Post on 18-Jan-2018
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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
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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
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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