We study the origin of 'frozen' photonic states in coupled Jaynes–Cummings–Hubbard arrays. For the case of half the array initially populated with photons while the other half is left empty, we show the emergence of a self-localized photon or 'frozen' states for specific values of the local atom–photon coupling. We analyse the dynamics in the quantum regime and discover important additional features that do not appear to be captured by a semi-classical treatment, which we analyse for different array sizes and filling fractions. We trace the origin of this interaction-induced photon 'freezing' to the suppression of the excitation of propagating modes in the system at large interaction strengths. We discuss in detail the possibility of experimentally probing the relevant transition by analysing the emitted photon correlations both in the idealized lossless case and more realistic scenarios when reasonable losses are included. We find a strong signature of the effect in the emitted photons statistics.
We study the origin of 'frozen' photonic states in coupled Jaynes–Cummings–Hubbard arrays. For the case of half the array initially populated with photons while the other half is left empty, we show the emergence of a self-localized photon or 'frozen' states for specific values of the local atom–photon coupling. We analyse the dynamics in the quantum regime and discover important additional features that do not appear to be captured by a semi-classical treatment, which we analyse for different array sizes and filling fractions. We trace the origin of this interaction-induced photon 'freezing' to the suppression of the excitation of propagating modes in the system at large interaction strengths. We discuss in detail the possibility of experimentally probing the relevant transition by analysing the emitted photon correlations both in the idealized lossless case and more realistic scenarios when reasonable losses are included. We find a strong signature of the effect in the emitted photons statistics.
We study the dynamics of an one dimensional array of Jaynes-Cummings-Hubbard system of arbitrary number of coupled cavities, each containing a two level atom that interacts with a field mode. In particular, we consider propagation of a single excitation quantum state for two different couplings of the photonic modes of the adjacent cavities, namely, a translation invariant closed chain of uniformly coupled cavities, and also a linear chain with nonuniform parabolically varying intercavity coupling where the interaction Hamiltonian is associated with the Jacobi matrix of the Krawtchouk polynomials. Using a description via the delocalized atomic and field modes we observe that for a large detuning of these two degrees of freedom atomic excitations propagate without populating the field modes, and vice versa. For the near-resonance scenario between these modes the atomic excitations, say, while propagating mix with the photonic states. In the context of the parabolic coupling between photons of adjacent cavities an arbitrary element of the time-dependent correlation function between two arbitrary cavities may be expressed in closed form for dominant values of the detuning parameter, when an exact transmission of the quantum state at pre-specified times is realized.
We study the dynamics of a one-dimensional array of the Jaynes–Cummings–Hubbard system of arbitrary number of coupled cavities, each containing a two-level atom that interacts with a field mode. In particular, we consider the propagation of a single-excitation quantum state for two different couplings between the localized photonic modes of the adjacent cavities, namely a translation invariant uniform coupling on a closed chain of cavities, and also a nonuniform parabolically varying intercavity coupling on a linear chain where the interaction Hamiltonian is associated with the Jacobi matrix of the relevant Krawtchouk polynomial. Using a description via the delocalized atomic and field modes, we observe that for a large detuning of these two degrees of freedom, atomic excitations propagate without populating the field modes, and vice versa. For the near-resonance scenario between these modes, the atomic excitations, say, while propagating mix with the photonic states. In the context of the parabolic coupling between photons of adjacent cavities, the time-dependent correlation function describing the propagation of the quantum state between two arbitrary sites may be expressed in closed form for dominant values of the detuning parameter, when an exact transmission of the quantum state at pre-specified times is realized.
We consider a generic model for interacting waveguide QED systems, where photons in a coupled-cavity array localize around atomic impurities while simultaneously interacting through local Kerr nonlinearities. This scenario appears naturally in nanophotonic crystals, circuit QED lattices, and ultracold atomic systems and is governed by the competition between attractive Jaynes-Cummings-mediated binding and intrinsic photon-photon repulsion. We analyze how this interplay affects the formation of localized few-photon bound states and determine the resulting many-body ground states for large periodic arrays of impurities and different filling factors. With the help of large-scale numerical simulations and approximate analytical models, we identify a rich phase diagram featuring Mott-like insulating states as well as superfluid phases with long-range correlations, which are mediated by an unbound, but strongly interacting photonic fluid.
