Ultrafast Excitation Exchange in a Maxwell Fish-Eye Lens.

The strong coupling of quantum emitters to a cavity mode has been of paramount importance in the development of quantum optics. Recently, also the strong coupling to more than a single mode of an electromagnetic resonator has drawn considerable interest. We investigate how this multimode strong coupling regime can be harnessed to coherently control quantum systems. Specifically, we demonstrate that a Maxwell fish-eye lens can be used to implement a pulsed excitation exchange between two distant quantum emitters. This periodic exchange is mediated by single-photon pulses and can be extended to a photon-exchange between two atomic ensembles, for which the coupling strength is enhanced collectively.

Driven-Dissipative Time Crystalline Phases in a Two-Mode Bosonic System with Kerr Nonlinearity.

For the driven-dissipative system of two coupled bosonic modes in a nonlinear cavity resonator, we demonstrate a sequence of phase transitions from a trivial steady state to two distinct dissipative time crystalline phases. These effects are already anticipated at the level of the semiclassical analysis of the Lindblad equation using the theory of bifurcations and are further supported by the full quantum treatment. The system is predicted to exhibit different dynamical phases characterized by an oscillating nonequilibrium steady state with nontrivial periodicity, which is a hallmark of time crystals. We expect that these phases can be directly probed in various cavity QED experiments.

Periodic Cavity State Revivals from Atomic Frequency Combs.

Spin ensembles with a comb-shaped spectrum have shown exciting properties as efficient quantum memories. Here, we present a rigorous theoretical study of such atomic frequency combs in the strong coupling limit of cavity QED, based on a full quantum treatment using tensor-network methods. Our results demonstrate that arbitrary multiphoton states in the cavity are almost perfectly absorbed by the spin ensemble and reemitted as parity-flipped states at periodic time intervals. Fidelity values near unity are achieved in these revived states by compensating for energy shifts induced by the strong spin-cavity coupling through adjustments of individual coupling values of the teeth in the atomic frequency comb.

Few-Mode Geometric Description of a Driven-Dissipative Phase Transition in an Open Quantum System.

By example of the nonlinear Kerr mode driven by a laser, we show that hysteresis phenomena in systems featuring a driven-dissipative phase transition can be accurately described in terms of just two collective, dissipative Liouvillian eigenmodes. The key quantities are just two components of a non-Abelian geometric connection, even though a single parameter is driven. This powerful geometric approach considerably simplifies the description of driven-dissipative phase transitions, extending the range of computationally accessible parameter regimes, and providing a new starting point for both experimental studies and analytical insights.

Variational Renormalization Group for Dissipative Spin-Cavity Systems: Periodic Pulses of Nonclassical Photons from Mesoscopic Spin Ensembles.

Mesoscopic spin ensembles coupled to a cavity offer the exciting prospect of observing complex nonclassical phenomena that pool the microscopic features from a few spins with those of macroscopic spin ensembles. Here, we demonstrate how the collective interactions in an ensemble of as many as a hundred spins can be harnessed to obtain a periodic pulse train of nonclassical light. To unravel the full quantum dynamics and photon statistics, we develop a time-adaptive variational renormalization group method that accurately captures the underlying Lindbladian dynamics of the mesoscopic spin-cavity system.

Hybrid Quantum Systems with Collectively Coupled Spin States: Suppression of Decoherence through Spectral Hole Burning.

Spin ensemble based hybrid quantum systems suffer from a significant degree of decoherence resulting from the inhomogeneous broadening of the spin transition frequencies in the ensemble. We demonstrate that this strongly restrictive drawback can be overcome simply by burning two narrow spectral holes in the spin spectral density at judiciously chosen frequencies. Using this procedure we find an increase of the coherence time by more than an order of magnitude as compared to the case without hole burning. Our findings pave the way for the practical use of these hybrid quantum systems for the processing of quantum information.

Optically induced orientational transitions in nematic liquid crystals with planar alignment.

A theoretical study of dynamical phenomena induced by linearly polarized light incident perpendicularly on a planar aligned nematic layer with the light intensity as the control parameter is reported. We find the threshold of the optically induced twist Fréedericksz transition as a function of the problem parameters. The critical light intensity was found substantially lower than predicted earlier by Santamato [Phys. Rev. A 36, 2389 (1987)]. We have demonstrated by a rigorous stability analysis that the bifurcation is stationary only for a thickness of the nematic layer smaller than a certain critical value and becomes a Hopf bifurcation in the opposite case. Above the Hopf bifurcation an oscillatory state appears. It becomes unstable at a secondary threshold through a heteroclinic bifurcation, and the director settles to a new stationary distorted state.

