Fact-checked by Grok 2 weeks ago

Cavity quantum electrodynamics

Cavity quantum electrodynamics (CQED) is the study of the interaction between atoms, ions, or artificial quantum emitters and the quantized electromagnetic field confined within a high-finesse optical or microwave cavity, enabling the modification of radiative processes such as spontaneous emission through control over the vacuum field fluctuations.^[1] In this regime, the coupling strength between the emitter and the cavity mode exceeds dissipation rates, leading to coherent energy exchange and the observation of quantum phenomena like vacuum Rabi splitting.^[2] CQED bridges quantum optics and atomic physics, providing a platform for fundamental tests of quantum mechanics and applications in quantum information processing.^[3] The theoretical foundation of CQED is rooted in the Jaynes–Cummings model^[4], introduced in 1963, which describes the dynamics of a two-level quantum system interacting with a single quantized mode of the electromagnetic field under the rotating-wave approximation. This model predicts key signatures of strong coupling, including Rabi oscillations even in the vacuum state (vacuum Rabi oscillations) and collapse-revival phenomena for coherent field states, where the atomic excitation probability exhibits periodic collapses and revivals due to the discrete photon number distribution.^[5] The strong coupling condition is met when the vacuum Rabi frequency (proportional to the dipole moment and field strength) surpasses both the atomic linewidth and the cavity decay rate, quantified by a cooperativity parameter C = g^2 / (\kappa \gamma) \gg 1, where g is the coupling rate, \kappa the cavity decay, and \gamma the atomic decay.^[2] Historically, the field emerged from early insights into cavity-modified emission rates, such as the Purcell effect proposed in 1946, which enhances spontaneous emission by a factor proportional to the cavity quality factor Q and mode density at the transition frequency.^[1] Experimental milestones in the 1980s included the first observations of modified spontaneous emission rates, including inhibition using Rydberg atoms between parallel mirrors at MIT (1985) and suppression for low-lying atomic states at Yale (1987), where lifetimes were extended by factors of up to 20 compared to free space.^[1] These advances culminated in demonstrations of single-atom masers and quantum nondemolition measurements of photon number, highlighting CQED's role in realizing open quantum systems with controlled decoherence.^[3] In modern contexts, CQED extends beyond atomic systems to solid-state platforms, including superconducting qubits in circuit QED and semiconductor quantum dots coupled to optical cavities, achieving ultrastrong coupling regimes where counter-rotating terms in the Hamiltonian become significant.^[6] Applications encompass quantum simulation of many-body physics, such as the Dicke model for superradiance, and scalable quantum networks for information transfer via photon-atom entanglement.^[7] Recent progress includes high-numerical-aperture resonators enabling near-unity single-photon absorption by single atoms (2025) and integration with color centers in diamond for room-temperature quantum interfaces.^[8] These developments underscore CQED's pivotal role in advancing quantum technologies.^[9]

Introduction

Definition and scope

Cavity quantum electrodynamics (cavity QED) is the study of the interaction between quantum emitters—such as neutral atoms, ions, or artificial atoms like superconducting qubits—and quantized electromagnetic fields confined in high-finesse cavities. These cavities, typically optical or microwave resonators, enhance the density of electromagnetic modes at specific frequencies, enabling strong coherent coupling that modifies fundamental processes like spontaneous emission. Unlike free-space quantum electrodynamics, where light-matter interactions occur in unbounded vacuum modes and are generally weak and irreversible, cavity QED focuses on controlled, reversible exchanges in confined geometries, spanning single-photon interactions to cooperative phenomena involving multiple emitters.^[10]^[11] The scope of cavity QED includes the exploration of quantum coherence, entanglement, and non-classical light generation, distinguishing it from broader quantum optics by its emphasis on cavity-mediated enhancements. Key parameters define system performance: the cavity quality factor Q = \omega_c / \kappa, where \omega_c is the cavity resonance frequency and \kappa the cavity decay rate, measures the photon's storage time and finesse of confinement. The cooperativity parameter C = g^2 / (\kappa \gamma), with g as the emitter-cavity vacuum Rabi coupling strength and \gamma the emitter's decay rate, quantifies the ratio of coherent interaction to dissipative losses, with C \gg 1 indicating dominant quantum effects.^[11]^[12] Cavity QED operates in distinct regimes based on these parameters. In the weak coupling regime (g \ll \kappa, \gamma), interactions manifest as modified emission rates through the Purcell effect, where decay is accelerated or suppressed depending on cavity detuning. The strong coupling regime (g \gg \kappa, \gamma), achievable with high Q and C > 1, allows observation of coherent vacuum Rabi splitting and dressed states, forming the basis for quantum information processing. This framework is canonically described by the Jaynes-Cummings model for a two-level emitter coupled to a single cavity mode.^[10]

Importance in quantum optics

Cavity quantum electrodynamics (QED) serves as a pivotal bridge between quantum mechanics and electromagnetism by confining electromagnetic fields within high-quality resonators, allowing precise manipulation of interactions between individual atoms or artificial emitters and single photons. This framework enables unprecedented control over light-matter coupling at the single-quantum level, where the exchange of excitations between the field and matter occurs on timescales faster than dissipation, fundamentally altering spontaneous emission rates and enabling reversible Rabi oscillations.^[13] Such control has been instrumental in realizing the strong coupling regime, a hallmark of cavity QED that amplifies quantum effects otherwise negligible in free space.^[14] In quantum information science, cavity QED contributes significantly by facilitating the generation of non-classical light states, such as single photons and squeezed vacuum, through coherent atom-photon interactions within the cavity. These systems support the creation of entanglement between atoms, photons, and even distant nodes via photon-mediated coupling, laying the groundwork for quantum networks and distributed quantum computing protocols. For instance, cavity QED architectures enable the deterministic transfer of quantum states between material qubits (e.g., atoms) and photonic qubits, essential for scalable quantum repeaters and secure communication.^[15]^[13] Furthermore, cavity QED provides profound insights into quantum measurement processes, decoherence mechanisms, and the quantum-classical boundary by allowing real-time observation of wave function collapse and environmental interactions. Non-demolition measurements of photon number states, achieved via atomic probes circulating through the cavity, reveal how information acquisition projects the field into definite Fock states, directly illustrating the measurement postulate. Studies of large coherent superpositions, or Schrödinger cat states, in these systems demonstrate decoherence as the irreversible loss of quantum coherence due to environmental coupling, quantifying the transition to classical behavior as the number of entangled quanta increases.^[3]^[13] The controlled environment of cavity QED also offers a robust platform for testing predictions of quantum electrodynamics, such as the granularity of the electromagnetic field and nonlinear photon statistics, with precision unattainable in open systems. By isolating few quanta in superconducting or optical cavities, experiments confirm QED tenets like vacuum Rabi splitting and photon blockade, validating theoretical models while probing subtle relativistic corrections in strong fields.^[13]^[3]

