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arXiv:1101.1420 · Physical Review A

Overcoming decoherence in the collapse and revival of spin Schrödinger-cat states

M. J. Everitt, William J. Munro, Timothy P. Spiller

Published Feb 8, 2012• 8 citations
arXivHTMLPDF

Abstract

In addition to being a very interesting quantum phenomenon, Schr\"odinger-cat-state swapping has the potential for application in the preparation of quantum states that could be used in metrology and other quantum processing. We study in detail the effects of field decoherence on a Schr\"odinger-cat-state-swapping system comprising a set of identical qubits, or spins, all coupled to a field mode. We demonstrate that increasing the number of spins actually mitigates the effects of field decoherence on the collapse and revival of a spin Schr\"odinger-cat state, which could be of significant utility in quantum metrology and other quantum processing.

DOI
10.1103/physreva.85.022113

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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.
We study the effects of continuous measurement of the field mode during the collapse and revival of spin Schr¨odinger cat states in the Tavis-Cummings model of N qubits (two-level quantum systems) coupled to a field mode. We show that a compromise between relatively weak and relatively strong continuous measurement will not completely destroy the collapse and revival dynamics while still providing enough signal-to-noise resolution to identify the signatures of the process in the measurement record. This type of measurement would in principle allow the verification of the occurrence of the collapse and revival of a spin Schr¨odinger cat state.
In its simplest form, decoherence occurs when a quantum state is entangled with a second state, but the results of measurements made on the second state are not accessible. As the second state has effectively ``measured'' the first, in this paper we argue that the quantum Fisher information is the relevant metric for predicting and quantifying this kind of decoherence. The quantum Fisher information is usually used to determine an upper bound on how precisely measurements on a state can be used to estimate a classical parameter, and as such it is an important resource. Quantum-enhanced metrology aims to create nonclassical states with large quantum Fisher information and utilize them in precision measurements. In the process of doing this it is possible for states to undergo decoherence; for instance atom-light interactions used to create coherent superpositions of atomic states may result in atom-light entanglement. Highly nonclassical states, such as spin-cat states (Schr\"odinger cat states constructed from superpositions of collective spins) are shown to be highly susceptible to this kind of decoherence. We also investigate the required field occupation of the second state, such that this decoherence is negligible.
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 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.