Quantum Structures of Matter and Light

The interplay of noise and nonlinearities plays an essential role in the dynamics of physical systems in nature. Their combined action is known to give rise to counterintuitive effects, such as the emergence of regular behavior as the noise level increases. Understanding their role in the quantum dynamics is an important question of fundamental research and crucial issue for quantum technological applications, where one aims at robust quantum coherent dynamics in systems of mesoscopic size. Therefore, the recent observation of stationary regular structures of photons and atoms in high-finesse optical resonators constitutes a prominent instance of pattern formation solely through quantum dynamics. Spatial order in fact results from the interplay between quantum noise and coherent multiple scattering of photons inside the resonator. It is a quantum nonlinear interaction between scattering particles that generates patterns of photons and atoms in the presence of noise and dissipation. Our goal is to provide insight over the semiclassical and the quantum limits of the composite dynamics, and in particular on the role of thermal and quantum noise and spatial disorder in the occurrence of selforganization of photons and atoms in cavity quantum electrodynamics. This will provide a basis for quantum technological applications, such as for quantum simulators, sensors, and metrology based on these systems.

The focus of the project research was a systematic and comprehensive understanding of spatial self-organization of atomic ensembles in single-mode and multi-mode optical resonators. The essential physics for the single-mode case was numerically predicted in [Domokos2002] and it was mapped to the Hamiltonian mean field model, the workhorse of statistical mechanics of long-range interacting systems [Schütz2014]. Multimode cavities have been increasingly attracting the attention of experimental and theoretical efforts for the perspectives they offer to study spin glasses and can be used for quantum simulation. Recent theoretical works by members of this consortium discussed quantum simulated annealing [Torggler2017, Torggler2018] and equilibrium and relaxation of thermal gases [Keller2017, Keller2018]. When distinct cavity modes with commensurate wavelengths are quasi-resonantly driven by laser fields, the equilibrium dynamics can be mapped to the generalized Hamiltonian mean field model, exhibiting four types of ordered phases [Keller2017] while relaxation is characterized by long-lived metastable states whose occurrence strongly depends on initial temperature, ramp speed, and number of atoms [Keller2018]. In the quantum regime, a dilutely filled N-site optical lattice near zero temperature within a high-Q multimode cavity can be mapped to a spin ensemble with tailorable interactions at all length scales, which allows for the implementation of quantum annealing dynamics relying on the all-to-all effective spin coupling controllable in real time. This system can simulate a quantum Hopfield associative memory scheme, whose physical properties can be monitored from the cavity output fields [Torggler2017]. Moreover, specific problems can be simulated with less resources. We proposed a special purpose quantum simulator with the aim to solve the N-queens completion problem with this system [Torggler2018]. This combinatorial problem may serve as a testbed to study possible quantum advantage in solving classical combinatorial problems in intermediate size near term quantum experiments.