Historical development

Early theoretical foundations

The foundations of cavity quantum electrodynamics (QED) trace back to the mid-20th century, when theoretical work began exploring how electromagnetic cavities could modify atomic emission processes. In 1946, Edward M. Purcell demonstrated that the spontaneous emission rate of an excited atom is altered by the density of electromagnetic modes in a resonant cavity, a phenomenon now known as the Purcell effect. This insight, derived from Fermi's golden rule applied to a quantized radiation field, predicted that emission could be enhanced or suppressed depending on the cavity's quality factor and mode volume, laying the groundwork for strong atom-field coupling studies.^[16] In 1954, Robert H. Dicke introduced the concept of superradiance, describing enhanced collective spontaneous emission in dense atomic ensembles, which highlighted the role of cavity boundaries in altering quantum electrodynamic processes and provided early theoretical motivation for confining fields to enhance light-matter interactions. Concurrently, the semiclassical Rabi model, originally developed by Isidor I. Rabi in the 1930s for magnetic resonance, was adapted in the 1950s to describe two-level atomic systems interacting with classical electromagnetic fields inside cavities. This model captured oscillatory energy exchange—Rabi flopping—between the atom and the field, offering a simplified framework for understanding coherent interactions without full quantization of the field. A pivotal fully quantum treatment emerged in 1963 with the Jaynes–Cummings model, which rigorously described the interaction of a two-level atom with a single quantized cavity mode under the rotating-wave approximation, predicting vacuum Rabi oscillations and other strong-coupling phenomena.^[17] Further theoretical advances in the 1970s and 1980s emphasized the potential of Rydberg atoms, with their large dipole moments and long lifetimes, for observing cavity-modified emission. A key proposal came in 1981 from Daniel Kleppner, who suggested using highly excited Rydberg atoms in microwave cavities to observe strong coupling regimes, where the atom-field interaction exceeds decay rates, potentially revealing nonclassical QED signatures like vacuum Rabi splitting. This theoretical vision bridged microscopic quantum optics with macroscopic cavities, inspiring subsequent developments.^[18]

Key experimental milestones

One of the earliest experimental demonstrations in cavity quantum electrodynamics involved the enhancement of spontaneous emission from a single Rydberg atom interacting with a high-Q superconducting microwave cavity, where the atom's lifetime was shortened by a factor of over 10 compared to free space, achieving a transient single-atom maser effect.^[19] In 1987, the Haroche group realized a two-photon micromaser using Rydberg atoms in a superconducting cavity, demonstrating coherent atom-field interactions and advancing toward the strong coupling regime in the microwave domain.^[20] During the 1990s, progress in optical cavities enabled the observation of vacuum Rabi splitting with neutral atoms; notably, in 1992, Kimble and colleagues reported normal-mode splitting in the transmission spectrum of a high-finesse optical cavity containing a single cesium atom, with a splitting of approximately 38 MHz corresponding to the atom-cavity coupling strength, confirming strong coupling for an individual atom in the optical domain.^[21] That same year, the Haroche group observed vacuum Rabi splitting in the microwave regime using Rydberg atoms, marking the first direct spectroscopic evidence of strong coupling.^[22] In 1996, they further demonstrated coherent vacuum Rabi oscillations on a single atom, showing reversible energy exchange.^[23] The advent of circuit quantum electrodynamics in the 2000s extended these milestones to solid-state systems; a seminal 2004 proposal by Blais et al. outlined using superconducting transmission-line resonators coupled to Cooper-pair box qubits to achieve strong coupling, predicting vacuum Rabi splittings on the order of 100 MHz.^[24] This was experimentally realized in 2004, with vacuum Rabi splitting observed in superconducting circuits. In 2007, Schuster et al. demonstrated the strong dispersive regime in a superconducting circuit, resolving individual photon number states in the cavity via dispersive shifts in the qubit frequency, with coupling strengths exceeding cavity and qubit decay rates by factors of 10 or more.^[25]^[26] These achievements culminated in the 2012 Nobel Prize in Physics awarded jointly to Serge Haroche and David J. Wineland for their pioneering work in cavity QED and ion trapping, particularly Haroche's demonstrations of non-destructive photon counting via atomic transits through the cavity and the generation of Schrödinger cat states representing superpositions of coherent photon fields.^[27]

Theoretical framework

Quantized cavity modes

In cavity quantum electrodynamics (QED), the electromagnetic field confined within a resonant cavity supports discrete modes that arise from the boundary conditions imposed by the cavity walls. These modes manifest as standing waves, with the allowed frequencies determined by the cavity geometry. For a one-dimensional Fabry-Pérot cavity of length L with perfectly reflecting mirrors, the fundamental mode frequency is given by \omega_c = \pi c / L, where c is the speed of light in vacuum; higher-order modes occur at integer multiples of this frequency. This discretization of the field spectrum is fundamental to cavity QED, as it enables precise control over light-matter interactions by selecting modes resonant with atomic transitions.^[28] The quantization of these cavity modes treats the electromagnetic field as a collection of independent harmonic oscillators, one for each mode. The Hamiltonian for a single free cavity mode of frequency \omega_c is H_c = \hbar \omega_c \left( a^\dagger a + \frac{1}{2} \right), where a^\dagger and a are the bosonic creation and annihilation operators satisfying the commutation relation [a, a^\dagger] = 1. The zero-point term \frac{1}{2} \hbar \omega_c accounts for the vacuum fluctuations inherent to the quantized field. This second-quantized description, originally developed for free-space fields and adapted to cavities, underpins the quantum treatment of cavity modes.^[29] The eigenstates of the number operator a^\dagger a are the Fock states |n\rangle, which represent definite photon number states with n = 0, 1, 2, \dots excitations in the mode; the vacuum state |0\rangle corresponds to the ground state with unavoidable zero-point energy. In contrast, coherent states |\alpha\rangle = e^{-|\alpha|^2/2} \sum_{n=0}^\infty \frac{\alpha^n}{\sqrt{n!}} |n\rangle, where \alpha is a complex amplitude, describe classical-like fields with Poissonian photon statistics, akin to those produced by lasers, and are superpositions of Fock states that maintain phase coherence over time. These states form the basis for describing the quantum statistics of light inside the cavity.^[30] Realistic cavities exhibit losses due to imperfect mirrors or coupling to external modes, characterized by a decay rate \kappa that quantifies the field's leakage. To model these open-system dynamics, the evolution of the cavity field density operator \rho is governed by the Lindblad master equation, incorporating dissipative terms such as \kappa \left( a \rho a^\dagger - \frac{1}{2} \{ a^\dagger a, \rho \} \right), which describe photon loss while preserving the positivity and trace of \rho. This framework is essential for analyzing decoherence in cavity QED experiments.^[31]

Jaynes-Cummings model

The Jaynes-Cummings model provides the foundational theoretical description of light-matter interaction in cavity quantum electrodynamics, focusing on a single two-level atom coupled to a single quantized mode of the electromagnetic field. Introduced in 1963, it incorporates the rotating-wave approximation to neglect rapidly oscillating counter-rotating terms, simplifying the dynamics while capturing essential quantum features such as energy exchange between the atom and the field.^[32] The model's Hamiltonian in the interaction picture, assuming resonant frequencies or small detuning, is given by

H = \hbar \omega_a \sigma^\dagger \sigma + \hbar \omega_c a^\dagger a + \hbar g (\sigma^\dagger a + \sigma a^\dagger),

where \sigma^\dagger and \sigma are the raising and lowering operators for the two-level atom (with transition frequency \omega_a), a^\dagger and a are the creation and annihilation operators for the cavity mode (with frequency \omega_c), and g is the vacuum Rabi frequency representing the coupling strength. This form arises from the minimal coupling interaction between the atomic dipole and the electric field, quantized within the cavity.^[32] To find the eigenstates and eigenvalues, known as dressed states, the Hamiltonian is diagonalized in the basis of uncoupled states |e, n\rangle (excited atom, n photons) and |g, n+1\rangle (ground-state atom, n+1 photons), where e and g denote the atomic levels. For a given manifold with total excitation number n+1, the eigenvalues are

