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arXiv:1212.6063 · Physical Review A

Cavity-QED simulation of qubit-oscillator dynamics in the ultrastrong-coupling regime

Arne L. Grimsmo, A. S. Parkins

Published Mar 14, 2013• 102 citations
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Abstract

We propose a quantum simulation of a two-level atom coupled to a single mode of the electromagnetic field in the ultrastrong-coupling regime based upon resonant Raman transitions in an atom interacting with a high finesse optical cavity mode. We show by numerical simulation the possibility of realizing the scheme with a single rubidium atom, in which two hyperfine ground states make up the effective two-level system, and for cavity QED parameters that should be achievable with, for example, microtoroidal whispering-gallery-mode resonators. Our system also enables simulation of a generalized model in which a nonlinear coupling between the atomic inversion and the cavity photon number occurs on an equal footing with the (ultrastrong) dipole coupling and can give rise to critical-type behavior even at the single-atom level. Our model takes account of dissipation, and we pay particular attention to observables that would be readily observable in the output from the system.

DOI
10.1103/physreva.87.033814

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We propose a quantum simulation of a two-level atom coupled to a single mode of the electromagnetic field in the ultrastrong-coupling regime based upon resonant Raman transitions in an atom interacting with a high finesse optical cavity mode. We show by numerical simulation the possibility of realizing the scheme with a single rubidium atom, in which two hyperfine ground states make up the effective two-level system, and for cavity QED parameters that should be achievable with, for example, microtoroidal whispering-gallery-mode resonators. Our system also enables simulation of a generalized model in which a nonlinear coupling between the atomic inversion and the cavity photon number occurs on an equal footing with the (ultrastrong) dipole coupling and can give rise to critical-type behavior even at the single-atom level. Our model takes account of dissipation, and we pay particular attention to observables that would be readily observable in the output from the system.
We consider a generalized version of the Rabi model that includes a nonlinear, dispersive-type atom-field interaction in addition to the usual linear dipole coupling, as well as cavity dissipation. An effective system of this sort arises, for example, in a quantum simulation of the Rabi model based upon Raman transitions in an optical cavity QED setting [A. L. Grimsmo and S. Parkins, Phys. Rev. A 87, 033814 (2013)]. For a range of the nonlinear interaction strength about a special value, degeneracies or near degeneracies of the states in the cavity-mode vacuum and single-photon subspaces, in combination with cavity loss, gives rise to an essentially closed cycle of excitations and photon emissions within these subspaces. Consequently, the cavity output field is strongly antibunched, while over this range of nonlinear strengths the atomic population undergoes an abrupt inversion. We develop a quantum-trajectory-based description of the system that models its key properties very well, and use a simple dressed-state picture to explain the novel structure of the cavity fluorescence spectrum. We also present numerical results for a potential realization of the system using a rubidium atom coupled strongly to a high-finesse optical cavity mode.
We propose a generalized system of nonequilibrium cavity QED with interacting dipoles coupled to a single-mode of an electromagnetic field in strong-, ultrastrong-, and deep-strong-coupling regimes. To illustrate the applicability of the system, an extended Dicke model is developed for atoms undergoing Raman transitions between the ground states in the presence of laser fields and considering dipole-dipole interactions; the latter has been neglected in many previous works. We have studied the effect of a ferroelectric and an antiferroelectric arrangement on the phase transition for both a finite and an infinite number of dipoles. An additional superradiant phase is observed in the deep-strong-coupling regime due to influence of the dipole-dipole interaction term. A high degree of dipole-dipole entanglement occurs for the antiferroelectric arrangement in the deep-strong regime, whereas it gets disentangled quite rapidly for the ferroelectric arrangement. A sharp transition of system parameters is observed in the ultrastrong-coupling regime and beyond. The dipole-dipole interaction also influences the spectra of the system, inducing a significant shift in the peaks, and modifies the average number of photons emitted.
We study a generic cavity-QED system where a set of (artificial) two-level dipoles is coupled to the electric field of a single-mode LCLCLC resonator. This setup is used to derive a minimal quantum mechanical model for cavity QED, which accounts for both dipole-field and direct dipole-dipole interactions. The model is applicable for arbitrary coupling strengths and allows us to extend the usual Dicke model into the nonperturbative regime of QED, where the dipole-field interaction can be associated with an effective fine-structure constant of order unity. In this regime, we identify three distinct classes of normal, superradiant, and subradiant vacuum states and discuss their characteristic properties and the transitions between them. Our findings reconcile many of the previous, often contradictory predictions in this field and establish a common theoretical framework to describe ultrastrong-coupling phenomena in a diverse range of cavity-QED platforms.
We investigate theoretically quantum effects of a cavity-atom system in which the upper two levels of a cascade-type three-level atom interact with a cavity field mode in the ultrastrong-coupling regime. By exploiting the virtual photons carried by atom-cavity dressed states, we indicate how two external driving fields induce Raman transitions such that a cavity photon pair can be generated with a high probability. We present analytical and numerical solutions of the system and determine the rate of photons transmitted out of the cavity. In addition, we show that the transmitted photons exhibit a bunching behavior in the steady state. Our scheme demonstrates that atom-cavity dressed states in the ultrastrong-coupling regime can serve as intermediate states to invoke nonlinear optical processes.
The prototypical system constituted by a two-level atom interacting with a quantized single-mode electromagnetic field is described by the quantum Rabi model (QRM). The QRM is potentially valid at any light-matter interaction regime, ranging from the weak (where the decay rates exceeds the coupling rate) to the deep strong coupling (where the interaction rate exceeds the bare transition frequencies of the subsystems). However, when reaching the ultrastrong coupling regime, several theoretical issues may prevent the correct description of the observable dynamics of such a system: (i) the standard quantum optics master equation fails to correctly describe the interaction of this system with the reservoirs; (ii) the correct output photon rate is no longer proportional to the intracavity photon number; and (iii) they appear to violate gauge invariance. Here, we study the photon flux emission rate of this system under the incoherent excitation of the two-level atom for any light-matter interaction strength and consider different effective temperatures. The dependence of the emission spectra on the coupling strength is the result of the interplay between energy levels, matrix elements of the observables, and the density of states of the reservoirs. Within this approach, we also study the occurrence of light-matter decoupling in the deep strong-coupling regime and show how all of the obtained results are gauge invariant.
We study a circuit QED setup where multiple superconducting qubits are ultrastrongly coupled to a single radio-frequency resonator. In this extreme parameter regime of cavity QED the dynamics of the electromagnetic mode is very slow compared to all other relevant timescales and can be described as an effective particle moving in an adiabatic energy landscape defined by the qubits. The focus of this paper is placed on settings with two or multiple qubits, where different types of symmetry-breaking transitions in the ground- and excited-state potentials can occur. Specifically, we show how the change in the level structure and the wave-packet dynamics associated with these transition points can be probed via conventional excitation spectra and Ramsey measurements performed at GHz frequencies. More generally, this analysis demonstrates that state-of-the-art circuit QED systems can be used to access a whole range of particlelike quantum-mechanical phenomena beyond the usual paradigm of coupled qubits and oscillators.