Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0906.4005 · New Journal of Physics

Dynamics of entanglement and ‘attractor’ states in the Tavis–Cummings model

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

Published Oct 26, 2009• 28 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/11/10/103047

Related papers

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

C. E. A. Jarvis, Denzil A. Rodrigues, Balazs L. Gyorffy +3 more

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'.

arXiv:0809.2025•Sep 11, 2008•1 citation

Collapse and revival of “Schrödinger cat” states

C. E. A. Jarvis, Denzil A. Rodrigues, Balazs L. Gyorffy +3 more

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.

Journal of the Optical Society of America B•May 11, 2010•8 citations

Collapse and Revival of `Schrödinger Cat' States

C. E. A. Jarvis, Denzil A. Rodrigues, Balazs L. Gyorffy +3 more

We study the dynamics of the Jaynes-Cummings Model for an array of $N_q$ two level systems (or qubits) interacting with a quantized single mode electromagnetic cavity (or quantum bus). For an initial cavity coherent state $| \alpha >$ 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.

•Dec 19, 2008•0 citations

Collapse and revival of entanglement between qubits coupled to a spin coherent state

Iskandar Bahari, Timothy P. Spiller, Shane Dooley +2 more

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.

arXiv:1612.06444•International Journal of Quantum Information•Feb 27, 2018•6 citations

Revivals and entanglement from initially entangled mixed states of a damped Jaynes-Cummings model

R. W. Rendell, A. K. Rajagopal

An exact density matrix of a phase-damped Jaynes-Cummings model (JCM) with entangled Bell-like initial states formed from a model two-state atom and sets of adjacent photon number states of a single-mode radiation field is presented. The entanglement of the initial states and the subsequent time evolution is assured by finding a positive lower bound on the concurrence of local $2\ifmmode\times\else\texttimes\fi{}2$ projections of the full $2\ifmmode\times\else\texttimes\fi{}\ensuremath{\infty}$ JCM density matrix. It is found that the time evolution of the lower bound of the concurrence systematically captures the corresponding collapse and revival features in atomic inversion, relative entropies of atomic and radiation, mutual entropy, and quantum deficit. The atom and radiation subsystems exhibit alternating sets of collapses and revivals in a complementary fashion due to the initially mixed states of the atom and radiation employed here. This is in contrast with the result obtained when the initial state of the dissipationless system is a factored pure state of the atom and radiation, where the atomic and radiation entropies are necessarily the same. The magnitudes of the entanglement lower bound and the atomic and radiation revivals become larger as both the magnitude and phase of the Bell-like initial state contribution increase. The time evolution of the entropy difference of the total system and that of the radiation subsystem exhibit negative regions called ``supercorrelated'' states which do not appear in the atomic subsystem. Entangled initial states are found to enhance this supercorrelated feature. Finally, the effect of phase damping is to randomize both the subsystems for asymptotically long times. It may be feasible to experimentally investigate the results presented here using the Rabi oscillation methods of microwave and optical cavity quantum electrodynamics since pure photon number states have recently been produced and observed.

arXiv:quant-ph/0301126•Physical Review A•Jun 30, 2003•45 citations

Collapse and Revival of `Schrödinger Cat' States

C. E. A. Jarvis, Denzil A. Rodrigues, Györffy, B. L. +3 more

We study the dynamics of the Jaynes-Cummings Model for an array of $N_q$ two level systems (or qubits) interacting with a quantized single mode electromagnetic cavity (or quantum bus). 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.

arXiv:0812.3766•Dec 19, 2008•0 citations
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 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 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.
An exact density matrix of a phase-damped Jaynes-Cummings model (JCM) with entangled Bell-like initial states formed from a model two-state atom and sets of adjacent photon number states of a single-mode radiation field is presented. The entanglement of the initial states and the subsequent time evolution is assured by finding a positive lower bound on the concurrence of local $2\ifmmode\times\else\texttimes\fi{}2$ projections of the full $2\ifmmode\times\else\texttimes\fi{}\ensuremath{\infty}$ JCM density matrix. It is found that the time evolution of the lower bound of the concurrence systematically captures the corresponding collapse and revival features in atomic inversion, relative entropies of atomic and radiation, mutual entropy, and quantum deficit. The atom and radiation subsystems exhibit alternating sets of collapses and revivals in a complementary fashion due to the initially mixed states of the atom and radiation employed here. This is in contrast with the result obtained when the initial state of the dissipationless system is a factored pure state of the atom and radiation, where the atomic and radiation entropies are necessarily the same. The magnitudes of the entanglement lower bound and the atomic and radiation revivals become larger as both the magnitude and phase of the Bell-like initial state contribution increase. The time evolution of the entropy difference of the total system and that of the radiation subsystem exhibit negative regions called ``supercorrelated'' states which do not appear in the atomic subsystem. Entangled initial states are found to enhance this supercorrelated feature. Finally, the effect of phase damping is to randomize both the subsystems for asymptotically long times. It may be feasible to experimentally investigate the results presented here using the Rabi oscillation methods of microwave and optical cavity quantum electrodynamics since pure photon number states have recently been produced and observed.
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.