Condensate
The term condensate has multiple meanings in science and engineering, referring to concentrated or transitioned states of matter in various contexts. These include quantum phenomena, thermodynamic processes, hydrocarbon products, and biological structures. The following sections outline key examples. In quantum physics, a Bose–Einstein condensate (BEC) is a state of matter that arises when a dilute gas of bosons is cooled to temperatures near absolute zero (−273.15 °C), causing many particles to occupy the same quantum state, exhibiting macroscopic quantum effects such as superfluidity. Predicted by Satyendra Nath Bose and Albert Einstein in the 1920s, the first BEC was experimentally realized in 1995 using rubidium-87 atoms.[1][2] Further details on BECs and other quantum condensates are covered in the dedicated section. In thermodynamics and chemistry, condensate typically denotes the liquid phase formed by the condensation of vapor, as in distillation processes where gases cool and liquefy. This is fundamental in applications like fractional distillation and chemical separation.[3] In petroleum engineering, natural gas condensate is a low-density mixture of liquid hydrocarbons (primarily pentanes and heavier) extracted from raw natural gas, valued for its use in gasoline blending and petrochemicals. Production involves separating it from gas streams at processing facilities.[4] In biology, biomolecular condensates are membrane-less, dynamic assemblies of proteins, RNA, and other molecules within cells, formed via liquid-liquid phase separation. These structures organize biochemical reactions, such as in stress granules or nucleoli, and play roles in gene regulation and cellular signaling.[5]In quantum physics
Bose–Einstein condensates
A Bose–Einstein condensate (BEC) is a distinct state of matter that emerges when a dilute gas of bosons, such as certain alkali metal atoms, is cooled to temperatures approaching absolute zero, triggering a quantum phase transition in which a macroscopic fraction of the particles coherently occupy the system's lowest-energy quantum state.[6] This condensation arises from Bose–Einstein statistics, which allow indistinguishable bosons to accumulate in the same state without the Pauli exclusion principle that governs fermions.[7] The phenomenon represents a direct manifestation of quantum mechanics on a macroscopic scale, where the de Broglie wavelength of the particles becomes comparable to the interparticle spacing, leading to wave-like collective behavior.[8] The theoretical foundation for BECs was laid in the mid-1920s. In 1924, Satyendra Nath Bose derived a new quantum statistics for photons to explain Planck's blackbody radiation law, treating light quanta as indistinguishable particles. Albert Einstein extended this framework in two papers later that year and in 1925, applying it to an ideal gas of massive, non-interacting bosons and predicting that below a critical temperature, a significant portion of the particles would "condense" into the ground state, forming a new phase of matter.[9] Despite early interest in systems like liquid helium, experimental verification proved challenging due to interactions and the need for extreme cooling. The breakthrough came in 1995, when Eric Cornell and Carl Wieman at JILA produced the first gaseous BEC using rubidium-87 atoms, followed by Wolfgang Ketterle's independent creation of a sodium-23 BEC at MIT.[10][11] Their achievements, which demonstrated BEC in dilute, weakly interacting atomic vapors, earned them the 2001 Nobel Prize in Physics.[6] For an ideal, non-interacting Bose gas, the critical temperature T_c marking the onset of condensation is derived from the condition where the maximum number of particles in excited states equals the total particle number, given by T_c = \frac{h^2}{2\pi m k_B} \left( \frac{n}{\zeta(3/2)} \right)^{2/3}, where h is Planck's constant, m is the boson mass, k_B is Boltzmann's constant, n is the particle number density, and \zeta(3/2) \approx 2.612 is the value of the Riemann zeta function at argument 3/2.[8] This formula highlights the dependence on density and mass, predicting T_c on the order of nanokelvins for typical atomic densities around $10^{12} to $10^{15} cm^{-3}. In real experiments, interactions slightly shift T_c, but the ideal gas model provides essential guidance.[12] Achieving BEC requires cooling techniques that reach temperatures below T_c, typically in the microkelvin to nanokelvin regime. Initial laser cooling uses Doppler and polarization gradient methods to slow atoms by absorbing and re-emitting photons, reducing their kinetic energy to around 100 μK.[12] Subsequent evaporative cooling in a magnetic trap selectively ejects the highest-energy atoms, allowing the remaining cloud to thermalize at lower temperatures via elastic collisions, often reaching 50–200 nK with condensate fractions exceeding 40%.[12] These methods, pioneered in the 1990s, enable the production of pure BECs with up to $10^7 atoms in milliseconds.