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Quantum Electronics and Laser Science Conference

Double well potentials for atomic qubit gates in a designer optical lattice

J. H. Huckans, Chad Fertig, Ian B. Spielman, J. V. Porto, William D. Phillips

Published Dec 10, 2005• 0 citations
Publisher

Abstract

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.

DOI
10.1109/qels.2005.1548806

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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.
We describe the design and implementation of a two-dimensional optical lattice of double wells suitable for isolating and manipulating an array of individual pairs of atoms in an optical lattice. Atoms in the square lattice can be placed in a double well with any of their four nearest neighbors. The properties of the double well (the barrier height and relative energy offset of the paired sites) can be dynamically controlled. The topology of the lattice is phase stable against phase noise imparted by vibrational noise on mirrors. We demonstrate the dynamic control of the lattice by showing the coherent splitting of atoms from single wells into double wells and observing the resulting double-slit atom diffraction pattern. This lattice can be used to test controlled neutral atom motion among lattice sites and should allow for testing controlled two-qubit gates.
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.
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 report on the experimental demonstration of dynamic control of the motional state of atoms in a 2D double-well optical lattice. First we describe experiments in which the atomic distributions obtained by loading Bose–Einstein condensates of rubidium atoms in the lattice are dynamically split by transforming a 2D lattice with period λ into a 2D lattice with period λ/2, and we show how this procedure allows for the study of the coherence and interaction properties of the system. Then we show how we can efficiently adiabatically transfer the population between adjacent sites of the lattice, as well as between different energy bands, by using dynamic modifications of the potential.
By means of optimal control techniques we model and optimize the manipulation of the external quantum state (center-of-mass motion) of atoms trapped in adjustable optical potentials. We consider in detail the cases of both noninteracting and interacting atoms moving between neighboring sites in a lattice of a double-well optical potentials. Such a lattice can perform interaction-mediated entanglement of atom pairs and can realize two-qubit quantum gates. The optimized control sequences for the optical potential allow transport faster and with significantly larger fidelity than is possible with processes based on adiabatic transport.
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.