E_{n,\pm} = \hbar \frac{\omega_c + \omega_a}{2} \pm \frac{\hbar}{2} \sqrt{\Delta^2 + 4 g^2 (n+1)},

with detuning \Delta = \omega_a - \omega_c. The corresponding dressed states are superpositions: |\psi_{n,\pm}\rangle = \cos(\theta_n/2) |e, n\rangle \pm \sin(\theta_n/2) |g, n+1\rangle, where \tan \theta_n = 2g\sqrt{n+1}/\Delta. These solutions reveal the hybridization of atomic and photonic excitations, leading to avoided crossings in the energy spectrum.^[32]^[33] A key prediction is the vacuum Rabi splitting, which occurs at resonance (\Delta = [0](/page/0)) for the lowest manifold (n=[0](/page/0)), yielding energy levels separated by $2g. This splitting manifests as a doublet in the system's transmission or absorption spectrum, distinguishing quantum coupling from classical behavior. For general n, the model predicts Rabi oscillations where the atom and field exchange energy at a frequency $2g \sqrt{n+1}, with the vacuum case (n=[0](/page/0)) oscillating purely at $2g.^[32]^[33]

Extensions to multi-level systems

The Jaynes-Cummings model provides a foundational description of light-matter interactions in cavity quantum electrodynamics by approximating the atomic system as a two-level entity and neglecting counter-rotating terms under the rotating-wave approximation, which holds for weak to moderate couplings. Extensions to more realistic scenarios incorporate multi-level atomic structures and full interactions, capturing effects relevant to ultrastrong coupling regimes and collective behaviors. These generalizations reveal richer dynamics, such as non-perturbative effects and phase transitions, essential for advanced quantum technologies.^[34] The quantum Rabi model extends the Jaynes-Cummings framework by including counter-rotating terms in the interaction Hamiltonian, given by \hat{H}_\text{int} = \hbar g (\hat{\sigma}^\dagger \hat{a} + \hat{\sigma} \hat{a}^\dagger + \hat{\sigma}^\dagger \hat{a}^\dagger + \hat{\sigma} \hat{a}), where the additional terms \hbar g (\hat{\sigma}^\dagger \hat{a}^\dagger + \hat{\sigma} \hat{a}) account for virtual photon processes. This full model becomes necessary in the ultrastrong coupling regime, where the coupling strength g approaches the cavity frequency \omega, typically g/\omega \gtrsim 0.1, as the rotating-wave approximation breaks down and leads to significant corrections in energy spectra and dynamics. The exact analytical solution of the quantum Rabi model, achieved through a transcendental G-function approach, reveals a fine-structured spectrum without level crossings, enabling precise predictions for systems like circuit QED implementations. For systems involving multiple atoms, the Dicke model generalizes the single-atom case to N two-level atoms collectively coupled to a single cavity mode, with the interaction Hamiltonian \hat{H}_\text{int} = \hbar g \sqrt{N} (\hat{J}_+ \hat{a} + \hat{J}_- \hat{a}^\dagger), where \hat{J}_\pm are collective spin operators. In the thermodynamic limit N \to \infty, this model predicts a superradiant phase transition at a critical coupling \lambda_c = \sqrt{\omega \omega_0 / 2}, where \lambda = g \sqrt{N}, shifting the system from a normal phase with zero photon occupation to a superradiant phase characterized by macroscopic cavity field occupation and broken \mathbb{Z}_2 symmetry. This equilibrium transition, first rigorously analyzed in the context of the Dicke maser, has implications for collective emission and quantum phase engineering, though realizations must navigate the no-go theorem in atomic systems due to the A^2 term in the full QED Hamiltonian.^[35] Incorporating three-level atomic systems, such as \Lambda- or V-configurations, further enriches cavity QED models by allowing coherent population transfer and dark-state dynamics. In a \Lambda-system, with ground states |g\rangle, |s\rangle and excited state |e\rangle, cavity-mediated stimulated Raman adiabatic passage (STIRAP) enables efficient, decoherence-resistant transfer from |g\rangle to |s\rangle via adiabatic following of a dark state |\text{D}\rangle = \cos\theta |g\rangle - \sin\theta |s\rangle, where the mixing angle \theta is controlled by pump and Stokes field intensities. Similarly, V-configurations support enhanced emission or absorption processes. These extensions facilitate applications in quantum state preparation and routing, with theoretical frameworks demonstrating near-unity fidelity in the adiabatic limit.^[34] In multi-level extensions, light-matter hybridization leads to polariton formation, where the eigenstates become hybrid quasiparticles combining photonic and atomic excitations. For a three-level atom, the polariton dispersion relations exhibit multiple avoided crossings, reflecting the coupling between cavity modes and atomic transitions, described by a generalized Hamiltonian that diagonalizes into polariton branches with energies E_\pm(k) \approx \frac{\hbar c k}{n} \pm \frac{\hbar \Omega}{2}, where \Omega is the Rabi splitting and k is the wavevector in extended cavities. These quasiparticles inherit mixed bosonic statistics, enabling phenomena like polariton blockade and superfluidity in driven-dissipative settings.^[29]

Experimental implementations

Microwave cavity QED

Microwave cavity quantum electrodynamics (QED) involves the interaction of Rydberg atoms with quantized modes of superconducting microwave cavities, enabling the study of quantum effects at the single-photon and single-atom level. These setups typically employ high-quality factor (Q > 10^8) superconducting cavities, such as niobium-coated copper Fabry-Pérot resonators with mirror diameters of about 5 cm separated by 2.7 cm, operated at cryogenic temperatures around 0.8 K to minimize thermal noise and achieve photon lifetimes exceeding 100 ms. Rydberg atoms, often circular states of rubidium with principal quantum numbers n ≈ 50–51, are sent through the cavity mode, leveraging their large electric dipole moments (on the order of 10^3 e a_0, where e is the electron charge and a_0 the Bohr radius) to attain single-atom vacuum Rabi coupling strengths of g/2π ≈ 25–50 kHz, well into the strong coupling regime where coherent atom-photon exchanges outpace dissipation.^[13] The advantages of this regime include exceptionally long coherence times for both atomic states (T_1, T_2 ≈ 30 ms in circular Rydberg levels) and cavity photons (up to 130 ms storage time), far surpassing many other quantum platforms and allowing for repeated non-destructive interactions. Single-photon detection is facilitated through quantum non-demolition (QND) measurements, where the dispersive phase shift induced by the cavity field on a probe atom's state is read out via field ionization after the atom exits the cavity, enabling resolution of photon numbers without absorbing the field.^[13] Pioneering experiments demonstrated photon number resolving detection in 1996, using a Rydberg atom to perform QND measurements on cavity fields, revealing the phase-dependent dispersion that distinguishes photon numbers and allowing the first observation of the decoherence of small Schrödinger cat states (superpositions of coherent fields with ≈5 photons and opposite phases). In the 2000s, these capabilities advanced to generate and manipulate larger cat states, such as in 2008 when tomographic reconstruction of the cavity Wigner function visualized non-classical field states and their progressive decoherence due to cavity losses, with cat sizes up to α ≈ 3.5 (≈20 photons total). A primary challenge in microwave cavity QED is the low operating frequencies (typically 40–50 GHz), which hinder direct integration with optical systems for quantum networking, necessitating inefficient frequency conversion schemes to bridge the microwave-to-optical gap.^[36]

