Entanglement of a qubit coupled to a resonator in the adiabatic regime

The time evolution of an entangled bi-partite qubit interacting with two independent photon baths in isolated cavities is not unitary. It is shown that the bi-partite qubit oscillates between pure and mixed states, and that the initial entanglement is lost and recovered in time by time as a consequence of its interaction with the baths.

Journal of Physics Conference SeriesMar 1, 20161 citation

Ground state of a resonant two-qubit cavity system in the ultrastrong-coupling regime

Kelvin M. C. Lee, C. K. Law

arXiv:1303.3367Physical Review AJul 8, 201321 citations

Entanglement of a qubit coupled to a resonator in the adiabatic regime

LIBERTI G, ZAFFINO R. L, Franco Piperno, Francesco Plastina

Published Jan 1, 2006• 0 citations

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Abstract

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Entanglement of a qubit coupled to a resonator in the adiabatic regime

Giuseppe Di Liberti, Rosa Letizia Zaffino, Franco Piperno +1 more

We discuss the ground state entanglement of a bi-partite system, composed by a qubit strongly interacting with an oscillator mode, as a function of the coupling strength, the transition frequency and the level asymmetry of the qubit. This is done in the adiabatic regime in which the time evolution of the qubit is much faster than the oscillator one. Within the adiabatic approximation, we obtain a complete characterization of the ground state properties of the system and of its entanglement content.We discuss the ground state entanglement of a bi-partite system, composed by a qubit strongly interacting with an oscillator mode, as a function of the coupling strength, the transition frequency and the level asymmetry of the qubit. This is done in the adiabatic regime in which the time evolution of the qubit is much faster than the oscillator one. Within the adiabatic approximation, we obtain a complete characterization of the ground state properties of the system and of its entanglement content.

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Adiabatic approximation for three qubits ultrastrongly coupled to a harmonic oscillator

Li-Tuo Shen, Rongxin Chen, Huai‐Zhi Wu +1 more

We study the system involving mutual interaction between three qubits and an oscillator within the ultrastrong coupling regime. We apply the adiabatic approximation approach to explore two extreme regimes: (i) the oscillator's frequency is far larger than each qubit's frequency and (ii) the qubit's frequency is far larger than the oscillator's frequency, and analyze the energy-level spectrum and the ground-state property of the qubit-oscillator system under the conditions of various system parameters. For the energy-level spectrum, we concentrate on studying the degeneracy in low-energy levels. For the ground state, we focus on its nonclassical properties that are necessary for preparing the nonclassical states. We show that the minimum qubit-oscillator coupling strength needed for generating the nonclassical states of the Schr\"odinger-cat type in the oscillator is just one half of that in the Rabi model. We find that the qubit-qubit entanglement in the ground state vanishes if the qubit-oscillator coupling strength is strong enough, for which the entropy of three qubits remains larger than 1. We also observe the phase-transition-like behavior in the regime where the qubit's frequency is far larger than the oscillator's frequency.We study the system involving mutual interaction between three qubits and an oscillator within the ultrastrong coupling regime. We apply the adiabatic approximation approach to explore two extreme regimes: (i) the oscillator's frequency is far larger than each qubit's frequency and (ii) the qubit's frequency is far larger than the oscillator's frequency, and analyze the energy-level spectrum and the ground-state property of the qubit-oscillator system under the conditions of various system parameters. For the energy-level spectrum, we concentrate on studying the degeneracy in low-energy levels. For the ground state, we focus on its nonclassical properties that are necessary for preparing the nonclassical states. We show that the minimum qubit-oscillator coupling strength needed for generating the nonclassical states of the Schr\"odinger-cat type in the oscillator is just one half of that in the Rabi model. We find that the qubit-qubit entanglement in the ground state vanishes if the qubit-oscillator coupling strength is strong enough, for which the entropy of three qubits remains larger than 1. We also observe the phase-transition-like behavior in the regime where the qubit's frequency is far larger than the oscillator's frequency.

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Quantum evolution of entanglement property in two-qubit and oscillator coupling system

Xia Jian-Ping, Xuezao Ren, Cong Hong-Lu +2 more

Under the non-rotating wave approximation, the quantum evolution of entanglement property of a two-qubit and oscillator coupling system is accurately investigated by the method of coherent-state orthogonalization expansion. The property of the ground state for qubit-oscillator system and the difference between qubit-oscillator entanglement and qubit-qubit entanglement when resonant vibration occurs are discussed. The calculation results show that when the external field is not taken into consideration, the qubit-qubit entanglement reduces from 1 to 0 rapidly with the increase of coupling strength, indicating the strong sensitivity of the entanglement to the coupling strength. On the contrary, with the increase of the coupling the qubit-oscillator entanglement rises from 0, but does not reach the maximum value 2. At the beginning, when the two qubits do not entangle, the vacuum field does not lead to the entanglement in weak coupling. However, the strong coupling can induce the sudden appearance of the entanglement.Under the non-rotating wave approximation, the quantum evolution of entanglement property of a two-qubit and oscillator coupling system is accurately investigated by the method of coherent-state orthogonalization expansion. The property of the ground state for qubit-oscillator system and the difference between qubit-oscillator entanglement and qubit-qubit entanglement when resonant vibration occurs are discussed. The calculation results show that when the external field is not taken into consideration, the qubit-qubit entanglement reduces from 1 to 0 rapidly with the increase of coupling strength, indicating the strong sensitivity of the entanglement to the coupling strength. On the contrary, with the increase of the coupling the qubit-oscillator entanglement rises from 0, but does not reach the maximum value 2. At the beginning, when the two qubits do not entangle, the vacuum field does not lead to the entanglement in weak coupling. However, the strong coupling can induce the sudden appearance of the entanglement.

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We give an analytical description of the dynamics of the three-qubit Dicke model using the adiabatic approximation in the parameter regime where the qubit transition frequencies are far off-resonance with the field frequency and the interaction strengths reach the ultrastrong-coupling regimes. Qualitative differences arise upon comparison to single- and two-qubit systems. Simple analytic formulas show that three revival sequences produce a three-frequency beat note in the time evolution of the population. We find an explicit way to estimate the dynamics for qubit-field and qubit-qubit entanglement inside the three-qubit system in the ultrastrong-coupling regime, and the resistance to sudden death proves that the entanglement in the Greenberger-Horne-Zeilinger state is more robust than that in the $W$ state.We give an analytical description of the dynamics of the three-qubit Dicke model using the adiabatic approximation in the parameter regime where the qubit transition frequencies are far off-resonance with the field frequency and the interaction strengths reach the ultrastrong-coupling regimes. Qualitative differences arise upon comparison to single- and two-qubit systems. Simple analytic formulas show that three revival sequences produce a three-frequency beat note in the time evolution of the population. We find an explicit way to estimate the dynamics for qubit-field and qubit-qubit entanglement inside the three-qubit system in the ultrastrong-coupling regime, and the resistance to sudden death proves that the entanglement in the Greenberger-Horne-Zeilinger state is more robust than that in the $W$ state.

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Additional Quantum Properties of Entangled Bipartite Qubit Systems Coupled to Photon Baths

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Ground state of a resonant two-qubit cavity system in the ultrastrong-coupling regime

Kelvin M. C. Lee, C. K. Law

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.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.

arXiv:1303.3367Physical Review AJul 8, 201321 citations

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