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Journal of Physics A Mathematical and Theoretical

Ground state of a cross-cavity quantum Rabi model

Li-Tuo Shen, Jingwen Yang, Zhi‐Cheng Shi, Zhi‐Rong Zhong, Canhua Xu

Published Feb 10, 2021• 4 citations
Publisher

Abstract

Abstract We study a cross-cavity quantum Rabi model with ultrastrong coupling, and its analytical ground state is demonstrated to be approximately obtained by using the rotating-transformation method. Our method requires making three unitary transformations to the original Hamiltonian and ignoring the three-party cross interaction. In near-resonance and ultrastrong-coupling regimes, the ground-state fidelity is higher than 99% for a ±20% detuning range. We analytically demonstrate that the entanglement in ground state first quadratically increases with the qubit-oscillator coupling strength, then gets close to the maximum value 1. The oscillator’s nonclassical property in the ground state is well explained by analytically solving the Wigner function.

DOI
10.1088/1751-8121/abe4eb

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We examine a generalized Rabi model formed by two identical qubits interacting with a common oscillator mode. In the near-resonance configuration where the oscillator frequency is close to the transition frequency of the qubit, we determine the ground state of the model approximately by using a variational method and a transformation method. Both methods are shown to approximate the ground state accurately for a range of coupling strengths in the ultrastrong-coupling regime. In addition, the accuracy of the approximation can be further improved by using perturbation theory. We also characterize the ground-state entanglement between the two qubits by calculating the negativity.
Abstract We apply a simple analytical method based on a unitary transformation to calculate the ground state, its excitation spectrum and quantum dynamic evolution of physical quantities for the double-photon quantum Rabi Hamiltonian over the wide coupling-strength range. The concise analytical method possesses the same mathematical simplicity as the approach of the rotating wave approximation (RWA). By quantitative comparison with the numerically exact result obtained by matrix diagonalization, we confirm that our calculated results obtained by transformed rotating-wave method are not only accurate in the weak coupling regime but also correct in intermediate strong-coupling case. In the intermediate ultrastrong-coupling regime, the calculated values of the ground state and lower lying excited states are nearly the same as the exact ones. It turns out that our calculation for the energy spectrum is beyond the ordinary-RWA. Meanwhile, we demonstrate the signatures resulting from the counter-rotating wave terms by monitoring the population, the coherence, the squeezing of the photon under the ultra-strong conditions. In particular, we find that when the frequency of the photon is much larger than the transition frequency of the system, the lineshape of the time evolution becomes complicated with the increase of the coupling strength, which may be verified experimentally.
We study the effect of inversion symmetry breaking on properties of the ground state of a qubit-oscillator system within the ultrastrong-coupling regime. We obtain the solution of the ground state through the approximate analytical approach, which, under the near-resonance condition, agrees well with the numerical simulation. We demonstrate that, due to the inversion symmetry breaking, the ground state becomes asymmetric and the qubit-oscillator entanglement entropy strongly depends on the mean dipole moments. Furthermore, we find that the attainable maximum entanglement entropy undergoes a sharp change across a critical point and the minimum value of the Wigner function has a quadratic dependence on the mean dipole moments.
We study the ground state of the two-qubit squeezed Rabi model. Two special transformations are found to diagonalize the system Hamiltonian when each qubit’s frequency is close to the field frequency, where both the squeezing and counterrotating-wave interactions are removed, leading to an effective integrable Hamiltonian. The analytical ground state is determined and matches with numerical solutions well for a range of squeezing strengths and qubit-field detunings in the ultrastrong-coupling regime. We demonstrate that the ground state exhibits a first-order quantum phase transition at a phase boundary linearly induced by the squeezed light. We characterize the two-qubit negativity analytically and find that its two-qubit entanglement increases with the increasing squeezing strength nonlinearly. The average photon numbers of the field mode and variances of position and momentum quadratures are also analyzed and discovered to have a nonlinear relation with the squeezing strength. Finally, we discuss the experimental scheme and realization possibility of the predicted results.
Abstract Quantum phase transition and entanglement in the Rabi model with a squeezed light are investigated. We find a special unitary-transformation method that removes the nonintegrable squeezing and counterrotating-wave interactions when the qubit frequency is close to the field frequency. The analytical ground state agrees well with the numerical solution. We demonstrate that the ground state exhibits a first-order quantum phase transition at a critical point induced linearly by the squeezed light. This quantum phase transition requires neither multiple qubits nor an infinite ratio of qubit frequency to field frequency, which solves a critical problem for the theory and experiment in Rabi model. As the qubit-field coupling strength increases, the ground-state entanglement reaches its maximum value at the critical point.