Time evolution of the one-dimensional Jaynes-Cummings-Hubbard Hamiltonian

Abstract

The Jaynes-Cummings-Hubbard (JCH) system describes a network of single-mode photonic cavities connected via evanescent coupling. Each cavity contains a single two level system which can be tuned in resonance with the cavity. Here we explore the behavior of single excitations (where an excitation can be either photonic or atomic) in the linear JCH system, which describes a coupled cavity waveguide. We use direct, analytic diagonalization of the Hamiltonian to study cases where inter-cavity coupling is either uniform or varies parabolically along the chain. Both excitations located in a single cavity, as well as one excitation as a Gaussian pulse spread over many cavities, are investigated as initial states. We predict unusual behavior of this system in the time domain, including slower than expected propagation of the excitation, and also splitting of the excitation into two distinct pulses, which travel at distinct speeds. In certain limits, we show that the JCH system mimics two Heisenberg spin chains.

Quantum-state transfer in staggered coupled-cavity arrays

“…For η = 0, we retrieve the CCA with uniform intercavity couplings usually considered in JCH models [27]. We also point out that, since N is even, for η → −1 + the two outermost cavities (corresponding to x = 1 and x = N , respectively) are weakly coupled to the remaining ones (bulk), a property which is crucial for our goals.…”

“…(26). Consider, in particular, the strong-coupling regime [27,32] such that g is far larger than the entire range of the field frequencies (ω a = 0, for simplicity). Then none of the coupling terms in Eq.…”

“…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].…”

Scattering and Bound States of two Polaritons in an Array of Coupled Cavities

“…It is predicted that, such systems can be used in quantum information processing [1][2][3][4][5] as well as the quantum simulation of many-body systems, e.g., the quantum phase simulation [10][11][12][13][14][15][16][17][18][19][20], quantum Hall effect [21] and Bose-Einstein condensate [22]. For the few-body physics of coupled cavities, many authors have studied the single-photon transmission in a 1D cavity array coupled with a single atom [1], and the dynamics of a single polariton in a 1D cavity array with each cavity coupled to an atom [2,7]. Recently, bound states of two polaritons in such a system with finite number of cavities was studied by Wong and Law by direct numerical diagonalization of the Hamiltonian [8].…”

“…In the recent years, the investigation of the physics in one-dimensional (1D) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] and two-dimensional (2D) [14][15][16][17][18][19][20][21][22][23] array of coupled cavities has attracted a lot of attention. It is predicted that, such systems can be used in quantum information processing [1][2][3][4][5] as well as the quantum simulation of many-body systems, e.g., the quantum phase simulation [10][11][12][13][14][15][16][17][18][19][20], quantum Hall effect [21] and Bose-Einstein condensate [22].…”