On the fluctuations of the number of atoms in the condensate
arXiv:2502.10880 · doi:10.1088/1361-6633/ae0e33
Abstract
Bose-Einstein condensation represents a remarkable phase transition, characterized by the formation of a single quantum subsystem. As a result, the statistical properties of the condensate are highly unique. In the case of a Bose gas, while the mean number of condensed atoms is independent of the choice of statistical ensemble, the microcanonical, canonical, or grand canonical variances differ significantly among these ensembles. In this paper, we review the progress made over the past 30 years in studying the statistical fluctuations of Bose-Einstein condensates. Focusing primarily on the ideal Bose gas, we emphasize the inequivalence of the Gibbs statistical ensembles and examine various approaches to this problem. These approaches include explicit analytic results for primarily one-dimensional systems, methods based on recurrence relations, asymptotic results for large numbers of particles, techniques derived from laser theory, and methods involving the construction of statistical ensembles via stochastic processes, such as the Metropolis algorithm. We also discuss the less thoroughly resolved problem of the statistical behavior of weakly interacting Bose gases. In particular, we elaborate on our stochastic approach, known as the hybrid sampling method. The experimental aspect of this field has gained renewed interest, especially following groundbreaking recent measurements of condensate fluctuations. These advancements were enabled by unprecedented control over the total number of atoms in each experimental realization. Additionally, we discuss the fluctuations in photonic condensates as an illustrative example of grand canonical fluctuations. Finally, we briefly consider the future directions for research in the field of condensate statistics.
arXiv comment33 pages + references, review
References in corpus (143)
- Theory of Bose-Einstein condensation in trapped gases
- Observation of resonance condensation of fermionic atom pairs
- The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
- Condensation of Pairs of Fermionic Atoms Near a Feshbach Resonance
- Berezinskii-Kosterlitz-Thouless Crossover in a Trapped Atomic Gas
- Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
- Quantum Mechanical Stabilization of a Collapsing Bose-Bose Mixture
- Bose-Einstein condensation of photons in an optical microcavity
- Observation of quantum droplets in a strongly dipolar Bose gas
- Regimes of quantum degeneracy in trapped 1D gases
- Cavity QED with a Bose-Einstein condensate
- Quantum-fluctuation-driven crossover from a dilute Bose-Einstein condensate to a macro-droplet in a dipolar quantum fluid
- Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
- Theory of the Weakly Interacting Bose Gas
- Quantum phases from competing short- and long-range interactions in an optical lattice
- Long-lived and transient supersolid behaviors in dipolar quantum gases
- Dipolar physics: A review of experiments with magnetic quantum gases
- Observation of Phase Fluctuations in Bose-Einstein Condensates
- Finite Temperature Models of Bose-Einstein Condensation
- Pair correlations in a finite-temperature 1D Bose gas
- The low-energy Goldstone mode in a trapped dipolar supersolid
- Observations of density fluctuations in an elongated Bose gas: ideal gas and quasi-condensate regimes
- Simulations of Bose fields at finite temperature
- Strong saturation absorption imaging of dense clouds of ultracold atoms
- Sub-Poissonian fluctuations in a 1D Bose gas: from the quantum quasi-condensate to the strongly interacting regime
- Phase Transition in the Number Partitioning Problem
- Quantum Supremacy of Many-Particle Thermal Machines
- Phase-fluctuating 3D condensates in elongated traps
- Quantum Monte Carlo Calculations for a large number of bosons in a harmonic trap
- Condensate fluctuations of a trapped, ideal Bose gas
- Direct Observation of Sub-Poissonian Number Statistics in a Degenerate Bose Gas
- The stochastic Gross-Pitaevskii equation II
- Principal problems in Bose-Einstein condensation of dilute gases
