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arXiv:0807.1144 · Physical Review A

Controlling entanglement by direct quantum feedback

Andre R. R. Carvalho, Andrew J. S Reid, J. J. Hope

Published Jul 18, 2008• 136 citations
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Abstract

We discuss the generation of entanglement between electronic states of two atoms in a cavity using direct quantum feedback schemes. We compare the effects of different control Hamiltonians and detection processes in the performance of entanglement production and show that the quantum-jump-based feedback proposed by Carvalho and Hope [Phys. Rev. A 76, 010301(R) (2007)] can protect highly entangled states against decoherence. We provide analytical results that explain the robustness of jump feedback, and also analyze the perspectives of experimental implementation by scrutinizing the effects of imperfections and approximations in our model.

DOI
10.1103/physreva.78.012334

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We discuss the generation of entanglement between electronic states of two atoms in a cavity using direct quantum feedback schemes. We compare the effects of different control Hamiltonians and detection processes in the performance of entanglement production and show that the quantum-jump-based feedback proposed by Carvalho and Hope [Phys. Rev. A 76, 010301(R) (2007)] can protect highly entangled states against decoherence. We provide analytical results that explain the robustness of jump feedback, and also analyze the perspectives of experimental implementation by scrutinizing the effects of imperfections and approximations in our model.
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 describe how feedback methods can be implemented to produce and stabilize entangled states of two atoms inside a cavity. Feedback control is used to engineer an effective environment dynamics, such that the entangled state to be protected is a steady state of the system. The control strategy is therefore robust with respect to external noises and fundamental decoherence sources, as spontaneous emission, for example. We also show that the scheme is mostly insensitive to practical imperfections, as detection inefficiencies and laser fluctuations.
We investigate the use of quantum-jump-based feedback to manipulate the stability of multipartite entangled dark states in an open quantum system. Using the model proposed in Phys. Rev. A 76, 010301(R) (2007) for a pair of atoms, we show a general strategy to produce many-body singlet stationary entangled states for larger number of atoms. In the case of four qubits, we propose a simple local feedback control that, although not optimal, is realistic and stabilizes a highly entangled state. We discuss the limitations and analyze alternative strategies within the framework of direct jump feedback schemes.
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.