Bogoliubov speed of sound for a dilute Bose-Einstein condensate in a 3d optical lattice

Abstract

We point out that the velocity of propagation of sound wavepackets in a Bose-Einstein condensate filling a three-dimensional cubic optical lattice undergoes a maximum with increasing lattice depth. For a realistic choice of parameters, the maximum sound velocity in a lattice condensate can exceed the sound velocity in a homogeneous condensate with the same average density by 30%. The maximum falls into the superfluid regime, and should be observable under currently achievable laboratory conditions. PACS numbers: 03.75.Lm 03.75.Kk 05.30.JpThere have been vigorous activities, and impressive achievements, concerning Bose-Einstein condensates in optical lattice potentials recently, both experimentally [1,2,3,4,5,6] and theoretically [7,8,9,10,11,12,13,14,15], culminating in the observation of the quantum phase transition from a superfluid to a Mott insulator with a condensate of 87 Rb atoms [5].On the theoretical side, substantial effort has been devoted to calculating the low-lying excitations of a condensate in an optical lattice, and thus the speed of sound, within the Bogoliubov theory [16,17,18]. In particular, it has been predicted that in a one-dimensional optical lattice the velocity of propagation of sound wavepackets decreases monotonically with increasing lattice depth [19,20]. In this letter, we argue that the situation is different for condensates in three-dimensional lattices: In this case the velocity of sound undergoes a pronounced maximum when the lattice is made successively deeper, which falls into the superfluid regime, and should be observable under currently achievable experimental conditions.We consider a 3d Bose-Einstein condensate subjected to a simple d-dimensional optical cosine latticewhere k L = 2π/λ denotes the wavenumber associated with the lattice-generating laser radiation of wavelength λ. For d = 1 we study the propagation of sound in the direction of the lattice, while assuming that the condensate remains homogeneous in the orthogonal plane. We also assume that the depth V 0 of the lattice be sufficiently deep so that only the lowest Bloch band needs to be taken into account. The velocity of sound propagation in a Bose-Einstein condensate filling the lattice then is given by the standard expression [19,20] where m * is the effective mass pertaining to the lowest band, and U is the inverse compressibility of the condensate in the lattice. In principle, also the effective mass m * appearing in eq. (2) does depend on the density of the condensate, and has to be determined by solving the Gross-Pitaevskii equation for the condensate in the lattice [7,11,13,18]. This is particularly pertinent if one considers a 1d lattice filled with an effectively 1d condensate, strongly confined by restoring potentials orthogonal to the lattice direction, so that the transversal degrees of freedom are frozen out entirely. If then each lattice site carries a comparatively large number of particles, nonlinear effects due to the meanfield interaction play a decisive role. In contrast, we focus here on trul...

Probing Sound Speed of an Optically-Trapped Bose Gas with Periodically Modulated Interactions by Bragg Spectroscopy

“…It's clear that if c 2 = 0, Eq. (3.1) recovers the sound speed in an OL [36,39,40] which decreases monotonically with v as it should be. In the presence of PMI with c 2 = 0, the second term and the last two terms in the square brackets in Eq.…”

Unusual behavior of sound velocity of a Bose gas in an optical superlattice at quasi-one-dimension

“…For instance, in recent proposals concerning the preparations of many-body states and nonequilibrium quantum phases based on engineering a superfluid reservoir [33][34][35][36], the sound velocity acts as a key parameter in determining the system-bath coupling. The control of sound velocity of a superfluid, such as by using various carefully configured external traps [16][17][18][19][20][21][22][23][24][25][26][27][28][29] , therefore constitutes an important ingredient of the reservoir engineering.…”

Scattering tightly bound dimers off a scattering potential

“…For ultra-cold atoms in an optical lattice [1,2,3] dynamical aspects include transverse resonances [4] density waves [5], the evolution of quantum fluctuations [6], the speed of sound [7,8] and time-resolved observation and control of superexchange interactions [9]. The aim of the present manuscript is to perform exact two-particle dynamics in an optical lattice similar to what has been suggested in Ref.…”