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arXiv:0809.2025

Collapse and Revival of Entanglement between Qubits Interacting via a Quantum Bus

C. E. A. Jarvis, Denzil A. Rodrigues, Balazs L. Gyorffy, Timothy P. Spiller, Short, A. J., James F. Annett

Published Sep 11, 2008• 1 citation
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Abstract

We study the dynamics of the Jaynes-Cummings Model for two level systems (or qubits) interacting with a quantized single mode electromagnetic cavity (or `quantum bus'). We show that there is a time in between the collapse and revival of Rabi oscillations when the state of the qubit sub-system, $| ψ\_{attractor} $, is largely independent of its initial state. This generalizes to many qubits the discovery by Gea-Banacloche for the one qubit case. The qubits in such `attractor' states are not entangled either with the field or among themselves, even if they were in the initial state. Subsequently the entanglement between the qubits revives. Finally, it is argued that the collapse and revival of entanglement and the persistence of `non-classicality' is a generic feature of multiple qubits interacting via a `quantum bus'.

DOI
10.48550/arxiv.0809.2025

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We study the dynamics of the Jaynes-Cummings Model for two level systems (or qubits) interacting with a quantized single mode electromagnetic cavity (or quantum bus'). We show that there is a time in between the collapse and revival of Rabi oscillations when the state of the qubit sub-system, $| ψ\_{attractor} $, is largely independent of its initial state. This generalizes to many qubits the discovery by Gea-Banacloche for the one qubit case. The qubits in such attractor' states are not entangled either with the field or among themselves, even if they were in the initial state. Subsequently the entanglement between the qubits revives. Finally, it is argued that the collapse and revival of entanglement and the persistence of non-classicality' is a generic feature of multiple qubits interacting via a quantum bus'.
We study the dynamics of the Jaynes–Cummings model for two two-level systems (or qubits) interacting with a quantized single mode electromagnetic cavity (or quantum bus), extending this to the macroscopic case of an array of Nq qubits. For an initial cavity coherent state |α⟩ and the qubit system in a specified “basin of attraction” in its Hilbert space, we demonstrate the oscillation of a superposition of two macroscopic quantum states between the qubit system and the field mode. From the perspective of either the qubit or the field system, there is collapse and revival of a “Schrödinger cat” state.
We study the time evolution of N q two-level atoms (or qubits) interacting with a single mode of a quantized radiation field. In the case of two qubits, we show that for a set of initial conditions the reduced density matrix of the atomic system approaches that of a pure state at , halfway between that start of the collapse and the first mini-revival peak, where t r is the time of the main revival. The pure state approached is the same for a set of initial conditions and is thus termed an 'attractor state'. The set itself is termed the 'basin of attraction' and we concentrate on its features. Extending to more qubits, we find that attractors are a generic feature of the multiqubit Jaynes–Cummings model (JCM) and we therefore generalize the discovery by Gea–Banacloche for the one-qubit case. We give the 'basin of attraction' for N q qubits and discuss the implications of the 'attractor' state in terms of the dynamics of N q -body entanglement. We observe both the collapse and revival and the sudden birth/death of entanglement depending on the initial conditions.
We study the dynamics of the Jaynes-Cummings Model for an array of NqN_qNq​ two level systems (or qubits) interacting with a quantized single mode electromagnetic cavity (or quantum bus). For an initial cavity coherent state ∣α>| α>∣α> and the qubit system in a specified `basin of attraction' in its Hilbert space, we demonstrate the oscillation of a superposition of two macroscopic quantum states between the qubit system and the field mode. From the perspective of either the qubit or the field system, there is collapse and revival of a `Schrödinger Cat' state.
We study the dynamics of the Jaynes-Cummings Model for an array of NqN_qNq​ two level systems (or qubits) interacting with a quantized single mode electromagnetic cavity (or quantum bus). For an initial cavity coherent state ∣α>| \alpha >∣α> and the qubit system in a specified `basin of attraction' in its Hilbert space, we demonstrate the oscillation of a superposition of two macroscopic quantum states between the qubit system and the field mode. From the perspective of either the qubit or the field system, there is collapse and revival of a `Schr\odinger Cat' state.
We extend the study of the Jayne–Cummings (JC) model involving a pair of identical two-level atoms (or qubits) interacting with a single mode quantized field. We investigate the effects of replacing the radiation field mode with a composite spin, comprising [Formula: see text] qubits, or spin-1/2 particles. This model is relevant for physical implementations in superconducting circuit QED, ion trap and molecular systems. For the case of the composite spin prepared in a spin coherent state, we demonstrate the similarities of this set-up to the qubits-field model in terms of the time evolution, attractor states and in particular the collapse and revival of the entanglement between the two qubits. We extend our analysis by taking into account an effect due to qubit imperfections. We consider a difference (or “mismatch”) in the dipole interaction strengths of the two qubits, for both the field mode and composite spin cases. To address decoherence due to this mismatch, we then average over this coupling strength difference with distributions of varying width. We demonstrate in both the field mode and the composite spin scenarios that increasing the width of the “error” distribution increases suppression of the coherent dynamics of the coupled system, including the collapse and revival of the entanglement between the qubits.
We extend study of the Jaynes-Cummings model involving a pair of identical two-level atoms (or qubits) interacting with a single mode quantised field. We investigate the effects of replacing the radiation field mode with a ‘big spin’, comprising a collection of N qubits, or spin-1/2 particles. We demonstrate the similarities of this set-up to the qubits-field model in terms of the qubits state probability, occurrence of attractor states, generation of Schr¨odinger cat state, and in particular the collapse and revival of the entanglement between the two qubits in the qubit subsystem. We extend our analysis by taking into account a decoherence effect due to qubit imperfections. We study two cases of ‘error’ in the system for both the field mode and ‘big spin’ cases. In the first part, we consider the case of systems with non-resonance frequencies, and secondly we let the systems evolve with a difference in the dipole interaction strengths of the two qubits. We average over the errors in both of these parameters with distributions of varying width. We demonstrate the effects of such error modeling in both the field mode and the ‘big spin’ scenarios. We discover that increasing the width \nof the ‘error’ distribution increases suppression of the coherent dynamics of the coupled system, including the collapse and revival of the entanglement between the qubits. We also find out that the decoherence effects are more significant in the system with difference in the coupling strength as opposed to the nonresonance case that has higher robustness against errors. At the end of the study, we investigate the qubit-big spin system with a modest value of N to identify the smallest size of the big spin that exhibits the important events in such interacting \nmodel.