Optical cavity QED

Optical cavity quantum electrodynamics (QED) encompasses experimental setups where neutral atoms, quantum dots, or molecules interact strongly with confined optical fields in high-finesse resonators operating at visible or near-infrared wavelengths. These systems typically employ Fabry-Pérot cavities formed by curved mirrors with finesses ranging from F \approx 10^5 to $10^6, enabling mode volumes on the order of (\lambda/2)^3 and long photon lifetimes to achieve the strong-coupling regime where the atom-cavity coupling rate g exceeds the decay rates of the atom and cavity.^[37] Microtoroid resonators, fabricated from silica or other dielectrics, offer similar high finesses and support whispering-gallery modes for compact integration.^[38] For solid-state emitters like quantum dots or color centers, evanescent coupling via near-field overlap with the cavity mode is commonly used, allowing precise positioning without direct embedding in some designs.^[39] Early demonstrations with neutral atoms highlighted the potential of optical cavities for probing fundamental light-matter interactions. In a seminal 1992 experiment, a single cesium atom was optically pumped and probed in a Fabry-Pérot cavity with F \approx 4 \times 10^4, revealing vacuum Rabi splitting in the transmission spectrum with a splitting of $2g/2\pi \approx 37 MHz, confirming strong coupling for an individual atom.^[21] This observation marked a key milestone, as the splitting arises from the coherent exchange of excitations between the atom and the single-photon cavity field, distinct from ensemble effects. Subsequent refinements in atom trapping extended these measurements to colder atoms with longer interaction times, enhancing the visibility of the Rabi doublet.^[40] Solid-state implementations leverage semiconductor quantum dots in micropillar cavities, where distributed Bragg reflectors confine light axially for high overlap with the emitter. A representative example involves InGaAs quantum dots in GaAs micropillars achieving strong coupling with g/2\pi \approx 25 GHz and vacuum Rabi splitting exceeding the linewidths, enabling observation of polariton dynamics at cryogenic temperatures.^[41] These setups benefit from compatibility with fiber-optic integration for efficient photon collection and routing, as well as potential room-temperature operation for certain robust emitters like carbon nanotubes or diamond defects, reducing cryogenic requirements compared to atomic systems.^[42] In 2003, researchers observed lasing from a single optically pumped cesium atom in a high-finesse optical cavity, demonstrating a threshold-like transition in photon output despite the single-emitter nature, with intracavity photon numbers reaching up to 4 above threshold. Such milestones underscore the enhanced spontaneous emission via the Purcell effect in these cavities, where the modified density of states boosts radiative rates by factors up to the finesse.^[43]

Circuit quantum electrodynamics

Circuit quantum electrodynamics (cQED) employs superconducting circuits to realize artificial atoms coupled to microwave cavities, enabling the study of light-matter interactions in a solid-state platform. The core setup involves Josephson junction-based qubits, such as transmon or flux qubits, integrated into coplanar waveguide resonators fabricated on silicon or sapphire substrates. These qubits act as nonlinear elements mimicking two-level systems, capacitively coupled to the resonator's electric field at points of maximum antinode strength. Typical vacuum Rabi coupling strengths reach g/2π up to 100 MHz, far exceeding cavity and qubit decay rates, thus achieving the strong coupling regime.^[6]^[44] A seminal demonstration of strong coupling in cQED was reported in 2004, where Wallraff et al. observed coherent vacuum Rabi oscillations between a superconducting qubit and a single microwave photon in an on-chip cavity, with coupling rates on the order of 10 MHz. This experiment established cQED as a viable analog to atomic cavity QED, directly mapping to the Jaynes-Cummings model for qubit-photon interactions. Subsequent advancements included dispersive readout techniques, where the qubit state induces a measurable shift in the cavity resonance frequency via the effective Hamiltonian term χ σ_z a† a, with χ representing the dispersive shift per photon (typically ~1-10 MHz). This state-dependent frequency pull enables high-fidelity qubit measurement without direct photon absorption, minimizing decoherence.^[44]^[6]^[6] The architecture of cQED offers distinct advantages for quantum technologies, including scalability through lithographic fabrication of multi-qubit arrays on a single chip, integration with control electronics, and ultrafast gate operations on nanosecond timescales driven by microwave pulses. These features facilitate the construction of quantum processors with dozens of qubits, supporting error-corrected computation. A 2021 comprehensive review underscores significant progress in multimode cQED systems, such as 3D cavities hosting multiple resonator modes for enhanced storage and entanglement, alongside hybrid integrations with spin qubits, mechanical oscillators, and optical photons to bridge microwave and optical domains.^[6]^[45]^[6]

Fundamental phenomena

Strong and weak coupling regimes

In cavity quantum electrodynamics (CQED), the interaction between a quantum emitter and a confined electromagnetic field is characterized by distinct coupling regimes determined by the relative strengths of the coherent coupling rate g and the dissipative rates of the cavity decay \kappa and the emitter decay \gamma. The weak coupling regime arises when g \ll \kappa, \gamma, where dissipation dominates and the primary effect is a modification of the emitter's spontaneous emission rate via the Purcell effect.^[46] In this regime, the cavity enhances or suppresses emission depending on the detuning, with the Purcell factor F_p quantifying the enhancement for a resonant emitter at the antinode of the field:

F_p = \frac{3}{4\pi^2} \frac{\lambda^3 Q}{V},

where \lambda is the emission wavelength, Q = \omega_c / \kappa is the cavity quality factor with cavity frequency \omega_c, and V is the effective mode volume.^[46] This regime is widely exploited in applications like microcavity lasers and single-photon sources, where the goal is efficient extraction of photons rather than coherent state manipulation.^[47] The strong coupling regime is achieved when g > \kappa, \gamma, enabling reversible, coherent energy exchange between the emitter and the cavity mode without significant loss to dissipation.^[47] Here, the eigenstates of the system hybridize into dressed states (polaritons), manifesting as an avoided crossing in the energy spectrum with a normal-mode splitting of $2g at resonance.^[47] For strong coupling to be experimentally observable and useful for quantum operations, the single-emitter cooperativity parameter must satisfy C = 4 g^2 / (\kappa \gamma) \gg 1, ensuring that the coherent interaction overwhelms decoherence. Vacuum Rabi oscillations, observed as coherent population transfer between the emitter and cavity, serve as a key signature of this regime.^[47] Beyond strong coupling lies the ultrastrong coupling regime, where g \sim 0.1 \omega_c, making the counter-rotating terms in the full quantum Rabi Hamiltonian non-negligible and invalidating the rotating-wave approximation used in the Jaynes-Cummings model.^[47] This leads to unique quantum effects, such as the Bloch-Siegert shift, a counter-rotating correction that asymmetrically displaces the energy levels of the hybridized states. Realized in systems like superconducting circuits and semiconductor microcavities, ultrastrong coupling enables exploration of non-perturbative light-matter physics, including ground-state modifications and enhanced nonlinearities.^[47]

Vacuum Rabi oscillations

Vacuum Rabi oscillations describe the coherent, reversible transfer of excitation between a two-level atom and a single mode of the quantized electromagnetic field in a cavity, starting from the vacuum state of the field. In the framework of the Jaynes-Cummings model, when the atom is prepared in its excited state |e⟩ and the cavity in the vacuum |0⟩, with the atomic transition resonant to the cavity frequency (detuning Δ = 0), the time evolution of the system is given by

|\psi(t)\rangle = \cos(gt) |e, 0\rangle - i \sin(gt) |g, 1\rangle,

where g is the light-matter coupling strength, also known as the vacuum Rabi frequency. The probability of finding the atom in the excited state is then P_e(t) = \cos^2(gt), exhibiting sinusoidal oscillations at angular frequency 2g.^[32] This dynamic reveals the quantized nature of the vacuum fluctuations, as the atom effectively "Rabi flops" with a single virtual photon borrowed from the vacuum.^[23] These oscillations occur in the strong coupling regime of cavity quantum electrodynamics, where the coherent exchange rate g exceeds both atomic and cavity decay rates. The first direct experimental observation of vacuum Rabi oscillations was achieved in 1996 using circular Rydberg atoms interacting with a high-quality superconducting microwave cavity, demonstrating damped sinusoidal variations in the atomic state population at a frequency of 2g/2π ≈ 50 kHz, with damping attributed to residual decoherence from cavity and atomic imperfections.^[23] The observed signal confirmed the predictions of the Jaynes-Cummings model, providing a definitive test of field quantization in a cavity.^[23] For systems initialized with the atom in |e⟩ and the cavity containing n photons (|e, n⟩), the oscillation generalizes to a detuning-dependent Rabi frequency \Omega_n = \sqrt{\Delta^2 + 4 g^2 n}, reducing to 2g√n on resonance (Δ = 0). This n-dependent scaling underlies phenomena such as collapse and revival of Rabi oscillations in coherent field states with mean photon number \bar{n}, where the frequency spreads as 2g√\bar{n}.^[32] Vacuum Rabi dynamics play a crucial role in generating Schrödinger cat states—superpositions of coherent field states |α⟩ and |-α⟩—through conditional measurements on the atom after partial interaction; for instance, detecting the atom in a superposition basis following resonant or dispersive coupling projects the cavity field into an even or odd parity cat state, as demonstrated in microwave cavity experiments.

