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arXiv:quant-ph/9910031 · Physical Review A

Entangling dipole-dipole interactions for quantum logic with neutral atoms

Gavin K. Brennen, Ivan Deutsch, Poul Jessen

Published May 16, 2000• 103 citations
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Abstract

We study a means of creating multiparticle entanglement of neutral atoms using pairwise controlled dipole-dipole interactions. For tightly trapped atoms the dipolar interaction energy can be much larger than the photon scattering rate and substantial coherent evolution of the two-atom state can be achieved before decoherence occurs. Excitation of the dipoles can be made conditional on the atomic states, allowing for deterministic generation of entanglement. We derive selection rules and a figure of merit for the dipole-dipole interaction matrix elements, for alkali atoms with hyperfine structure and trapped in localized center of mass states. Different protocols are presented for implementing two-qubit quantum logic gates such as the controlled-phase and swap gates. We analyze the error probability of our gate designs, finite due to decoherence from cooperative spontaneous emission and coherent couplings outside the logical basis. Outlines for extending our model to include the full molecular interactions potentials are discussed.

DOI
10.1103/physreva.61.062309

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We study a means of creating multiparticle entanglement of neutral atoms using pairwise controlled dipole-dipole interactions. For tightly trapped atoms the dipolar interaction energy can be much larger than the photon scattering rate and substantial coherent evolution of the two-atom state can be achieved before decoherence occurs. Excitation of the dipoles can be made conditional on the atomic states, allowing for deterministic generation of entanglement. We derive selection rules and a figure of merit for the dipole-dipole interaction matrix elements, for alkali atoms with hyperfine structure and trapped in localized center of mass states. Different protocols are presented for implementing two-qubit quantum logic gates such as the controlled-phase and swap gates. We analyze the error probability of our gate designs, finite due to decoherence from cooperative spontaneous emission and coherent couplings outside the logical basis. Outlines for extending our model to include the full molecular interactions potentials are discussed.
We study the deterministic entanglement of a pair of neutral atoms trapped in an optical lattice by coupling to excited-state molecular hyperfine potentials. Information can be encoded in the ground-state hyperfine levels and processed by bringing atoms together pairwise to perform quantum logical operations through induced electric dipole-dipole interactions. The possibility of executing both diagonal- and exchange-type entangling gates is demonstrated for two three-level atoms and a figure of merit is derived for the fidelity of entanglement. The fidelity for executing a CPHASE gate is calculated for two 87Rb{}^{87}\mathrm{Rb}87Rb atoms, including hyperfine structure and finite atomic localization. The main source of decoherence is spontaneous emission, which can be minimized for interaction times fast compared to the scattering rate and for sufficiently separated atomic wave packets. Additionally, coherent couplings to states outside the logical basis can be constrained by the state-dependent trapping potential.
Summary form only given. Controlled interactions between pairs of neutral atoms in optical lattices allow for the creation of highly entangled multiparticle states and the implementation of quantum logic gates. Such systems benefit from suppressed decoherence because neutrals couple weakly to the environment and from the possibility of processing with the massively parallel quantum registers in the atomic ensemble. The main source of decoherence is spontaneous emission which can be made negligible if the two atom interactions are performed fast compared to the scattering rate. We have shown the possibility of using induced electric dipole-dipole interactions between pairs of atoms to perform the two qubit gates /spl radic/(SWAP) and CPHASE with high fidelity.
Summary form only given. Controlled coherent interactions between pairs of neutral atoms can be designed in tight micro-traps such as optical lattices which allow the creation of highly entangled multiparticle states. Such systems benefit from suppressed decoherence because neutrals couple weakly to the environment and the interactions are strictly pairwise. The main source of decoherence is spontaneous emission which can be made negligible if the two atom interactions are performed fast compared to the scattering rate.We have shown the possibility of using induced electric dipole-dipole interactions between pairs of atoms to perform quantum logic gates with high fidelity.
Summary form only given. Optical lattices provide new opportunities to create entangled states of neutral atoms for quantum information processing. Such systems have some attractive features: decoherence is suppressed because neutrals couple weakly to the environment, and operations can be performed in parallel on a large ensemble of trapped atoms, thus offering avenues for scaling to many qubits. The main source of decoherence is spontaneous emission, but this can be negligible if all manipulations are performed rapidly compared to the photon scattering rate. We consider here the possibility of using resonantly induced electric dipole-dipole interactions to engineer two-qubit operations such as the swap gate and the controlled-phase which, together with single qubit operations, can perform arbitrary quantum computations.
Summary form only given.Quantum logic gates require qubits that can interact strongly with each other and with external fields while minimizing unwanted coupling to the decohering environment. Neutral atoms trapped in a far-off resonance optical lattice satisfy these criteria. The adjustable parameters of the lattice (e.g., laser polarization, frequency, intensity) allow one to design interactions for which atoms interact strongly via dipole-dipole interactions during logical interactions but otherwise are isolated from each other and the environment. Dissipation arising from spontaneous photon scattering can be suppressed to an arbitrary degree given sufficient laser power and large detuning from atomic resonance. Thus, by bringing two atoms in close proximity, one can simultaneously achieve strong coherent coupling with small photon scattering rates.
We present a detailed analysis and design of a neutral atom quantum logic device based on atoms in optical traps interacting via dipole-dipole coupling of Rydberg states. The dominant physical mechanisms leading to decoherence and loss of fidelity are enumerated. Our results support the feasibility of performing single- and two-qubit gates at MHz rates with decoherence probability and fidelity errors at the level of ${10}^{\ensuremath{-}3}$ for each operation. Current limitations and possible approaches to further improvement of the device are discussed.