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arXiv:1111.3457 · Optics Letters

Jaynes–Cummings photonic superlattices

Stefano Longhi

Published Aug 24, 2011• 36 citations
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Abstract

A classical realization of the Jaynes-Cummings (JC) model, describing the interaction of a two-level atom with a quantized cavity mode, is proposed based on light transport in engineered waveguide superlattices. The optical setting enables us to visualize in Fock space dynamical regimes not yet accessible in quantum systems, providing new physical insights into the deep strong coupling regime of the JC model. In particular, bouncing of photon number wave packets in Hilbert space and revivals of populations are explained as generalized Bloch oscillations in an inhomogeneous tight-binding lattice.

DOI
10.1364/ol.36.003407

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A classical realization of the Jaynes-Cummings (JC) model, describing the interaction of a two-level atom with a quantized cavity mode, is proposed based on light transport in engineered waveguide superlattices. The optical setting enables us to visualize in Fock space dynamical regimes not yet accessible in quantum systems, providing new physical insights into the deep strong coupling regime of the JC model. In particular, bouncing of photon number wave packets in Hilbert space and revivals of populations are explained as generalized Bloch oscillations in an inhomogeneous tight-binding lattice.
The interaction of a two-level atom with a single-mode quantized field is one of the simplest models in quantum optics. Under the rotating wave approximation, it is known as the Jaynes-Cummings model and without it as the Rabi model. Real-world realizations of the Jaynes-Cummings model include cavity, ion trap and circuit quantum electrodynamics. The Rabi model can be realized in circuit quantum electrodynamics. As soon as nonlinear couplings are introduced, feasible experimental realizations in quantum systems are drastically reduced. We propose a set of two photonic lattices that classically simulates the interaction of a single two-level system with a quantized field under field nonlinearities and nonlinear couplings as long as the quantum optics model conserves parity. We describe how to reconstruct the mean value of quantum optics measurements, such as photon number and atomic energy excitation, from the intensity and from the field, such as von Neumann entropy and fidelity, at the output of the photonic lattices. We discuss how typical initial states involving coherent or displaced Fock fields can be engineered from recently discussed Glauber-Fock lattices. As an example, the Buck-Sukumar model, where the coupling depends on the intensity of the field, is classically simulated for separable and entangled initial states.
We study the quantum dynamics of a two-level system interacting with a quantized harmonic oscillator in the deep strong coupling regime (DSC) of the Jaynes-Cummings model, that is, when the coupling strength g is comparable or larger than the oscillator frequency ω (g/ω≳1). In this case, the rotating-wave approximation cannot be applied or treated perturbatively in general. We propose an intuitive and predictive physical frame to describe the DSC regime where photon number wave packets bounce back and forth along parity chains of the Hilbert space, while producing collapse and revivals of the initial population. We exemplify our physical frame with numerical and analytical considerations in the qubit population, photon statistics, and Wigner phase space.
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.
A classical analog simulator of the two-site Hubbard-Holstein model, describing the dynamics of two correlated electrons coupled with local phonons, is proposed based on light transport in engineered optical waveguide arrays. Our photonic analog simulator enables us to map the temporal dynamics of the quantum system in Fock space into spatial propagation of classical light waves in the evanescently coupled waveguides of the array. In particular, in the strong correlation regime the periodic temporal dynamics, related to the excitation of Holstein polarons with equal energy spacing, can be visualized as a periodic self-imaging phenomenon of the light beam along the waveguide array and explained in terms of generalized Bloch oscillations of a single particle in a semi-infinite inhomogeneous tight-binding lattice.