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arXiv:1911.05087 · Advanced Quantum Technologies

Quantum Simulation of Non‐Perturbative Cavity QED with Trapped Ions

Tuomas Jaako, Juan José García‐Ripoll, Peter Rabl

Published Feb 3, 2020• 7 citations
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Abstract

Abstract The simulation of non‐perturbative cavity‐QED effects is discussed using systems of trapped ions. Specifically, the implementation of extended Dicke models with both collective dipole‐field and direct dipole–dipole interactions is addressed, which represent a minimal set of models for describing light–matter interactions in the ultrastrong and deep‐strong coupling regime. It is shown that this approach can be used in state‐of‐the‐art trapped ion setups to investigate excitation spectra or the transition between sub‐ and superradiant ground states, which are currently not accessible in any other physical system. The analysis also reveals the intrinsic difficulty of accessing this non‐perturbative regime with larger numbers of dipoles, which makes the simulation of many‐dipole cavity QED a particularly challenging test case for future quantum simulation platforms.

DOI
10.1002/qute.201900125

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•Jan 1, 2018•28 citations
Abstract The simulation of non‐perturbative cavity‐QED effects is discussed using systems of trapped ions. Specifically, the implementation of extended Dicke models with both collective dipole‐field and direct dipole–dipole interactions is addressed, which represent a minimal set of models for describing light–matter interactions in the ultrastrong and deep‐strong coupling regime. It is shown that this approach can be used in state‐of‐the‐art trapped ion setups to investigate excitation spectra or the transition between sub‐ and superradiant ground states, which are currently not accessible in any other physical system. The analysis also reveals the intrinsic difficulty of accessing this non‐perturbative regime with larger numbers of dipoles, which makes the simulation of many‐dipole cavity QED a particularly challenging test case for future quantum simulation platforms.
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 propose the analog quantum simulation of generalized Dicke models in trapped ions. By combining bicromatic laser interactions on multiple ions we can generate all regimes of light-matter coupling in these models, where here the light mode is mimicked by a motional mode. We present numerical simulations of the three-qubit Dicke model both in the weak field (WF) regime, where the Jaynes-Cummings behavior arises, and the ultrastrong coupling (USC) regime, where a rotating-wave approximation cannot be considered. We also simulate the two-qubit biased Dicke model in the WF and USC regimes and the two-qubit anisotropic Dicke model in the USC regime and the deep-strong coupling regime. The agreement between the mathematical models and the ion system convinces us that these quantum simulations can be implemented in the laboratory with current or near-future technology. This formalism establishes an avenue for the quantum simulation of many-spin Dicke models in trapped ions.
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 propose the quantum simulation of the quantum Rabi model in all parameter regimes by means of detuned bichromatic sideband excitations of a single trapped ion. We show that current setups can reproduce, in particular, the ultrastrong and deep strong coupling regimes of such a paradigmatic light-matter interaction. Furthermore, associated with these extreme dipolar regimes, we study the controlled generation and detection of their entangled ground states by means of adiabatic methods. Ion traps have arguably performed the first quantum simulation of the Jaynes-Cummings model, a restricted regime of the quantum Rabi model where the rotating-wave approximation holds. We show that one can go beyond and experimentally investigate the quantum simulation of coupling regimes of the quantum Rabi model that are difficult to achieve with natural dipolar interactions.
Abstract Light-matter interactions are an established field that is experiencing a renaissance in recent years due to the introduction of exotic coupling regimes. These include the ultrastrong and deep-strong coupling regimes, where the coupling constant is smaller and of the order of the frequency of the light mode, or larger than this frequency, respectively. In the past few years, quantum simulations of light-matter interactions in all possible coupling regimes have been proposed and experimentally realized, in quantum platforms such as trapped ions, superconducting circuits, cold atoms, and quantum photonics. We review this fledgling field, illustrating the benefits and challenges of the quantum simulations of light-matter interactions with quantum technologies.
Abstract Recent technological developments have made it increasingly easy to access the non-perturbative regimes of cavity quantum electrodynamics known as ultrastrong or deep strong coupling, where the light–matter coupling becomes comparable to the bare modal frequencies. In this work, we address the adequacy of the broadly used single-mode cavity approximation to describe such regimes. We demonstrate that, in the non-perturbative light–matter coupling regimes, the single-mode models become unphysical, allowing for superluminal signalling. Moreover, considering the specific example of the quantum Rabi model, we show that the multi-mode description of the electromagnetic field, necessary to account for light propagation at finite speed, yields physical observables that differ radically from their single-mode counterparts already for moderate values of the coupling. Our multi-mode analysis also reveals phenomena of fundamental interest on the dynamics of the intracavity electric field, where a free photonic wavefront and a bound state of virtual photons are shown to coexist.