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arXiv:1105.2835

Exact Entanglement Dynamics Beyond the Rotating Wave Approximation

Seyed Mohammad Hashemi Rafsanjani, Shantanu Agarwal, Joseph H. Eberly

Published May 13, 2011• 0 citations
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Abstract

The entanglement dynamics of two remote qubits is examined analytically. The qubits interact arbitrarily strongly with separate harmonic oscillators in the idealized degenerate limit of the Jaynes-Cummings Hamiltonian. In contrast to well known non-degenerate RWA results, it is shown that ideally degenerate qubits cannot induce bipartite entanglement between their partner oscillators.

DOI
10.48550/arxiv.1105.2835

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The entanglement dynamics of two remote qubits is examined analytically. The qubits interact arbitrarily strongly with separate harmonic oscillators in the idealized degenerate limit of the Jaynes-Cummings Hamiltonian. In contrast to well known non-degenerate RWA results, it is shown that ideally degenerate qubits cannot induce bipartite entanglement between their partner oscillators.
We study the dynamics of two qubits interacting with a single mode of a harmonic oscillator beyond the rotating wave approximation in the ideally degenerate regime. Exact analytic expressions are obtained for state properties of interest, including qubit entanglement for a certain class of initial states of the oscillator and the qubits. Qualitative differences and similarities in the evolution of the qubits in the degenerate regime when the oscillator is treated quantum mechanically and classically are discussed.
We generalize the dispersive theory of the Jaynes-Cummings model beyond the frequently employed rotating-wave approximation (RWA) in the coupling between the two-level system and the resonator. For a detuning sufficiently larger than the qubit-oscillator coupling, we diagonalize the non-RWA Hamiltonian and discuss the differences to the known RWA results. Our results extend the regime in which dispersive qubit readout is possible. If several qubits are coupled to one resonator, an effective qubit-qubit interaction of Ising type emerges, whereas RWA leads to isotropic XYXYXY interaction. This impacts on the entanglement characteristics of the qubits.
The interaction of qubits with quantized modes of electromagnetic fields has been largely addressed in the quantum optics literature under the rotating wave approximation (RWA), where rapid oscillating terms in the qubit-mode interaction picture Hamiltonian can be neglected. At the same time, it is generally accepted that, provided the interaction is sufficiently strong or for long times, the RWA tends to describe physical phenomena incorrectly. In this work, we extend the investigation of the validity of the RWA to a more involved setup where two qubit-mode subsystems are brought to interaction through their harmonic coordinates. Our treatment is all analytic thanks to a sequence of carefully chosen unitary transformations, which allows us to diagonalize the Hamiltonian within and without the RWA. By also considering qubit dephasing, we find that the purity of the two-qubit state presents non-Markovian features which become more pronounced as the coupling between the modes gets stronger and the RWA loses its validity. In the same regime, there occurs fast generation of entanglement between the qubits, which is also not correctly described under the RWA. The setup and results presented here clearly show the limitations of the RWA in a scenario amenable to exact description and free from numerical uncertainties. Consequently, it may be of interest for the community working with cavity or circuit quantum electrodynamic systems in the strong coupling regime.
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We analyze the dynamics of the quantum Rabi model for two qubits interacting through a common bosonic field (resonator), focusing on the generation and detection of maximally entangled states. We obtain analytical results for the unitary dynamics of this system in the slow-qubit (or degenerate) regime, considering ultra-strong coupling between qubits and resonator mode, for which the rotating wave approximation (RWA) is no longer applicable. We also numerically investigate the dynamics beyond the slow-qubit condition in order to study the validity of the model in the presence of less strict conditions.