1 Trey Porto Joint Quantum Institute NIST / University of Maryland LASSP Seminar Cornell Oct. 30...
-
Upload
sabrina-clark -
Category
Documents
-
view
220 -
download
1
Transcript of 1 Trey Porto Joint Quantum Institute NIST / University of Maryland LASSP Seminar Cornell Oct. 30...
1
Trey Porto Joint Quantum Institute
NIST / University of Maryland
LASSP SeminarCornell
Oct. 30 2007
Controlled exchange interactions between pairs of atoms in an
optical lattice
•Quantum information processingw/ neutral atoms
•Correlated many-body physicsw/ neutral atoms
•Engineering new optical trapping and control techniques
Research Directions
This Talk
Sub-lattice RF addressing in a lattice-independent Bloch-sphere control of atoms in sub-lattices
Controlled exchange-mediated interactions-using exchange to get spin-dependent entangling (SWAP)
Outline
-Description of the lattice
- Demonstrations of toolsdouble well splitting, controlled
motion, sub-lattice spin addressing
-Putting it all together:controlled two-atom exchange
swapping
Outline
-Description of the lattice
- Demonstrations of toolsdouble well splitting, controlled
motion, sub-lattice spin addressing
-Putting it all together:controlled two-atom exchange
swapping
Motivation for the double-well lattice:Isolate pairs of atoms in controllable potential, to test
- demonstrate addressing ideas - controlled interactions, at 2-
atom level
Provide new possibilities for cold atom
lattice physics
Double-Well Lattice
Phase Stable 2D Double Well
‘’ ‘’
Basic idea:Combine two different period lattices with adjustable
- intensities - positions
Mott insulator single atom/site
+ = A B
rε =y
+
=
/2
rε =z
nodes
16E2 sin4 kx / 2( )
4E2 cos2 kx +φ( ) +1( )
BEC
Mirror
z
y
x
Folded retro-reflection is phase stable
Polarization Controlled 2-period Lattice
Sebby-Strabley et al., PRA 73 033605 (2006)
Add an independent, deep vertical lattice
Provides an independent array of 2D systems
Polarization Controlled 2-period Lattice
Light Shifts
Scalar
Vector
∝ I
e
hg
Ω2 ~I
Intensity and state
dependent light shift
δU
Pure scalar, Intensity lattice
Intensity + polarization
Effective B field, with -scale spatial structure
Flexibility to tune scalar vs. vector component
mF
€
rμ ⋅
rB
Red detuning attractiveBlue detuningrepulsive
Optical standing wave
Vector Light Shifts
x
y z
rε =x
rε =x
Example: lin || lin
no elipticity, intensity modulation
rε =x
rε =y
Example: lin lin⊥
no intensity modulation, alternating circular polarization
rBeff
Position dependent effective magnetic field
F =1,mF =0
F =1,mF =−1
F =1,mF =1
Vector light shift + bias B-field:controllable
state-dependent barriersstate-dependent tilts
Use for site-dependent RF addressing
State Dependent Potential
For the demonstrations
shown here, we use these 2 states in
87Rb
We use the quadratic Zeeman shift
to isolate a pseudo spin-1/2
~34 MHz
~34.3 MHz
~50 gauss
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- interesting Band-structure
Lattice Features
cos2 (x + y)cos (x−y) cos4 (x)
Outline
-Description of the lattice
- Demonstrations of toolsdouble well splitting, controlled
motion, sub-lattice spin addressing
-Putting it all together:controlled two-atom exchange
swapping
q
E
x
Lattice can be turned on/off in different time scales
Sudden: (<< 100 μs) (“pulsing” lattice)
Eigenstate projection
Intermediate:Fast compared to interaction/tunneling,Slow compared to non-interacting band
“Map” band distribution
Slow compared to all times: (>> few ms)
complete adiabaticity(“adiabatic”)
Dynamic Lattice Amplitude Control
Time of flight imaging
py
px
Reciprocal Lattices and Brillouin Zones
‘’ lattice ‘/2’ lattice
Band-adiabatic load in 500μs, snap off
300 ms500 μs
Brillouin Zone mapping
phase incoherent
500 μs 20 μs
Double Slit Diffraction
Slowly load mostly- lattice, snap off
Coherently split single well
Single slit diffraction
load in ~300 msphase scrambled
QuickTime™ and aAnimation decompressor
are needed to see this picture.
