1 Trey Porto Joint Quantum Institute NIST / University of Maryland ICAP 2008 Coherent control of pairs of atoms in a double-well optical lattice

Optically trapped neutral atoms Quantum information Many-body physics Two motivating directions Light to trap and control atoms

Optical Trapping: Lattice Tweezer “Bottom up” individual atom control, add more traps “Top Down” start massively parallel add complexity combine approaches to meet in the middle Holographic techniques

Optical Trapping: Lattice Tweezer “Bottom up” individual atom control, add more traps “Top Down” start massively parallel add complexity combine approaches to meet in the middle Holographic techniques This talk

Double Well Lattice Quantum information Many-body physics Two motivating directions for double well lattices Paredes next talk Bloch Hot Topics II

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

Controlled two-neutral atom interactions Two individually trapped atoms Arrays of pairs of atoms in double-well lattice Toward two qubit gates Browaeys Monday

Provide test-bed for scalable ideas e.g. sub-wavelength addressing Demonstrate spin-controlled 2-neutral atom interactions Goals (also a platform for quantum information using global/parallel control)

2D Double Well ‘ ’ ‘  ’ Basic idea: Combine two different period lattices with adjustable - intensities - positions += AB 2 control parameters

+ = /2 nodes  BEC Mirror Folded retro-reflection is phase stable Polarization Controlled 2-period Lattice Sebby-Strabley et al., PRA (2006)

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

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

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 Different from recent work in Mainz Folling et al. Nature (2007)

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

Basis Measurements Release from lattice Allow for time-of flight Absorption Imaging gives momentum distribution

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

Basis Measurements Absorption Imaging give momentum distribution

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

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

Lattice Brillioun Zone Mapping

Provide test-bed for scalable ideas e.g. sub-wavelength addressing Demonstrate spin-controlled 2-neutral atom interactions Goals

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 Different from recent work in Mainz Folling et al. Nature (2007)

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

Can be coupled with perpendicular RF fields Effective magnetic field Aside: dressed spin-dependent lattice Haycock, Jessen, PRL (2000) Sub wavelength structure: Yi, Daley, Pupillo, Zoller NJP (2008)

Aside: dressed spin-dependent lattice RF coupling N. Lundblad et al. PRL 100, (2008) Effective B-field lattice RF-dressed lattice

Intensity modulation effective magnetic field Polarization modulation Scalar vs. Vector Light Shifts Optical Magnetic Resonance Imaging

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

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

Example: Addressable One-qubit gates  Optical Magnetic Resonance Imaging

Example: Addressable One-qubit gates Optical Magnetic Resonance Imaging

Example: Addressable One-qubit gates RF,  wave or Raman Optical Magnetic Resonance Imaging

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

Provide test-bed for scalable ideas e.g. sub-wavelength addressing Demonstrate spin-controlled 2-neutral atom interactions Goals

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

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

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

optical 87 Rb Choices for qubit states Field sensitive states m F = -2 m F = -1

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

Dynamic vibrational control Problem : 87 Rb has very weak spin-dependent interactions Approach: Use symmetry & “exchange” interactions

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)

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 )

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 )

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

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

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

+ - Symmetrized, merged two qubit states interaction energy

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

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

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

Basis Measurements Stern-Gerlach + “Vibrational-mapping”

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)

- 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

- 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

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

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.

Move to clock states m F = -2 m F = m F = -2 m F = -1 OR e.g. 2-body loss becomes important: p-wave loss dominant!

Quantum control techniques Gate control parameters unoptimized optimized De Chiara, Calarco et al. PRA 77, (2008)

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

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

Postdocs Jenni Sebby-Strabley Marco Anderlini Ben Brown Patty Lee Nathan Lundblad John Obrecht BenJenni Marco Patty Double-well People Patty Nathan John Ian Spielman, Bill Phillips Former postdocs/students Bruno Laburthe Chad Fertig Ken O’Hara Johnny Huckans

The End

Dynamic vibrational control

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

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)

Aside: Dressed spin-dependent latttices RF coupling N. Lundblad et al. PRL 100, (2008) Effective B-field latticeRF-dressed lattice

Coherent Evolution First  /2Second  /2 RF

Controlled Exchange Interactions

Sweep Low  High Sweep High  Low Faraday signals.

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