1 Trey Porto Joint Quantum Institute NIST / University of Maryland Open quantum systems: Decoherence and Control ITAMP Nov. 20-22 2008 Coherent Control

1

Trey Porto Joint Quantum Institute

NIST / University of Maryland

Open quantum systems: Decoherence and ControlITAMP

Nov. 20-22 2008

Coherent Control of Atoms in a Double-Well Optical Lattice

Desire: Coherent Control

Vibrational Control (external)

Spin Control (internal)

Our system: optically tapped cold neutral atoms

Desire: Coherent Control

Vibrational Control

Spin Control

MergingMoving

Auxiliary state controlqubit state control

Control Testbed: 2D Double Well

‘’ ‘’

Two different period lattices with adjustable

- intensities - positions

+ = A B

2 control parameters

rε =y

+

=

/2

rε =z

nodes

16E2 sin4 kx / 2( )

4E2 cos2 kx +φ( )+1( )

BEC

Mirror

Folded retro-reflection is phase stable

Polarization Controlled 2-period Lattice

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

Vibrational control of atoms in a double-well lattice

Sub-lattice addressing (sub-wavelength optical MRI)

Controlled spin-exchange2-neutral atom interactions

Testbed Demonstrations

QuickTime™ and aAnimation decompressor

are needed to see this picture.

Controlled 2-atom spin-exchange



Controlled 2-atom spin-exchange

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)

Toward 2-qubit gate1.5

1.0

0.5

0.0

Time (ms)

-2 0 2 Momentum (ph. rec./sqrt(2))

1.5

1.0

0.5

0.0-2 0 2

Momentum (ph. rec./sqrt(2))

- Initial Mott state preparation(~30% holes)

- Imperfect vibrational motion ~85%

- Imperfect projection onto T0, S ~95%

- Sub-lattice spin control >95%

- Field stability T2 ~300 s

Global exchange interaction current limitations:

Toward 2-qubit gate1.5

1.0

0.5

0.0

Time (ms)


1.5

1.0

0.5

0.0-2 0 2


- Initial Mott state preparation(~30% holes)

- Imperfect vibrational motion ~85%

- Imperfect projection onto T0, S ~95%

- Sub-lattice spin control >95%

- Field stability T2 ~300 s

Filtering/state preparation

Coherent quantum control

Move to clock statesT2*= 60 ms, T2 >

300ms Coherent Hyperfine control

Global exchange interaction current limitations:

Outline

I. Vibrational Control

II.Spin Control



~0.5 ms transfer time

fidelity limited by vibrational energy scale

competes with spin-coherence times.

mapped at t0

from ‘’ lattice mapped at tf

from ‘/2’ lattice

Adiabatic vibrational transfer



Adiabatic vibrational transfer

1.5

1.0

0.5

0.0

Time (ms)


1.5

1.0

0.5

0.0-2 0 2


For the spin-exchange, we compromised: with vibrational fidelity

F ~0.80 to 0.85

Improve spin-coherence and vibrational control

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coherent quantum control techniques improve both speed and fidelity

Coherent Quantum Control

Step 1: reasonable model of the system

Measured populations as a function of tilt during merge

Coherent Quantum Control

Step 1: reasonable model of the system

With G. De Chiara and T. Calarco

Measured populations as a function of merge time

Optimized Control





Step 2: optimize the control theoretically

Gate control parameters

Un-optimized left well projections

Unwanted excitation

unoptimized

optimizedQuickTime™ and a

Animation decompressorare needed to see this picture.

Ask for 150 s optimization time




Quantum control techniques

unoptimized

optimized



Optimized at very short merge time and only for vibrational motion!(Longer times and full optimization should be better.)




QuickTime™ and a decompressor




Quantum control techniques

unoptimized

optimized



Experimental consideration: band width of

feedback




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Quantum control techniquesStep 3: Implement optimization

Outline

I. Vibrational Control

II.Spin Control

Sub-Wavelength Addressing

State dependent light shift looks like local B-field

rBeff

Polarization modulation in an optical lattice

Polarization modulation in a focused beam

rBeff

Sub-lattice addressing in a double-well

Make the lattice spin-dependent

Apply RF resonant with local Zeeman shift

OPTICAL MRI

Sub-lattice addressing in a double-well

1.0

0.8

0.6

0.4

0.2

0.0

P1 /(P

1+P

2)

34.3134.3034.2934.2834.2734.2634.25freq_(MHz)_0063_0088

Right Well Left Well

Left sites

Right sites

≈ 1kGauss/cm !

