Cavity QED Arrays Research Articles

Atom-light entanglement for precise field sensing in the optical domain

Macroscopic arrays of cold atoms trapped in optical cavities can reach the strong atom-light collective coupling regime thanks to the simultaneous interactions of the cavity mode with the atomic ensemble. In a recent work we reported a protocol that takes advantage of the strong and collective atom-light interactions in cavity QED systems for precise electric field sensing in the optical domain. We showed that it can provide between $10$-$20$~dB of metrological gain over the standard quantum limit in current cavity QED experiments operating with long-lived alkaline-earth atoms. Here, we give a more in depth discussion of the protocol using both exact analytical calculations and numerical simulations, and describe the precise conditions under which the predicted enhancement holds after thoroughly accounting for both photon loss and spontaneous emission, natural decoherence mechanisms in current experiments. The analysis presented here not only serves to benchmark the protocol and its utility in cavity QED arrays but also sets the conditions required for its applicability in other experimental platforms such as arrays of trapped ions.

Coding closed and open quantum systems in MATLAB: applications in quantum optics and condensed matter

We develop a package of numerical simulations implemented in MATLAB to solve complex many-body quantum systems. We focus on widely used examples that include the calculation of the magnetization dynamics for the closed and open Ising model, dynamical quantum phase transition in cavity QED arrays, Markovian dynamics for interacting two-level systems, and the non-Markovian dynamics of the pure-dephasing spin-boson model. These examples will be useful for undergraduate and graduate students with a medium or high-level background in MATLAB, and also for researchers interested in numerical studies applied to quantum optics and condensed matter systems.

Engineering indefinitely long-lived localization in cavity-QED arrays

By exploiting the nonlinear nature of the Jaynes Cumming's interaction, one can get photon population trapping in cavity-QED arrays. However, the unavoidable dissipative effects in a realistic system would destroy the self-trapped state by continuous photon leakage. To circumvent this issue, we show that a careful engineering of drive, dissipation and Hamiltonian results in achieving indefinitely sustained self-trapping. We show that the intricate interplay between drive, dissipation, and light-matter interaction results in requiring an optimal window of drive strengths in order to achieve such non-trivial steady states. We treat the two-cavity and four-cavity cases using exact open quantum many-body calculations. Additionally, in the semiclassical limit we scale up the system to a long 1-D chain and demonstrate localization de-localization transition in a driven-dissipative system. Although, our analysis is performed keeping cavity-QED systems in mind, our work is applicable to other driven-dissipative systems where nonlinearity plays a defining role.

Nonlocality dynamics for an eight-qubit model in cavity QEDs

We study the nonlocality dynamics for an eight-qubit model in cavity QED, where four atoms are confined in four different cavities, all of them initially prepared in the maximally correlated state of four qubits, which corresponds to the atomic degrees of freedom. The nonlocality evolution for the latter states will show that the corresponding maximal violation of a multipartite Bell inequality will experience revivals at precise times, defining, in analogy with entanglement, nonlocality sudden deaths, as well as nonlocality sudden rebirths. The present contribution paves the way to describe, by employing the nonlocality multipartite correlation measure, collective complex behavior displayed by slightly interacting cavity QED arrays.

Effective spin physics in two-dimensional cavity QED arrays

We investigate a strongly correlated system of light and matter in two-dimensional cavity arrays. We formulate a multimode Tavis–Cummings (TC) Hamiltonian for two-level atoms coupled to cavity modes and driven by an external laser field which reduces to an effective spin Hamiltonian in the dispersive regime. In one-dimension we provide an exact analytical solution. In two-dimensions, we perform mean-field study and large scale quantum Monte Carlo simulations of both the TC and the effective spin models. We discuss the phase diagram and the parameter regime which gives rise to frustrated interactions between the spins. We provide a quantitative description of the phase transitions and correlation properties featured by the system and we discuss graph-theoretical properties of the ground states in terms of graph colourings using Pólya’s enumeration theorem.

Localization attractors in active quasiperiodic arrays

In dissipationless linear lattices, spatial disorder or quasiperiodic modulations in on-site potentials induce localization of the eigenstates and block the spreading of wave packets. Quasiperiodic inhomogeneities allow for the metal–insulator transition at a finite modulation amplitude already in one dimension. We go beyond the dissipationless limit and consider nonlinear quasi-periodic arrays that are additionally subjected to dissipative losses and energy pumping. We find finite excitation thresholds for oscillatory phases in both metallic and insulating regimes. In contrast to disordered arrays, the transition in the metallic and weakly insulating regimes display features of the second order phase transition accompanied by a large-scale cluster synchronization. In the limit of strong localization, we find the existence of globally stable asymptotic states consisting of several localized modes. These localization attractors and chaotic synchronization effects can be potentially implemented with polariton condensate lattices and cavity-QED arrays.

Anderson attractors in active arrays.

In dissipationless linear media, spatial disorder induces Anderson localization of matter, light, and sound waves. The addition of nonlinearity causes interaction between the eigenmodes, which results in a slow wave diffusion. We go beyond the dissipationless limit of Anderson arrays and consider nonlinear disordered systems that are subjected to the dissipative losses and energy pumping. We show that the Anderson modes of the disordered Ginsburg-Landau lattice possess specific excitation thresholds with respect to the pumping strength. When pumping is increased above the threshold for the band-edge modes, the lattice dynamics yields an attractor in the form of a stable multi-peak pattern. The Anderson attractor is the result of a joint action by the pumping-induced mode excitation, nonlinearity-induced mode interactions, and dissipative stabilization. The regimes of Anderson attractors can be potentially realized with polariton condensates lattices, active waveguide or cavity-QED arrays.

First-order superfluid–Mott-insulator transition for quantum-optical switching in cavity-QED arrays with two cavity modes

We theoretically investigated the ground states of coupled arrays of cavity-quantum-electrodynamical (cavity-QED) systems in the presence of two photon modes. Within the Gutzwiller-type variational approach, we found the first-order quantum phase transition between Mott-insulating and superfluid phases as well as the conventional second-order one. The first-order phase transition was found only for specific types of emitter models, and its physical origin is clarified based on the analytic arguments which are allowed in the perturbative and semiclassical limits. The first-order transition of the correlated photons is accompanied with discontinuous change in the emitter states, not only with the appearance of intercavity coherence in the superfluid phase. We also discuss the condition for the first-order transition to occur, which can lead to a strategy for future design of quantum-optical switching devices with cavity-QED arrays.

Bright solitons in cavity-QED arrays containing two-level atoms

We examine the problem of polariton soliton formation in the array of weakly coupled optical cavities, each containing an ensemble of ultracold non-interacting two-level atoms. An effective complex Ginzburg-Landau equation (GLE) is derived in the continuum limit taking into account the effects of cavity field dissipation and atomic polarization dephasing. Bright solitons are found to be supported under perturbations only in the upper (optical) branch of polaritons, for which the corresponding group velocity is controlled by tuning the atom-light detuning. With the help of perturbation theory for solitons, we also demonstrate that the group velocity of these polariton solitons is suppressed by the diffusion process.