Sound propagation in a cylindrical Bose-condensed gas

Zaremba, E.

doi:10.1103/physreva.57.518

Cited by 137 publications

(223 citation statements)

References 12 publications

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“…This effect, predicted in Refs. [24,25] and observed numerically in [26] goes beyond the quasi-1D approach: it occurs when the excitation has a wavelength allowing exploration of side regions of the condensate that have lower local sound velocity. Hence, it cannot be reproduced by using the adiabatic ansatz (1).…”

Section: Transmission Modesmentioning

confidence: 99%

Bose-Einstein beams: Coherent propagation through a guide

2001

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We compute the stationary profiles of a coherent beam of Bose-Einstein condensed atoms propagating through a guide. Special emphasis is put on the effect of a disturbing obstacle present in the trajectory of the beam. The obstacle considered (such as a bend in the guide, or a laser field perpendicular to the beam) results in a repulsive or an attractive potential acting on the condensate. Different behaviors are observed when the beam velocity (with respect to the speed of sound), the size of the obstacle (relative to the healing length) and the intensity and sign of the potential are varied. The existence of bound states of the condensate is also considered.

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Section: Transmission Modesmentioning

confidence: 99%

Bose-Einstein beams: Coherent propagation through a guide

2001

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“…Low-lying excitations are found using standard Bogoliubov theory [5], after averaging over the transverse degrees of freedom [6]. The Bogoliubov spectrum for the excitation frequencies is ω B k = (ω k (ω k + 2M c 2 1d /h)) 1/2 ≈ c 1D k for small k, with the free particle energyhω k = h 2 k 2 /2M and the 1D speed of sound c 1D = µ/2M [19]. The Fourier component for phase fluctuations with wavevector k is…”

Section: Momentum Distribution and Correlation Function Of Quasicondementioning

confidence: 99%

Momentum distribution and correlation function of quasicondensates in elongated traps

et al. 2003

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We calculate the spatial correlation function and momentum distribution of a phase-fluctuating, elongated three-dimensional condensate, in a trap and in free expansion. We take the inhomogeneous density profile into account via a local density approximation. We find an almost Lorentzian momentum distribution, in stark contrast with a Heisenberg-limited Thomas-Fermi condensate.PACS numbers: 03.75. Fi,05.30.Jp Low-dimensional, degenerate Bose gases are expected to have significantly different coherence properties than their three-dimensional (3D) counterparts. In onedimensional (1D) uniform systems, no true condensate can exist at any temperature T because of a large population of low-lying states that destroys phase coherence (see [1] and references therein). For a trapped gas, the situation is different: the finite size of the sample naturally introduces a low-momentum cutoff, and at sufficiently low temperature T ≪ T φ , a phase coherent sample can exist [1]. Above T φ , the degenerate cloud is a so-called quasicondensate: the density has the same smooth profile as a true condensate, but the phase fluctuates in space and time. As shown in [2], this analysis holds also for 3D condensates in elongated traps even if, strictly speaking, radial motion is not frozen. Such 3D, phase-fluctuating condensates have been recently observed experimentally in equilibrium [3] and nonequilibrium [4] samples.Phase fluctuations of the condensate are caused mainly by long-wavelength (or low-energy) collective excitations [1,2,5]. In elongated traps, the lowest energy modes are 1D excitations along the long axis of the trap [6]. Furthermore, in the long-wavelength limit, density fluctuations are small and can be neglected for the calculation of the correlation function [1,7]. Then, the single-particle density matrix is, assuming cylindrical symmetry,We have introduced ∆φ 2 (Z, s) = [φ(z) − φ(z ′ )] 2 , the variance of the phase difference between two points z,z ′ on the axis of the trap, with mean coordinate Z = (z + z ′ )/2 and relative distance s = z − z ′ , and the overlap function χ = n 0 (ρ, z)n 0 (ρ, z ′ ), where n 0 is the (quasi)condensate density. The variance ∆φ 2 (Z, s), the key quantity to characterize the spatial fluctuations of the phase of the condensate, has been calculated in [2], and an analytical form has been given, which is valid ‡ UMRA 8501 du CNRS * e-mail: fabrice.gerbier@iota.u-psud.fr † current address:Department of Physics, University of Toronto, Canada.near the center of the trap (i.e. for Z, s ≪ L, with L the condensate half-length). The first goal of this paper is to find an analytical approximation for the variance ∆φ 2 (Z, s) valid across the whole sample. This is motivated by the fact that coherence measurements with quasi-condensates [10,11] are quite sensitive to the inhomogeneity of the sample. In position space, interferometry [12,13] gives access to the spatial correlation functionEquivalently, one can measure the axial (i.e. integrated over transverse momenta) momentum distribution P(p z ),...

