1

Trey Porto Joint Quantum Institute

NIST / University of Maryland

DAMOP2008

Controlled interaction between pairs of atoms in a

double-well optical lattice

Neutral atom quantum computing

•Well characterized qubits

•Ability to (re)initialize

•Decoherence times longer than operation times

•A universal set of gates1) One-qubit 2) Two-qubit

•State specific readout

All in a Scalable Architecture

Minimal Requirements

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)

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. d’Optique

This talk(Last year)

2D Double Well

‘’ ‘’

Basic idea:Combine two different period lattices with adjustable

- intensities - positions

+ = A B

2 control parameters

See also Folling et al. Nature 448 1029 (2007)

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 …

Sebby-Strabley, et al., PRA 73 033605 (2006)

Sebby-Strabley, et al., PRL 98 200405 (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

cos2 (x + y)cos (x−y) cos4 (x)

This talk: Isolated a double-well sites

Focus on a single double-well

negligible coupling/tunneling between double-wells

Basis Measurements

Release from latticeAllow for time-of flight

(possibly with field gradient)

Absorption Imaginggives momentum distribution

Basis Measurements

Absorption Imaginggive momentum distribution

All atoms in an excited vibrational level

Basis Measurements

Absorption Imaginggive momentum distribution

All atoms in ground vibrational level

Basis Measurements

Absorption Imaginggive momentum distribution

Stern-GerlachSpin measurement

B-Field gradient

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

cos2 (x + y)cos (x−y) cos4 (x)

Compare to recent work of Folling et al. Nature 448

1029 (2007)

rε =x Intensity modulation

rε =x

rε =y

rBeff

effective magnetic field

Polarization modulation

Scalar vs. Vector Light Shifts

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

1.0

0.8

0.6

0.4

0.2

0.0

P1 /(P

1+P

2)

34.3134.3034.2934.2834.2734.2634.25

freq_(MHz)_0063_0088

Right Well Left Well

Left sites

Right sites

≈ 1kGauss/cm !

Lee et al., Phys. Rev. Lett. 99 020402

(2007)

Example: Addressable One-qubit gates

Example: Addressable One-qubit gates

Example: Addressable One-qubit gates

RF, wave or Raman

Example: Addressable One-qubit gates

Zhang, Rolston Das Sarma, PRA, 74 042316 (2006)

optical

87Rb

F =

F =1

F =I +1 /

F =I −1 /

Choices for qubit states

Field sensitive states

0 1

-1 0

2

Work at high field, quadratic Zeeman isolates two of the F=1 states

1mF = -2

mF = -1

Easily controlled with RFqubit states are sub-lattice addressable

optical

87Rb

F =

F =1

F =I +1 /

F =I −1 /

Choices for qubit states

Field insensitive statesat B=0

0 1

-1 0

21mF = -2

mF = -1

controlled with wavequbit states are not sub-lattice addressable

need auxiliary states

optical

87Rb

F =

F =1

F =I +1 /

F =I −1 /

Choices for qubit states

Field insensitive statesat B=3.2 Gauss

0 1

-1 0

21mF = -2

mF = -1

controlled with wavequbit states are not sub-lattice addressable

need auxiliary states

Dynamic vibrational control

QuickTime™ and aAnimation decompressor

are needed to see this picture.

Merge pairs of atoms to control interactions

Maintain separate orbital (vibrational) states:qubits are always labeled and distinct.

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

€

L,0

€

R,1

2 “orbital” states (L, R)2 spin states (0,1)

qubit labelqubit

€

L,1

€

R,0

€

L,0

€

R,1

QuickTime™ and aAnimation decompressor

are needed to see this picture.

4 states( + other higher orbital states )

€

=1

€

= 0

Single particle states in a double-well

€

g,0

€

e,1

2 “orbital” states (g, e)2 spin states (0,1)

qubit labelqubit

€

g,1

€

e,0

€

g,0

€

e,1

4 states( other states = “leakage )

Two particle states in a double-well

Two (identical) particle states have

- interactions

- symmetry

€

L0,R1

€

L1,R0

€

L0,R0

€

L1,R1

Separated two qubit states

single qubit energy

€

=1

€

= 0

L= left, R = right

Merged two qubit states

single qubit energyBosons must be symmetric under particle exchange

€

(r1,r2) =ψ (r2,r1)

€

=1

€

= 0

e= excited, g = ground

€

eg + ge( ) 00

+- €

eg + ge( ) 01 + 01( )

€

eg − ge( ) 01 − 01( )