Purcell effect

The Purcell effect describes the alteration of an excited quantum emitter's spontaneous emission rate due to the modified photonic density of states within a resonant cavity, enabling control over decay dynamics that is absent in free space. In free space, the emission rate \gamma_0 arises from the continuous broadband density of electromagnetic modes, but a cavity confines light to discrete modes with a Lorentzian lineshape, peaking sharply at the cavity resonance frequency \omega_c. When the emitter's transition frequency \omega_0 aligns with \omega_c, the local density of states (LDOS) increases dramatically, accelerating emission; conversely, detuning suppresses it. This phenomenon, central to weak-coupling cavity quantum electrodynamics, underpins strategies for engineering light-matter interactions without requiring coherent Rabi oscillations. The quantitative description in the weak-coupling limit (g \ll \kappa, \gamma_0) relies on Fermi's golden rule, where the emission rate \gamma_c into the cavity mode is \gamma_c = \frac{ g^2 \kappa }{ \Delta^2 + \kappa^2/4 } \approx \frac{4 g^2}{\kappa} on resonance (\Delta = \omega_0 - \omega_c = 0), with g the vacuum Rabi coupling and \kappa = \omega_c / [Q](/page/Q) the cavity decay rate. Equivalently, the enhancement factor F_p = \gamma_c / \gamma_0 = \frac{3 [Q](/page/Q) \lambda^3}{4 \pi^2 V} (assuming optimal dipole orientation and refractive index n=1), where \lambda is the emission wavelength, [Q](/page/Q) the quality factor, and V the mode volume; this form highlights the trade-off between long photon lifetime (high [Q](/page/Q)) and strong confinement (low V). For large F_p \gg 1, the total rate approximates \gamma_c \approx F_p \gamma_0, directing most emission into the cavity mode. Off resonance, for |\Delta| \gg \kappa/2, the LDOS falls below the free-space value, yielding inhibition with \gamma_c / \gamma_0 < 1, potentially quenching emission by factors of 10 or more in tuned cavities.^[48] Early experimental verification occurred in the 1980s using mirror-based cavities to probe atomic and molecular lifetimes. Drexhage, Kuhn, and Schäfer demonstrated tunable fluorescence decay rates of dye molecules near dielectric mirrors, observing enhancements and inhibitions aligning with boundary-modified LDOS predictions, with lifetime changes up to 50% depending on distance to the reflector. In microwave cavities, Rydberg atoms showed inhibited emission when detuned from the mode, confirming reduced rates by factors of 2–3 compared to free space. Modern nanophotonic implementations, such as quantum dots in photonic crystal nanocavities or micropillars, routinely achieve F_p > 50, with lifetime reductions from nanoseconds to picoseconds; for instance, InAs quantum dots in L3 photonic crystal cavities have exhibited F_p \approx 100, validating the scaling with Q/V.^[49] In single-photon sources, the Purcell effect boosts the mode-coupling efficiency via the \beta-factor, \beta = \frac{\gamma_c}{\gamma_c + \gamma_0} \approx \frac{F_p}{F_p + 1}, enabling near-unity values for indistinguishable photons. This has enabled deterministic sources with g^{(2)}(0) < 0.05 and extraction efficiencies >70%, critical for quantum networks; examples include telecom-wavelength quantum dots in circular Bragg gratings achieving \beta > 0.9 through tailored F_p \approx 20.^[50]^[51]

Applications

Quantum information processing

Cavity quantum electrodynamics (QED) enables quantum information processing by facilitating strong interactions between qubits and photons within a confined electromagnetic field, allowing for the implementation of entangling operations essential for quantum computing and communication. In particular, cavities mediate interactions between distant qubits, enabling two-qubit gates without direct coupling. For instance, controlled-NOT (CNOT) gates can be realized through cavity-mediated interactions, where the cavity field swaps states between qubits via dispersive coupling, achieving high fidelities in experimental setups. In circuit QED systems using superconducting qubits, such CNOT gates have demonstrated fidelities exceeding 99%, as reported in implementations with fluxonium qubits that maintain stability over extended periods without recalibration.^[52] These cavity-mediated interactions also underpin quantum communication protocols, notably in quantum repeaters designed to extend entanglement over long distances. By entangling atoms with cavity modes, single atoms can store and retrieve photonic qubits, forming the basis for entanglement swapping and purification in repeater nodes. Proposals and demonstrations in cavity QED utilize atom-cavity systems to generate high-fidelity Bell states between flying photons and stationary atomic qubits, mitigating photon loss in optical fibers. For example, schemes employing coherent light and atom-cavity chains have shown potential for efficient repeater operation with error rates below the threshold for fault tolerance.^[53]^[54] Beyond gates and repeaters, cavity QED supports nonlinear photon control devices like single-photon transistors, where a single atom conditionally blocks or transmits cavity photons. In these systems, an atom in the cavity ground state allows resonant photon transmission, but excitation to a Rydberg state induces a phase shift or absorption, effectively gating the photon flux with high on-off contrast. Experimental realizations in microwave cavities coupled to superconducting qubits have achieved ultra-high gain, where one gate photon controls multiple signal photons, enabling photon blockade with extinction ratios exceeding 20 dB.^[55]^[56] To enhance scalability, 2010s research proposed bosonic codes encoded in cavity modes for quantum error correction, leveraging the infinite-dimensional Hilbert space of harmonic oscillators to protect against photon loss and dephasing. Cat codes, introduced in 2013, stabilize superpositions of coherent states in driven nonlinear cavities, correcting bit-flip errors via continuous syndrome measurements while being resilient to phase errors. Similarly, binomial codes from 2016 encode logical qubits in Fock state superpositions, offering protection against both loss and dephasing with hardware-efficient decoding. These codes, implemented in circuit QED platforms, have demonstrated extended qubit lifetimes beyond native decoherence times, paving the way for fault-tolerant quantum processors.

