Laboratoire de Physique Théorique
Toulouse - UMR 5152

The field of quantum simulation, which aims to use one quantum system to simulate another, has grown rapidly in recent years as an alternative to the universal quantum computer. The emphasis so far has been on the use of regular systems which seem a priori easier to control. However, it has been known for the last century that many systems display varying degrees of chaos. Chaotic systems exhibit exponential sensitivity to initial conditions and typical ergodic trajectories in phase space. In practice, most systems present a mixed phase space in which chaotic and regular zones coexist. Although the evolution of a chaotic system is difficult to predict, the instability of these systems makes them very versatile because a small disturbance can induce completely different evolutions. More surprisingly, this instability can be exploited to bring the system to a desired state at minimal cost, a process known as “control of chaos”.

In [1], a team of theoreticians and experimentalists from the LPT and LCAR in Toulouse and LPTMS in Orsay have shown that the use of chaotic dynamics in a system of cold atoms opens up possibilities for quantum simulation that are difficult to achieve by other means. To do this, the authors use a time-modulated optical lattice. For moderately strong modulation, this creates a mixed phase space with regular islands surrounded by a chaotic sea. The quantum mechanics of such a system leads to quantum states that are either localized on islands or spread out in the chaotic sea. The position and number of regular islands as well as the size of the chaotic sea can be finely adjusted by the time modulation.

The key phenomenon of purely quantum origin used in [1] is the modification of the tunnel effect in such a mixed system. Indeed, quantum states can cross classical barriers through a process similar to the standard tunneling effect called dynamical tunneling. This phenomenon can be strongly affected by the presence of chaotic states, which causes large variations in the tunneling rate over a short range of parameters, leading to resonances. This chaos-assisted tunneling effect has been observed experimentally with great precision for classical waves. For quantum waves, it was carried out in pioneering experiments a few years ago, but the experimental limits made it impossible to clearly observe the resonances that characterize it.

In [1], ultra-cold atoms are placed in a 1D optical lattice whose depth is periodically modulated in time. The results obtained show that this makes it possible to experimentally produce an effective superlattice and to observe for the first time the resonances of the chaos assisted tunnel effect between spatially separated stable islands. This allows to control this tunneling effect, going from complete suppression to a large increase in a small range of parameters.

In the context of cold atoms, the tunnel resonances observed are independent of the species, unlike the Feshbach resonances, which modify the strength of interactions between atoms, but are delicate to handle. The results of [1] should make it possible to probe models with a new type of long-range hoppings for quantum simulation. Indeed, the tunnel effect assisted by chaos is mediated by quantum states delocalized in the chaotic sea which surrounds all the sites of the lattice. This therefore leads to long-distance transfers through the system. Such long-range models have been studied a lot theoretically in condensed matter, and present a rich phenomenology such as multifractality, glassy physics, high TC superconductivity, etc. The protocol presented in [1] proposes for the first time a strategy to emulate such models with cold atoms.

See also the associated CNRS news

[1] M. Arnal, G. Chatelain, M. Martinez, N. Dupont, O. Giraud, D. Ullmo, B. Georgeot, G. Lemarié, J. Billy and D. Guéry-Odelin, "Chaos-assisted tunneling resonances in a synthetic Floquet superlattice", Science Advances Vol. 6, eabc4886 (2020)

Figure : The amplitude modulation of the depth of the lattice generates a mixed phase space with regular islands (blue closed orbits) surrounded by a chaotic sea (red zone). The wave packet can be placed on a regular island (for example the one on the right). Then, the wave packets go back and forth between the two stable symmetrical islands (tunnel rate J), ​​leading to the two wave packets R and L.