Optically trapped quasi-two-dimensional Bose gases in a random environment: Quantum fluctuations and superfluid density

Abstract

We investigate a dilute Bose gas confined in a tight one-dimensional (1D) optical lattice plus a superimposed random potential at zero temperature. Accordingly, the ground state energy, quantum depletion and superfluid density are calculated. The presence of the lattice introduces a crossover to the quasi-2D regime, where we analyze asymptotically the 2D behavior of the system, particularly the effects of disorder. We thereby offer an analytical expression for the ground state energy of a purely 2D Bose gas in a random potential. The obtained disorder-induced normal fluid density nn and quantum depletion n d both exhibit a characteristic 1/ ln 1/n2Da 2 2D dependence. Their ratio nn/n d increases to 2 compared to the familiar 4/3 in lattice-free 3D geometry, signifying a more pronounced contrast between superfluidity and Bose-Einstein condensation in low dimensions. Conditions for possible experimental realization of our scenario are also proposed.

Step-by-step dimensional crossover of an optically-trapped quantum gas with disorder

“…In comparison, the red solid line denotes the one-step dimensional crossover from 3D to pure 2D studied in Ref. [13] with the red dotted curve being the pure 2D asymptotic behavior. y-direction optical lattices and t = t 1 + t 2 , V is volume and g being the re-normalized coupling constant due to the optical lattice.…”

“…Refs. [12][13][14] have investigated the quantum phases along a characteristic 3D to 2D crossover and the visualization of dimensional effects in collective excitations. The strategy of previous research [10][11][12][13][14][15][16][17] on dimensional effects, called by one-step dimensional crossover, is limited on exploring separate 1D or 2D behaviors from 3D by the tight confinement.…”

“…[12][13][14] have investigated the quantum phases along a characteristic 3D to 2D crossover and the visualization of dimensional effects in collective excitations. The strategy of previous research [10][11][12][13][14][15][16][17] on dimensional effects, called by one-step dimensional crossover, is limited on exploring separate 1D or 2D behaviors from 3D by the tight confinement. Instead, the aim of this Letter is to investigate, by the strategy of the step-by-step dimensional crossover, the effects on the equilibrium quantum phases due to the gradual dimensional crossover from the 3D to quasi-2D and then 1D.…”

“…Model.-At zero temperature, an optically-trapped BEC can be well described by the N -body Hamiltonian [10][11][12][13]…”

“…Directly following Refs. [11,13], we proceed to expand the field operators of Hamiltonian (1) by the expression Ψ(r) = k âk e −ikzz φ kx (x)φ ky (y) as follows…”