- Finite temperature correlations and density profiles of an inhomogeneous interacting 1D Bose gas
- Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate, and measure levels
- The critical temperature of a trapped, weakly interacting Bose gas
- Anomalous fluctuations of the condensate in interacting Bose gases
- Observation of grand-canonical number statistics in a photon Bose-Einstein condensate
- Finite temperature correlations in the Lieb-Liniger 1D Bose gas
- Generalized Hydrodynamics in the 1D Bose gas: theory and experiments
- Statistical physics of Bose-Einstein condensed light in a dye microcavity
- Observation of deviations from ideal gas thermodynamics in a trapped Bose-Einstein condensed gas
- Breaking of ensemble equivalence in networks
- Improved detection of small atom numbers through image processing
- Effects of Interactions on the Critical Temperature of a Trapped Bose Gas
- Condensate Fluctuations in Trapped Bose Gases: Canonical vs. Microcanonical Ensemble
- Critical temperature of a trapped Bose gas: comparison of theory and experiment
- Multi-mode description of an interacting Bose-Einstein condensate
- Anomalous fluctuations in phases with a broken continuous symmetry
- Non-destructive Faraday imaging of dynamically controlled ultracold atoms
- Quantum and thermal effects in dark soliton formation and dynamics in a 1D Bose gas
- Non-local pair correlations in the 1D Bose gas at finite temperature
- Fluctuations of composite observables and stability of statistical systems
- Canonical Bose gas simulations with stochastic gauges
- Spatial nonlocal pair correlations in a repulsive 1D Bose gas
- When Superconductivity Crosses Over: From BCS to BEC
- Fermion-boson transmutation and comparison of statistical ensembles in one dimension
- The stochastic projected Gross-Pitaevskii equation
- Canonical Statistics of Trapped Ideal and Interacting Bose Gases
- Maxwell's Demon at work: Two types of Bose condensate fluctuations in power-law traps
- A comparison between microscopic methods for finite temperature Bose gases
- Preparation of ultracold atom clouds at the shot noise level
- A Monte Carlo Formulation of the Bogolubov Theory
- Observation of Atom Number Fluctuations in a Bose-Einstein Condensate
- Adiabatic approximation and fluctuations in exciton-polariton condensates
- A quantum Langevin model for non-equilibrium condensation
- Bose-Einstein Condensation, Fluctuations, and Recurrence Relations in Statistical Mechanics
- Quantum mixtures of ultracold gases of neutral atoms
- Calibrating High Intensity Absorption Imaging of Ultracold Atoms
- Can a Bose gas be saturated?
- Properties of the stochastic Gross-Pitaevskii equation: Projected Ehrenfest relations and the optimal plane wave basis
- Machine learning discovery of new phases in programmable quantum simulator snapshots
- Dipolar Bose-Einstein condensates at Finite temperature
- Ensemble equivalence for general many-body systems
- Interaction Effects on Number Fluctuations in a Bose-Einstein Condensate of Light
- The saddle-point method for condensed Bose gases
- Finite temperature analysis of a quasi2D dipolar gas
- Photon number-resolved measurement of an exciton-polariton condensate
- Temperature Dependent Density Profiles of Dipolar Droplets
- Non-diffusive phase spreading of a Bose-Einstein condensate at finite temperature
- Calorimetry of a Bose-Einstein condensed photon gas
- Fully quantum scalable description of driven dissipative lattice models
- Condensation of N interacting bosons: Hybrid approach to condensate fluctuations
- Condensed Fraction of an Atomic Bose Gas Induced by Critical Correlations
- Condensate statistics in interacting Bose gases: exact results
- Gaussian concentration bound and Ensemble equivalence in generic quantum many-body systems including long-range interaction
- Anomalous condensate fluctuations in strongly interacting superfluids
- Single-exposure absorption imaging of ultracold atoms using deep learning
- No Anomalous Fluctuations Exist in Stable Equilibrium Systems
- Quantum simulation of traversable wormhole spacetimes in a dc-SQUID array
- Linear density response in the random phase approximation for confined Bose vapours at finite temperature
