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Physical Review A

Dynamics of interacting Dicke model in a coupled-cavity array

Fazal Badshah, Shahid Qamar, Mauro Paternostro

Published Sep 9, 2014• 16 citations
Publisher

Abstract

We consider the dynamics of an array of mutually interacting cavities, each containing an ensemble of $N$ two-level atoms. By exploring the possibilities offered by ensembles of various dimensions and a range of atom-light and photon-hopping values, we investigate the generation of multisite entanglement, as well as the performance of excitation transfer across the array, resulting from the competition between on-site nonlinearities of the matter-light interaction and intersite photon hopping. In particular, for a three-cavity interacting system it is observed that the initial excitation in the first cavity completely transfers to the ensemble in the third cavity through the hopping of photons between the adjacent cavities. Probabilities of the transfer of excitation of the cavity modes and ensembles exhibit characteristics of fast and slow oscillations governed by coupling and hopping parameters, respectively. In the large-hopping case, by seeding an initial excitation in the cavity at the center of the array, a tripartite W state, as well as a bipartite maximally entangled state, is obtained, depending on the interaction time. Population of the ensemble in a cavity has a positive impact on the rate of excitation transfer between the ensembles and their local cavity modes. In particular, for ensembles of five to seven atoms, tripartite W states can be produced even when the hopping rate is comparable to the cavity-atom coupling rate. A similar behavior of the transfer of excitation is observed for a four-coupled-cavity system with two initial excitations.

DOI
10.1103/physreva.90.033813

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We consider the dynamics of an array of mutually interacting cavities, each containing an ensemble of NNN two-level atoms. By exploring the possibilities offered by ensembles of various dimensions and a range of atom-light and photon-hopping values, we investigate the generation of multisite entanglement, as well as the performance of excitation transfer across the array, resulting from the competition between on-site nonlinearities of the matter-light interaction and intersite photon hopping. In particular, for a three-cavity interacting system it is observed that the initial excitation in the first cavity completely transfers to the ensemble in the third cavity through the hopping of photons between the adjacent cavities. Probabilities of the transfer of excitation of the cavity modes and ensembles exhibit characteristics of fast and slow oscillations governed by coupling and hopping parameters, respectively. In the large-hopping case, by seeding an initial excitation in the cavity at the center of the array, a tripartite W state, as well as a bipartite maximally entangled state, is obtained, depending on the interaction time. Population of the ensemble in a cavity has a positive impact on the rate of excitation transfer between the ensembles and their local cavity modes. In particular, for ensembles of five to seven atoms, tripartite W states can be produced even when the hopping rate is comparable to the cavity-atom coupling rate. A similar behavior of the transfer of excitation is observed for a four-coupled-cavity system with two initial excitations.
We study quantum state transfer and multipartite entanglement generation in the ensembles of qubits enclosed by a one-dimensional system of coupled optical cavities. Each cavity contains N qubits whose interaction with the quantum field of their respective cavity is governed by the Dicke Lipkin–Meshkov–Glick model. An excitation initially seeded in the ensemble at the end of the one-dimensional chain of coupled cavities transfers to the corresponding ensemble of the last cavity with success that depends on the mode-ensemble coupling χ , ensemble-mode detuning δ , photon hopping rate λ , and size of a given ensemble N . Suitable choices of such parameters enable overcoming the freezing effect induced by the choice of a far-off detuning regime. We identify working points at which three-ensemble W states and two-ensemble maximally entangled states emerge in the multipartite entanglement dynamics. This study provides a basis for manipulation of quantum states in a multipartite coupled cavity arrangement that may be useful in understanding very complex systems in the field of quantum information processing.
The dynamical behavior of a coupled cavity array is investigated when each cavity contains a three-level atom. For the uniform and staggered intercavity hopping, the whole system Hamiltonian can be analytically diagonalized in the subspace of single-atom excitation. The quantum-state transfer along the cavities is analyzed in detail for distinct regimes of parameters, and some interesting phenomena including binary transmission and selective localization of the excitation population are revealed. We demonstrate that the uniform coupling is more suitable for the quantum-state transfer. It is shown that the initial state of polariton located in the first cavity is crucial to the transmission fidelity, and the local entanglement depresses the state transfer probability. Exploiting the metastable state, the distance of the quantum-state transfer can be much longer than that of Jaynes-Cummings-Hubbard model. A higher transmission probability and longer distance can be achieved by employing a class of initial encodings and final decodings.
The dynamics of a system composed of two coupled cavities, each containing a single two-level atom, is studied over a wide range of detuning and coupling values. A description of the field in terms of delocalized modes reveals that the detuning between the atoms and these modes is controlled by the coupling between the cavities; this detuning in turn governs the nature of the dynamics. If the atoms are highly detuned from both delocalized field modes, the dynamics become dispersive and an excitation may be transferred from the first atom to the second without populating the field. In the case of resonance between the atoms and one of the delocalized modes, state transfer between the atoms requires intermediate excitation of the field. Thus, the interaction between the two atoms can be controlled by adjusting the coupling between the cavities.
We study the one-excitation dynamics of a coupled cavity system composed of three cavities, each containing a two-level atom. By adjusting the atom–cavity detuning Δ, cavity–cavity hopping rate v and the initial atomic excitation residential, a wide variety of time-evolution behaviors can be realized. Under certain conditions, the two-atom maximally entangled states and three-atom W states can be obtained. The results provide a theoretical basis for the manipulation of quantum states in such a system and will contribute to the understanding of more complex systems.
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Abstract We investigate a hybrid quantum system consisting of two coupled optical cavities, each containing an ensemble of coherently pumped artificial or real two-level atoms. The system is modelled within the dressed-state formalism, accounting for coherent driving and dissipative interactions with independent electromagnetic reservoirs. Focusing on the regime where the Rabi frequency greatly exceeds the collective spontaneous emission and cavity decay rates, respectively, we derive the equations of motion characterizing the system and analyse its steady-state behaviours. Special attention is given to the scenario in which only one cavity contains a pumped multi-atom ensemble, and as a consequence, coherent excitation transfer to the second cavity occurs via cavity–cavity coupling. In this case, the mean photon number in the second cavity mode scales proportional to the squared number of atoms, i.e., N2 from the first cavity. The proposed model offers insight into light–matter interaction in composite systems and suggests viable mechanisms for engineering collective interactions and non-local excitation transport in quantum optical platforms.