The quantum Rabi model is a widespread description of the coupling between a two-level system and a quantized single mode of an electromagnetic resonator. Issues about this model's gauge invariance have been raised. These issues become evident when the light-matter interaction reaches the so-called ultrastrong coupling regime. Recently, a modified quantum Rabi model able to provide gauge-invariant physical results (e.g., energy levels, expectation values of observables, quantum probabilities) in any interaction regime was introduced [O. Di Stefano, A. Settineri, V. Macr\`{\i}, L. Garziano, R. Stassi, S. Savasta, and F. Nori, Nat. Phys. 15, 803 (2019)]. Here we provide an alternative derivation of this result, based on the implementation in two-state systems of the gauge principle, which is the principle from which all the fundamental interactions in quantum field theory are derived. The adopted procedure can be regarded as the two-site version of the general method used to implement the gauge principle in lattice gauge theories. Applying this method, we also obtain the gauge-invariant quantum Rabi model for asymmetric two-state systems, and the multimode gauge-invariant quantum Rabi model beyond the dipole approximation.The quantum Rabi model is a widespread description of the coupling between a two-level system and a quantized single mode of an electromagnetic resonator. Issues about this model's gauge invariance have been raised. These issues become evident when the light-matter interaction reaches the so-called ultrastrong coupling regime. Recently, a modified quantum Rabi model able to provide gauge-invariant physical results (e.g., energy levels, expectation values of observables, quantum probabilities) in any interaction regime was introduced [O. Di Stefano, A. Settineri, V. Macr\`{\i}, L. Garziano, R. Stassi, S. Savasta, and F. Nori, Nat. Phys. 15, 803 (2019)]. Here we provide an alternative derivation of this result, based on the implementation in two-state systems of the gauge principle, which is the principle from which all the fundamental interactions in quantum field theory are derived. The adopted procedure can be regarded as the two-site version of the general method used to implement the gauge principle in lattice gauge theories. Applying this method, we also obtain the gauge-invariant quantum Rabi model for asymmetric two-state systems, and the multimode gauge-invariant quantum Rabi model beyond the dipole approximation.

arXiv:2006.06583Physical Review AMay 7, 202138 citations

GAUGE INVARIANCE PROPERTIES OF AN INTERACTING BOSE SYSTEM.

FERDINANDO DE PASQUALE, Eugenio Tabet

Jan 1, 19671 citation

Quantum simulations of gauge theories with ultracold atoms: Local gauge invariance from angular-momentum conservation

Erez Zohar, J. I. Cirac, Benni Reznik

Quantum simulations of high-energy physics, and especially of gauge theories, is an emerging and exciting direction in quantum simulations. However, simulations of such theories, compared to simulations of condensed matter physics, must satisfy extra restrictions, such as local gauge invariance and relativistic structure. In this paper we discuss these special requirements, and present a method for quantum simulation of lattice gauge theories using ultracold atoms. This method allows us to include local gauge invariance as a fundamental symmetry of the atomic Hamiltonian, arising from natural atomic interactions and conservation laws (and not as a property of a low-energy sector). This allows us to implement elementary gauge invariant interactions for three lattice gauge theories: U(1) (compact QED), ${\mathbb{Z}}_{N}$ and SU $(N)$ (Yang-Mills), which can be used to build quantum simulators in $1+1$ dimensions. We also present a loop method, which uses the elementary interactions as building blocks in the effective construction of quantum simulations for $d+1$ dimensional lattice gauge theories ( $d>1$ ), but unlike in previous proposals, here gauge invariance and Gauss's law are natural symmetries, which do not have to be imposed as a constraint. We discuss in detail the quantum simulation of $2+1$ dimensional compact QED and provide a numerical proof of principle. The simplicity of the already gauge-invariant elementary interactions of this model suggests it may be useful for future experimental realizations.Quantum simulations of high-energy physics, and especially of gauge theories, is an emerging and exciting direction in quantum simulations. However, simulations of such theories, compared to simulations of condensed matter physics, must satisfy extra restrictions, such as local gauge invariance and relativistic structure. In this paper we discuss these special requirements, and present a method for quantum simulation of lattice gauge theories using ultracold atoms. This method allows us to include local gauge invariance as a fundamental symmetry of the atomic Hamiltonian, arising from natural atomic interactions and conservation laws (and not as a property of a low-energy sector). This allows us to implement elementary gauge invariant interactions for three lattice gauge theories: U(1) (compact QED), ${\mathbb{Z}}_{N}$ and SU$(N)$ (Yang-Mills), which can be used to build quantum simulators in $1+1$ dimensions. We also present a loop method, which uses the elementary interactions as building blocks in the effective construction of quantum simulations for $d+1$ dimensional lattice gauge theories ($d>1$), but unlike in previous proposals, here gauge invariance and Gauss's law are natural symmetries, which do not have to be imposed as a constraint. We discuss in detail the quantum simulation of $2+1$ dimensional compact QED and provide a numerical proof of principle. The simplicity of the already gauge-invariant elementary interactions of this model suggests it may be useful for future experimental realizations.

arXiv:1303.5040Physical Review AAug 27, 2013205 citations

A microscopic theory of the interacting bose system

精久松田

Jan 1, 19760 citations

Gauge-invariant time-dependent perturbation theory. II. degenerate case

Kuo‐Ho Yang

For pt.I see ibid., vol.15, p.1201 (1982). The author formulates a manifestly gauge-invariant time-dependent perturbation theory for a nonrelativistic spinless charged particle interacting with a classical external electromagnetic radiation field. The treatment of the degenerate bound states and the states in the continuum is considered. It is found that the gauge-invariant and the conventional perturbative solutions agree on the net transition rates but disagree on the transition amplitudes and transition probabilities. The treatment of a realistic physical system can be obtained by combining the treatment here with that for a nondegenerate system.For pt.I see ibid., vol.15, p.1201 (1982). The author formulates a manifestly gauge-invariant time-dependent perturbation theory for a nonrelativistic spinless charged particle interacting with a classical external electromagnetic radiation field. The treatment of the degenerate bound states and the states in the continuum is considered. It is found that the gauge-invariant and the conventional perturbative solutions agree on the net transition rates but disagree on the transition amplitudes and transition probabilities. The treatment of a realistic physical system can be obtained by combining the treatment here with that for a nondegenerate system.

Journal of Physics A Mathematical and GeneralApr 1, 198311 citations

Density and Phase Variables in the Theory of Interacting Bose Systems

Paul Berdahl

Springer eBooksJan 1, 19742 citations

{\mathbb{Z}}_{N}

and SU

(N)

(Yang-Mills), which can be used to build quantum simulators in

1+1

dimensions. We also present a loop method, which uses the elementary interactions as building blocks in the effective construction of quantum simulations for

d+1

dimensional lattice gauge theories (

d>1

), but unlike in previous proposals, here gauge invariance and Gauss's law are natural symmetries, which do not have to be imposed as a constraint. We discuss in detail the quantum simulation of

2+1

dimensional compact QED and provide a numerical proof of principle. The simplicity of the already gauge-invariant elementary interactions of this model suggests it may be useful for future experimental realizations.