- Observation of Microcanonical Atom Number Fluctuations in a Bose-Einstein Condensate
- Sub-atom shot noise Faraday imaging of ultracold atom clouds
- Number-of-particle fluctuations in systems with Bose-Einstein condensate
- Finite-temperature trapped dipolar Bose gas
- Microcanonical fluctuations of the condensate in weakly interacting Bose gases
- The grand canonical catastrophe as an instance of condensation of fluctuations
- Asymptotics of the number partitioning distribution
- Full counting statistics of interacting lattice gases after an expansion: The role of the condensate depletion in the many-body coherence
- Optimized fringe removal algorithm for absorption images
- Statistical properties of one dimensional attractive Bose gas
- Statistical properties of one dimensional Bose gas
- Fluctuation-dissipation relation for a Bose-Einstein condensate of photons
- Particle fluctuations in nonuniform and trapped Bose gases
- Fluctuations of a weakly interacting Bose-Einstein condensate
- Fluctuations of the Condensate in Ideal and Interacting Bose Gases
- Appropriate probe condition for absorption imaging of ultracold Li atoms
- Physical interpretation of the canonical ensemble for long-range interacting systems in the absence of ensemble equivalence
- Classical field records of a quantum system: their internal consistency and accuracy
- Analysis and calibration of absorptive images of Bose-Einstein condensate at non-zero temperatures
- Effective statistical fringe removal algorithm for high-sensitivity imaging of ultracold atoms
- Grand-canonical condensate fluctuations in weakly interacting Bose-Einstein condensates of light
- Statistical Properties of Interacting Bose Gases in Quasi-2D Harmonic Traps
- Condensation vs Ordering: From the Spherical Models to BEC in the Canonical and Grand Canonical Ensemble
- Analytic thermodynamic properties of the Lieb-Liniger gas
- Critical fluctuations in a confined driven-dissipative quantum condensate
- Bose-Einstein condensate fluctuations versus an interparticle interaction
- Optimally focused cold atom systems obtained using density-density correlations
- Bose-Einstein condensation and non-extensive statistics
- Fluctuation dynamics of an open photon Bose-Einstein condensate
- Anomalous fluctuations of two-dimensional Bose-Einstein condensates
- Classical fields in the one-dimensional Bose gas: applicability and determination of the optimal cutoff
- Continuum of classical-field ensembles from canonical to grand canonical and the onset of their equivalence
- Correlations of quasi-2D dipolar ultracold gas at finite temperatures
- Fermi-Dirac statistics and the number theory
- Self-similar analytical solution of the critical fluctuations problem for the Bose-Einstein condensation in an ideal gas
- Suppression of Bogoliubov momentum pairing and emergence of non-Gaussian correlations in ultracold interacting Bose gases
- Spatial calibration of high-density absorption imaging
- Complex wave fields in the interacting one-dimensional Bose gas
- Measurement of the order parameter and its spatial fluctuations across Bose-Einstein condensation
- Full quantum theory of nonequilibrium phonon condensation and phase transition
- Mesoscopic density grains in the 1d interacting Bose gas from the exact Yang-Yang solution
- Atom Number Fluctuations in Bose Gases -- Statistical analysis of parameter estimation
- Anomalous particle-number fluctuations in a three-dimensional interacting Bose-Einstein condensate
- Equivalence of ensembles, condensation and glassy dynamics in the Bose-Hubbard Hamiltonian
- Condensation of N bosons IV: A simplified Bogoliubov master equation analysis of fluctuations in an interacting Bose gas
- Statistical properties of cold bosons in a ring trap
- Berezinskii-Kosterlitz-Thouless phase induced by dissipating quasisolitons
- Canonical vs. Grand Canonical Ensemble for Bosonic Gases under Harmonic Confinement
- Number-of-Particle Fluctuations and Stability of Bose-Condensed Systems
- Condensate fluctuations in the dilute Bose gas
- Mechanism for sound dissipation in a two-dimensional degenerate Fermi gas
- Bose-Einstein condensation in canonical ensemble with fixed total momentum