Adaptive multifrequency light collection by self-ordered mobile scatterers in optical resonators

Abstract

Mobile light scatterers in a high-Q optical cavity transversely illuminated by laser light close to a cavity resonance form ordered patterns, which maximize light scattering into the cavity and induce optical selftrapping. We show that a generalized form of such crystallization dynamics appears in multicolored pump fields with several cavity modes. Here the particles arrange in spatial patterns maximizing total light collection into the resonator. For changing input frequencies and strengths the particles dynamically adapt to the current illumination. Interestingly the system keeps some memory on past configurations, so that a later renewed application of the same pattern exhibits faster adaptation towards optimal collective scattering. In a noisy environment particles explore larger regions of configuration space spending most of the time close to optimum scattering configurations. This adaptive self-ordering dynamics should be implementable in a wide range of systems ranging from cold atoms in multimode cavities or nanofiber traps to molecules or mobile nano-particles within an optical resonator.

Quenches across the self-organization transition in multimode cavities

“…The blue (red) lines correspond to simulations using equation (1)(equation (22)). The black dashed lines denote the values of the order parameters obtained by the free energy, equation (16). In (a) the blue (red) line corresponds to 250 (500) trajectories.…”

“…We further note that for  t k 10 3 the order parameters undergo a three-stage dynamics, as for the sudden quench (we attribute the fluctuations to the statistics of the trajectories). For slower ramps, the mean value of the order parameters tends exponentially towards the steady state, which approaches the free energyʼs global minimum in equation (16) for t k > 10 4 . We believe that this behavior is determined by the ramp duration τ with respect to the time scale of the transient dynamics, and thus by the time the parameters a ( ) t n spend close to the transition point.…”

“…The corresponding time evolution of the mean kinetic energy per particle is displayed in figure 18 and it shows that for = T T 2 ini 0 (and even more for = T T 5 ini 0 ) the system stays relatively hot over time and as a function of the ramp duration τ (in units of k 1 ) for the same parameters as in figure 11. The dashed horizontal lines show the steady-state value predicted by the free energy, equation (16). scales of the order of k 10 4 .…”

“…In section 4 we analyze the dynamics of the distributions from the spatially homogeneous to the organized ones with different momentum widths. In section 5 we compare the predictions of the stochastic differential equations we employ with an extended approach including the dynamical evolution of the field modes introduced in [15,16]. Conclusions are drawn and future perspectives are discussed in section 6.…”

Quantum annealing with ultracold atoms in a multimode optical resonator

“…For classical point particles one finds that the coupled atom-cavity dynamics can be designed as a self-optimizing light collection system with learning and memory capacity [19]. Similarly, generalizing the system to fixed multilevel atoms and using degenerate modes, Gopalakrishnan and coworkers previously proposed to simulate a quantum version of the Hopfield model [20][21][22].…”