€

eg + ge( ) 11

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

r1 = r2

€

U ≅ 0

r1 = r2

€

U ≠ 0

See Hayes, Julliene and Deutsch, PRL 98 070501 (2007)

Exchange and the swap gate

+- +=

0,1

1,0

0,0

1,1

0,1 + i 1,0

0,1 −i 1,0

0,0

1,1

Start in

€

g0,e1 ≡ 0,1

“Turn on” interactions spin-exchange dynamics Universal

entangling operation

€

e iUt / h

Basis Measurements

Stern-Gerlach + “Vibrational-mapping”

Swap Oscillations

Onsite exchange -> fast140s swap time ~700s total manipulation time

Population coherence preserved for >10 ms.( despite 150s T2*! )

Anderlini et al. Nature 448 452 (2007)

- Initial Mott state preparation(30% holes -> 50% bad pairs)

- Imperfect vibrational motion~85%- Imperfect projection onto T0, 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 T0, S

- Sub-lattice spin control

- Field stability

Current (Improvable) Limitations

Filtering pairs

Coherent quantum control

Composite pulsing

Clock States

Move to clock states

0 1

-1 021

mF = -2

mF = -1 0 1

-1 021

mF = -2

mF = -1

T2 ~ 280 ms (prev. 300 s)

OR

Improved frequency resolution

Improved coherence times

Move to clock states

0 1

-1 021

mF = -2

mF = -1 0 1

-1 021

mF = -2

mF = -1

OR

Requires auxiliary statesPlus wave/RF mapping between states

e.g.e.g.

Two-body decay considerations

0 1

-1 021

mF = -2

mF = -1 0 1

-1 021

mF = -2

mF = -1

ORe.g.

e.g.

2-body loss becomes important:

p-wave loss dominant!

Quantum control techniques

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Example: optimized merge for exchange gate

Gate control parameters

unoptimized

optimized

QuickTime™ and aAnimation decompressor

are needed to see this picture.

Quantum control techniques

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Example: optimized merge for exchange gate

Gate control parameters

unoptimized

optimized QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

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, 052333 (2008)

Faraday rotation: improved diagnostics

€

θ

€

′ θ

polarizationanalyzer

Real-time, single-shot spectroscopy

Example: single-shot spectrogramof 10 MHz frequency

sweep

34.2 34.3 34.4 34.5 34.6 34.7 34.80

100

200

300

Fourier Power (au)

Frequency (MHz)

Faraday rotation: improved diagnostics

34.2 34.3 34.4 34.5 34.6 34.7 34.80

100

200

300

Fourier Power (au)

Frequency (MHz)

1.0

0.8

0.6

0.4

0.2

0.0

P1 /(P

1+P

2)

34.3134.3034.2934.2834.2734.2634.25

freq_(MHz)_0063_0088

Right Well Left Well

Left sites

Right sites

Single shot measurement Multiple-shot spectroscopyvs.

More than 30 times less efficient

quadratic Zeeman

Sub-lattice spectroscopy

Future

Longer term:

-individual addressinglattice + “tweezer”

- use strength of parallelism, e.g. quantum cellular automata

Postdocs

Jenni Sebby-Strabley Marco Anderlini Ben Brown Patty Lee

Nathan LundbladJohn Obrecht

Ben JenniMarco

Patty

People

Patty

NathanJohn

Ian Spielman, Bill Phillips

The End

Coherent Evolution

First /2 Second /2

RF RF

T−1 = ↓↓

T1 = ↑↑

T0 = ↑↓ + ↓↑

S = ↑↓ −↓↑

Controlled Exchange Interactions

34.2 34.3 34.4 34.5 34.6 34.7 34.80

100

200

300

400

50049.15 GQuadratic-Zeeman Shift: 350.3(7) kHz

Fourier Power (au)

Frequency (MHz)

34.2 34.3 34.4 34.5 34.6 34.7 34.80

100

200

300

Fourier Power (au)

Frequency (MHz)

34.2 34.3 34.4 34.5 34.6 34.7 34.80

30

60

90

120

150

Fourier Power (au)

Frequency (MHz)

34.63 34.64 34.65 34.66 34.67 34.68 34.69 34.70 34.710

30

60

90

120

150

State-dependent Shift: 26.1(13) kHz

Fourier Power (au)

Frequency (MHz)

Sweep Low HighSweep 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 echoConsiderations:

filteringcoherent quantum controldipolar lossdetailed lattice

characterizationfaraday