[8] BECs display profound quantum properties due to their macroscopic occupation of a single quantum state. The system exhibits phase coherence over the entire cloud, analogous to a matter-wave laser, enabling long-range order and stimulated emission of atoms.[7] Superfluidity emerges, characterized by frictionless flow and quantized vortices, while matter-wave interference produces high-contrast fringes when multiple condensates overlap, confirming the wavelike nature of massive particles.[7] These traits stem from the condensate's description by a macroscopic wavefunction governed by the Gross–Pitaevskii equation, which incorporates weak interparticle interactions.[13] The unique coherence and tunability of BECs have opened avenues for applications in precision metrology and quantum technologies. They serve as ultrasensitive probes in atom interferometers for measuring gravitational acceleration with uncertainties below $10^{-9} g or testing general relativity through equivalence principle violations.[7] In quantum simulation, BECs mimic condensed-matter systems, such as Hubbard models for correlated electrons, aiding studies of exotic phases like supersolids.[7] Recent developments up to 2025 have expanded BEC capabilities beyond dilute atomic gases. Loading BECs into optical lattices—periodic potentials formed by interfering laser beams—has enabled simulations of lattice models with unprecedented control, revealing anomalous particle number fluctuations near superfluid-Mott insulator transitions in experiments reported in 2025.[14] In 2024, the first Bose–Einstein condensate of dipolar molecules was produced at temperatures below 10 nK, enabling studies of strongly interacting quantum gases.[15] Photonic BECs, realized in driven-dissipative microcavities filled with dye molecules, achieve condensation at room temperature, offering insights into non-equilibrium quantum phases and potential for integrated photonic devices, as demonstrated in 2021 studies of modified condensation dynamics.[16] In space, the 2017 MAIUS mission aboard a sounding rocket produced the first microgravity BEC of rubidium atoms, generating high-fidelity matter waves over 6 minutes of free fall to enhance interferometry sensitivity for fundamental physics tests.[17]Other quantum condensates
Other quantum condensates encompass a variety of systems where quantum coherence emerges through mechanisms distinct from the direct Bose-Einstein condensation of non-interacting bosons, often involving composite particles or pairing to overcome fermionic statistics. These states exhibit macroscopic quantum phenomena such as superfluidity and coherence, but arise in contexts ranging from ultracold atomic gases to solid-state materials and high-energy physics vacuums. Fermionic condensates form when fermions, which obey the Pauli exclusion principle and cannot occupy the same quantum state, pair up to create bosonic-like molecules or pairs that then condense into a coherent state, enabling superfluid behavior in ultracold atomic gases. This pairing is typically induced via Feshbach resonances, tunable magnetic interactions that bind fermionic atoms into weakly bound pairs. The first experimental realization occurred in 2003 using a gas of potassium-40 atoms cooled to near absolute zero, where resonance pairing led to a condensate of fermionic atom pairs exhibiting long-range coherence.[18] In superconductivity, Cooper pair condensates arise when electrons—fundamental fermions—pair through attractive interactions mediated by lattice phonons, forming a bosonic condensate that allows zero-resistance current flow and the Meissner effect. This phenomenon is described by the Bardeen-Cooper-Schrieffer (BCS) theory, proposed in 1957, which models the superconducting transition as the condensation of these pairs below a critical temperature. The theory's key result is the energy gap equation for the pairing amplitude \Delta, \Delta = V \sum_k \frac{\Delta}{2E_k} \tanh\left(\frac{\beta E_k}{2}\right), where V is the interaction strength, E_k = \sqrt{\epsilon_k^2 + \Delta^2} is the quasiparticle energy with \epsilon_k the single-particle energy relative to the Fermi level, \beta = 1/(k_B T), and the sum runs over momentum states near the Fermi surface. This self-consistent equation determines the gap \Delta(T), which vanishes above the critical temperature and sets the scale for superconducting properties like the binding energy of pairs, approximately $2\Delta(0) \approx 3.5 k_B T_c.[19] Exciton-polariton condensates represent hybrid light-matter systems where excitons (electron-hole pairs in a semiconductor) couple strongly to cavity photons, forming half-light, half-matter quasiparticles known as polaritons, which are bosons due to their composite nature and can condense into a coherent state. These condensates enable lasing without population inversion, as the bosonic stimulation amplifies emission from the lower polariton branch. The first unambiguous observation occurred in 2006 in a cadmium telluride-based semiconductor microcavity under non-resonant optical pumping, where polaritons accumulated in the zero-momentum ground state above a critical density, showing thermalization and quadratic dispersion characteristic of Bose-Einstein condensation.