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arXiv:1706.07781 · Physical Review A

Cold-atom-based implementation of the quantum Rabi model

Philipp Schneeweiß, Alexandre Dareau, C. Sayrin

Published Aug 8, 2018• 46 citations
arXivHTMLPDF

Abstract

The interaction of a two-level system (TLS) with a single bosonic mode (BM) is one of the most fundamental processes in quantum optics. Microscopically, it is described by the quantum Rabi model (QRM). Here we propose a versatile implementation of this model based on single trapped cold atoms. Assuming realistic experimental conditions, we show that our approach is not restricted to the Jaynes-Cummings regime but also allows exploring the regimes of ultrastrong coupling, deep strong coupling, and dispersive deep strong coupling. In contrast to most other QRM platforms, all important system parameters, i.e., the emitter-field detuning and the coupling strength of the emitter to the mode, can be dynamically tuned over a wide range. The quantum state of the BM and the TLS can be prepared and read-out using standard cold-atom techniques, enabling the study of the QRM and its dynamics with unprecedented control. Our scheme implements the TLS using atomic Zeeman states, while the atom's vibrational states in the trap represent the BM. The coupling is mediated by a suitable fictitious magnetic field pattern. Finally, we show that our scheme also enables the implementation of important generalizations, namely, the driven QRM, the QRM with quadratic coupling, or the Dicke model.

DOI
10.1103/physreva.98.021801

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The interaction of a two-level system (TLS) with a single bosonic mode (BM) is one of the most fundamental processes in quantum optics. Microscopically, it is described by the quantum Rabi model (QRM). Here we propose a versatile implementation of this model based on single trapped cold atoms. Assuming realistic experimental conditions, we show that our approach is not restricted to the Jaynes-Cummings regime but also allows exploring the regimes of ultrastrong coupling, deep strong coupling, and dispersive deep strong coupling. In contrast to most other QRM platforms, all important system parameters, i.e., the emitter-field detuning and the coupling strength of the emitter to the mode, can be dynamically tuned over a wide range. The quantum state of the BM and the TLS can be prepared and read-out using standard cold-atom techniques, enabling the study of the QRM and its dynamics with unprecedented control. Our scheme implements the TLS using atomic Zeeman states, while the atom's vibrational states in the trap represent the BM. The coupling is mediated by a suitable fictitious magnetic field pattern. Finally, we show that our scheme also enables the implementation of important generalizations, namely, the driven QRM, the QRM with quadratic coupling, or the Dicke model.
The quantum Rabi model describes the coupling of a two-state system to a bosonic field mode. Recent theoretical work has pointed out that a generalized periodic version of this model, which maps onto Hamiltonians applicable in superconducting qubit settings, can be quantum simulated with cold trapped atoms. Here, we experimentally demonstrate atomic dynamics predicted by the periodic quantum Rabi model far in the deep strong-coupling regime. The two-state system is represented by two Bloch bands of cold atoms in an optical lattice, and the bosonic mode by oscillations in a superimposed optical dipole trap potential. The observed dynamics beyond the usual quantum Rabi physics becomes relevant when the edge of the Brillouin zone is reached, and evidence for collapse and revival of the initial state is revealed at extreme coupling conditions. Published by the American Physical Society 2024
In the last decades, the experimental and theoretical study of light-matter interactions in confined quantum systems has allowed to considerably widen and deepen our understanding of the quantum world.The simplest fully-quantized light-matter interaction is the quantum Rabi model (QRM), where a two-level system is coupled to a single bosonic mode.The implementation of quantum-optical systems in which the interaction strength overcomes losses brought a revolution to this research area.Under this condition, dubbed strong coupling (SC) regime, quantum processes can be observed at the single-photon level, and even exploited to perform Quantum Information tasks.Recent developments in solid-state Quantum Technologies have made possible to push the line further, achieving the ultrastrong coupling (USC) regime of the QRM, in which the interaction strength is comparable with the bare frequencies of the interacting systems.In the USC regime of the QRM, light and matter degrees of freedom merge into collective bound states called polaritons, the system ground state is not the vacuum and excitations are not conserved.The growing interest in USC-related phenomena is mainly motivated by the fundamental counterintuitive modifications to light-matter interactions entailed by this regime.At the same time, the USC regime is also expected to provide computational benefits in terms of operational speed, coherence time, and noise protection.In this Thesis, we theoretically analyze novel quantum phenomena emerging in the USC regime, which can be observed using nowadays technology and can motivate foreseeable improvements.The results here presented have been derived using two conceptually different approaches.On one side, we have analyzed interesting models that can be implemented in superconducting circuits, a quantum platform where the USC regime can be naturally achieved.In particular, we focused on excitation transfer across USC impurities, entanglement generation via modulation of electrical boundary conditions and quantum state engineering in ultrastrongly-coupled systems.On the other hand, we have developed methods to reproduce the physics of light-matter interactions in the USC regime, by tailoring the Hamiltonian of atomic systems, like trapped ions and cold atoms.These proposals take profit of the specific features of such quantum platforms, in order to implement regimes and measurements that are not directly accessible.We believe that this Thesis will contribute to develop a thorough understanding of quantum phenomena related to the USC regime of light-matter interaction, and that it will foster the dialog between experimental and theoretical research in this area.I would like to thank first my PhD supervisor Prof. Enrique Solano, for his constant support and invaluable guidance.Countless thought-provoking discussions held with him during my PhD studies have contributed to develop my critical skills, and his advice has covered all facets of nowadays top-level research.
The coupling of a two-level system with an electromagnetic field, whose fully quantized version is the quantum Rabi model, is among the central topics of quantum physics. When the coupling strength becomes large enough that the field mode frequency is reached, the deep strong coupling regime is approached, and excitations can be created from the vacuum. Here we demonstrate a periodic variant of the quantum Rabi model in which the two-level system is encoded in the Bloch band structure of cold rubidium atoms in optical potentials. With this method we achieve a Rabi coupling strength of 6.5 times the field mode frequency, which is far in the deep strong coupling regime, and observe a subcycle timescale raise in bosonic field mode excitations. In a measurement recorded in the basis of the coupling term of the quantum Rabi Hamiltonian, a freezing of dynamics is revealed for small frequency splittings of the two-level system, as expected when the coupling term dominates over all other energy scales, and a revival for larger splittings. Our work demonstrates a route to realize quantum-engineering applications in yet unexplored parameter regimes.
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 propose a quantum simulation of the quantum Rabi model in an atomic quantum dot, which is a single atom in a tight optical trap coupled to the quasiparticle modes of a superfluid Bose-Einstein condensate. This widely tunable setup allows us to simulate the ultrastrong coupling regime of light-matter interaction in a system which enjoys an amenable characteristic time scale, paving the way for an experimental analysis of the transition between the Jaynes-Cummings and the quantum Rabi dynamics using cold-atom systems. Our scheme can be naturally extended to simulate multiqubit quantum Rabi models. In particular, we discuss the appearance of effective two-qubit interactions due to phononic exchange, among other features.
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.