1 trey porto joint quantum institute nist / university of maryland university of minnesota 26 march...
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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
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g0,g1
€
g0,g0€
g1,e0
€
g1,e1
€
g0,e1
€
g0,e0€
e1,g0
€
e1,g1
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e0,g1
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e0,g0€
e1,e0
€
e1,e1
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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