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Quantum Simulation of Multifractality using time-Modulated Optical Lattices

thesis proposal 2022-funding secured

par Bertrand Georgeot - 15 avril

Toutes les versions de cet article : English , English

PhD advisor : Bertrand Georgeot, LPT et Gabriel Lemarié

Contact : Bertrand Georgeot (georgeot(at) ; +33 (0)5 61 55 65 63)

Cold atom gases in optical lattices are part of the major experimental systems allowing the quantum simulation of fundamental problems of condensed matter. In particular, the temporal modulation of these lattices has aroused great interest recently because it makes it possible to induce new quantum effects which do not exist in the absence of modulation, such as topological effects or the time crystal phenomenon. As a result, these modulated lattices have become one of the key tools in quantum simulation. The thesis project that we propose follows this direction, aiming at quantum simulating a paradigmatic effect of disordered quantum systems : multifractality. Multifractal states normally appear in systems of great complexity, at the disorder-induced metal-insulator Anderson transition, or in the many-body localized phase. They have spectacular properties : they are both delocalized (thus allowing transport) but spatially strongly inhomogeneous (they are ``nonergodic’’). Nevertheless, they are extremely difficult to observe experimentally.

In this PhD project, we wish to explore a new type of system, based on time-modulated optical lattices, where multifractality could be controlled and therefore made strong enough to be observable even at the relatively short times accessible to experiments. Our proposal is based on the expertise of our group on the control of multifractality in theoretical models called ``pseudo-integrable’’ [1][2] We have preliminary results that suggest that ``quasi-integrable’’ models could be quantum-simulated by means of some type of experimentally feasible sawtooth temporal modulation. The first objective of the thesis will be to confirm this theoretically and then to determine an adequate protocol allowing the experimental observation of multifractality. It should be noted that such an observation would in itself represent a quite remarkable scientific result.

The system envisioned should make it possible to control the multifractality of the states (contrary to the rare existing experimental observations) : they can be made more inhomogeneous or less (“weak” or “strong” multifractality). This is a crucial feature in view of possible applications to quantum technologies. The second objective of the thesis will be to develop these control possibilities in order to reach the regime where these states could be used for such quantum technologies.

The third objective of the thesis is to study an important aspect of the planned experiments, the effects of interactions between cold atoms, in the presence of multifractality. In condensed matter, multifractality has a remarkable effect on superconductivity : it induces an increase in the critical temperature below which superconductivity appears, in other words it promotes superconductivity. We intend to study whether similar effects can occur within the cold atom system we are considering.

The thesis will take place within the framework of a collaboration established between the theoretical group of B. Georgeot at the LPT Toulouse and the group of cold atoms of D. Guéry-Odelin, J. Billy and B. Peaudecerf at LCAR in Toulouse. This collaboration has acquired internationally recognized expertise in quantum simulation using modulated lattices, as evidenced by our two recent publications on the first observation of chaos-assisted tunneling resonances [3] and how this effect can be used for quantum simulation [4]. The project will require both analytical computations and numerical simulations. During the PhD, stays at Majulab laboratory in Singapore will be organized.

References :

[1] Martinez, M., G. Lemarié, B. Georgeot, C. Miniatura, and O. Giraud, Phys. Rev. Research 3, L032044 (2021).

[2] Bilen, A. M. B. Georgeot, O. Giraud, G. Lemarié, and I. García-Mata, Phys. Rev. Research 3, L022023 (2021).

[3] M. Arnal, G. Chatelain, M. Martinez, N. Dupont, O. Giraud, D. Ullmo, B. Georgeot, G. Lemarié, J. Billy and D. Guéry-Odelin, Science Advances 6, eabc4886 (2020) (arXiv:2003.10387).

[4] Martinez, M., Giraud, O., Ullmo, D., Billy, J., Guéry-Odelin, D., Georgeot, B. and Lemarié, G., Phys. Rev. Lett. 126, 174102 (2021).