Breakdown of gauge invariance in ultrastrong-coupling cavity QED

Bernardis, Daniele De; Pilar, Philipp; Jaako, Tuomas; Liberato, Simone De; Rabl, Peter

doi:10.1103/physreva.98.053819

Cited by 178 publications

(266 citation statements)

References 141 publications

(250 reference statements)

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“…1. The fundamental limitations of the fewlevel approximation have been presented in a variety of recent publications 16,23,26,43,44 . While this approximation results in a strongly simplified problem, it has the advantage that exact numerical results, although nontrivial to obtain, are still achievable with a reasonable computational effort.…”

Section: Electron-photon Correlated Systemsmentioning

confidence: 99%

Benchmarking semiclassical and perturbative methods for real-time simulations of cavity-bound emission and interference

Hoffmann

Schäfer

Säkkinen

et al. 2019

The Journal of Chemical Physics

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We benchmark a selection of semiclassical and perturbative dynamics techniques by investigating the correlated evolution of a cavity-bound atomic system to assess their applicability to study problems involving strong light-matter interactions in quantum cavities. The model system of interest features spontaneous emission, interference, and strong coupling behaviour, and necessitates the consideration of vacuum fluctuations and correlated light-matter dynamics. We compare a selection of approximate dynamics approaches including fewest switches surface hopping, multi-trajectory Ehrenfest dynamics, linearized semiclasical dynamics, and partially linearized semiclassical dynamics. Furthermore, investigating self-consistent perturbative methods, we apply the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy in the second Born approximation. With the exception of fewest switches surface hopping, all methods provide a reasonable level of accuracy for the correlated light-matter dynamics, with most methods lacking the capacity to fully capture interference effects.Here we broaden our scope by investigating the performance of a comprehensive class of approximate quantum dynamics methods for simulating spontaneous emission in an optical cavity, including Ehrenfest meanfield theory 33,34 , Tully's surface hopping algorithm 35 , fully linearized 36 and partially linearized 37,38 semilclassical dynamics techniques, and a selection of approximate closures for the quantum mechanical Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. Through benchmark comparisons with exact numerical results, we assess the accuracy and efficiency of each method and highlight the possibilities and theoretical challenges involved with extending these approaches towards realistic systems.The remainder of this work is divided into four sections: Sec. II gives a short overview of general quantum mechanical arXiv:1909.07177v2 [quant-ph]

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Section: Electron-photon Correlated Systemsmentioning

confidence: 99%

Benchmarking semiclassical and perturbative methods for real-time simulations of cavity-bound emission and interference

Hoffmann

Schäfer

Säkkinen

et al. 2019

The Journal of Chemical Physics

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confidence: 99%

“…One important conclusion that can be drawn from these controversies is that, once the light-matter coupling becomes non-perturbative, the validity of the two-level approximation for the atomic dipoles depends explicitly on the choice of gauge. In particular, it has been shown [6] that in the electric dipole gauge (the multipolar gauge in the dipole approximation) the two-level approximation can be performed as long as the Rabi frequency remains much smaller than the energies of the off-resonant higher-energy levels. However, it can dramatically fail in the Coulomb gauge, even for systems with an extremely anharmonic spectrum [6].…”

mentioning

confidence: 99%

Resolution of gauge ambiguities in ultrastrong-coupling cavity quantum electrodynamics

Stefano¹,

Settineri²,

Macrì³

et al. 2019

Nat. Phys.

