Quantum Control and Information Processing in Optical Lattices

 

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P. S. Jessen, D.L. Haycock, G. Klose, G. Smith, I.H. Deutsch, and G.K. Brennen
 

Neutral atoms offer a promising platform for single- and many-body quantum control, as required for quantum information processing. This includes excellent isolation from the decohering influence of the environment, and the existence of well developed techniques for atom trapping and coherent manipulation. We present a review of our work to implement quantum control and measurement for ultra-cold atoms in far-off resonance optical lattice traps. In recent experiments we have demonstrated coherent behavior of mesoscopic spinor wavepackets in optical double-well potentials, and carried out quantum state tomography to reconstruct the full density matrix for the atomic spin degrees of freedom. This model system shares a number of important features with proposals to implement quantum logic and quantum computing in optical lattices. We present a theoretical analysis of a protocol for universal quantum logic via single qubit operations and an entangling gate based on electric dipole-dipole interactions. Detailed calculations including the full atomic hyperfine structure suggests that high-fidelity quantum gates are possible under realistic experimental conditions.
 

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Measuring the Quantum State of a Large Angular Momentum

 

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G. Klose, G. Smith, and Poul S. Jessen

Optical Sciences Center, University of Arizona, Tucson, AZ 85721
 

We demonstrate a general method to measure the quantum state of an angular momentum of arbitrary magnitude. The (2F+1) x (2F+1) density matrix is completely determined from a set of Stern-Gerlach measurements with (4F+1) different orientations of the quantization axis. We implement the protocol for laser cooled Cesium atoms in the 6 S1/2 (F=4) hyperfine ground state and apply it to a variety of test states prepared by optical pumping and Larmor precession. A comparison of input and measured states shows typical reconstruction fidelities greater than about 0.95.
 

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Quantum Computing with Neutral Atoms in an Optical Lattice

 

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Ivan H. Deutsch¹, Gavin K. Brennen¹ and Poul S. Jessen²

1. Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131
2. Optical Sciences Center, University of Arizona, Tucson, AZ 85721
 

We present a proposal for quantum information processing with neutral atoms trapped in optical lattices as qubits. Initialization and coherent control of single qubits can be achieved with standard laser cooling and spectroscopic techniques. We consider entangling two-qubit logic gates based on optically induced dipole-dipole interactions, calculating a figure-of-merit for various protocols. Massive parallelism intrinsic to the lattice geometry makes this an intriguing system for scalable, fault-tolerant quantum computation.
 

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Mesoscopic Quantum Coherence in an Optical Lattice

 

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D. L. Haycock¹, P.M. Alsing², I. H. Deutsch², J. Grondalskik² and P. S. Jessenk¹

1. Optical Sciences Center, University of Arizona, Tucson, AZ 85721
2. Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131
 

We observe the quantum coherent dynamics of atomic spinor wave packets in the double-well potentials of a far-off resonance optical lattice. With appropriate initial conditions the system Rabi oscillates between the left and right localized states of the ground doublet, and at certain times the wave packet corresponds to a coherent superposition of these mesoscopically distinct quantum states. The atom/optical double-well potential is a flexible and powerful system for further study of quantum coherence, quantum control and the quantum/classical transition.
 

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Entangling Dipole-Dipole Interactions and Quantum Logic in Optical Lattices

 

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Gavin K. Brennen and Ivan H. Deutsch Center for Advanced Studies, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131 Poul S. Jessen Optical Sciences Center, University of Arizona, Tucson, Arizona 85721
 

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.
 

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Quantum Transport in Magneto-Optical Double-Potential Wells

 

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I. H. Deutsch, P. M. Alsing, J. Grondalski, S. Ghose, D. L. Haycock, and Poul S. Jessen
 

We review the quantum transport of ultra-cold alkali atoms trapped in a one dimensional optical lattice of double-potential wells, engineered through a combination of ac-Stark shifts and Zeeman interactions. The system is modeled numerically through analysis of the band-structure and integration of the time dependent Schrdinger equation. By these means we simulate coherent control of the atomic wavepackets. We present results from ongoing experiments on laser cooled Cesium, including the demonstration of quantum state preparation and coherent tunneling. Entanglement between the internal and motional degrees of freedom allows us to access the tunneling dynamics by Stern-Gerlach measurements of the ground state magnetic populations. Schemes to extend this into a full reconstruction of the density matrix for the ground state angular momentum are presented. We further consider the classical dynamics of our system, which displays deterministic chaos. This has important implications for the distinction between classical and quantum mechanical transport.
 

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Quantum Logic Gates in Optical Lattices

 

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Gavin K. Brennen, Carlton M. Caves, Poul S. Jessen*, and Ivan H. Deutsch Center for Advanced Studies, Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM 87131 * Optical Sciences Center, University of Arizona, Tucson, AZ 85721
 

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 the logical operations, thereby suppressing decoherence.
 

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Resolved-Sideband Raman Cooling to the Ground State of an Optical Lattice

 

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S.E. Hamann, D.L. Haycock, G. Klose, P.H. Pax, I.H. Deutsch* and P.S. Jessen Optical Sciences Center, University of Arizona, Tucson, AZ 85721 *Center for Advanced Studies, Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM 87131
 

We trap neutral Cs atoms in a two-dimensional optical lattice and cool them close to the zero-point motion by resolved-sideband Raman cooling. Sideband cooling occurs via transitions between the vibrational manifolds associated with a pair of magnetic sublevels and the required Raman coupling is provided by the lattice potential itself. We obtain mean vibrational excitations nx ny 0.01, corrensponding to a population ~98% in the vibrational ground state. Atoms in the ground state of an optical lattice provide a new system in which to explore quantum state control and subrecoil laser cooling.
 

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Enhanced laser cooling and state preparation in an optical lattice with magnetic field

 

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D.L. Haycock, S.E. Hamann, G. Klose, G.Raithel* and P.S. Jessen Optical Sciences Center, University of Arizona, Tucson, AZ 85721 *National Institute of Standards and Technology, PHYS A167, Gaithersburg, MD 20899
 

We demonstrate that weak magnetic fields can significantly enhance laser cooling and sate preparation of Cs atoms in a one-dimensional optical lattice. A field parallel to the lattice axis increases the vibrational ground state population of the stretched state |m=F> to 28%. A transverse field ireduces the kinetic temperature. Quantum Monte-Carlo simulations agree with the experiment, and predict 45% ground state population for optimal parallel and transverse fields. Our results show that coherent mixing and local energy relaxation play important roles in laser cooling of large-F atoms.
 

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Quantum State Control in Optical Lattices

 

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Ivan H. Deutsch Center for Advanced Studies, Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM 87131 Poul S. Jessen Optical Sciences Center, University of Arizona, Tucson, AZ 85721
 

We study the means to prepare and coherently manipulate atomic wave packets in optical lattices, with particular emphasis on alkalis in the far-detuned limit. We derive a general, basis independent expression for the lattice potential operator, and show that its off-diagonal elements can be tailored to couple the vibrational manifolds of separate magnetic sublevels. Using these couplings one can evolve the state of a trapped atom in a quantum coherent fashion, and prepare pure quantum states by resolved-sideband Raman cooling. We explore the use of atoms bound in optical lattices to study quantum tunneling and the generation of macroscopic superposition states in a double-well potential. Far-off-resonance optical potentials lend themselves particularly well to reservoir engineering via well controlled fluctuations in the potential, making the atom/lattice system attractive for the study of decoherence and the connection between classical and quantum physics.
 

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