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Optics Express

Thermo-optic effect induced tunable phase controlled propagation of solitons in a Jaynes-Cummings-Hubbard model

Yujuan Xiao, Tianjun Li, Yujie Zhang, Anshou Zheng

Published Jun 24, 2024• 1 citation
Publisher

Abstract

The manipulation of light propagation has garnered significant attention in discrete periodic photon structures. In this study, we investigate the impact of an adjustable phase on soliton behavior within a one-dimensional (1D) coupled cavity array. Each cavity is doped with two-level qubits, and the system can be effectively described by a Jaynes-Cummings-Hubbard model (JC-Hubbard model). By numerically exploring the photonic phase, we reveal that it introduces an additional degree of flexibility in controlling soliton propagation. This flexibility encompasses dispersion relations, propagation direction, transverse velocity, and stability conditions. We observe that soliton styles transition with changes in the tunneling phase. At a phase of 0, solitons form due to the delicate balance between spatial dispersion and system nonlinearity. When the phase increases to π/2, solitons vanish because spatial dispersion is significantly suppressed. The underlying theory explains this suppression, which arises from the opposite phase ±θ. Interestingly, standard temporal solitons emerge in the discrete periodic cavity array. Our investigation has broader applicability extending to various discrete structures, encompassing but not limited to waveguide arrays and optomechanical cavity arrays.

DOI
10.1364/oe.525317

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The manipulation of light propagation has garnered significant attention in discrete periodic photon structures. In this study, we investigate the impact of an adjustable phase on soliton behavior within a one-dimensional (1D) coupled cavity array. Each cavity is doped with two-level qubits, and the system can be effectively described by a Jaynes-Cummings-Hubbard model (JC-Hubbard model). By numerically exploring the photonic phase, we reveal that it introduces an additional degree of flexibility in controlling soliton propagation. This flexibility encompasses dispersion relations, propagation direction, transverse velocity, and stability conditions. We observe that soliton styles transition with changes in the tunneling phase. At a phase of 0, solitons form due to the delicate balance between spatial dispersion and system nonlinearity. When the phase increases to π/2, solitons vanish because spatial dispersion is significantly suppressed. The underlying theory explains this suppression, which arises from the opposite phase ±θ. Interestingly, standard temporal solitons emerge in the discrete periodic cavity array. Our investigation has broader applicability extending to various discrete structures, encompassing but not limited to waveguide arrays and optomechanical cavity arrays.
ABSTRACT The manipulation of light in periodic structures is fundamental to the development of discrete photonics and provides a versatile platform for controlling light propagation in integrated and quantum photonic systems. This work reports the experimental observation of discrete one‐dimensional (1D) solitons in a photonic lattice, optically induced in warm rubidium vapor. The lattice is generated by the interference of two coupling laser fields intersecting at a small angle, which creates a spatially modulated 1D refractive index. When a probe beam is focused into a single lattice site, discrete diffraction is observed. By increasing the probe intensity, discrete solitons emerge as a result of the balance between discrete diffraction and self‐focusing within the nonlinear atomic medium. Experimental results are supported by numerical simulations, in which the refractive index is modeled via optical Bloch equations for a multilevel atomic system driven by the coupling and probe fields in a configuration. These results, combined with the inherent controllability of gain and loss in atomic vapors, suggest that this platform provides a versatile foundation for exploring non‐Hermitian nonlinear dynamics in photonic lattices.
We theoretically study the single-photon transport properties in periodic and position-disordered Jaynes–Cummings (or JC) arrays of waveguide-coupled microtoroidal ring resonators, each interacting with a single two-level quantum emitter. Employing the real-space formalism of quantum optics, we focus on various parameter regimes of cavity quantum electrodynamics (cQED) to gain better control of single-photon propagation in such a many-body quantum optical setting. As for some of the key findings, we observe that the periodic setting leads to the formation of the band structure in the photon transmission spectra, which is most evident in the strong coupling regime of cQED. However, under resonant conditions with no losses, the application of Bloch’s theorem indicates that the width of forbidden gaps can be altered by tuning the emitter-cavity coupling to small values. Moreover, in the disordered case, we find that the single-photon transmission curves show the disappearance of band formation. However, spectral features originating from cQED interactions observed for the single atom-cavity problem remain robust against weak-disordered conditions. The results of this work may find application in the study of quantum many-body effects in the optical domain as well as in different areas of quantum computation and quantum networking.
Abstract Controllable single-photon scattering in a one-dimensional waveguide coupled to a Jaynes–Cummings structure containing a time-modulated two-level atom interacting with a single-mode cavity is investigated. The photon transmission and reflection amplitudes are calculated by using an effective Floquet Hamiltonian in real space. The results show that the coupling between the atom and the cavity mode can dynamically be tuned via periodically modulating the atomic transition frequency. As a consequence, the scattering behaviors of the waveguide photons can be actively manipulated, and a controllable single-photon switch with high on-off ratio could be realized. More interestingly, the switch works well within a wide frequency region, i.e., the transmission of both resonant and off-resonant waveguide photons can be effectively switched on or off with appropriate system parameters. Furthermore, the proposed dynamically tunable switching scheme is robust against atomic dissipation associated with the help of atom-cavity coupling mismatch. Such single-photon device can be used as an elementary unit for various quantum information processing.
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.
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 intercavity 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.