QuickTime™ and aAnimation decompressor
are needed to see this picture.
split in ~200 μscoherent split
Double slit diffraction
Time dependence of diffraction
time
Contrast collapse:Not factorizable into a product state
LL + LR + RL + RR
L + R( ) L + R( ) =
e−iUt LL + LR + RL + e−iUt RR
split
++
Time dependence of diffraction
time
N > 1
N =1
0.0 0.2 0.4 0.6 0.8 1.0 1.2 Time (ms)
In 3D lattice, see:Greiner et al.Nature, 419 (2002)
Sebby-strabley, PRL 98, 200405 (2007)
Loading (Slowly) One Atom Per Site
Step 1: (for most experiments)
Start with a Bose-Einstein condensate,slowly turn on the lattice
Load one atom per site using the Mott-Insulator transition
or
Well “fermionized”, but some holes
Probe: Selective Removal of Sites
Load right well expel left
Load left well expel left
band map
band map
QuickTime™ and aAnimation decompressor
are needed to see this picture.
QuickTime™ and aAnimation decompressor
are needed to see this picture.
QuickTime™ and aAnimation decompressor
are needed to see this picture.
~ ms transfer time
atoms can be put on the same site, (but different vibrational level), allowed to interact, and then separated adiabatically
mapped at t0
from ‘’ lattice mapped at tf
from ‘/2’ lattice
Adiabatic transfer “excitation”
Start with atoms in m=-1
Apply RF to spin flip to m=0
“Evaporate” m=0 atoms
Measure m=-1 occupation in the left or right well.
sub-lattice addressing by light shift gradient
Sub-Lattice Addressing
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
Start with atoms in m=-1
Apply RF to spin flip to m=0
“Evaporate” m=0 atoms
Measure m=-1 occupation in the left or right 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
Sub-Lattice Addressing
Right well
Left well
Lee et al., PRL 99, 020402 (2007)
Example: Addressable One-qubit gates
Atoms at sub- spacing-focused beam sees
several sites
- state dependent shifts
effective field gradients
Example: Addressable One-qubit gates
Atoms at sub- spacing-focused beam sees
several sites
- state dependent shifts
effective field gradients
RF, μwave or Raman
Example: Addressable One-qubit gates
Atoms at sub- spacing-focused beam sees
several sites
- state dependent shifts
effective field gradients
- frequency addressing
State selective motion/splitting
Start with either m=-1 or m=0Selectively and coherently
split wavefunction
m=0 on left m=-1 on right
or
Outline
-Description of the lattice
- Demonstrations of toolsdouble well splitting, controlled
motion, sub-lattice spin addressing
-Putting it all together:controlled two-atom exchange
swapping
Putting it all together: a swap gate
Step 1: load single atoms into sites
Step 2: spin flip atoms on right
Step 3: combine wells into same site
Step 4: wait for time T
Step 5: measure state occupation(vibrational + internal)
1)
2)
3)
4)
QuickTime™ and aAnimation decompressor
are needed to see this picture.
Exchange Gate:
0,1 + 1,0
00
1,1
0,1 −1,0
0,1
1,0
exchange split by energy U
0,0
1,1
projection1,0
swap
projection triplet
singlet
Exchange Gate:
0,1 + 1,0
00
1,1
0,1 −1,0
0,1
1,0
exchange split by energy U
0,0
1,1
projection1,0
swap
projection triplet
singlet
r1 = r2r1 = r2
€
U ≅ 0
€
U ≠ 0
Exchange Gate:
0,1 + 1,0
00
1,1
0,1 −1,0
0,1
1,0
exchange split by energy U
0,0
1,1
projection1,0
projection triplet
singlet
0,1 + i 1,0
0,1 −i 1,0
0,0
1,1
swap0,1 −i 1,0
swap
Swap Oscillations
Onsite exchange -> fast140μs swap time ~700μs total manipulation time
Population coherence preserved for >10 ms.( despite 150μs T2*! )
Anderlini, Nature 448 452 (2007)
- Initial Mott state preparatio(30% holes -> 50% bad pairs)
- Imperfect vibrational motion~85%
- Imperfect projection onto T0, S ~95%
- Sub-lattice spin control >95%
- Field stabilitymove to clock states
(state-dependent control through intermediate states)
Current (Improvable) Limitations
Coherent collisional gatesNeighboring atoms are
-spatially isolated
or-in “activated”
states
Example: Two-qubit control
Optical tweezer adiabatically brings neighboring atoms together.
