Cloud shape of a molecular Bose–Einstein condensate in a disordered trap: a case study of the dirty boson problem

Abstract

We investigate, both experimentally and theoretically, the static geometric properties of a harmonically trapped Bose-Einstein condensate of 6 Li 2 molecules in laser speckle potentials. Experimentally, we measure the in situ column density profiles and the corresponding transverse cloud widths over many laser speckle realizations. We compare the measured widths with a theory that is non-perturbative with respect to the disorder and includes quantum fluctuations. Importantly, for small disorder strengths we find quantitative agreement with the perturbative approach of Huang and Meng, which is based on Bogoliubov theory. For strong disorder our theory perfectly reproduces the geometric mean of the measured transverse widths. However, we also observe a systematic deviation of the individual measured widths from the theoretically predicted ones. In fact, the measured cloud aspect ratio monotonously decreases with increasing disorder strength, while the theory yields a constant ratio. We attribute this discrepancy to the utilized local density approximation, whose possible failure for strong disorder suggests a potential future improvement.

Non-equilibrium evolution of Bose-Einstein condensate deformation in temporally controlled weak disorder

“…Recently, it has been demonstrated that the Huang-Meng theory can be verified quantitatively by using the homogeneous results within a local density approximation (LDA) [33]. Here we demonstrate that the above time-dependent results can also be extended to the case of inhomogeneous condensates in disordered traps, provided that the disorder correlation length is much smaller than the spatial extent of the atomic cloud.…”

“…The consideration of scenarios when the disorder correlation function has a non-zero correlation length σ showed that both condensate and superfluid depletions decrease with increasing σ, in particular for the case of a Gaussian [21,[27][28][29], Lorentzian [30], or laser speckle disorder [31,32]. Quite recently, the predictions of the Huang-Meng theory were experimentally confirmed by analyzing the cloud shape of a molecular 6 Li BEC in a disordered trap [33]. Furthermore, building on an equilibrium inhomogeneous Bogoliubov theory [34], the results presented in [35] clarified the relation between the condensate depletion and condensate deformation in the presence of a weak, possibly random, external potential.…”

“…which has the same strength R(k = 0) = R as in the delta-correlated case. Experimental realization of such a disorder can be achieved by using laser speckles [33,45,46]. Since the dynamical effects are revealed already during switching on, we simply consider the driving function (20).…”

“…Since, by our presumption, the disorder correlation length σ is much smaller than the characteristic condensate width L 0 , the perturbative corrections of the condensate wave function Ψ 1 (x, t) and Ψ * 1 (x, t) vary in space much more rapidly than Ψ 0 (x). Hence, in order to determine them from (37) we employ LDA, in the sense of [33], by treating Ψ 0 (x) as a constant background quantity Ψ 0 that will, at the end of the calculation, be restored to its original value at the point x. In the same spirit, we can make the estimates…”

Two-body mobility edge in the Anderson-Hubbard model in three dimensions: Molecular versus scattering states

“…Finally, our approach can be adapted to investigate the transport properties of other kinds of two-particle systems subject to quenched randomness, like Cooper pairs in strongly disordered atomic gases [81] or superconductors [82][83][84]. Investigations of the steady-state and out-of-equilibrium properties of a Fermi gas undergoing the BCS-BEC crossover in the presence of a random potential [85] are already under way [86][87][88][89].…”