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Kluwer Academic Publishers eBooks

Quantum Gates Using Motional States in an Optical Lattice

Éric Charron, Eite Tiesinga, Frederick H. Mies, Carl J. Williams

Published Feb 24, 2006• 2 citations
Publisher

Abstract

We study an implementation of a two-qubit universal quantum gate with neutral 87 Rb atoms trapped in a far-detuned two-color optical lattice. The qubit states |O〉 and |1〉 represent the ground and first excited motional states of an atom in a laser induced potential well. By varying the ratio of the laser intensities of the two colors, the barrier between two neighboring atoms is lowered, creating two-particle entanglement. We predict the duration of operation of a conditional π-phase gate with a time-dependent configuration interaction model.

DOI
10.1007/0-306-47114-0_35

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We study an implementation of a two-qubit universal quantum gate with neutral 87 Rb atoms trapped in a far-detuned two-color optical lattice. The qubit states |O〉 and |1〉 represent the ground and first excited motional states of an atom in a laser induced potential well. By varying the ratio of the laser intensities of the two colors, the barrier between two neighboring atoms is lowered, creating two-particle entanglement. We predict the duration of operation of a conditional π-phase gate with a time-dependent configuration interaction model.
We propose a new system for implementing quantum logic gates: neutral atoms trapped in a very far-off-resonance optical lattice. Pairs of atoms are made to occupy the same well by varying the polarization of the trapping lasers, and then a near-resonant electric dipole is induced by an auxiliary laser. A controlled-NOT can be implemented by conditioning the target atomic resonance on a resolvable level shift induced by the control atom. Atoms interact only during logical operations, thereby suppressing decoherence.
We propose a two-qubit phase gate for ultracold atoms in a tilted double-well optical lattice. Such a lattice is capable of confining pairs of atoms in a two-dimensional array of double-well potentials where both the barrier height and the energy difference of the minima of the two wells (known as the ``tilt'') can be controlled. The four lowest single-particle motional states can be used to form spatially separated qubits. We present a time-dependent scheme to manipulate the tilt to induce tunneling oscillations which produce a collisional phase gate. Numerical simulations demonstrate that this gate can be performed with high fidelity.
Using four coherent laser beams we make two different 2D optical lattices with polarization-dependent periodicity. The lattices are coincident, and by shifting one with respect to the other, we create an array of double well potentials. We have designed a 2D optical lattice for /sup 87/Rb atoms consisting of an array of double well potentials. This lattice should allow us to test two-qubit gates and in general permit atomic control in support of nearest neighbor interaction physics such as the Ising model and quantum cellular automata.
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.
Arrays of qubits encoded in the ground-state manifold of neutral atoms trapped in optical (or magnetic) lattices appear to be a promising platform for the realization of a scalable quantum computer. Two-qubit conditional gates between nearest-neighbor qubits in the array can be implemented by exploiting the Rydberg blockade mechanism, as was shown by D. Jaksch et al. [Phys. Rev. Lett. 85, 2208 (2000)]. However, the energy shift due to dipole-dipole interactions causing the blockade falls off rapidly with the interatomic distance, and protocols based on direct Rydberg blockade typically fail to operate between atoms separated by more than one lattice site. In this work, we propose an extension of the protocol of Jaksch et al. for controlled-ZZZ and controlled-not gates which works in the general case where the qubits are not nearest neighbors in the array. Our proposal relies on the Rydberg excitation hopping along a chain of ancilla noncoding atoms connecting the qubits on which the gate is to be applied. The dependence of the gate fidelity on the number of ancilla atoms, the blockade strength, and the decay rates of the Rydberg states is investigated. A comparison between our implementation of a distant controlled-not gate and one based on a sequence of nearest-neighbor two-qubit gates is also provided.