Resonant atom-field interaction in large-size coupled-cavity arrays

Abstract

We consider an array of coupled cavities with staggered inter-cavity couplings, where each cavity mode interacts with an atom. In contrast to large-size arrays with uniform-hopping rates where the atomic dynamics is known to be frozen in the strong-hopping regime, we show that resonant atom-field dynamics with significant energy exchange can occur in the case of staggered hopping rates even in the thermodynamic limit. This effect arises from the joint emergence of an energy gap in the free photonic dispersion relation and a discrete frequency at the gap's center. The latter corresponds to a bound normal mode stemming solely from the finiteness of the array length. Depending on which cavity is excited, either the atomic dynamics is frozen or a JaynesCummings-like energy exchange is triggered between the bound photonic mode and its atomic analogue. As these phenomena are effective with any number of cavities, they are prone to be experimentally observed even in small-size arrays.

Quantum phase transitions for two coupled cavities with dipole-interaction atoms

“…The simulation of the strongly correlated many-body systems described by Bose-Hubbard model has received great advances in optical lattices [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and coupled-cavity systems [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Both of them depend on the competition between the local interaction and the nonlocal tunneling, but there are also some differences between these two basic models.…”

Quantum-state transfer in staggered coupled-cavity arrays

“…(2). We can now tackle the problem perturbatively by interpretingV ± as a perturbation in a defect-free staggered CCA consisting of an odd number of cavities, a model which can be exactly solved in the single-excitation subspace [29].…”

“…[29], forV ± = 0 (no defect) the spectrum ofĤ (±) hop comprises a pair of bands (separated by a gap ω) alongside a discrete frequency ω b = 0 falling in the middle of the gap. The latter corresponds to a bound eigenstate |α b , which is localized in the vicinity of only one of the array edges (which of the two depends on the sign of η).…”

“…These describe a pair of energy bands separated by a band gap ω 4J , with the identity holding only when |η| = 1 The eigenstates corresponding to ω kμ are worked out as [29] …”

“…From this perspective, a key issue is the study of excitation transport-in the form of photonic, atomic, or polaritonic excitations-as well as quantum-state transfer (QST) [21,22] across CCAs [23][24][25][26][27][28][29][30][31][32][33][34][35]. Nontrivial dynamics are also exhibited * gmaalmeidaphys@gmail.com by CCAs featuring only a single cavity coupled to an atom [36][37][38][39][40][41].…”