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Physical Review A

Steady atomic entanglement with different quantum feedbacks

Jungang Li, Jian Zou, Bin Shao, Cai Jin-Fang

Published Jan 31, 2008• 37 citations

Abstract

We consider a model of two driven and collectively damped atoms with different quantum feedbacks. We find that the steady entanglement depends on the initial condition in the case of symmetric feedback but is independent of the initial condition in the case of nonsymmetric feedback. We also find that in the process of the transition from the symmetric feedback to the nonsymmetric feedback, the entanglement between the two atoms is discontinuous. Without the feedback (symmetric case), in the symmetric subspace the steady entanglement between the two atoms will be very small; then we apply a feedback just to one of the atoms (nonsymmetric case), the steady entanglement will increase greatly, which can reach $C\ensuremath{\approx}0.82$. It is very interesting that if we withdraw the feedback, the strong steady entanglement will remain, i.e., the whole process is irreversible, and reminds us of the hysteresis phenomena.

DOI: 10.1103/physreva.77.012339

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We consider a model of two driven and collectively damped atoms with different quantum feedbacks. We find that the steady entanglement depends on the initial condition in the case of symmetric feedback but is independent of the initial condition in the case of nonsymmetric feedback. We also find that in the process of the transition from the symmetric feedback to the nonsymmetric feedback, the entanglement between the two atoms is discontinuous. Without the feedback (symmetric case), in the symmetric subspace the steady entanglement between the two atoms will be very small; then we apply a feedback just to one of the atoms (nonsymmetric case), the steady entanglement will increase greatly, which can reach

C\ensuremath{\approx}0.82

. It is very interesting that if we withdraw the feedback, the strong steady entanglement will remain, i.e., the whole process is irreversible, and reminds us of the hysteresis phenomena.

The dynamics of two identical atoms is studied, which is resonantly coupled to a single-mode cavity under two different quantum feedback controls, i.e., the symmetric feedback control and the nonsymmetric feedback control. Correspondingly, the quantum discord of the system is induced to reach steady values under these two kinds of feedback controls. Furthermore, in some cases, the steady value of quantum discord of the system under symmetric feedback control is much larger than the steady value under nonsymmetric feedback control. The situation is just the opposite when the initial state is |eg〉. It is also found that the feedback is not good for getting a high discord when the initial state is in the form of Werner-like state (d = 0).

We consider a model consisting of three two-level atoms in a heavily damped cavity. We show that the quantum-jump-based feedback can be used to generate a steady entangled state of three atoms against decoherence. When the feedback acts on just one of the atoms, it can protect a maximally entangled state of other two atoms. When the feedback acts on three atoms, by choosing appropriate parameters we can obtain a decoherence-free subspace spanned by two vectors, and by using quantum trajectory Monte Carlo wave function method we find that the maximally entangled state of three atoms in this decoherence-free subspace can be obtained for some specific initial conditions.

We consider a model consisting of two (two-level) atoms which are placed in two separated heavily damped cavities respectively. We show that the quantum-jump-based feedback based on joint measurement can be used to generate a steady entangled state between two atoms against decoherence. We analyse the effects of general local control Hamiltonians in the performance of entanglement production and show that by choosing a proper control Hamiltonian the steady maximal entanglement between two separated atoms can be protected.

We study a hybrid quantum open system consisting of two interacting subsystems formed by one two-level atom (qubit) and one three-level atom (qutrit). The quantum open system is coupled to an external environment (cavity) via the qubit-cavity interaction. It is found that the feedback control on different parts of the system (qubit or qutrit) gives dramatically different asymptotical behaviors of the open system dynamics. We show that the local feedback control mechanism acting on the qutrit subsystem is superior than that on the qubit in the sense of improving the entanglement. Particularly, the qutrit-control scheme may result in an entangled steady state, depending on the initial state.

We study a physical system for creation of quantum correlations by quantum feedback control. The system is composed of two three-level atoms, each of which interacts with one of two coupled cavities. By appropriately choosing the feedback strength, we show that an arbitrary initial state can be deterministically driven to a steady-state that has a nonzero quantum discord or entanglement. It is also found that the effect of atomic spontaneous emission on quantum correlations is suppressed efficiently by increasing the frequency detuning.