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1 Trey Porto Joint Quantum Institute NIST / University of Maryland DAMOP 2008 Controlled interaction between pairs of atoms in a double-well optical lattice

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Neutral atom quantum computing Well characterized qubits Ability to (re)initialize Decoherence times longer than operation times A universal set of gates 1) One-qubit 2) Two-qubit State specific readout All in a Scalable Architecture Minimal Requirements

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Demonstrate controlled, coherent, 2-neutral atom interactions Provide a test bed for some scalable ideas e.g. sub-wavelength addressing Short Term Goal (also a potential platform for quantum information using global/parallel control)

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Goal: demonstrate controlled, coherent, 2-neutral atom interactions Two individually trapped atoms Arrays of pairs of atoms in double-well lattice Neutral atom quantum processing This year: U. Wisc. Inst. dOptique This talk (Last year)

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2D Double Well Basic idea: Combine two different period lattices with adjustable - intensities - positions += AB 2 control parameters See also Folling et al. Nature (2007)

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Add an independent, deep vertical lattice 3D lattice = independent array of 2D systems 3D confinement Mott insulator single atom per /2 site

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Add an independent, deep vertical lattice 3D lattice = independent array of 2D systems 3D confinement Mott insulator single atom/ /2 site Many more details handled by the postdocs… Make BEC, load into lattice, Mott insulator, control over 8 angles … Sebby-Strabley, et al., PRA (2006) Sebby-Strabley, et al., PRL (2007)

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X-Y directions coupled - checkerboard topology - not sinusoidal (in all directions) (e.g., leads to very different tunneling) - spin-dependence in sub-lattice - blue-detuned lattice is different from red-detuned - non-trivial Band-structure Unique Lattice Features

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This talk: Isolated a double-well sites Focus on a single double-well negligible coupling/tunneling between double-wells

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Basis Measurements Release from lattice Allow for time-of flight (possibly with field gradient) Absorption Imaging gives momentum distribution

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Basis Measurements Absorption Imaging give momentum distribution All atoms in an excited vibrational level

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Basis Measurements Absorption Imaging give momentum distribution All atoms in ground vibrational level

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Basis Measurements Absorption Imaging give momentum distribution Stern-Gerlach Spin measurement B-Field gradient

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X-Y directions coupled - checkerboard topology - not sinusoidal (in all directions) (e.g., leads to very different tunneling) - spin-dependence in sub-lattice - blue-detuned lattice is different from red-detuned - non-trivial Band-structure Unique Lattice Features Compare to recent work of Folling et al. Nature (2007)

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Intensity modulation effective magnetic field Polarization modulation Scalar vs. Vector Light Shifts

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Sub-lattice addressing in a double-well Make the lattice spin-dependent Apply RF resonant with local Zeeman shift

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Sub-lattice addressing in a double-well Left sites Right sites 1kGauss/cm ! Lee et al., Phys. Rev. Lett (2007)

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Example: Addressable One-qubit gates

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Example: Addressable One-qubit gates

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RF, wave or Raman

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Example: Addressable One-qubit gates Zhang, Rolston Das Sarma, PRA, (2006)

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optical 87 Rb Choices for qubit states Field sensitive states Work at high field, quadratic Zeeman isolates two of the F=1 states 1 m F = -2 m F = -1 Easily controlled with RF qubit states are sub-lattice addressable

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optical 87 Rb Choices for qubit states Field insensitive states at B= m F = -2 m F = -1 controlled with wave qubit states are not sub-lattice addressable need auxiliary states

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optical 87 Rb Choices for qubit states Field insensitive states at B=3.2 Gauss m F = -2 m F = -1 controlled with wave qubit states are not sub-lattice addressable need auxiliary states

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Dynamic vibrational control Merge pairs of atoms to control interactions Maintain separate orbital (vibrational) states: qubits are always labeled and distinct.

