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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