Mark Acton (grad)

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Mark Acton (grad) Kathy-Anne Brickman
(grad) Louis Deslauriers (grad) Patricia Lee
(grad) Martin Madsen (grad) David Moehring
(grad) Steve Olmschenk (grad) Daniel Stick (grad)
US National Security Agency
US Advanced Research and Development Activity
David Hucul (undergrad) Rudy Kohn
(undergrad) Mark Yeo (undergrad)
US Army Research Office
NSF
Boris Blinov (postdoc) Paul Haljan
(postdoc) Winfried Hensinger (postdoc) Chitra
Rangan (postdoc/theory to U. Windsor) Luming
Duan (Prof., UM) Jim Rabchuk (Visiting Prof.,
West. Illinois Univ.)
National Science Foundation
FOCUS
FOCUS Center
http//iontrap.physics.lsa.umich.edu/
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Trapped Atomic Ions I Quantum computing and
motional quantum gates
Christopher Monroe FOCUS Center Department of
Physics University of Michigan
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There's Plenty of Room at the Bottom (1959 APS
annual meeting)
Richard Feynman
When we get to the very, very small world say
circuits of seven atoms - we have a lot of new
things that would happen that represent
completely new opportunities for design. Atoms on
a small scale behave like nothing on a large
scale, for they satisfy the laws of quantum
mechanics
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A quantum computer hosts quantum bits that can
store superpositions of 0 and 1 classical
bit 0 or 1 quantum bit ?0? ?1?
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GOOD NEWS quantum parallel processing on 2N
inputs
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GOOD NEWS! quantum interference
depends on all inputs
quantum logic gates
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Key resource Quantum Entanglement
not just a choice of basis e.g. ?? - ??
vs. 0,0? must be able to access subsystems
individually (see Bell ?)
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very hard to quantify (esp. mixed states)
?1 ????? ????? ?2 ????? ?????
????? ????? ????? ?????
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Quantum computer hardware requirements

• Must make states like
• 0000? 1111?

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Quantum Information and Atomic Physics
controlled coupling
N qubits
to gt99 accuracy
provided things have been done right
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Trapped Atomic Ions
199Hg
0.3 mm
J. Bergquist, NIST
J. Bergquist (NIST)
Ion Trap QC Groups
Aarhus Boulder (NIST) Munich (MPQ) Hamburg Innsbru
ck
Los Alamos McMaster Michigan Oxford Teddington
(NPL)
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2 Cd ions
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Atomic Ion Internal Energy Levels (think
HYDROGEN)
Ca, Sr, Ba, Yb
P
Energy
D
??
t ? 1 sec
optical (1015 Hz)
??
S
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Hyperfine Structure States of relative
electron/nuclear spin
State ??
State ??
N S
N S
N S
S N
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111Cd atomic structure
2,2
2,1
2P3/2
l215nm
??
0,0
2S1/2
14.53 GHz
1,1
1,0
1,-1
??
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111Cd qubit measurement
g/2p 50 MHz
2,2
2,1
2P3/2
l215nm
??
0,0
2S1/2
14.53 GHz
1,1
1,0
1,-1
bright
??
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111Cd qubit measurement
g/2p 50 MHz
2,2
2,1
2P3/2
99.7 detection efficiency
l215nm
??
0,0
2S1/2
14.53 GHz
1,1
1,0
1,-1
dark
??
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111Cd qubit manipulation microwaves
2,2
2,1
2P3/2
l215nm
microwaves
??
0,0
2S1/2
14.53 GHz
1,1
1,0
1,-1
??
coupling rate gm
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Microwave Rabi Flopping
t
measure fluorescence (bright or dark)
prepare 00
mwaves
gm ? 10-100kHz
sweep t
1.0
0.8
0.6
Prob(1000)
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Time t (ms)
1.0
0.8
0,0
0.6
Prob(1100)
0.4
1,1
1,0
1,-1
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Time (ms)
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Single shot Rabi Flopping
increment t
t
measure fluorescence (bright or dark)
prepare 00
mwaves
1
0.8
0.6
Prob(1000)
0.4
0.2
0
0
50
100
150
200
250
300
350
400
t (ms)
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Microwave Ramsey Inteferometry
p/2
p/2
t
measure fluorescence
prepare 00
mwaves
sweep t
1.0
0.8
0.6
Prob(??)
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Time (ms)
1.0
0.8
0,0
Prob(??)
0.6
0.4
1,1
1,0
1,-1
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Time (ms)
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111Cd qubit manipulation optical Raman
transitions
2,2
2,1
g/2p 50 MHz
2P3/2
?
?/2p ? 0.1-1 THz
coherent coupling rate (good) gR
g1g2/D direct coupling to P (bad) Rdec g
g1g2/D2 want small g/D (but DltDFS!)
l215nm
??
0,0
2S1/2
14.53 GHz
1,1
1,0
1,-1
??
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0.3 mm
J. Bergquist, NIST
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40Ca
Thanks R. Blatt, Univ. Innsbruck
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Another Qubit The quantized motion of a single
mode of oscillation
? harmonic motion of a collective single mode
described by quantum states n?m 0?m, 1?m,
2?m,..., where E hw(n½) PHONONS FORMALLY
EQUIVALENT TO PHOTONS ? motional data-bus
quantum bit spans n?m 0?m and 1?m