Cavity-enhanced spectroscopies

Cavity-enhanced spectroscopies leverage the high-finesse optical cavities central to cavity quantum electrodynamics (CQED) to achieve ultrasensitive detection of light-matter interactions, enabling measurements of trace absorbers that would be undetectable in free-space spectroscopy. By confining photons within the cavity for extended times, these techniques amplify absorption signals, with effective path lengths reaching kilometers despite compact setups. This enhancement stems from the cavity's quality factor Q, which quantifies the photon lifetime and directly boosts sensitivity to molecular or atomic transitions. A cornerstone method is cavity ring-down spectroscopy (CRDS), which measures the decay time of light intensity after the input pulse is extinguished, providing an absolute determination of the absorption coefficient \alpha. The ring-down time \tau is given by

\tau = \frac{L}{c(1 - R + \alpha L)},

where L is the cavity length, c is the speed of light, and R is the mirror reflectivity; for low absorption (\alpha L \ll 1 - R), \tau approximates the empty-cavity lifetime, allowing precise extraction of \alpha from deviations. This technique, pioneered in the late 1980s, achieves sensitivities down to $10^{-10} cm^{-1}, corresponding to parts-per-million (ppm) levels for many gases. In the CQED context, CRDS exploits high-Q cavities (Q > 10^6) to probe weak molecular transitions without requiring coherent excitation, distinguishing it from resonant CQED phenomena. For even weaker absorbers, such as single molecules, normal-mode splitting in the cavity transmission spectrum serves as a spectroscopic signature of light-matter coupling. In the strong-coupling regime, the interaction vacuum Rabi frequency $2g exceeds the cavity decay rate \kappa and atomic linewidth \gamma, splitting the bare cavity resonance into two peaks separated by $2g; for N non-interacting particles, the collective coupling scales as g \sqrt{N}, enabling detection at low densities where individual contributions are resolvable. This has been demonstrated for single atoms, with splitting observed in optical cavities at room temperature, and extended to molecules in microcavities for single-particle resolution. Collective effects from strong coupling further enhance visibility for sparse ensembles, allowing sub-ppm detection thresholds. These methods found key developments in the 1990s, when advancements in stable optical cavities enabled continuous-wave CRDS and integrating cavity-enhanced absorption spectroscopy, routinely achieving ppm-level sensitivity for atmospheric trace species. Applications span trace gas detection, such as monitoring greenhouse gases like CO_2 or pollutants like NO_2 at parts-per-billion levels using mid-infrared cavities. In biological sensing, high-Q cavities (Q > 10^9) integrated with whispering-gallery modes or Fabry-Pérot resonators enable label-free detection of biomolecules, such as proteins or DNA, via refractive index shifts or fluorescence enhancement, with sensitivities to single-molecule events in aqueous environments.

Polaritonic chemistry

Polaritonic chemistry explores how the strong coupling between molecular vibrations and cavity photons in quantum electrodynamics (QED) frameworks alters chemical reactivity and molecular properties at the ground state, without requiring external excitation. In this regime, molecular ensembles interact collectively with infrared (IR) cavity modes, forming hybrid light-matter states known as vibrational polaritons that redistribute energy and modify reaction pathways. These effects arise from the non-equilibrium distribution of photonic and vibrational excitations, enabling control over processes like energy transfer and bond dynamics in organic systems. Vibrational strong coupling occurs when the interaction strength between molecular vibrational dipoles and the cavity field exceeds the decay rates of both, leading to the formation of polaritons in IR cavities tuned to molecular transition frequencies. For molecular ensembles, this coupling manifests as collective Rabi splitting, where the absorption spectrum shows symmetric peaks split by an amount proportional to the square root of the number of molecules, often reaching tens of wavenumbers in experiments with liquid or solid samples. For instance, in organic crystals, collective intermolecular vibrations in the terahertz range have demonstrated strong coupling with Rabi splittings of ~2 cm⁻¹ (68 GHz), highlighting the scalability with molecular density.^[57] Significant alterations in chemical reaction rates have been observed under these conditions, with changes occurring without modifications to the molecular ground-state geometry. Experiments on Förster-type excitation energy transfer in molecular dimers showed significant modifications to transfer efficiency within cavities, rendering the process nearly distance-independent over hundreds of nanometers, in stark contrast to the 1/R⁶ decay in free space. This demonstrates how polaritons can facilitate resonant amplification of energy transfer, with rate modifications scaling with coupling strength and detuning. In ground-state reactions, such as unimolecular dissociations, collective vibrational strong coupling has been linked to rate changes of up to 50% in model systems, attributed to modified vibrational landscapes.^[58]^[59] The theoretical foundation relies on non-perturbative QED treatments that incorporate the full dipole self-energy, accounting for virtual photon exchanges and cavity-induced renormalization of molecular potentials. These approaches reveal that polaritonic effects stem from the coherent mixing of photonic and molecular degrees of freedom, leading to shifts in the dipole self-energy that alter reaction barriers without perturbative approximations. Ultrastrong coupling regimes, where the coupling exceeds 10% of the transition frequency, further amplify these shifts in vibrational modes.^[60]^[61] In the 2020s, studies on cavity-modified photochemistry in organic molecules have advanced this field, showing polariton-mediated enhancements in photoisomerization rates for systems like spiropyrans embedded in Fabry-Pérot cavities. These works indicate that while some rate changes arise from non-polaritonic field enhancements, true polaritonic effects dominate in strong coupling, with up to twofold increases in quantum yields for isomerization. Such findings underscore the potential for designing cavity environments to steer photochemical outcomes in synthetic organic reactions. As of 2025, polaritonic effects have been demonstrated to influence selectivity in catalytic processes, further expanding applications in synthetic chemistry.^[62]^[63]

Recent advances

Scalable quantum networks

Cavity quantum electrodynamics (QED) serves as a foundational platform for scalable quantum networks by enabling efficient interfaces between matter qubits and photonic channels, facilitating distributed quantum information processing across multiple nodes. In these architectures, individual atoms or ensembles trapped in optical cavities act as quantum memories that generate and store entanglement with flying qubits in the form of photons, allowing for the interconnection of remote quantum processors. This approach leverages the strong light-matter coupling in cavity QED to overcome the limitations of direct qubit-qubit interactions over long distances, paving the way for quantum repeaters and large-scale entanglement distribution. A key enabler of these networks is the generation of atom-photon entanglement, where the success probability for efficient interfaces scales approximately with the single-atom cooperativity parameter C \approx g^2 / \kappa \gamma, with g the vacuum Rabi frequency, \kappa the cavity decay rate, and \gamma the atomic decay rate. High cooperativity (C \gg 1) ensures near-deterministic mapping of atomic states onto photons, essential for heralded entanglement protocols that detect successful emission without destroying the quantum information. For instance, in 2022 experiments using optical cavities with Rydberg atoms, atom-photon entanglement was achieved with fidelities exceeding 91.9%, demonstrating robust links suitable for network integration. Circuit QED offers a complementary scalable platform, extending these principles to superconducting qubits for hybrid implementations. Modular architectures in cavity QED link arrays of qubit nodes via photonic interconnects, with proposals enabling networks of 100+ nodes through multiplexing and optical tweezer arrays for neutral atoms. These designs feature quantum processing units and repeaters spaced approximately 50 km apart, where cavity-enhanced entanglement generation supports high-rate distribution over continental scales. A 2023 proposal outlines neutral atom arrays in cavities as processing nodes, achieving link efficiencies greater than unity for 1000 km distances via parallel temporal modes and entanglement purification. Significant challenges in realizing these networks include mitigating photon loss during transmission, addressed through error correction codes and heralded protocols that confirm successful entanglement before swapping. Heralded entanglement swapping extends short-distance links into long-range connections by fusing elementary pairs at intermediate nodes, with fidelity preserved via purification to counter decoherence. Loss mitigation strategies, such as multimode cavities and quantum error correction, are critical to scaling beyond prototype systems while maintaining overall network fidelity above 80%.

