Disordered quantum gases

Quantum boomerang effect

In collaboration with Dominique Delande, we discovered in 2018 a surprising quantum-mechanical effect in spatially disordered potentials: If one launches a wave packet in a given direction through the disorder, its average trajectory performs a “quantum boomerang” : the center of mass of the launched wave packet initially moves forward in a ballistic manner, then makes a U-turn and finally returns to its initial position (see figure). The term “quantum” means this effect can by no means be described classically. The U-turn of the center of mass is indeed a consequence of quantum interferences in the disorder, leading to Anderson localization. The initial discovery and theoretical description of the quantum boomerang effect was presented in [Prat, Delande, Cherroret, Phys. Rev. A 99, 023629 (2019)]. Following this, we also studied how the boomerang effect is impacted by interactions between the quantum particles forming the wave packet [Janarek et al., Phys. Rev. A 102, 013303 (2020)] and by spin-orbit coupling [Janarek et al., Acta Physica Polonica 144, 415 (2023)]. In subsequent work, we explored the quantum boomerang effect for different types of disorder [Tessieri et al., Phys. Rev. A 103, 063316 (2021)] and, in particular, in collaboration with Patrizia Vignolo from INPHYNI, demonstrated that the effect also occurs in a quantum-chaotic system known as the kicked rotor. This result led, in 2021, to a first experimental demonstration in David Weld’s group at the University of California.
See also Phys.org, NewScientist, TheConversation, and the Wikipedia Page for popularizing articles about the quantum boomerang effect.

Weakly interacting disordered Bose gases

Our team has developed an expertise in the interplay between disordered and interactions in Bose gases. In seminal works, we have for instance investigated how the dynamics of bosonic wave packets was affected by interactions in the vicinity of the Anderson transition in 3D [Cherroret et al., Phys. Rev. Lett. 112, 170603 (2014) ; Cherroret, J. of Phys.: Cond. Mat. 29, 024002 (2016)]. More recently, we have focused on the general problem of thermalization for a weakly interacting Bose gas following the quench of a disorder potential [Scoquart et al., 2020 EPL 132 66001, Scoquart et al., Phys. Rev. Research 2, 033349 (2020)]. In [Scoquart, Delande, Cherroret, Phys. Rev. A 106, L021301 (2022)], in particular, we studied the time evolution of the spatial coherence of the Bose gas after such a quench, until it reached a stationary value signaling the end of the dynamics. With this approach, we were able to construct the long-time stationary disorder-temperature phase diagram of the gas. This phase diagram is presented in the figure on the right. At the end of the post-quench dynamics, the Bose gas thermalizes, depending on the strength of the disorder, either in a superfluid phase, characterized by quasi long-range order, or in a “normal” phase, characterized by an exponentially decaying coherence. These two phases are separated by a Kosterlitz-Thouless transition, with a corresponding critical temperature decreasing with the strength of the disorder quench.
Several aspects of the dynamics of weakly interacting disordered Bose gases have been discussed in the review paper [Cherroret, Annals of Physics 435, 168543 (2021)]

Coherent forward scattering effect

When a wave is scattered coherently in a disordered environment, phase information is not lost, only converted into an intricate interference pattern. After averaging over randomness, interference is scrambled except in the backscattering direction of the velocity distribution where there is a narrow peak, a phenomenon known as coherent backscattering (CBS).

We have shown in the team that when the wave propagates in even stronger disorder and begins to halt its progression due to Anderson localization, the CBS signal is complemented by a spectacular peak in the opposite, forward direction. At long times, the velocity distribution freezes into a symmetric, twin-peak structure, retaining a long-term memory of the initial direction.  This coherent forward scattering (CFS, see picture) peak has been discovered in [Karpiuk et al., Phys. Rev. Lett. 109, 190601 (2012)], through numerical simulations of the momentum distribution of a wave packet launched inside a random potential, as done in cold-atom experiments. Further theoretical approaches of CFS have been developed as short and long times in 2D [Ghosh et al., Phys. Rev. A 90, 063602 (2014)] and in 3D [Ghosh et al., Phys. Rev. A 95, 041602(R) (2017) ; Phys. Rev. Lett. 115, 200602 (2015)].

Coherent forward scattering is expected to be quite general, observable with many different types of waves under the right circumstances. Further studies will certainly improve our understanding of the behavior of waves when they undergo Anderson localization.