1 trey porto joint quantum institute nist / university of maryland university of minnesota 26 march...

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 processingw/ neutral atoms

•Correlated many-body physicsw/ neutral atoms

•Engineering new optical trapping and control techniques

Research Directions

This talk

Quantum Information Requirements

Quantum computing classical bits ( 0, 1 ) quantum states

€

ψ =a 0 + b1

(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 controlworlds best clocks (~10-17 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 coherentqubit

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

contactLocally 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

∝ I

e

hg

Ω2 ~I

Intensity and state

dependent light shift

U

Pure scalar, Intensity lattice

Intensity + polarization

Effective B field, with -scale spatial structure

mF

€

r ⋅

rB

€

∝

Red detuning attractiveBlue detuningrepulsive

Optical standing wave

optical guitar string

rε =x Intensity modulation

rε =x

rε =y

rBeff

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

givesspread in

€

vk

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

+ = A B

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

€

L,0

€

R,1

2 “orbital” states (ψL, ψR)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 (ψg, ψe)2 spin states (0,1)

qubit labelqubit

€

g,1

€

e,0

€

g,0

€

e,1

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

€

g1,g0

€

g1,g1

€

g0,g1

€

g0,g0€

g1,e0

€

g1,e1

€

g0,e1

€

g0,e0€

e1,g0

€

e1,g1

€

e0,g1

€

e0,g0€

e1,e0

€

e1,e1

€

e0,e1

€

e0,e0

Two particle states in a double-well

€

g1,g0

€

g1,g1

€

g0,g1

€

g0,g0€

g1,e0

€

g1,e1

€

g0,e1

€

g0,e0€

e1,g0

€

e1,g1

€

e0,g1

€

e0,g0€

e1,e0

€

e1,e1

€

e0,e1

€

e0,e0

Avoid double-occupied orbitals

4 two-particle states of interestone-to-one with qubit states( + many other “leakage” orbitals… )

Quantum-indistinguishable pairs of states

€

L0,R1

€

L1,R0

€

L0,R0

€

L1,R1

Separated two qubit states

single qubit energy

Merged two qubit states

single qubit energyBosons must be symmetric under particle exchange

€

ψ(r1,r2) =ψ (r2,r1)

€

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

Symmetry + Interaction = Exchange

r1 = r2r1 = r2

€

U ≅ 0

€

U ≠ 0

Simple exchange interactions: (x)-function interactions

-

+

Symmetry spin-dependent spectrum, even if interactions are spin-independent

Exchange and the swap gate

+- +=

0,1 + 1,0

00

1,1

0,1 −1,0

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

exchange energy U

projection triplet

singlet

Universal entangling operation

Exchange and the swap gate

QuickTime™ and aAnimation decompressor

are needed to see this picture.

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)

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

RF RF

Left sites

Right sites

Sub-lattice dependent spectroscopy

Step 2: spin flip

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

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 -> fast140s swap time ~700s total manipulation time

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

Coherent Evolution

First /2 Second /2

RF RF

- 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 stabilitymoved to clock states(demonstrated >10ms T2*, >100ms

T2 )

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 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 Jenni

Marco

Patty

People

The End

T−1 = ↓↓

T1 = ↑↑

T0 = ↑↓ + ↓↑

S = ↑↓ −↓↑

Controlled Exchange Interactions