Collective Modes in the Cooperative Jahn–Teller Model: Path Integral Approach

Ivanov, Peter A.

doi:10.1007/s10909-015-1295-9

Cited by 4 publications

(4 citation statements)

References 36 publications

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“…, where the phase f remains undetermined which is a result of arbitrariness in the choice of a direction of spontaneous symmetry breaking [41], (see appendix A). In the symmetry-broken phase the energy spectrum of the TMD model contains one gapless Godstone mode and two gapped amplitude modes [41,43,44].…”

Section: Quantum Phase Transitionmentioning

confidence: 99%

“…In this work we investigate signatures of chaos and transition to equilibration and thermalization in the twomode Dicke (TMD) model, which consists of an ensemble of N two-state atoms and two bosonic modes which interact via dipolar coupling. The TMD model shows a quantum phase transition between a normal phase and a superradiant phase [41][42][43][44]. For the  2 -symmetric TMD model the superradiant phase is characterized by macroscopical excitations of one of the bosonic modes, whereas the other mode is with zero mean-field bosonic excitations.…”

Section: Introductionmentioning

confidence: 99%

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Quantum chaos and thermalization in the two-mode Dicke model

Kirkova

Ivanov

2023

Phys. Scr.

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We discuss the onset of quantum chaos and thermalization in the two-mode Dicke model, which describes the dipolar interaction between an ensemble of spins and two bosonic modes. The two-mode Dicke model exhibits normal to superradiant quantum phase transition with spontaneous breaking either of a discrete or continuous symmetry. We study the behaviour of the fidelity out-of-time-order correlator (FOTOC) derived from the Loschmidt echo signal in the quantum phases of the model. We show that the exponential growth of the FOTOC in the beginning of the time evolution cannot be related to a classical unstable point in the general case. Furthermore, we find that the collective spin observable in the two-mode Dicke model quickly saturates to its long-time average value, and shows very good agreement between its diagonal ensemble average and microcanonical average even for a small number of spins. We show that the temporal fluctuations of the expectation value of the collective spin observable around its average are small and decrease with the effective system size, which leads to thermalization of the spin system.

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Section: Quantum Phase Transitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum chaos and thermalization in the two-mode Dicke model

Kirkova

Ivanov

2023

Phys. Scr.

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“…In the U(1)-symmetric case the superradiant phase for g > g c is characterized by â † â /S = 2(g/ω) 2 (1 − g 4 c /g 4 ) cos 2 (φ ), b † b /S = 2(g/ω) 2 (1 − g 4 c /g 4 ) sin 2 (φ ) and Ŝz /S = −g 2 c /g 2 , where the phase φ remains undetermined which is a result of arbitrariness in the choice of a direction of spontaneous symmetry breaking [32], (see Appendix A). In the symmetrybroken phase the energy spectrum of the TMD model contains one gapless Godstone mode and two gapped amplitude modes [32,34,35].…”

Section: B Quantum Phase Transitionmentioning

confidence: 99%

“…In this work we investigate signatures of chaos and transition to equilibration and thermalization in the two-mode Dicke (TMD) model, which consists of an ensemble of N two-state atoms and two bosonic modes which interact via dipolar coupling. The TMD model shows a quantum phase transition between a normal phase and a superradiant phase [32][33][34][35]. For the Z 2 -symmetric TMD model the superradiant phase is characterized by macroscopical excitations of one of the bosonic modes, whereas the other mode is with zero mean-field bosonic excitations.…”

Section: Introductionmentioning

confidence: 99%

Quantum chaos and thermalization in the two-mode Dicke model

Kirkova¹,

Ivanov²

2022

Preprint

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We discuss the onset of quantum chaos and thermalization in the two-mode Dicke model, which describes the dipolar interaction between an ensemble of spins and two bosonic modes. The two-mode Dicke model exhibits normal to superradiant quantum phase transition with spontaneous breaking either of a discrete or continuous symmetry. We study the behaviour of the fidelity out-of-time-order correlator derived from the Loschmidt echo signal in the quantum phases of the model and show that its exponential growth cannot be related to a classical unstable point in the general case. Moreover, we find that the collective spin observable in the two-mode Dicke model quickly saturates to its long-time average value, and shows very good agreement between its diagonal ensemble average and microcanonical average even for a small number of spins. We show that the temporal fluctuations of the expectation value of the collective spin observable around its average are small and decrease with the effective system size, which leads to thermalization of the spin system.

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Synchronization of networked Jahn–Teller systems in SQUIDs

Gül

2016

Int. J. Mod. Phys. B

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We consider the nonlinear effects in Jahn-Teller system of two coupled resonators interacting simultaneously with flux qubit using Circuit QED. Two frequency description of Jahn Teller system that inherits the networked structure of both nonlinear Josephson Junctions and harmonic oscillators is employed to describe the synchronous structures in multifrequency scheme. Emergence of dominating mode is investigated to analyze frequency locking by eigenvalue spectrum. Rabi Supersplitting is tuned for coupled and uncoupled synchronous configurations in terms of frequency entrainment switched by coupling strength between resonators. Second order coherence functions are employed to investigate self-sustained oscillations in resonator mode and qubit dephasing. Snychronous structure between correlations of priviledged mode and qubit is obtained in localization-delocalization and photon blockade regime controlled by the population imbalance.

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Collective Modes in the Cooperative Jahn–Teller Model: Path Integral Approach

Cited by 4 publications

References 36 publications

Quantum chaos and thermalization in the two-mode Dicke model

Quantum chaos and thermalization in the two-mode Dicke model

Quantum chaos and thermalization in the two-mode Dicke model

Synchronization of networked Jahn–Teller systems in SQUIDs

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