192

302

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Gauge invariance is the cornerstone of modern quantum field theory [1][2][3][4]. Recently, it has been shown that the quantum Rabi model, describing the dipolar coupling between a two-level atom and a quantized electromagnetic field, violates this principle [5][6][7]. This widely used model describes a plethora of quantum systems and physical processes under different interaction regimes [8,9]. In the ultrastrong coupling regime, it provides predictions which drastically depend on the chosen gauge. This failure is attributed to the finite-level truncation of the matter system. We show that a careful application of the gauge principle is able to restore gauge invariance even for extreme lightmatter interaction regimes. The resulting quantum Rabi Hamiltonian in the Coulomb gauge differs significantly from the standard model and provides the same physical results obtained by using the dipole gauge. It contains field operators to all orders that cannot be neglected when the coupling strength is high. These results shed light on subtleties of gauge invariance in the nonperturbative and extreme interaction regimes, which are now experimentally accessible, and solve all the long-lasting controversies arising from gauge ambiguities in the quantum Rabi and Dicke models [5,[10][11][12][13][14][15][16][17][18].arXiv:1809.08749v3 [quant-ph]

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“…This gauge ambiguity becomes particularly important in the (ultra) strong coupling regime. It has been found that the QRM derived in a gauge where the qubit-resonator coupling is mediated by the flux variables leads to different predictions than the one where the coupling is mediated by the charge variables [10][11][12].…”

mentioning

confidence: 99%

Optimal gauge for the multimode Rabi model in circuit QED

Roth

Hassler

DiVincenzo

2019

Phys. Rev. Research

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In circuit QED, a Rabi model can be derived by truncating the Hilbert space of the anharmonic qubit coupled to a linear, reactive environment. This truncation breaks the gauge invariance present in the full Hamiltonian. We analyze the determination of an optimal gauge such that the differences between the truncated and the full Hamiltonian are minimized. Here, we derive a simple criterion for the optimal gauge. We find that it is determined by the ratio of the anharmonicity of the qubit to an averaged environmental frequency. We demonstrate that the usual choices of flux and charge gauge are not necessarily the preferred options in the case of multiple resonator modes.Circuit QED [1, 2] is a central subject of quantum information science that has deepened our understanding of light-matter interaction [3][4][5]. Most implementations consist of a two-level system (qubit) that is coupled to a linear environment. The qubit is formed by the two lowest energy levels of an anharmonic multilevel-system. For the physics of interest only the qubit subspace is important. The Schrieffer-Wolff (SW) transformation [6,7] is the standard method to perturbatively derive an effective Hamiltonian description within this subspace. For most purposes, it is sufficient to consider the effective Hamiltonian only to first order, yielding the well known quantum Rabi model (QRM). However, since the Hamiltonian of the non-truncated system is unique only up to a unitary transformation, the effective description is gauge dependent to every finite order [8,9]. This gauge ambiguity becomes particularly important in the (ultra) strong coupling regime. It has been found that the QRM derived in a gauge where the qubit-resonator coupling is mediated by the flux variables leads to different predictions than the one where the coupling is mediated by the charge variables [10][11][12].In this work, we look at the issue from a different perspective. We use the gauge degree of freedom to find an optimal gauge such that the results of the effective model are as close as possible to full model. Importantly, we take account of the need for a multimode description [13][14][15][16] in the quest for achieving the ultra-strong coupling regime [17][18][19][20]. To increase the flexibility, we not only consider the extremal cases of purely flux or charge mediated coupling but perform a general gauge transformation that smoothly interpolates between the two. A similar transformation has been used in [21] to extend the Jaynes-Cummings model into the ultra-strong coupling regime.We find that already the second order term of the effective Hamiltonian within the SW method is a good indicator of the validity of the QRM. Based on this observation, we derive a simple analytical criterion for the optimal gauge and benchmark it against numerical sim- FIG. 1. (a) Circuit diagram of a qubit with potential U (φq), capacitance Cq, and inductance Lq that is coupled to a general reactive environment. In the Forster form, the latter is represented by N resonators with capacitance...

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Breakdown of gauge invariance in ultrastrong-coupling cavity QED

Cited by 178 publications

References 141 publications

Benchmarking semiclassical and perturbative methods for real-time simulations of cavity-bound emission and interference

Benchmarking semiclassical and perturbative methods for real-time simulations of cavity-bound emission and interference

Resolution of gauge ambiguities in ultrastrong-coupling cavity quantum electrodynamics

Optimal gauge for the multimode Rabi model in circuit QED

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