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.
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 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.
A system of two coupled cavities with N - 1 photons is shown to be dynamically equivalent to an array of N coupled cavities containing one photon. Every transition in the two cavity system has a dual phenomenon in terms of photon transport in the cavity array. This duality is employed to arrive at the required coupling strengths and nonlinearities in the cavity array so that controlled photon transfer is possible between any two cavities. This transfer of photons between two of the cavities in the array is effected without populating the other cavities. The condition for perfect transport enables perfect state transfer between any two cavities in the array. Further, possibility of high fidelity generation of generalized NOON states in two coupled cavities, which are dual to the Bell states of the photon in the cavity array, is established.
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.
Based on two-photon exchange interaction between
n coupled optical cavities each of them containing a single three level atom, the
n-qubit and
n-photonic state transfer is investigated. In fact, following the approach of Ref.\cite{Alex1}, we consider
n coupled cavities instead of two cavities and generalize the discussions about quantum state transfer, photon transition between cavities and entanglement generations between
n atoms. More clearly, by employing the consistency of number of photons (the symmetry of Hamiltonian), the hamiltonian of the system is reduced from
3n dimensional space into 2n dimensional one. Moreover, by introducing suitable basis for the atom-cavity state space based on Fourier transform, the reduced Hamiltonian is block-diagonalized, with 2 dimensional blocks. Then, the initial state of the system is evolved under the corresponding Hamiltonian and the suitable times
T at which the initially unentangled atoms, become maximally entangled, are determined in terms of the hopping strength
ξ between cavities.