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arXiv:1402.0522 · Physical Review A

Dissipative preparation of large W states in optical cavities

Ryan Sweke, Ilya Sinayskiy, Francesco Petruccione

Published Apr 19, 2013• 44 citations
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Abstract

Two schemes are proposed for the dissipative preparation of large $W$ 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.

DOI
10.1103/physreva.87.042323

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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 \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ 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.
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.
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 propose an analytical treatment method of generation of multipartite W-type states with a single-resonant interaction of the atoms with the cavity mode in cavity QED, under the consideration of very weak decay from the excited atomic level and from the cavity mode. By manipulating different coupling strengths between the atoms and the cavity mode, we show how to deterministically produce W states, including the standard W state and the one with arbitrary coefficients. The corresponding analytical expressions are given, indicating that the detrimental influence from the atomic spontaneous emission is three times that from the cavity decay. The experimental feasibility of our scheme is also discussed by using current cavity QED techniques.
We propose a dissipative scheme to generate a maximally entangled state for two $\ensuremath{\Lambda}$-type atoms trapped in an optical cavity. Different from the unitary-dynamics-based scheme, our work shows that both atomic spontaneous emission and cavity decay are no longer detrimental, but necessary for entanglement generation. The scheme is independent of initial states and does not require precise time control. A final numerical simulation with two groups of experimental parameters indicates that the present scheme is feasible and the performance could be better than the unitary-dynamics-based scheme.
Feasible schemes for implementing quantum swap gates of both coherent-state qubits and photonic qubits are proposed using a Λ-type atomic ensemble trapped in a bimodal optical cavity. In both protocols, the decoherence from atomic spontaneous emission is negligible due to the fact that the excited states of the atoms are adiabatically eliminated under large detuning condition and the swap gates can be created in a single step. In our schemes, the required atoms—cavity interaction time decreases with the increase of the number of atoms, which is very important in view of decoherence. The experimental feasibilities of the schemes are also discussed.