Lee et al., PRL 99 020402 (2007)

optical

87Rb

F =

F =1

F =I +1

F =I −1

Choices for qubit states

Field sensitive states0 1

-1 02

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

1mF = -2

mF = -1

Easily controlled with RFOptical MRI works

optical

87Rb

F =

F =1

F =I +1

F =I −1

Choices for qubit states

Field sensitive states0 1

-1 02

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

1mF = -2

mF = -1

Easily controlled with RFOptical MRI works

Problems:- field sensitive states

= very bad qubit

- Optical MRI field affects

neighboring qubit states

T*2 = 120 s

optical

87Rb

F =

F =1

F =I +1

F =I −1

Other Choices for qubit States

Field insensitive statesat B=0

0 1

-1 021

mF = -2

mF = -1

optical

87Rb

F =

F =1

F =I +1

F =I −1

Other Choices for qubit States

0 1

-1 021

mF = -2

mF = -1

Field insensitive statesat B=3.2 Gauss

Clock States

Improve coherence time by moving to clock states

€

F =1,mF = 0 ↔ F = 2,mF = 0

€

F =1,mF = −1 ↔ F = 2,mF =1Switch to clock states:

•Field insensitive

• wave control

•Optical MRI addressing does not directly work on clock states

Clock State Coherence

T2 ~ 300 ms (prev. 300 s)


3.2 Gauss

Clock State Coherence

T*2 ~ 20 ms

(prev. 150 s)


T*2 ~ 60 ms

(prev. 150 s)

3.2 Gauss

Time (ms)

Time (ms)

Contrast

Contrast

Optical Addressing of Clock States

Need a technique to address clock states

Transitions between clock states are MRI-addressable

Develop techniques to addressably map qubit states

Field sensitive transitions

€

α 1 + β 2

€

α a + β b

€

1

€

a

€

2

€

b

Field insensit

ive

Field insensit

ive

Field sensitiv

e

Hyperfine Manifold Control

Develop techniques for robust Hyperfine manifold control

qubit mapping not entirely trivial

- near degeneracies- quadratic shifts

Theory input from I. Deutsch

Symmetry breakingwave

€

1

€

a

€

2

€

b

Field insensit

ive

Field insensit

ive

Field sensitiv

e€

α 1 + β 2

€

α a + β b

Example: single-site qubit addressing

€

ψi= U ψ

i( )Memory qubits are distinct from

“activated” qubits

Goal: arbitrary qubit rotation on a single site

Field & positioninsensitive

€

α 1 + β 2

€

α a + β b


€

ψi= U ψ

i( )


qubit mapping is position sensitive

Memory qubits are distinct from “activated” qubits

€

α 1 + β 2

€

α a + β b


€

ψi= U ψ

i( )


Isolated qubit control


€

α 1 + β 2

€

α a + β b


€

ψi= U ψ

i( )


Reverse process

€

α 1 + β 2

€

α a + β b



€

ψi= U ψ

i( )Memory qubits are distinct from

“activated” qubits


€

α 1 + β 2

€

α a + β b

Attractive approach:- field insensitive states

= good qubit

- No cross-talkOptical MRI field does

not affect neighboring sites

- Optical MRI mapping is asimple -pulse: very

amenable to robust pulse control

“Activated” Qubit Mapping

Sub-Lattice Qubit Mapping

Demonstrate these techniques in our double-well lattice

Mapped Ramsey

Step 1: verify clean Ramsey fringe on clock

Phase / Open and close 2-pulse Ramsey sequence on

Popu

lati

on

Mapped Ramsey

Step 2: Ramsey fringe preserved with OMRI field

-Open Ramsey on , -add left/right field gradient, -close Ramsey sequence on

Mapped Ramsey

Step 2: Ramsey fringe preserved with OMRI field

Phase

Population

Population

Left

Right

Left sites

Right sites

-Open Ramsey on , -add left/right field gradient, -close Ramsey sequence on

Mapped Ramsey

Step 2b: determine optical field strength

Left sites

Rightsites

Mapped Ramsey

Step 3: Map qubit on left, maintaining coherence

-Open Ramsey on , -add left/right field gradient,

map to , only on left -close Ramsey sequence right: left:

Mapped Ramsey


Left sites

Right sites



Mapped Ramsey


Left sitesRight sites



Use quadratic Zeeman effect to avoid leakage

Mapped Ramsey




LEFT RIGHT

Mapped Ramsey Sequence !!




LEFT

RIGHT

Mapped Ramsey Sequence !!




LEFT

RIGHT

Should be improvable with robust (composite) pulse

techniques

Example Composite Pulse Improvements

-pulseCORPSE pulse

detuning insensitivity

Example Composite Pulse Improvements

-pulseCORPSE pulse

detuning insensitivity

Want arbitrary Unitary control +

Insensitivity to errors

Future Direction

Collaboration with Inst. d’Optique

BEC production

transport atom cloud

Separate chamber

Comercial aspheres

PostdocsJohn ObrechtNathan

Lundblad

Double-well Team

Patty

Nathan

John

Former postdocs/studentsBruno Laburthe Chad Fertig Jenni Sebby-StrableyMarco Anderlini Ben Brown Patty LeeKen O’Hara Johnny Huckans

The End

€

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

Lattice Brillioun Zone Mapping

Example: Addressable One-qubit gates

Optical Magnetic Resonance Imaging




RF, wave or Raman



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


Documents

1 Trey Porto Joint Quantum Institute NIST / University of Maryland Open quantum systems: Decoherence and Control ITAMP Nov. 20-22 2008 Coherent Control