Absence of Vacuum Induced Berry Phases without the Rotating Wave Approximation in Cavity QED

Larson, Jonas

doi:10.1103/physrevlett.108.033601

Cited by 70 publications

(48 citation statements)

References 54 publications

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“…Others have also noted that the RWA and non-RWA can lead to physically different conclusions, e.g. in the context of Berry phases in cavity QED [41].…”

Section: Numerical Resultsmentioning

confidence: 99%

Quantum adiabatic Markovian master equations

et al. 2012

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Abstract. We develop from first principles Markovian master equations suited for studying the time evolution of a system evolving adiabatically while coupled weakly to a thermal bath. We derive two sets of equations in the adiabatic limit, one using the rotating wave (secular) approximation that results in a master equation in Lindblad form, the other without the rotating wave approximation but not in Lindblad form. The two equations make markedly different predictions depending on whether or not the Lamb shift is included. Our analysis keeps track of the various time and energy scales associated with the various approximations we make, and thus allows for a systematic inclusion of higher order corrections, in particular beyond the adiabatic limit. We use our formalism to study the evolution of an Ising spin chain in a transverse field and coupled to a thermal bosonic bath, for which we identify four distinct evolution phases. While we do not expect this to be a generic feature, in one of these phases dissipation acts to increase the fidelity of the system state relative to the adiabatic ground state.

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“…Others have also noted that the RWA and non-RWA can lead to physically different conclusions, e.g. in the context of Berry phases in cavity QED [41].…”

Section: Numerical Resultsmentioning

confidence: 99%

Quantum adiabatic Markovian master equations

et al. 2012

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“…Explicitly, the Rabi model has been experimentally simulated in optical waveguides [9], superconducting circuit systems [10][11][12][13], and solid-state semiconductors [14][15][16][17][18], which provides a perfect test bed to explore the physics of light-matter interaction in the deep strong coupling regime. Another significance of the analytic achievement is that it offers some insight into the involved physics, e.g., the vacuum-induced Berry phase [19], and the quantum phase transition in the related multi-mode Rabi model, i.e., the spin-boson model [20,21], for which an exact solution is quite difficult to obtain, and a wellestablished approximate method is desirable.…”

Section: Introductionmentioning

confidence: 99%

Mean photon number dependent variational method to the Rabi model

Liu

Ying

et al. 2015

New J. Phys.

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We present a mean photon number dependent variational method, which works well in the whole coupling regime if the photon energy is dominant over the spin-flipping, to evaluate the properties of the Rabi model for both the ground state and excited states. For the ground state, it is shown that the previous approximate methods, the generalized rotating-wave approximation (only working well in the strong coupling limit) and the generalized variational method (only working well in the weak coupling limit), can be recovered in the corresponding coupling limits. The key point of our method is to tailor the merits of these two existing methods by introducing a mean photon number dependent variational parameter. For the excited states, our method yields considerable improvements over the generalized rotating-wave approximation. The variational method proposed could be readily applied to more complex models, for which it is difficult to formulate an analytic formula. by considering the RWA-type interaction in the reformulated Hamiltonian in the displaced oscillator basis. This scheme was named 'generalized RWA' (GRWA). Although the GRWA works well in a quite broad parameter regime, especially in the strong coupling regime, it does not work well in the weak coupling regime, especially for the positive detuning case. In addition, the mean photon number predicted by the GRWA is independent of the frequency of the two-level system, which is actually not true. As an improvement, a generalized variational method (GVM) [31,32] has been introduced, where the displacement of the displaced oscillator basis is determined by minimizing the ground state energy. Indeed, the GVM evidently improves the GRWA in the weak coupling regime with positive detuning, and yields a frequency dependent ground state mean photon number. However, for strong coupling and intermediate coupling regimes, the GVM is no longer applicable. Moreover the GVM is limited to the ground state.Obviously, the merit of the GRWA and the AA comes from the introduction of the displaced oscillator basis, which captures the essential physics in the large coupling regime. However, its disadvantage lies in fixing the displacement, which leads to a frequency independent mean photon number of the obtained ground state. On the contrary, the GVM frees the displacement, but it does not introduce the displaced oscillator basis and has been excessively simplified in the analytic treatment. In the present work, we combine the merits of the GRWA and the GVM to obtain a novel analytic method. We start from the GRWA formula but further introduce a mean photon number dependent variational method to determine the displacement. As a result, our approximation method is applicable in both weak and strong coupling regimes. In the weak coupling regime, it recovers the result of the GVM and in the strong coupling regime it recovers the GRWA. In the intermediate coupling, it provides a natural crossover from the GVM to the GRWA. This variational method is not only valid for the ground state, b...

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“…In the presence of noise in the field, B(t) = B 0 (t) + B 1 (t), the component of B 1 along the tangent to C 0 (t) induces reparametrization of C 0 (t) and, hence, leaves ϕ geo invariant, but the normal component changes the shape of C 0 (t) and modifies, in general, ϕ geo . The statistics of ϕ geo were first computed analytically in [10], considering B 1 as a classical stochastic field, with subsequent numerical [12] and experimental [13] confirmations of the results, while the subtler case of B 1 being a quantum operator was treated in [1], with some qualitative differences showing up (see also [14] for earlier work treating B as a quantum field, [17,18,30] for subsequent theoretical debate, and the recent experimental observation reported in [15]).…”

Section: Introductionmentioning

confidence: 89%

When geometric phases turn topological

Aguilar¹,

Chryssomalakos²,

Guzmán-González³

et al. 2020

J. Phys. A: Math. Theor.

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Geometric phases, accumulated when a quantum system traces a cycle in quantum state space, do not depend on the parametrization of the cyclic path, but do depend on the path itself. In the presence of noise that deforms the path, the phase gets affected, compromising the robustness of possible applications, e.g., in quantum computing. We show that for a special class of spin states, called anticoherent, and for paths that correspond to a sequence of rotations in physical space, the phase only depends on topological characteristics of the path, in particular, its homotopy class, and is therefore immune to noise.

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Absence of Vacuum Induced Berry Phases without the Rotating Wave Approximation in Cavity QED

Cited by 70 publications

References 54 publications

Quantum adiabatic Markovian master equations

Quantum adiabatic Markovian master equations

Mean photon number dependent variational method to the Rabi model

When geometric phases turn topological

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