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Experimental requirements Step 1: load single atoms into sites Step 2: independently control spins Step 3: combine wells into same site, wait for time T Step 4: measure state occupation (orbital + spin) 1) 2) 3) 4)

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Single particle states in a double-well 2 orbital states ( L, R ) 2 spin states (0,1) qubit label qubit 4 states( + other higher orbital states )

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Single particle states in a double-well 2 orbital states ( g, e ) 2 spin states (0,1) qubit label qubit 4 states( other states = leakage )

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Two particle states in a double-well Two (identical) particle states have - interactions - symmetry

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Separated two qubit states single qubit energy L= left, R = right

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Merged two qubit states single qubit energy Bosons must be symmetric under particle exchange e= excited, g = ground

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+ - Symmetrized, merged two qubit states interaction energy

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+ - Symmetrized, merged two qubit states Spin-triplet, Space-symmetric Spin-singlet, Space-Antisymmetric

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+ - Symmetrized, merged two qubit states Spin-triplet, Space-symmetric Spin-singlet, Space-Antisymmetric r 1 = r 2 See Hayes, Julliene and Deutsch, PRL (2007)

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Exchange and the swap gate + - += Start in Turn on interactions spin-exchange dynamics Universal entangling operation

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Basis Measurements Stern-Gerlach + Vibrational-mapping

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Swap Oscillations Onsite exchange -> fast 140 s swap time ~700 s total manipulation time Population coherence preserved for >10 ms. ( despite 150 s T2*! ) Anderlini et al. Nature (2007)

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- Initial Mott state preparation (30% holes -> 50% bad pairs) - Imperfect vibrational motion ~ 85% - Imperfect projection onto T 0, S ~ 95% - Sub-lattice spin control >95% - Field stability Current (Improvable) Limitations

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- Initial Mott state preparation (30% holes -> 50% bad pairs) - Imperfect vibrational motion - Imperfect projection onto T 0, S - Sub-lattice spin control - Field stability Current (Improvable) Limitations Filtering pairs Coherent quantum control Composite pulsing Clock States

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Move to clock states m F = -2 m F = m F = -2 m F = -1 T 2 ~ 280 ms (prev. 300 s) OR Improved frequency resolution Improved coherence times

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Move to clock states m F = -2 m F = m F = -2 m F = -1 OR Requires auxiliary states Plus wave/RF mapping between states e.g.

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Two-body decay considerations m F = -2 m F = m F = -2 m F = -1 OR e.g. 2-body loss becomes important: p-wave loss dominant!

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Quantum control techniques Example: optimized merge for exchange gate Gate control parameters unoptimized optimized

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Quantum control techniques Example: optimized merge for exchange gate Gate control parameters unoptimized optimized Optimized at very short 150 s merge time and only for vib. motion! (Longer times and full optimization should be better.) De Chiara et al., PRA 77, (2008)

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Faraday rotation: improved diagnostics polarization analyzer Real-time, single-shot spectroscopy Example: single-shot spectrogram of 10 MHz frequency sweep

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Faraday rotation: improved diagnostics Left site s Righ t sites Single shot measurementMultiple-shot spectroscopy vs. More than 30 times less efficient quadratic Zeeman Sub-lattice spectroscopy

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Future Longer term: -individual addressing lattice + tweezer - use strength of parallelism, e.g. quantum cellular automata

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Postdocs Jenni Sebby-Strabley Marco Anderlini Ben Brown Patty Lee Nathan Lundblad John Obrecht BenJenni Marco Patty People Patty Nathan John Ian Spielman, Bill Phillips

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The End

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Coherent Evolution First /2Second /2 RF

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Controlled Exchange Interactions

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Sweep Low High Sweep High Low Faraday signals.

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Outline - Demonstration of controlled Exchange oscillations -Intro to lattice - lattice. - state dependence. - qubit choice. -Demonstrations -Exchange oscillations -Theory of exchange - future directions with clock states. Better T2 and spin echo Considerations: filtering coherent quantum control dipolar loss detailed lattice characterization faraday

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