Hybrid quantum systems

Hybrid quantum systems in cavity quantum electrodynamics (QED) integrate photonic cavities with diverse quantum platforms, such as mechanical oscillators, solid-state spins, and condensed-matter excitations, to harness collective light-matter interactions for advanced quantum control and simulation. Optomechanical cavities exemplify this integration, where radiation pressure mediates coupling between optical cavity modes and mechanical resonators. The interaction strength is enhanced by intracavity photons, yielding an effective coupling rate g_{om} = g_0 \sqrt{n}, with g_0 denoting the vacuum optomechanical coupling and n the mean photon number. This regime enables quantum ground-state cooling of mechanical modes and bidirectional state transfer between photons and phonons, as demonstrated in experiments with silicon nitride membranes and Fabry-Pérot cavities.^[64]^[65] Spin-cavity interfaces represent another key hybrid architecture, particularly using nitrogen-vacancy (NV) centers in diamond as robust quantum emitters coupled to optical microcavities. These systems achieve Purcell-enhanced emission rates of several fold, facilitating efficient spin-photon entanglement and coherent readout. NV centers serve as long-lived quantum memories with coherence times up to milliseconds, interfaced via evanescent fields in photonic crystal cavities or microspheres. Such hybrids support scalable quantum repeaters by enabling deterministic photon-spin mapping.^[66] Recent progress has expanded hybrid cavity QED to multimode circuit platforms and low-dimensional materials. In 2024, multimode superconducting circuit QED with a Josephson junction demonstrated emergent quantum phase transitions, simulating many-body criticality through tunable photon-mediated interactions across multiple resonator modes. Cavity control of 2D materials, such as transition metal dichalcogenides in hyperbolic van der Waals cavities, has revealed strong excitonic polaritons with Rabi splittings up to 100 meV, altering transport and optical properties. Complementing these, the 2025 QED-SA-CASSCF method advances theoretical modeling of molecular hybrids, extending state-averaged complete active space self-consistent field theory to include cavity photons for ab initio polariton calculations in strongly coupled organic systems.^[67]^[68]^[69]

