Second-order correlation function of a phase fluctuating Bose-Einstein condensate (original) (raw)

Measurement of the Spatial Correlation Function of Phase Fluctuating Bose-Einstein Condensates

Physical Review Letters, 2003

We measure the intensity correlation function of two interfering spatially displaced copies of a phase fluctuating Bose-Einstein Condensate (BEC). It is shown that this corresponds to a measurement of the phase correlation properties of the initial condensate. Analogous to the method used in the stellar interferometer experiment of Hanbury Brown and Twiss, we use spatial intensity correlations to determine the phase coherence lengths of elongated BECs. We find good agreement with our prediction of the correlation function and confirm the expected coherence length.

Measurement of the Coherence of a Bose-Einstein Condensate

Physical Review Letters, 1999

We present experimental and theoretical studies of the coherence properties of a Bose-Einstein condensate (BEC) using an interference technique. Two optical standing wave pulses of duration 100 ns and separation Dt are applied to a condensate. Each standing wave phase grating makes small copies of the condensate displaced in momentum space. The quantum mechanical amplitudes of each copy interfere, depending on Dt and on spatial phase variations across the condensate. We find that the behavior of a trapped BEC is consistent with a uniform spatial phase. A released BEC, however, exhibits large phase variation across the condensate.

Spatial coherence and density correlations of trapped Bose gases

Physical Review A, 1999

We study first and second order coherence of trapped dilute Bose gases using appropriate correlation functions. Special attention is given to the discussion of second order or density correlations. Except for a small region around the surface of a Bose-Einstein condensate the correlations can be accurately described as those of a locally homogeneous gas with a spatially varying chemical potential. The degrees of first and second order coherence are therefore functions of temperature, chemical potential, and position. The second order correlation function is governed both by the tendency of bosonic atoms to cluster and by a strong repulsion at small distances due to atomic interactions. In present experiments both effects are of comparable magnitude. Below the critical temperature the range of the bosonic correlation is affected by the presence of collective quasi-particle excitations. The results of some recent experiments on second and third order coherence are discussed. It is shown that the relation between the measured quantities and the correlation functions is much weaker than previously assumed. 03.75.Fi,05.30.Jp Typeset using REVT E X

Phase fluctuations in Bose–Einstein condensates

Applied Physics B, 2001

We demonstrate the existence of phase fluctuations in elongated Bose-Einstein Condensates (BECs) and study the dependence of those fluctuations on the system parameters. A strong dependence on temperature, atom number, and trapping geometry is observed. Phase fluctuations directly affect the coherence properties of BECs. In particular, we observe instances where the phase coherence length is significantly smaller than the condensate size. Our method of detecting phase fluctuations is based on their transformation into density modulations after ballistic expansion. An analytic theory describing this transformation is developed.

Matter-Wave Interferometry with Phase Fluctuating Bose-Einstein Condensates

Physical Review Letters, 2007

Elongated Bose-Einstein condensates (BECs) exhibit strong spatial phase fluctuations even well below the BEC transition temperature. We demonstrate that atom interferometers using such condensates are robust against phase fluctuations, i.e. the relative phase of the split condensate is reproducible despite axial phase fluctuations. However, larger phase fluctuations limit the coherence time, especially in the presence of some asymmetries in the two wells of the interferometer.

Characterizing the coherence of Bose-Einstein condensates and atom lasers

Optics Express, 1997

For a dilute, interacting Bose gas of magnetically-trapped atoms at temperatures below the critical temperature T 0 for Bose-Einstein condensation, we determine the second-order coherence function g (2) (r 1 , r 2) within the framework of a finite-temperature quantum field theory. We show that, because of the different spatial distributions of condensate and thermal atoms in the trap, g (2) (r 1 , r 2) does not depend on |r 1 − r 2 | alone. This means that the experimental determinations of g (2) reported to date give only its spatial average. Such an average may underestimate the degree of coherence attainable in an atom laser by judicious engineering of the output coupler.

Phase-Fluctuating 3D Bose-Einstein Condensates in Elongated Traps

Physical Review Letters, 2001

We find that in very elongated 3D trapped Bose gases, even at temperatures far below the BEC transition temperature Tc, the equilibrium state will be a 3D condensate with fluctuating phase (quasicondensate). At sufficiently low temperatures the phase fluctuations are suppressed and the quasicondensate turns into a true condensate. The presence of the phase fluctuations allows for extending thermometry of Bose-condensed gases well below those established in current experiments. 03.75.Fi,05.30.Jp Phase coherence properties are among the most interesting aspects of Bose-condensed gases. Since the discovery of Bose-Einstein condensation (BEC) in trapped ultra-cold clouds of alkali atoms [1], various experiments have proved the presence of phase coherence in trapped condensates. The MIT group [2] has found the interference of two independently prepared condensates, once they expand and overlap after switching off the traps. The MIT [3], NIST [4] and Munich [5] experiments provide evidence for the phase coherence of trapped condensates through the measurement of the phase coherence length and/or single particle correlations.

Loss and revival of phase coherence in a Bose Einstein condensate moving through an optical lattice

Journal of Physics B-atomic Molecular and Optical Physics, 2004

We investigate the phase coherence of a trapped Bose-Einstein condensate that undergoes a dynamical superfluid-insulator transition in the presence of a one-dimensional optical lattice. We study the evolution of the condensate after a sudden displacement of the harmonic trapping potential by solving the Gross-Pitaevskii equation, and comparing the results with the prediction of two effective 1D models. We show that, owing to the 3D nature of the system, the breakdown of the superfluid current above a critical displacement is not associated to a sharp transition, but there exists a range of displacements for which the condensate can recover a certain degree of coherence. We also discuss the implications on the interference pattern after the ballistic expansion as measured in recent experiments at LENS.

Characterization and control of phase fluctuations in elongated Bose-Einstein condensates

Applied Physics B: Lasers and Optics, 2003

Quasi one dimensional Bose-Einstein condensates (BECs) in elongated traps exhibit significant phase fluctuations even at very low temperatures. We present recent experimental results on the dynamic transformation of phase fluctuations into density modulations during time-of-flight and show the excellent quantitative agreement with the theoretical prediction. In addition we confirm that under our experimental conditions, in the magnetic trap density modulations are strongly suppressed even when the phase fluctuates. The paper also discusses our theoretical results on control of the condensate phase by employing a time-dependent perturbation. Our results set important limitations on future applications of BEC in precision atom interferometry and atom optics, but at the same time suggest pathways to overcome these limitations.

Hanbury Brown and Twiss correlations across the Bose–Einstein condensation threshold

Nature Physics, 2012

Hanbury Brown and Twiss correlations-correlations in farfield intensity fluctuations-yield fundamental information on the quantum statistics of light sources, as demonstrated after the discovery of photon bunching 1-3 . Drawing on the analogy between photons and atoms, similar measurements have been performed for matter-wave sources, probing density fluctuations of expanding ultracold Bose gases 4-8 . Here we use two-point density correlations to study how coherence is gradually established when crossing the Bose-Einstein condensation threshold. Our experiments reveal a persistent multimode character of the emerging matter-wave as seen in the non-trivial spatial shape of the correlation functions for all probed source geometries, from nearly isotropic to quasi-onedimensional, and for all probed temperatures. The qualitative features of our observations are captured by ideal Bose gas theory 9 , whereas the quantitative differences illustrate the role of particle interactions.