Superfluids, Fluctuations and Disorder

Abstract

We present a field-theory description of ultracold bosonic atoms in presence of a disordered external potential. By means of functional integration techniques, we aim to investigate and review the interplay between disordered energy landscapes and fluctuations, both thermal and quantum ones. Within the broken-symmetry phase, up to the Gaussian level of approximation, the disorder contribution crucially modifies both the condensate depletion and the superfluid response. Remarkably, it is found that the ordered (i.e. superfluid) phase can be destroyed also in regimes where the random external potential is suitable for a perturbative analysis. We analyze the simplest case of quenched disorder and then we move to present the implementation of the replica trick for ultracold bosonic systems. In both cases, we discuss strengths and limitations of the reviewed approach, paying specific attention to possible extensions and the most recent experimental outputs.

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

“…Thus, the adiabatic switch on followed by the sudden quench down and the sudden quench up followed by the adiabatic switch off scenarios lead both to the same final condensate deformation of 3q HM /2. Furthermore, the largest dynamically generated deformation is three times larger than the equilibrium one (26) and it occurs by suddenly switching the disorder on and off.…”

“…the particle density. The sufficient condition for it is that the Huang-Meng deformation (26) for the delta-correlated disorder of the same strength R = R(k = 0) is much smaller than n. This places the following requirement on the disorder strength…”

“…After accounting for the disorder perturbatively they found that superfluidity persists in spite of it, although the superfluid depletion turned out to be larger than the condensate depletion. Their work was subsequently expanded by many others, using the original approach of second quantization [20][21][22][23] or employing the functional integral framework and the replica method [24][25][26]. 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].…”

“…Figure 1: Temporal evolution of condensate deformation(21) in units of the equilibrium deformation(26) for exponential temporal increase (20) of delta-correlated disorder potential(25), with the time scales 10 3 τ 1 = τ 2 = 10 −3 τ 3 = τ MF ≡ ħ h/(g n).…”

Special Issue on Quantum Optics for Fundamental Quantum Mechanics

“…In this Special Issue, four review papers concern some of the most interesting aspects of this field: both fundamental aspects, such a as quantum non-locality [3], uncertainty relations [10], ultra-cold bosonic atoms [11] and applicative ones, such as topological carriers of information [12].…”