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arXiv:1402.0529 · Journal of Physics B Atomic Molecular and Optical Physics

Dissipative preparation of generalized Bell states

Ryan Sweke, Ilya Sinayskiy, Francesco Petruccione

Published May 9, 2013• 13 citations
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Abstract

A scheme is presented for the dissipative preparation of generalized Bell states of two qubits, within the context of cavity QED. In the suggested protocol the dissipative processes of spontaneous emission and cavity loss are no longer undesirable, but essential to the required dynamics. Extremely long-lived target states are achieved, with fidelities of near unity, utilizing cooperativities corresponding to currently available optical cavities. Furthermore, the suggested protocol exhibits excellent scaling of relevant characteristics, with respect to cooperativity, such that improved results may be obtained as the development of experimental capabilities continues.

DOI
10.1088/0953-4075/46/10/104004

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A scheme is presented for the dissipative preparation of generalized Bell states of two qubits, within the context of cavity QED. In the suggested protocol the dissipative processes of spontaneous emission and cavity loss are no longer undesirable, but essential to the required dynamics. Extremely long-lived target states are achieved, with fidelities of near unity, utilizing cooperativities corresponding to currently available optical cavities. Furthermore, the suggested protocol exhibits excellent scaling of relevant characteristics, with respect to cooperativity, such that improved results may be obtained as the development of experimental capabilities continues.
We propose a novel scheme for the preparation of a maximally entangled state of two atoms in an optical cavity. Starting from an arbitrary initial state, a singlet state is prepared as the unique fixed point of a dissipative quantum dynamical process. In our scheme, cavity decay is no longer undesirable, but plays an integral part in the dynamics. As a result, we get a qualitative improvement in the scaling of the fidelity with the cavity parameters. Our analysis indicates that dissipative state preparation is more than just a new conceptual approach, but can allow for significant improvement as compared to preparation protocols based on coherent unitary dynamics.
Two schemes are proposed for the dissipative preparation of large WWW states, of the order of ten qubits, within the context of cavity QED. By utilizing properties of the irreducible representations of su(3), we are able to construct protocols in which it is possible to restrict the open-system dynamics to a fully symmetric irreducible subspace of the total Hilbert space and hence obtain analytic solutions for effective ground-state dynamics of arbitrary-size ensembles of $\ensuremath{\Lambda}$ atoms within an optical cavity. In the proposed schemes, the natural decay processes of spontaneous emission and photon loss are no longer undesirable, but essential to the required dynamics. All aspects of the proposed schemes relevant to implementation in currently available optical cavities are explored, especially with respect to increasing system size.
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A new mechanism is proposed for dissipatively preparing maximal Bell entangled state of two atoms in an optical cavity. This scheme integrates the spontaneous emission, the light shift of atoms in the presence of dispersive microwave field, and the quantum Zeno dynamics induced by continuous coupling, to obtain a unique steady state irrespective of initial state. Even for a large cavity decay, a high-fidelity entangled state is achievable at a short convergence time, since the occupation of the cavity mode is inhibited by the Zeno requirement. Therefore, a low single-atom cooperativity C=g2/(κγ) is good enough for realizing a high fidelity of entanglement in a wide range of decoherence parameters. As a straightforward extension, the feasibility for preparation of two-atom Knill–Laflamme–Milburn state with the same mechanism is also discussed.
We propose various schemes for the dissipative preparation of a maximally entangled steady state of two atoms in an optical cavity. Harnessing the natural decay processes of cavity photon loss and spontaneous emission, we use an effective operator formalism to identify and engineer effective decay processes, which reach an entangled steady state of two atoms as the unique fixed point of the dissipative time evolution. We investigate various aspects that are crucial for the experimental implementation of our schemes in present-day and future cavity quantum electrodynamics systems and analytically derive the optimal parameters, the error scaling and the speed of convergence of our protocols. Our study shows promising performance of our schemes for existing cavity experiments and favorable scaling of fidelity and speed with respect to the cavity parameters.
We present a scheme for the dissipative preparation of an entangled steady state of two superconducting qubits in a circuit quantum electrodynamics (QED) setup. Combining resonator photon loss---a dissipative process already present in the setup---with an effective two-photon microwave drive, we engineer an effective decay mechanism which prepares a maximally entangled state of the two qubits. This state is then maintained as the steady state of the driven, dissipative evolution. The performance of the dissipative state preparation protocol is studied analytically and verified numerically. In view of the experimental implementation of the presented scheme we investigate the effects of potential experimental imperfections and show that our scheme is robust to small deviations in the parameters. We find that high fidelities with the target state can be achieved both with state-of-the-art three-dimensional, as well as with the more commonly used two-dimensional transmons. The promising results of our study thus open a route for the demonstration of a highly entangled steady state in circuit QED.