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Chinese Physics B

First-order quantum phase transition and entanglement in the Jaynes–Cummings model with a squeezed light

Chun-Qi Tang, Li-Tuo Shen

Published Feb 8, 2023• 0 citations
Publisher

Abstract

We study the quantum phase transition and entanglement in the Jaynes–Cummings model with squeezed light, utilize a special transformation method to obtain the analytical ground state of the model within the near-resonance regime, and numerically verify the validity of the analytical ground state. It is found that the ground state exhibits a first-order quantum phase transition at the critical point linearly induced by squeezed light, and the ground state entanglement reaches its maximum when the qubit-field coupling strength is large enough at the critical point.

DOI
10.1088/1674-1056/acb9f0

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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.
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.
We follow the passage from complex amplitude bistability to phase bistability in the driven dissipative Jaynes-Cummings oscillator. Quasi -distribution functions in the steady state are employed, for varying qubit-cavity detuning and drive parameters, in order to track a first-order dissipative quantum phase transition up to the critical point marking a second-order transition and spontaneous symmetry breaking. We demonstrate the photon blockade breakdown in the dispersive regime, and find that the coexistence of cavity states in the regime of quantum bistability is accompanied by pronounced qubit-cavity entanglement. Focusing on the effect of quantum-activated switching for both coupled degrees of freedom, we move from a region of minimal entanglement in the dispersive regime, where we derive analytical perturbative results, to the threshold behaviour of spontaneous dressed-state polarization at resonance.
We investigate spin squeezing (SS) and the quantum Fisher information (QFI) for the Jaynes–Cummings–Dicke (JCD) model in a two-component atomic Bose–Einstein condensate (BEC) inside an optical cavity. Analytical expressions for spin squeezing and the reciprocal of the quantum Fisher information per particle (RMQFI) are derived using the frozen spin approximation. It is shown that in the superradiant phase near the critical point, maximum squeezing and maximum quantum entanglement occur and thus the critical point emerges as a useful resource for precision measurements. In the presence of decoherence and particle loss, we show that gradually with time, even though the ability of squeezing and entanglement generation are weakened, yet significant amounts are still present which can be relevant to quantum information processing and precision spectroscopy.
We investigate spin squeezing (SS) and the quantum Fisher information (QFI) for the Jaynes-Cummings Dicke (JC-Dicke) model in a two component atomic Bose-Einstein condensate (BEC) inside an optical cavity. Analytical expressions for spin squeezing and the reciprocal of the quantum Fisher information per particle (RMQFI) are derived using the frozen spin approximation. It is shown that in the superradiant phase near the critical point, maximum squeezing and maximum quantum entanglement occurs. The present study is relevant to quantum information processing and precision spectroscopy.