We investigate the nonequilibrium dynamics of a Josephson-coupled Jaynes-Cummings dimer in the presence of Kerr nonlinearity, which can be realized in the cavity and circuit quantum electrodynamics systems. The semiclassical dynamics is analyzed systematically to chart out a variety of photonic Josephson oscillations and their regime of stability. Different types of transitions between the dynamical states lead to the self-trapping phenomenon, which results in photon population imbalance between the two cavities. We also study the dynamics quantum mechanically to identify characteristic features of different steady states and to explore fascinating quantum effects, such as spin dephasing, phase fluctuation, and revival phenomena of the photon field, as well as the entanglement of spin qubits. For a particular "self-trapped" state, the mutual information between the atomic qubits exhibits a direct correlation with the photon population imbalance, which is promising for generating photon mediated entanglement between two non interacting qubits in a controlled manner. Under a sudden quench from stable to unstable regime, the photon distribution exhibits phase space mixing with a rapid loss of coherence, resembling a thermal state. Finally, we discuss the relevance of the new results in experiments, which can have applications in quantum information processing and quantum technologies.
Strong effective photon-photon interactions mediated by atom-photon couplings have been routinely achievable in QED setups for some time now. Recently, there have been several proposals to push the physics of interacting photons into many- body distributed architectures. The essential idea is to coherently couple together arrays of QED resonators, such that photons can hop between resonators while interacting with each other inside each resonator. These proposed structures have attracted intense theoretical attention while simultaneously inspiring experimental efforts to realise this novel regime of strongly-correlated many-body states of light. A central challenge of both theoretical and practical importance is to understand the physics of such coupled resonator arrays (CRAs) beyond equilibrium, when unavoidable (or sometimes even desired) photon loss processes are accounted for. This thesis presents several studies whose purpose can roughly be divided in two aims. The first part studies just what constitutes a valid physical and computational representation of non-equilibrium driven-dissipative CRAs. Addressing these ques- tions constitutes essential groundwork for further investigations of CRA phenomena, as numerical experiments are likely to guide and interpret near-future experimen- tal array observations. The relatively small body of existing work on CRAs out of equilibrium has often truncated their full, rich physics. It is important to establish the effects and validity of these approximations. To this end we introduce powerful numerical algorithms capable of efficiently simulating the full dynamics of CRAs, and use them to characterise the non-equilibrium steady states of arrays reached under the combined influence of dissipation and pumping. Having established the rigour necessary to realistically describe CRAs, we exam- ine two novel phenomena observable in near-future small arrays. Firstly we relate a counter-intuitive ‘super bunching’ in the statistics of photons emitted from arrays engineered to demonstrate strong effective photon-photon repulsion at the single and two-photon level, to an interplay between the underlying eigen-structure and details of the non-equilibrium operation. Secondly we characterise a dynamical phenomenon in which domains of ‘frozen’ photons remain trapped in sufficiently nonlinear arrays. Finally we present a preliminary characterisation of a previously unexplored phase diagram of arrays under coherent two-photon pumping. Com- petition between the coherence injected by the pumping, photon interactions and delocalisation processes lead to interesting new physical signatures.
We study the non-equilibrium behavior of optically driven dissipative coupled resonator arrays. Assuming each resonator is coupled with a two-level system via a Jaynes–Cummings interaction, we calculate the many-body steady state behavior of the system under coherent pumping and dissipation. We propose and analyze the many-body phases using experimentally accessible quantities such as the total excitation number, the emitted photon spectra and photon coherence functions for different parameter regimes. In parallel, we also compare and contrast the expected behavior of this system assuming the local nonlinearity in the cavities is generated by a generic Kerr effect as described by the Bose–Hubbard (BH) model rather than a Jaynes–Cummings interaction. We find that the behavior of the experimentally accessible observables produced by the two models differs for realistic regimes of interactions even when the corresponding nonlinearities are of similar strength. We analyze in detail the extra features available in the Jaynes–Cummings–Hubbard (JCH) model originating from the mixed nature of the excitations and investigate the regimes where the BH approximation would faithfully match the JCH physics. We find that the latter is true for values of the light–matter coupling and losses beyond the reach of current technology. Throughout the study we operate in the weak pumping, fully quantum mechanical regime where approaches such as mean field theory fail, and instead use a combination of quantum trajectories and the time evolving block decimation algorithm to compute the relevant steady state observables. In our study we have assumed small to medium size arrays (from 3 up to 16 sites) and values of the ratio of coupling to dissipation rate g / γ ∼ 20, which makes our results implementable with current designs in circuit QED and with near future photonic crystal set ups.