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arXiv:1311.0982 · Physical Review A

Adiabatic approximation for three qubits ultrastrongly coupled to a harmonic oscillator

Li-Tuo Shen, Rongxin Chen, Huai‐Zhi Wu, Zhen‐Biao Yang

Published Feb 10, 2014• 4 citations
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Abstract

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.

DOI
10.1103/physreva.89.023810

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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 consider a system composed of a two-level system (i.e., a qubit) and a harmonic oscillator in the ultrastrong-coupling regime, where the coupling strength is comparable to the qubit and oscillator energy scales. Special emphasis is placed on the possibility of preparing nonclassical states in this system. These nonclassical states include squeezed states, Schr\"odinger-cat states, and entangled states. We start by comparing the predictions of a number of analytical methods that can be used to describe the system under different assumptions, thus analyzing the properties of the system in various parameter regimes. We then examine the ground state of the system and analyze its nonclassical properties. We finally discuss some questions related to the possible experimental observation of the nonclassical states and the effect of decoherence.
We study the Rabi model composed of three qubits coupled to a harmonic oscillator without involving the rotating-wave approximation. We show that the ground state of the three-qubit Rabi model can be analytically treated by using the transformation method, and the transformed ground state agrees well with the exactly numerical simulation under a wide range of qubit-oscillator coupling strengths for different detunings. We use the pairwise entanglement to characterize the ground-state entanglement between any two qubits and show that it has an approximately quadratic dependence on the qubit-oscillator coupling strength. Interestingly, we find that there is no qubit-qubit entanglement for the ground state if the qubit-oscillator coupling strength is large enough.
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 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 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 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 WWW state.