I. Bose-Einsten condensate

Phase transitions are ubiquitous in physics, encompassing thermal phenomena such as the boiling of water to magnetic transitions in solids. They include cosmological transitions in the early universe and the transition to a quark-gluon plasma during high-energy collisions. Quantum phase transitions, particularly intriguing, occur at temperatures close to absolute zero and are driven by quantum rather than thermal fluctuations. The intensity of the fluctuations is highly sensitive to the dimensionality of physical systems, which determines the existence and nature of phase transitions. Low-dimensional systems often exhibit phase transition suppression, while high-dimensional systems tend to exhibit mean-field behavior. The Anderson localization-delocalization transition stands out among quantum phase transitions because it is thought to retain its non-mean-field character in all dimensions.

Recent experiments mark the first-ever observation and characterization of the Anderson transition in four dimensions, using ultracold atoms as quantum simulators with synthetic dimensions. We characterize the universal dynamics near the phase transition. We measure the critical exponents describing the scale-invariant properties of the critical dynamics, which obey Wegner's scaling law. Our work constitutes the first experimental demonstration that the Anderson transition is not of the mean-field type in four dimensions. This flagship research topic of the Quantum Gases team is the result of long-standing collaborations with researchers from LKB Paris (Dominique Delande, Nicolas Cherroret) and NUS Singapore (G. Lemarié).

See also:

• Exploring the criticality of a 4D quantum phase transition:  arXiv:2402.06573

• Studying the shape of the localized asymptotic distribution: Eur. Phys. J. D 76 103 (2022)

• Realization of an ideal disordered Floquet system: New J. Phys. 21 035008 (2019)

• Scaling function of 2D Anderson localization: PRL 115 240603 (2015)

Quantum chaos, characterized by the behavior of quantum systems whose classical limits are chaotic, does not always lead to sensitivity to initial conditions. Under certain conditions, these systems may undergo a dynamical phase transition, suddenly changing their behavior with respect to the memory of initial conditions. Before a certain critical time tE, the system is chaotic and does not retain this memory; after this time, quantum interference increases the probability of returning to the initial state. The time tE is related to the notion of ‘Ehrenfest time’ τE, corresponding to the classical-quantum transition of the system. Using an atomic hit rotator experiment with laser-cooled Cs atoms, we observed a sudden change in the system’s behavior, co-incident with this transition: before the critical time, the system undergoes a chaotic motion in phase space and its memory of initial states is erased; after the critical time, quantum interference increases the probability that a chaotic trajectory returns to the initial state, thus allowing the system to recover its initial memory [PRL 121 134101 (2018)].

These results come from a theoretical collaboration with Chushun Tian, ​​a researcher at the Chinese Academy of Sciences.

The localization properties of disordered systems are sensitive to their Hamiltonian symmetry characteristics. However, this issue has been little explored experimentally so far. Through precise temporal control of potential modulations, we have demonstrated the realization of an artificial gauge field in a synthetic (time) dimension of a periodically excited disordered quantum (Floquet) system. By tuning the strength of this gauge field, we can control the time-reversal symmetry properties of the system, which we probe through the experimental observation of three telltale and symmetry-sensitive signatures of localization. The first two are coherent backscattering (CBS) [PRL 118 184101 (2017)], marker of weak localization, and coherent forward scattering (CFS), a true interference signature of Anderson localization, which we observed experimentally for the first time [Nat. Commun. 9 1382 (2018)]. The third is the direct measurement of the scaling function β(g) in two different symmetry classes, allowing to demonstrate its universality as well as the one-parameter scaling hypothesis. [PRA 97 061601 (2018)]