Sound speed of a Bose-Einstein condensate in an optical lattice

Abstract

The speed of sound of a Bose-Einstein condensate in an optical lattice is studied both analytically and numerically in all three dimensions. Our investigation shows that the sound speed depends strongly on the strength of the lattice. In the one-dimensional case, the speed of sound falls monotonically with increasing lattice strength. The dependence on lattice strength becomes much richer in two and three dimensions. In the two-dimensional case, when the interaction is weak, the sound speed first increases then decreases as the lattice strength increases. For the three dimensional lattice, the sound speed can even oscillate with the lattice strength. These rich behaviors can be understood in terms of compressibility and effective mass. Our analytical results at the limit of weak lattices also offer an interesting perspective to the understanding: they show the lattice component perpendicular to the sound propagation increases the sound speed while the lattice components parallel to the propagation decreases the sound speed. The various dependence of the sound speed on the lattice strength is the result of this competition.Comment: 15pages 6 figure

Collective excitations of a trapped Bose-Einstein condensate in the presence of weak disorder and a two-dimensional optical lattice

“…It's worth mentioning here that one can also employ the compressibility-based definition for sound velocity [20,21,26,[35][36][37] to investigate the beyond-mean-fieldeffect induced shift. In our case, the normal component of fluid is pinned by the quenched disorder and doesn't directly participate in the propagation of the density disturbance.…”

“…which accounts for the increased inertia of the system along the direction of optical lattice [20,21]. The ground state density within the TF approximation is obtained by putting δµ = 0 that yields [5,8]:…”

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

“…Theoretical studies have shown: (i) when D=1, the sound velocity always decreases monotonically with increasing V 1 [18][19][20][21][22][23][24]. (ii) for D=2 and 3, when c exceeds a critical value, the sound speed first increases to a maximum value and then decreases with increasing V 1 [25,26]. When D=3, the sound velocity can even oscillate with respect to V 1 [26].…”

“…Ever since the first achievement of Bose-Einstein condensate (BEC) in atomic gases, the sound velocity has been one of the first things to be studied theoretically [1] and experimentally [7][8][9][10][11] on a BEC in the presence of harmonic traps [12][13][14][15], optical lattices [16][17][18][19][20][21][22][23][24][25][26][27] and disorder [28,29], etc. More recently, the studies on the sound velocity have been renewed, which are much more in line with its important applications in quantum simulations involving superfluid [30][31][32].…”

“…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.…”