1 trey porto joint quantum institute nist / university of maryland open quantum systems: decoherence...

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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

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Controlled 2-atom spin-exchange

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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)

-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

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

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~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

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Adiabatic vibrational transfer

1.5

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))

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

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Step 2: optimize the control theoretically

Gate control parameters

Un-optimized left well projections

Unwanted excitation

unoptimized

optimizedQuickTime™ and a

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Ask for 150 s optimization time

With G. De Chiara and T. Calarco

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Quantum control techniques

unoptimized

optimized

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

Step 2: optimize the control theoretically

Gate control parameters

With G. De Chiara and T. Calarco

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Quantum control techniques

unoptimized

optimized

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Experimental consideration: band width of

feedback

Step 2: optimize the control theoretically

Gate control parameters

With G. De Chiara and T. Calarco

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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)

Improve coherence time by moving to clock states

3.2 Gauss

Clock State Coherence

T*2 ~ 20 ms

(prev. 150 s)

Improve coherence time by moving to clock states

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

Example: single-site qubit addressing

€

ψi= U ψ

i( )

Goal: arbitrary qubit rotation on a single site

qubit mapping is position sensitive

Memory qubits are distinct from “activated” qubits

€

α 1 + β 2

€

α a + β b

Example: single-site qubit addressing

€

ψi= U ψ

i( )

Goal: arbitrary qubit rotation on a single site

Isolated qubit control

Memory qubits are distinct from “activated” qubits

€

α 1 + β 2

€

α a + β b

Example: single-site qubit addressing

€

ψi= U ψ

i( )

Goal: arbitrary qubit rotation on a single site

Reverse process

€

α 1 + β 2

€

α a + β b

Memory qubits are distinct from “activated” qubits

Example: single-site qubit addressing

€

ψi= U ψ

i( )Memory qubits are distinct from

“activated” qubits

Goal: arbitrary qubit rotation on a single site

€

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

Step 3: Map qubit on left, maintaining coherence

Left sites

Right sites

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

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

Mapped Ramsey

Step 3: Map qubit on left, maintaining coherence

Left sitesRight sites

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

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

Use quadratic Zeeman effect to avoid leakage

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:

LEFT RIGHT

Mapped Ramsey Sequence !!

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:

LEFT

RIGHT

Mapped Ramsey Sequence !!

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:

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

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, 74 042316 (2006)

Optical Magnetic Resonance Imaging