References

[1]
[PDF] Cavity Quantum Electrodynamics - MIT
The recent research on atom-vacuum interactions belongs to a new field of atomic physics and quantum optics called cavity quantum electrodynamics.
[2]
A Quick Introduction to the strong coupling regime of Cavity ... - arXiv
Dec 1, 2014 · Here, the essentials of the strong coupling regime of Cavity Quantum Electrodynamics (QED) are reviewed for cavities tuned with a single atomic transition.
[3]
Cavity Quantum Electrodynamics - Scientific American
Oct 9, 2012 · Atoms and photons in small cavities behave completely unlike those in free space. Their quirks illustrate some of the principles of quantum physics.
[4]
Collapse and revival of the state vector in the Jaynes-Cummings ...
Dec 31, 1990 · The evolution of the atomic state in the resonant Jaynes-Cummings model (a two-level atom interacting with a single mode of the quantized ...Missing: paper | Show results with:paper
[5]
Circuit quantum electrodynamics | Rev. Mod. Phys.
May 19, 2021 · This review surveys the development over the last 15 years of circuit quantum electrodynamics, the nonlinear quantum optics of microwave ...
[6]
Cavity quantum materials | Applied Physics Reviews - AIP Publishing
This brief review provides an overview of the state of the art of cavity platforms and highlights recent theoretical proposals and first experimental ...II. CAVITY QED AND... · Cavity light–matter coupling · Cavity control of collective...
[7]
Cavity QED in a high NA resonator | Science Advances
Feb 26, 2025 · We present a high–numerical aperture, lens-based resonator that pushes the single-atom single-photon absorption probability near its fundamental limit.
[8]
Cavity quantum electrodynamics with color centers in diamond
This paper reviews recent progress in coupling individual diamond defects to optical resonators, focusing on cQED platforms with a clear potential for quantum ...2. Cavity Qed With... · 4. Open Fabry--Perot... · 5. Nanophotonic Cavities
[9]
From cavity to circuit quantum electrodynamics | Nature Physics
Mar 2, 2020 · Circuit quantum electrodynamics focuses on the interaction of small superconducting circuits, tailored to behave as two-level quantum systems.Missing: 2020 | Show results with:2020
[10]
https://www.nature.com/articles/s41567-020-0812-1
[11]
Cavity QED Based on Strongly Localized Modes: Exponentially ...
Sep 3, 2025 · Our results demonstrate that this cavity QED system enables ultralong vacuum Rabi oscillations and a strong photon blockade effect. The proposed ...
[12]
None
Summary of each segment:
[13]
In the right place | Nature Photonics
Nov 30, 2006 · Cavity quantum electrodynamics (QED) uses optical resonators to enhance these interactions. To take advantage of such enhanced properties in ...
[14]
[PDF] Cavity QED Approaches
Apr 2, 2004 · Importance to Quantum Information Processing ... [1]. Cavity Quantum Electrodynamics, P.!Berman, Ed. (Academic Press ...
[15]
Observation of Cavity-Enhanced Single-Atom Spontaneous Emission
It has been observed that the spontaneous-emission lifetime of Rydberg atoms is shortened by a large ratio when these atoms are crossing a high- Q ...
[16]
Observation of normal-mode splitting for an atom in an optical cavity
Feb 24, 1992 · Observation of normal-mode splitting for an atom in an optical cavity. R. J. Thompson, G. Rempe, and H. J. Kimble.Missing: paper | Show results with:paper
[17]
Cavity quantum electrodynamics for superconducting electrical circuits
Jun 29, 2004 · We propose a realizable architecture using one-dimensional transmission line resonators to reach the strong-coupling limit of cavity quantum electrodynamics in ...
[18]
The Nobel Prize in Physics 2012 - NobelPrize.org
The Nobel Prize in Physics 2012 was awarded jointly to Serge Haroche and David J. Wineland for ground-breaking experimental methods.
[19]
Resolution of superluminal signalling in non-perturbative cavity ...
When only the coupling to the lowest mode of frequency ωc = πc/L is ... High-cooperativity cavity QED with magnons at microwave frequencies. Phys. Rev ...
[20]
Theoretical Advances in Polariton Chemistry and Molecular Cavity ...
Aug 8, 2023 · We review recent advances made in resolving gauge ambiguities, the correct form of different QED Hamiltonians under different gauges, and their ...
[21]
Generation of arbitrary Fock states via resonant interactions in cavity ...
Apr 16, 2008 · Abstract: We propose a scheme to generate arbitrary Fock states |N> in a cavity QED using N resonant Rydberg atoms.
[22]
High-purity single-photon generation based on cavity QED
Mar 7, 2025 · We describe the cavity decay and atomic spontaneous decay with Lindblad operators: L ̂ ex = 2 κ ex | g , 0 〉〈 g , 1 | corresponds to the ...
[23]
[PDF] Comparison of Quantum and Semiclassical Radiation Theory with ...
1963. Jaynes and Cummings: Quantum and Semiclassical Radiation Theories tions to find the transient response to an arbitrary small perturbation. Thus ...
[24]
(PDF) The Jaynes-Cummings Model - ResearchGate
Aug 6, 2025 · The Jaynes-Cummings model (JCM), a soluble fully quantum mechanical model of an atom in a field, was first used (in 1963) to examine the classical aspects of ...
[25]
Stimulated Raman adiabatic passage in physics, chemistry, and ...
Mar 8, 2017 · This article reviews the many applications of STIRAP emphasizing the developments since 2001, the time when the last major review on the topic ...
[26]
On the superradiant phase transition for molecules in a quantized ...
On the superradiant phase transition for molecules in a quantized radiation field: the dicke maser model ... Lieb. J. Math. Phys., 7 (1966), p. 1016.
[27]
Coherent Conversion Between Microwave and Optical Photons—An ...
Dec 12, 2019 · Spatially separated quantum technologies will need to communicate using optical channels, rather than at the microwave frequencies which ...
[28]
A fiber Fabry–Perot cavity with high finesse - IOPscience
We have realized a fiber-based Fabry–Perot cavity with CO 2 laser-machined mirrors. It combines very small size, high finesse , small waist and mode volume.
[29]
A single-atom quantum switch for coherent light fields | Phys. Rev. A
Nov 11, 2014 · Microtoroidal cavity QED with fiber overcoupling and strong atom-field coupling: A single-atom quantum switch for coherent light fields. Scott ...
[30]
Evanescent-Vacuum-Enhanced Photon-Exciton Coupling and ...
Feb 17, 2017 · An evanescent optical mode existing in various nanophotonic structures always acts as a cavity mode rather than an electromagnetic vacuum in ...
[31]
None
Nothing is retrieved...<|separator|>
[32]
Observation of the Vacuum Rabi Spectrum for One Trapped Atom
Dec 3, 2004 · The transmission spectrum for one atom strongly coupled to the field of a high finesse optical resonator is observed to exhibit a clearly resolved vacuum Rabi ...
[33]
Fiber-pigtailing quantum-dot cavity-enhanced light emitting diodes
Sep 28, 2021 · The coupling process, fully carried out at room temperature, involves a spatial scanning technique, where the fiber facet is positioned relative ...
[34]
Cavity QED with Diamond Nanocrystals and Silica Microspheres
A solid-state cavity QED system circumvents the complexity of trapping single atoms in a microresonator and can potentially enable scalable device fabrications.
[35]
Strong coupling of a single photon to a superconducting qubit using ...
Sep 9, 2004 · Here we perform an experiment in which a superconducting two-level system, playing the role of an artificial atom, is coupled to an on-chip cavity.
[36]
Ultrafast quantum computation in ultrastrongly coupled circuit QED ...
Mar 10, 2017 · We propose a scheme to accelerate the nontrivial two-qubit phase gate in a circuit QED system, where superconducting flux qubits are ultrastrongly coupled to a ...
[37]
Atoms and molecules in cavities, from weak to strong coupling in ...
In Cavity QED—The Molecular Dimer Case we study systems that contain nuclear, electronic, and photonic degrees of freedom explicitly. First, we consider a model ...
[38]
[PDF] Cavity Quantum Electrodynamics in the Ultrastrong Coupling Regime
This field of quantum optics which studies the interaction between the quantum light emitters and cavity modes is also known nowadays as Cavity Quantum Electro- ...<|control11|><|separator|>
[39]
Quantum Rabi Oscillation: A Direct Test of Field Quantization in a ...
Mar 11, 1996 · We have observed the Rabi oscillation of circular Rydberg atoms in the vacuum and in small coherent fields stored in a high Q cavity.Missing: experiment | Show results with:experiment
[40]
None
Summary of each segment:
[41]
Time Resolved Fluorescence Measurements of Fluorophores Close ...
K. H. Drexhage, H. Kuhn, and F. P. Schäfer, Variation of the fluorescence decay time of a molecule in front of a mirror, Ber. Bunsen-Ges. Phys. Chem ...
[42]
Spontaneous emission in micro- or nanophotonic structures - PhotoniX
Sep 16, 2021 · ... which is so-called Purcell effect. Its emission enhancement is defined as Purcell factor [3, 5, 7]. F = γ γ 0 = 3 4 π 2 ( λ n ) 3 Q V . (3).Missing: γ_c / λ³ / π²
[43]
Purcell-enhanced single photons at telecom wavelengths from a ...
Feb 23, 2024 · Quantum dots are promising candidates for telecom single photon sources due to their tunable emission across the different low-loss telecommunications bands.
[44]
24 Days-Stable CNOT Gate on Fluxonium Qubits with Over 99.9 ...
Over the past decade, researchers have been dedicated to developing robust entangling gates with over 99.9% fidelity on superconducting qubits, aiming to ...
[45]
Dynamical quantum repeater using cavity QED and optical coherent ...
Nov 11, 2013 · In the framework of cavity QED, we propose a quantum repeater scheme that uses coherent light and atoms coupled to optical cavities.
[46]
A scheme of quantum repeaters with single atom and cavity-QED
Feb 15, 2010 · Here, we propose a new quantum repeaters protocol which is based on single atom-cavity QED. We use simple long-life two-level atoms to store ...
[47]
Single-photon transistor based on cavity electromagnetically ...
Mar 18, 2019 · A scheme is presented to realize a single-photon transistor based on cavity quantum electrodynamics (QED) with Rydberg atomic ensemble.
[48]
An ultra-high gain single-photon transistor in the microwave regime
Oct 15, 2022 · Our device consists of two microwave cavities dispersively coupled to a superconducting qubit. A single gate photon imprints a phase shift on ...
[49]
Strong coupling of collective intermolecular vibrations in organic ...
Jul 19, 2019 · Here we demonstrate strong coupling with collective, inter-molecular vibrations occurring in organic materials in the low-terahertz region.
[50]
Modification of excitation and charge transfer in cavity quantum ...
Modification of excitation and charge transfer in cavity quantum-electrodynamical chemistry. Christian Schäfer angel.rubio@mpsd.mpg.de, Michael Ruggenthaler ...
[51]
Chemical reactivity under collective vibrational strong coupling
Dec 9, 2022 · In this paper, we study the unimolecular dissociation reactions of many molecules, collectively interacting with an infrared cavity mode, through their ...
[52]
Understanding Polaritonic Chemistry from Ab Initio Quantum ...
In this review, we present the theoretical foundations and first-principles frameworks to describe quantum matter within quantum electrodynamics (QED) in ...
[53]
Can We Observe Nonperturbative Vacuum Shifts in Cavity QED?
Jul 7, 2023 · In this Letter we investigate the ground-state energy shift of a single dipole due to its coupling to the electromagnetic vacuum in a confined ...
[54]
Non‐Polaritonic Effects in Cavity‐Modified Photochemistry - Thomas
Nov 23, 2023 · Non-Polaritonic Effects in Cavity-Modified Photochemistry. Philip A. Thomas,. Corresponding Author. Philip A. Thomas. p.thomas2@exeter.ac.uk.
[55]
Vibration-Cavity Polariton Chemistry and Dynamics - Annual Reviews
Apr 20, 2022 · In this work we review the ability of vibration-cavity polaritons to modify chemical and physical processes including chemical reactivity, as ...
[56]
Cavity Optomechanics | alphaXiv
... g = g 0 n ˉ cav g = g_0\sqrt{\bar{n}_{\text{cav}}} g=g0nˉcav is the enhanced coupling rate. True quantum coherent coupling demands g > { Γ m n ˉ th , κ } g > ...
[57]
[PDF] Spectrometric reconstruction of mechanical-motional states in ...
The second term in. Hopc describes the radiation-pressure coupling, and g0 is the single-photon optomechanical coupling strength [47]. The annihilation and ...
[58]
Optically Coherent Nitrogen-Vacancy Defect Centers in Diamond ...
Mar 20, 2023 · Nitrogen-vacancy defect centers (NV) in diamond act as quantum memories and can be interfaced with coherent photons as demonstrated in entanglement protocols.
[59]
Emergent quantum phase transition of a Josephson junction ...
Jun 27, 2024 · Here we investigate the emergent criticality of a junction coupled to a multimode resonator when the number of modes is increased.
[60]
Cavity Quantum Electrodynamics with Hyperbolic van der Waals ...
May 26, 2023 · We propose and discuss a promising platform to achieve this goal based on a two-dimensional electronic material encapsulated by a planar cavity ...
[61]
A Complete Active Space Self-Consistent Field Approach for ...
Jul 7, 2025 · In this work, we extend the complete active space self-consistent field (CASSCF) approach to polaritonic systems.