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“…Several efforts are also focusing on the creation of quantum computers [9] and ultrasensitive interferometers [10]. In this paper we study the propagation of sound waves on top of a Bose-Einstein condensate at rest in a one-dimensional lattice.The propagation of sound in a harmonically trapped condensate without lattice has been already observed experimentally [11,12] and studied theoretically [13,14,15,16]. Generally speaking, it is important to study the propagation of sound also in the non linear regime, where density fluctuations are comparable to the background density of the condensate.…”

mentioning

confidence: 99%

“…The propagation of sound in a harmonically trapped condensate without lattice has been already observed experimentally [11,12] and studied theoretically [13,14,15,16]. Generally speaking, it is important to study the propagation of sound also in the non linear regime, where density fluctuations are comparable to the background density of the condensate.…”

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confidence: 99%

Propagation of sound in a Bose-Einstein condensate in an optical lattice

et al. 2004

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We study the propagation of sound waves in a Bose-Einstein condensate trapped in a onedimensional optical lattice. We find that the velocity of propagation of sound wavepackets decreases with increasing optical lattice depth, as predicted by the Bogoliubov theory. The strong interplay between nonlinearities and the periodicity of the external potential raise new phenomena which are not present in the uniform case. Shock waves, for instance, can propagate slower than sound waves, due to the negative curvature of the dispersion relation. Moreover, nonlinear corrections to the Bogoliubov theory appear to be important even with very small density perturbations, inducing a saturation on the amplitude of the sound signal.The study of Bose Einstein condensates in optical lattices is a very active field of research, both from the theoretical and experimental sides. The presence of the lattice can drammatically modify the behaviour of the system with respect to the uniform case, giving rise to new phenomena like, for instance, a Mott-insulator superfluid phase transition [1,2] or the occurence of dynamical instabilities [3,4,5,6,7,8]. Several efforts are also focusing on the creation of quantum computers [9] and ultrasensitive interferometers [10]. In this paper we study the propagation of sound waves on top of a Bose-Einstein condensate at rest in a one-dimensional lattice.The propagation of sound in a harmonically trapped condensate without lattice has been already observed experimentally [11,12] and studied theoretically [13,14,15,16]. Generally speaking, it is important to study the propagation of sound also in the non linear regime, where density fluctuations are comparable to the background density of the condensate. The reason is that only large amplitude wavepackets can be realistically observed experimentally. It turns out, however, that nonlinear effects in the sound propagation are particolarly interesting also from the theorethical point of view. For instance, the formation of shock waves in front of a bright sound wavepacket (positive density variation) a uniform or harmonically trapped condensates has been studied in [16], and analitycal solutions have also been discussed in [17,18,19]. In the presence of a periodic potential, theoretical aspects of the propagation of sound have been so far explored only in the linear regime [5,20,21,22,23,24,25,26,27,28,29,30]. The main question addressed in this work is the strong interplay between nonlinear effects and the periodicity of the external potential.We assume a fully coherent condensate described by an effective one-dimensional Gross-Pitaevskii (GP) equation. In the uniform case, the spectrum of elementary excitations is given by the well-known Bogoliubov dispersion relation ω(q) = q 2 /2m (q 2 /2m + 2U ), where q is the momentum of the excitation, m the atomic mass and U = gn the inverse compressibility with g = 4πh 2 a/m the interaction strength and n the density. For momenta q smaller than the inverse of the healing length ξ = 1/ √ 8πan, the excitation spec...

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Sound propagation in a cylindrical Bose-condensed gas

Cited by 137 publications

References 12 publications

Bose-Einstein beams: Coherent propagation through a guide

Bose-Einstein beams: Coherent propagation through a guide

Momentum distribution and correlation function of quasicondensates in elongated traps

Propagation of sound in a Bose-Einstein condensate in an optical lattice

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