1 Trey Porto Joint Quantum Institute NIST / University of Maryland University of Minnesota 26 March 2008 Controlled exchange interactions in a double-well optical lattice

Quantum information processing w/ neutral atoms Correlated many-body physics w/ neutral atoms Engineering new optical trapping and control techniques Research Directions This talk

Quantum Information Requirements Quantum computing classical bits ( 0, 1 ) quantum states (Plus measurement, scalable architecture, ……) Need (at minimum) - well characterized, coherent quantum states + control over those states - conditional “logic” = coherent interactions between qubits

Internal state coherence and control worlds best clocks (~ precision!) For many single qubit applications, only internal degrees of freedom need to be controlled Atoms: Ideal quantum bits Gas of Atoms Internal states provide coherent qubit optical RF,  wave

Need External (motional) Control Controlled interactions and individual addressing require atom trapping

Localized pair-wise interactions Need External (motional) Control Contact interactions (short range  (x)-function) - atoms brought in contact Locally shift resonance Address as in MRI Individual addressing - localized atoms - localized fields

Localized pair-wise interactions Need External (motional) Control Individual addressing - localized atoms - localized fields Our handle: LIGHT!

Light Shifts Scalar Vector ee h gg  Intensity and state dependent light shift Pure scalar, Intensity lattice Intensity + polarization Effective B field, with -scale spatial structure Red detuning attractive Blue detuningrepulsive Optical standing wave optical guitar string

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

Optical Trapping: Lattice Tweezer Counter-propagating: Lattice Focused beams: Tweezer Any intensity pattern is a potential (think holograms). Light = Quadratic phase gives spread in Light = Sum of  -functions in k -space

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

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

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 Many more details handled by the postdocs… Make BEC, load into lattice, Mott insulator, control over 8 angles …

Single particle states in a double-well Focus on a single double-well minimal coupling/tunneling between double-wells

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 )

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

Two particle states in a double-well Two (identical) particle states have - interactions - symmetry 4 x 4 = 16 two-particle states

Two particle states in a double-well

Avoid double-occupied orbitals 4 two-particle states of interest one-to-one with qubit states ( + many other “leakage” orbitals… ) Quantum-indistinguishable pairs of states

Separated two qubit states single qubit energy

Merged two qubit states single qubit energy Bosons must be symmetric under particle exchange

+ - Symmetrized, merged two qubit states interaction energy

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

Symmetry + Interaction = Exchange r 1 = r 2 Simple exchange interactions:  (x) -function interactions - + Symmetry spin-dependent spectrum, even if interactions are spin-independent

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

Exchange and the swap gate

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

RF Left sites Right sites Sub-lattice dependent spectroscopy Step 2: spin flip

Basis Measurements Release from lattice Allow for time-of flight (possibly with field gradient) 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 All atoms in ground vibrational level

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

Basis Measurements Stern-Gerlach + “Vibrational-mapping” Step 3: merge control Step 4: basis measure

Putting it all together Step 1: load single atoms into sites Step 2: spin flip atoms on right Step 3: combine wells into same site, wait for time T Step 4: measure state occupation (orbital + spin) 1) 2) 3) 4)

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

Coherent Evolution First  /2Second  /2 RF

- 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 moved to clock states (demonstrated >10ms T 2 *, >100ms T 2 ) Current (Improvable) Limitations

Future Short term: - improve using clock states - incorporate quantum control techniques - interact longer chains

Future Example: Limited addressing + pairwise Ising = maximally entangled GHZ state Longer term: -individual addressing lattice + “tweezer” - use strength of parallelism, e.g. quantum cellular automata

Postdocs Jenni Sebby-Strabley Marco Anderlini Ben Brown Patty Lee Nathan Lundblad John Obrecht BenJenni Marco Patty People

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Controlled Exchange Interactions