Optimal control of atom transport for quantum gates in optical lattices

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.

[1]  J J García-Ripoll,et al.  Implementation of spin Hamiltonians in optical lattices. , 2004, Physical review letters.

[2]  William D. Phillips,et al.  Controlled exchange interaction between pairs of neutral atoms in an optical lattice , 2007, Nature.

[3]  V. Krotov,et al.  Global methods in optimal control theory , 1993 .

[4]  Stuart A. Rice,et al.  Optical Control of Molecular Dynamics , 2000 .

[5]  Tommaso Calarco,et al.  Robust optimal quantum gates for Josephson charge qubits. , 2007, Physical review letters.

[6]  Immanuel Bloch,et al.  Exploring quantum matter with ultracold atoms in optical lattices , 2005 .

[7]  P. Zoller,et al.  Quantum computations with atoms in optical lattices: marker qubits and molecular interactions , 2004, quant-ph/0403197.

[8]  Sublattice addressing and spin-dependent motion of atoms in a double-well lattice. , 2007, Physical review letters.

[9]  I Bloch,et al.  Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. , 2001, Physical review letters.

[10]  W. Phillips,et al.  Controlled atom dynamics in a double-well optical lattice , 2006 .

[11]  J. Crank,et al.  A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type , 1947 .

[12]  I Bloch,et al.  Time-Resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices , 2007, Science.

[13]  S. Rolston,et al.  Collisional deexcitation in a quasi-two-dimensional degenerate bosonic gas , 2005, cond-mat/0509079.

[14]  P. Zoller,et al.  Entanglement of Atoms via Cold Controlled Collisions , 1998, quant-ph/9810087.

[15]  Physical Review , 1965, Nature.

[16]  A lattice of double wells for manipulating pairs of cold atoms. , 2006, cond-mat/0602103.

[17]  P J Lee,et al.  Preparing and probing atomic number states with an atom interferometer. , 2007, Physical review letters.

[18]  Gerard L. G. Sleijpen,et al.  A Jacobi-Davidson Iteration Method for Linear Eigenvalue Problems , 1996, SIAM Rev..

[19]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[20]  T. Hänsch,et al.  Controlled collisions for multi-particle entanglement of optically trapped atoms , 2003, Nature.

[21]  T. Hänsch,et al.  Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms , 2002, Nature.

[22]  J J García-Ripoll,et al.  Speed optimized two-qubit gates with laser coherent control techniques for ion trap quantum computing. , 2003, Physical review letters.

[23]  Carlton M. Caves,et al.  QUANTUM LOGIC GATES IN OPTICAL LATTICES , 1999 .

[24]  Phillips,et al.  Adiabatic cooling of cesium to 700 nK in an optical lattice. , 1995, Physical review letters.

[25]  H. Rabitz,et al.  Optimal control of quantum-mechanical systems: Existence, numerical approximation, and applications. , 1988, Physical review. A, General physics.

[26]  Maxim Olshanii.  Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons , 1998 .

[27]  David J. Tannor,et al.  Loading a Bose-Einstein condensate onto an optical lattice: An application of optimal control theory to the nonlinear Schrödinger equation , 2002 .

[28]  D. Jaksch,et al.  Fast initialization of a high-fidelity quantum register using optical superlattices , 2007, cond-mat/0702645.

[29]  J. W. Thomas.  Numerical Partial Differential Equations , 1999 .

[30]  Samuel H. Tersigni,et al.  Wavepacket dancing: Achieving chemical selectivity by shaping light pulses , 1989 .

[31]  Kristian Helmerson,et al.  Diffraction of a Released Bose-Einstein Condensate by a Pulsed Standing Light Wave , 1999 .