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arXiv:1902.08328 · Physical Review A

Comparison between continuous- and discrete-mode coherent feedback for the Jaynes-Cummings model

Nikolett Német, Alexander Carmele, A. S. Parkins, Andreas Knorr

Published Aug 6, 2019• 23 citations
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Abstract

Using the example of the Jaynes-Cummings model, we present a comparison between time-delayed coherent feedback mediated by reservoirs with continuous- and discrete-mode structures and work out their qualitative differences. In contrast to the discrete-mode case, the continuous-mode case results in the well-known single-delay dynamics which can, e.g., stabilize Rabi oscillations. The discrete-mode case, however, shows population trapping, not present in the continuous-mode model. Given these differences, we discuss the cavity output spectra and show how these characteristic properties are spectrally identifiable. This work demonstrates the fundamental difference between the continuous-mode case, which represents a truly dissipative mechanism, and the discrete-mode case that is in principle based on a coherent excitation exchange process.

DOI
10.1103/physreva.100.023805

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Using the example of the Jaynes-Cummings model, we present a comparison between time-delayed coherent feedback mediated by reservoirs with continuous- and discrete-mode structures and work out their qualitative differences. In contrast to the discrete-mode case, the continuous-mode case results in the well-known single-delay dynamics which can, e.g., stabilize Rabi oscillations. The discrete-mode case, however, shows population trapping, not present in the continuous-mode model. Given these differences, we discuss the cavity output spectra and show how these characteristic properties are spectrally identifiable. This work demonstrates the fundamental difference between the continuous-mode case, which represents a truly dissipative mechanism, and the discrete-mode case that is in principle based on a coherent excitation exchange process.
In this proceeding we show how to formulate the quantum stochastic Schrodinger equation (QSSE) of the Jaynes-Cummings-model, where the cavity mode is subject to coherent feedback as control mechanism. We start from the Jaynes-Cummings Hamiltonian and the Hamiltonian for feedback on the cavity mode and derive the QSSE and show how to represent the system state as a matrix product state in order to derive a numerically tractable model for the case of the Jaynes-Cummings model subject to feedback. We compare the dynamics for stabilization of the Rabi oscillation with the solution of the Schrodinger equation in the single excitation regime. Furthermore, we compare this with the behavior for the case with two excitations in the system.
We investigate the coherence and steady-state properties of the Jaynes-Cummings model subjected to time-delayed coherent feedback in the regime of multiple excitations. The introduced feedback qualitatively modifies the dynamical response and steady-state quantum properties of the system by enforcing a non-Markovian evolution. This leads to recovered collapses and revivals as well as non-equilibrium steady states when the two-level system (TLS) is directly driven by a laser. The latter are characterized by narrowed spectral linewidth and diverging correlation functions that are robust against the time delay and feedback phase choices. These effects are also demonstrated in experimentally accessible quantities such as the power spectrum and the second-order correlation function g(2)(τ)g^{(2)}(τ)g(2)(τ) in standard and widely available photon-detection setups.
Recent numerical and analytical results have been obtained for the dynamics of a VVV-type system, and of a model molecular system, interacting with the thermal states of a cavity with a single mode or with a few discrete modes [D. Avisar and A. D. Wilson-Gordon, Phys. Rev. A 93, 033843 (2016)]. The authors speculate that these results may be relevant to excitation with natural incoherent radiation, such as sunlight, which has a continuous spectrum. We claim that this is incorrect, as are their comments about prior work on natural incoherent radiation that does properly deal with a continuous spectrum. Specifically, while their results obtained for the Jaynes-Cummings systems may be of interest for excitation by thermal states of cavities with a few modes, the discrete nature of their field modes produces dynamics that are fundamentally different from those induced by natural sunlight. Hence, we show here that the criticisms leveled in their paper regarding prior treatments that dealt with the continuous spectrum of natural incoherent radiation, as well as their speculation that excitation with continuous-mode thermal radiation can induce long-lived molecular coherences, are incorrect.
The purpose of this article is to study two-photon dynamics induced by the coherent feedback control of a cavity quantum electrodynamics (cavity-QED) system coupled to a waveguide. In this setup, the two-level system in the cavity can work as a photon source, and the photon emitted into the waveguide can reinteract with the cavity-QED system many times after the transmission and reflection in the waveguide, during which the feedback can tune the number of the photons in and out of the cavity. We analyze the dynamics of two-photon processes in this coherent feedback network in two scenarios: the continuous mode coupling scheme and the discrete periodic mode coupling scheme between the waveguide and cavity. The difference of these coupling schemes is due to their relative scales and the number of semitransparent mirrors for coupling. Specifically, in the continuous mode coupling scheme, the generation of two-photon states is influenced by the length of the feedback loop by the waveguide and the coupling strength between the waveguide and the cavity-QED system. By tuning the length of the waveguide and the coupling strength, we are able to generate two-photon states efficiently. In the discrete periodic mode coupling scheme, the Rabi oscillation in the cavity can be stabilized and there are no notable two-photon states in the waveguide.
A spontaneously decaying two-level atom in an evacuated high-Q cavity undergoes Rabi oscillations. This phenomenon has been observed experimentally as enhanced or inhibited spontaneous emission. In the standard Jaynes-Cummings model the atom is assumed to interact with only a single cavity mode. By retaining the infinite set of cavity modes the propagation of the spontaneously emitted radiation may be calculated. Such an analysis yields a clear physical picture of Rabi oscillations. These vacuum-field Rabi oscillations are compared with Rabi oscillations of a one-electron atom induced by coherent radiation. We show that the same wave packet analysis explains both types of Rabi oscillation. The limit in which a multimode cavity may be approximated as a single-mode cavity is discussed.