Coherent collisional shift
Coherent collisional gatesNeighboring atoms are
-spatially isolated
or-in “activated”
states
Example: Two-qubit control
Optical tweezer adiabatically brings neighboring atoms together.
Atoms are separated after an interaction time.
Coherent collisional shift
Coherent collisional gatesNeighboring atoms are
-spatially isolated
or-in “activated”
states
Example: Two-qubit control
Toward “Scalable” Quantum Computing
Test bed for addressable two qubit ideas
Test and extend ideas to addressingadd tweezers
registration is essential
Using Parallelism
Quantum Cellular Automatalimited addressability (e.g. on the edges)distinct entangling, nearest neighbor rules
Formally equivalent to circuit Qcomp
Individually address only the edge atoms
B-rulesA-rules
Using Parallelism
Measurement Based or“One way” or “Cluster State” Qcomp
-Create a parallel-entangled cluster state-measurements + 1-qubit rotations
Entangled with each of its neighbors
Tools for lattice systems
State preparation, e.g.- ‘filter’ cooling- constructing anti-ferromagnetic
state.
Diagnostics, e.g.- number distributions (including
holes)- neighboring spin correlations
Realizing lattice Hamiltonians, e.g.- band structure engineering- ‘stroboscopic’ techniques- coupled 1D-lattice “ladder”
systems- RVB physics
. . .
Postdocs
Jenni Sebby-Strabley Marco Anderlini Ben Brown Patty Lee
Nathan LundbladJohn Obrecht
Ben Jenni
Marco
Patty
People
Lasercooling GroupI. Spielman K. Helmerson P. Lett T. Porto
W. Phillips
10-5
10-4
10-3
10-2
10-1
100
4J/E
R
2520151050V/ER
"out of plane" lattice
"in-plane" lattice
Different tunneling
Different J but similar U and vibrational spacing
Same input power
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
2D Mott-insulator
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Quite good comparison to a homogeneous theory (no free parameters)
Sengupta and Dupuis, PRA 71, 033629
Momentum distribution
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
2D Mott-insulator
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Bimodal fit disappears quite sharply
position agrees with theory
(no fit distinction between thermal/depletion)
-10
-5
0
Potential [ER]
-4-3-2-10
Potential [ER]
8006004002000-200-400Position [nm]
10-6
10-5
10-4
10-3
10-2
10-1
V / U
2 34560.012 3456 0.12 3456 1t/U
5% Tilt15% Tilt3 ER Lattice Depth
Wannier function control
Two band Hubbard modelstate-dependent control of: t/U, /U, position of -lattice
t
Ian Spielman
Characterizing Holes
In a fixed period lattice,difficult to measure “holes”
Isolated holes in /2 Combine holes with neighbors
mF =−1
mF =1
mF =0
Can be coupled with perpendicular DC or RF fields
couples spin to Bloch state motion
Purely vector part of
with no coupling (large Zeeman splitting)
lin lin⊥
Coupling spin and motion
Connection between single-particle base states and correlated physics when you put in interactions.
Designing Bose-Hubbard Hamiltonians
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
State selective motion/splitting
Start with either m=-1 or m=0
Selectively split sites
Tilt dependence of transfer efficiency
or
Coherent State-Dependent “Splitting”
-600
-400
-200
0
200
400
600
Y (μ)m
-600 -400 -00 0 00 400 600 (X μ )m
Site specificRF excitation
Double-slitdiffraction
/2 pulse
(Actually, folded into a spin-echo sequence)
Lee et al., PRL 99, 020402 (2007)