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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Two-qubit quantum gates in an optical lattice with polarization gradient

M. A. Duenas, Ángela M. Guzmán

Published Oct 21, 2004• 0 citations
Publisher

Abstract

We study a dipole-dipdole collision between two atoms confined in adjacent minima of the two sublattices of an optical lattice with polarization gradient. A qubit consists of the two lowest atomic vibrational states of the optical lattice potential. The inter-atomic distance is changed adiabatically by rotating the polarization of the lasers that originate the optical lattice. In an elastic collision the two-qubit quantum states undergo controllable phase shifts that allow for the implementation of quantum gates. We obtain the truth-table for a quantum logic phase gate and calculate probability losses caused by the non-hermitian effective dipole-dipole interaction Hamiltonian.

DOI
10.1117/12.590617

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We study a dipole-dipdole collision between two atoms confined in adjacent minima of the two sublattices of an optical lattice with polarization gradient. A qubit consists of the two lowest atomic vibrational states of the optical lattice potential. The inter-atomic distance is changed adiabatically by rotating the polarization of the lasers that originate the optical lattice. In an elastic collision the two-qubit quantum states undergo controllable phase shifts that allow for the implementation of quantum gates. We obtain the truth-table for a quantum logic phase gate and calculate probability losses caused by the non-hermitian effective dipole-dipole interaction Hamiltonian.
Experimental realizations of a two-qubit quantum logic gate based on cold atom collisions have been elusive mainly due to the decoherence effects introduced during the quantum gate operation, which cause transitions out of the two-qubit space and lead to a decreased gate operation fidelity. This type of decoherence effects, due to the non closeness of the interacting two-qubit system, are characteristic of the electromagnetic interaction, since the electromagnetic vacuum acts as a reservoir whose eigenmodes might become active during the gate operation. To describe the cold-atom collision we consider the quantum non-Hermitian dipole-dipole interaction instead of the less realistic s-scattering approach widely used in the literature. By adding an ancillary qubit, we take advantage of the spatial modulation of the non-Hermitian part of the interaction potential to obtain a "resonant" condition that should be satisfied to achieve lossless operation of a specific two-qubit quantum phase-gate. We demonstrate that careful engineering of the collision is required to obtain a specific truth table and to suppress the effects inherent in the openness of the system arising from the electromagnetic interaction.
Steps towards implementing a collision-based two-qubit gate in optical lattices have previously been realized by the parallel merging of all pairs of atoms in a periodicity two superlattice. In contrast, we propose an architecture which allows for the merger of a selected qubit pair in a long-periodicity superlattice structure consisting of two optical lattices with close-lying periodicity. We numerically optimize the gate time and fidelity, including the effects on neighboring atoms and in the presence of experimental sources of error. Furthermore, the superlattice architecture induces a differential hyperfine shift, allowing for single-qubit gates. The fastest possible single-qubit gate times, given a maximal tolerable rotation error on the remaining atoms at various values of the lattice wavelengths, are identified. We find that robust single- and two-qubit gates with gate times of a few hundred microseconds and with error probabilities $\ensuremath{\sim}$${10}^{\ensuremath{-}3}$ are possible.
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.
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.
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.