[20] Quark condensates appear in quantum chromodynamics (QCD) as a non-perturbative vacuum effect where the strong interaction breaks chiral symmetry spontaneously, leading to a nonzero vacuum expectation value for the quark bilinear operator \langle \bar{q} q \rangle, which generates effective masses for light quarks and underlies hadron structure. This chiral symmetry breaking, analogous to superconductivity in the Nambu-Jona-Lasinio model, results in the quark-antiquark pairs forming a scalar condensate in the QCD vacuum, with the magnitude |\langle \bar{q} q \rangle| \approx (250 \, \mathrm{MeV})^3 estimated from lattice QCD simulations and sum rules. The original conceptualization dates to 1961, modeling quarks (then nucleons) with a four-fermion interaction that dynamically generates the condensate and Goldstone modes like pions. Unlike Bose-Einstein condensates of composite bosons, fermionic and related condensates require attractive pairing mechanisms to convert fermionic statistics into effective bosonic behavior, allowing macroscopic occupation of a single quantum state. For instance, atomic fermionic condensates rely on tunable s-wave pairing, while Cooper pairs involve phonon-mediated attraction; in contrast, exciton-polaritons inherit bosonic statistics from their light-matter hybridization without needing explicit pairing. Additionally, these systems can achieve condensation at higher temperatures than dilute atomic BECs—for example, exciton-polariton condensates form at millikelvin to even room temperatures due to their light effective mass and cavity confinement, facilitating studies of nonequilibrium quantum fluids.[21]In thermodynamics and chemistry
Vapor-liquid condensation
Vapor-liquid condensation is a reversible phase transition in which gas molecules, typically in the form of vapor, lose sufficient kinetic energy through cooling or compression to form liquid droplets, serving as the inverse process of evaporation.[22] This phenomenon occurs when the vapor reaches saturation, where the rate of condensation equals the rate of evaporation, establishing dynamic equilibrium.[23] In practical terms, it manifests in everyday scenarios such as the formation of dew on cool surfaces or fog in humid air, where water vapor condenses into visible liquid particles.[24] The thermodynamic foundation of vapor-liquid condensation is described by the Clausius-Clapeyron equation, which relates the change in vapor pressure with temperature along the coexistence curve:\frac{dP}{dT} = \frac{L}{T \Delta V}
where L is the latent heat of vaporization, T is the absolute temperature, and \Delta V is the change in specific volume between the vapor and liquid phases.[25] This equation quantifies the driving force for condensation, driven by reductions in temperature or increases in pressure that shift the system toward the liquid phase to minimize free energy. The dew point, defined as the temperature at which condensation begins for a given vapor pressure, marks the onset of this transition and is a key indicator of saturation in moist air.[26] Condensation typically initiates through nucleation, the formation of stable liquid clusters from vapor molecules, governed by classical nucleation theory. Homogeneous nucleation occurs spontaneously in a pure supersaturated vapor without external surfaces, requiring significant energy to overcome the free energy barrier for cluster formation. In contrast, heterogeneous nucleation predominates in real systems, catalyzed by impurities, aerosols, or container walls that lower the activation energy. The critical nucleus radius, beyond which clusters grow rather than evaporate, is given by
r^* = \frac{2\sigma}{\Delta G_v}
where \sigma is the surface tension between liquid and vapor, and \Delta G_v is the bulk free energy difference per unit volume driving the phase change.[27] Key factors influencing condensation include the degree of supersaturation—the excess vapor pressure above the equilibrium value—and temperature gradients that promote cooling and vapor clustering. High supersaturation accelerates nucleation rates, while gentle temperature decreases favor larger droplet growth over rapid fog formation. These principles underpin natural processes like dew accumulation on grass during clear nights or the initial droplet formation in clouds.[28] Early experimental studies of vapor-liquid condensation in the 19th century, notably by French physicist Henri Victor Regnault, provided precise measurements of vapor pressures and latent heats for water and other substances, establishing foundational data for thermodynamic models. Regnault's work from the 1840s to 1860s refined saturation vapor pressure tables, enabling accurate predictions of condensation behavior. These measurements played a crucial role in advancing cloud physics, where condensation drives precipitation and atmospheric stability.