1 trey porto joint quantum institute nist / university of maryland university of minnesota 26 march...
TRANSCRIPT
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1
Trey Porto Joint Quantum Institute
NIST / University of Maryland
University of Minnesota 26 March 2008
Controlled exchange interactions in a
double-well optical lattice
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•Quantum information processingw/ neutral atoms
•Correlated many-body physicsw/ neutral atoms
•Engineering new optical trapping and control techniques
Research Directions
This talk
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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
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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
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Need External (motional) Control
Controlled interactions and individual addressing require atom trapping
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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
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Localized pair-wise interactions
Need External (motional) Control
Individual addressing- localized atoms- localized fields
Our handle: LIGHT!
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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
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rε =x Intensity modulation
rε =x
rε =y
rBeff
Varying effective
magnetic field
Polarization modulation
Scalar vs. Vector Light Shifts
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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
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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
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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
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2D Double Well
‘’ ‘’
Basic idea:Combine two different period lattices with adjustable
- intensities - positions
+ = A B
2 control parameters
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Add an independent, deep vertical
lattice
3D lattice=
independent array of 2D systems
3D confinement
Mott insulator single atom per /2 site
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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 …
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Single particle states in a double-well
Focus on a single double-well
minimal coupling/tunneling between double-wells
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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
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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 )
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Sub-lattice addressing in a double-well
Make the lattice spin-dependent
Apply RF resonant with local Zeeman shift
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Two particle states in a double-well
Two (identical) particle states have
- interactions
- symmetry
4 x 4 = 16 two-particle states
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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
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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
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€
L0,R1
€
L1,R0
€
L0,R0
€
L1,R1
Separated two qubit states
single qubit energy
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Merged two qubit states
single qubit energyBosons must be symmetric under particle exchange
€
ψ(r1,r2) =ψ (r2,r1)
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€
eg + ge( ) 00
+- €
eg + ge( ) 01 + 01( )
€
eg − ge( ) 01 − 01( )
€
eg + ge( ) 11
Symmetrized, merged two qubit states
interaction energy
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+-
Symmetrized, merged two qubit states
Spin-triplet,Space-symmetric
Spin-singlet,Space-Antisymmetric
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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
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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
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Exchange and the swap gate
QuickTime™ and aAnimation decompressor
are needed to see this picture.
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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)
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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
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Basis Measurements
Release from latticeAllow for time-of flight
(possibly with field gradient)
Absorption Imaginggives momentum distribution
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Basis Measurements
Absorption Imaginggive momentum distribution
All atoms in an excited vibrational level
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Basis Measurements
Absorption Imaginggive momentum distribution
All atoms in ground vibrational level
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Basis Measurements
Absorption Imaginggive momentum distribution
Stern-GerlachSpin measurement
B-Field gradient
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Basis Measurements
Stern-Gerlach + “Vibrational-mapping”
Step 3: merge control
Step 4:basis measure
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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)
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Swap Oscillations
Onsite exchange -> fast140s swap time ~700s total manipulation time
Population coherence preserved for >10 ms.( despite 150s T2*! )
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Coherent Evolution
First /2 Second /2
RF RF
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- 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
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Future
Short term:
- improve using clock states- incorporate quantum control techniques- interact longer chains
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Future
Example: Limited addressing + pairwise Ising = maximally entangled GHZ state
Longer term:
-individual addressinglattice + “tweezer”
- use strength of parallelism, e.g. quantum cellular automata
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Postdocs
Jenni Sebby-Strabley Marco Anderlini Ben Brown Patty Lee
Nathan LundbladJohn Obrecht
Ben Jenni
Marco
Patty
People
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The End
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T−1 = ↓↓
T1 = ↑↑
T0 = ↑↓ + ↓↑
S = ↑↓ −↓↑
Controlled Exchange Interactions