Light-driven liquid-crystalline nonlinear oscillator under optical periodic forcing.

An all-optically driven strategy to govern a liquid-crystalline collective molecular nonlinear oscillator is discussed. It does not require external feedback of any kind while the oscillator and a time-dependent perturbation both are sustained by incident light. Various dynamical regimes such as frequency-locked, quasiperiodic, forced, and chaotic are observed, in agreement with a theoretical approach developed in the limit of the plane-wave approximation.

Ultralong relaxation times in bistable hybrid quantum systems.

Nonlinear systems, whose outputs are not directly proportional to their inputs, are well known to exhibit many interesting and important phenomena that have profoundly changed our technological landscape over the last 50 years. Recently, the ability to engineer quantum metamaterials through hybridization has allowed us to explore these nonlinear effects in systems with no natural analog. We investigate amplitude bistability, which is one of the most fundamental nonlinear phenomena, in a hybrid system composed of a superconducting resonator inductively coupled to an ensemble of nitrogen-vacancy centers. One of the exciting properties of this spin system is its long spin lifetime, which is many orders of magnitude longer than other relevant time scales of the hybrid system. This allows us to dynamically explore this nonlinear regime of cavity quantum electrodynamics and demonstrate a critical slowing down of the cavity population on the order of several tens of thousands of seconds-a time scale much longer than observed so far for this effect. Our results provide a foundation for future quantum technologies based on nonlinear phenomena.

Granular elasticity: general considerations and the stress dip in sand piles.

Granular materials are predominantly plastic, incrementally nonlinear, preparation-dependent, and anisotropic under shear. Nevertheless, their static stress distribution is well accounted for, in the whole range up to the point of failure, by a judiciously tailored isotropic nonanalytic elasticity theory termed granular elasticity. The first purpose of this paper is to carefully expound this view. Then granular elasticity is employed to consider the stress distribution in two-dimensional sand piles (or sand wedges). Starting from a uniform density, the pressure at the bottom of the pile is found to show a single central peak. It turns into a pressure dip, if some density inhomogeneity, with the center being less compact, is assumed. These two pressure distributions are remarkably similar to recent measurements, made in piles obtained, respectively, by rainlike pouring and funneling. In an accompanying paper, the stress distributions in silos and under point loads, calculated using the same method, are also found to agree with experiments.

Granular elasticity: stress distributions in silos and under point loads.

An elastic-strain-stress relation, the result of granular elasticity as introduced in the preceding paper, is employed here to calculate the stress distribution (a) in cylindrical silos and (b) under point loads assuming uniform density. In silos, the ratio k{J} between the horizontal and vertical stress is found to be constant (as conjectured by Janssen) and given as k{J}=1-sin phi (with phi the Coulomb yield angle), in agreement with a construction industry standard usually referred to as the Jaky formula. Next, the stress distribution at the bottom of a granular layer exposed to a point force at its top is calculated. The results include both vertical and oblique point forces, which agree well with simulations and experiments using rainlike preparation. Moreover, the stress distribution of a sheared granular layer exposed to the same point force is calculated and again found in agreement with given data.

Dip of the granular shear stress.

Recent experiments reveal an unexpected dip of the shear stress as the shear rate increases, from the rate-independent regime to Bagnold flow. Employing granular solid hydrodynamics, it is shown that in uniform systems, such dips occur for given pressure or normal stress, but not for given density. If the shear rate is strongly nonuniform, enforcing a constant volume does not prevent the local density to vary, and a stress dip may still occur.

Delocalization and spreading in a nonlinear Stark ladder.

We study the evolution of a wave packet in a nonlinear Stark ladder. In the absence of nonlinearity all normal modes are spatially localized giving rise to an equidistant eigenvalue spectrum and Bloch oscillations. Nonlinearity induces frequency shifts and mode-mode interactions and destroys localization. For large strength of nonlinearity we observe single-site trapping as a transient, with subsequent explosive spreading, followed by subdiffusion. For moderate nonlinearities an immediate subdiffusion takes place. Finally, for small nonlinearities we find linear Stark localization as a transient, with subsequent subdiffusion. For single-mode excitations and weak nonlinearities, stability intervals are predicted and observed upon variation in the dc bias strength, which affects the short- and the long-time dynamics.