2
1
0
logical 0?m
logical 1?m
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Coupling (internal) qubits to (external) bus qubit
??
??
??
??
??
radiation tuned to w0-w
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excitation on 1st lower (red) motional sideband
(n0)
w few MHz
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excitation on 1st lower (red) motional sideband
(n0)
P3/2

2
1
0

S1/2
??
2
1
0
??
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P3/2
P3/2


2
2
1
1
0
0


S1/2
S1/2
??
??
2
2
1
1
0
0
??
??
Mapping (??? ???) 0?m ? ?? (?0?m
?1?m)
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P3/2
P3/2


2
2
1
1
0
0


S1/2
S1/2
??
??
2
2
1
1
0
0
??
??
Mapping (??? ???) 0?m ? ?? (?0?m
?1?m)
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Spin-motion coupling some math
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stationary terms arise in H at particular values
of d
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Raman spectrum of single 111Cd ion (start in
??)
Blue sideband ?,n? ? ?,n-1?
Red Sideband ?,n? ? ?,n1?
1.0
Doppler Cooling
P?
0.5
0.0
-3.6 3.6
d/2p (MHz)
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Raman Sideband Laser-Cooling
.
.
n
n-1
??
??
n-1
n-1
??
??
stimulated Raman p-pulse on blue sideband
spontaneous Raman recycling
?Dn? ? wrecoil/wtrap ltlt 1
Dn-1
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Raman spectrum of single 111Cd ion (3.6 MHz
trap)
Blue sideband ?,n? ? ?,n-1?
Red Sideband ?,n? ? ?,n1?
1.0
Doppler Cooling
P?
?n? ? 6
0.5
0.0
-3.6 3.6
d/2p (MHz)
1.0
Doppler Raman Cooling
P?
?n? lt 0.05
0.5
0.0
-3.6 3.6
d/2p (MHz)
x0 3 nm
L. Deslauriers et al., Phys. Rev. A 70, 043408
(2004)
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Decoherence of Trapped Ion Motion
Heating of a single Cd ion from n?0
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Linear Trap (100 mm to nearest electrode)
Heating rate d?n?/dt (quanta/msec)
1
Heating Rate d?n?/dt (quanta/msec)
0.1
Quadrupole Trap (160 mm to nearest electrode)
0.01
1
2
3
4
5
6
Trap Frequency (MHz)
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Heating history in 3-6 MHz traps
heating rate (quanta/msec)

2
10
111Cd Michigan (2003)
9Be
1
10
199Hg NIST (1989)
9Be NIST (1995-)
137Ba
10
0
40Ca Innsbruck (1999)
137Ba IBM-Almaden (2002)
-1
10
111Cd
199Hg
-2
10
40Ca
-3
10
0.04
0.1
0.2
0.3
0.6
Distance to nearest trap electrode mm
Q. Turchette, et. al., Phys. Rev. A 61, 063418-8
(2000) L. Deslauriers et al., Phys. Rev. A 70,
043408 (2004)
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Electric Field Noise History in 3-6 MHz traps
Heating due to fluctuating patch potentials (?)
SE(w) ? 10-12 (V/m)2/Hz
137Ba
9Be
2
10
d
10
1
111Cd
199Hg
0
10
1/d 4
40Ca
10
-1
est. thermal noise
1/d4 guide-to-eye
-2
10
0.04
0.1
0.2
0.3
0.6
Trap dimension mm
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• Quantum Gate Schemes for Trapped Ions
• Cirac-Zoller
• Mølmer-Sørensen
• Fast Impulsive Gates

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Universal Quantum Logic Gates with Trapped
Ions
Cirac and Zoller, Phys. Rev. Lett. 74, 4091
(1995)
n0
Step 1 Laser cool collective motion to rest
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Universal Quantum Logic Gates with Trapped
Ions
Cirac and Zoller, Phys. Rev. Lett. 74, 4091
(1995)
j
k
laser
Step 2 Map jth qubit to collective motion
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Universal Quantum Logic Gates with Trapped
Ions
Cirac and Zoller, Phys. Rev. Lett. 74, 4091
(1995)
j
k
laser
Step 3 Flip kth qubit depending upon motion
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Universal Quantum Logic Gates with Trapped
Ions
Cirac and Zoller, Phys. Rev. Lett. 74, 4091
(1995)
j
k
n0
laser
Step 4 Remap collective motion to jth qubit
(reverse of Step 1)
Net result ??j ??j ??k ? ??j ??k
??j??k
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Demonstrations of Cirac-Zoller CNOT Gate

• CNOT between motion and spin (1 ion) F85
• C.M., et. al., Phys. Rev. Lett. 75, 4714
  (1995)

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During the gate (at some point), the state of
an ion qubit and motional bus state is
? a??0?m b ??1?m
Decoherence Kills the Cat
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Direct coupling between ??? and ??? with
bichromatic excitation ?
???
e
??? eif???
?2
uniform illumination
???
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Bichromatic coupling to sidebands
Mølmer/Sørensen Milburn/Schneider/James (1999)
???
n
e
n1
???, ???
n
n-1
uniform illumination
???
n
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Mølmer/Sørensen 2-ion entangling quantum gate
a super p/2-pulse
n1
n
???
n-1
n
???
n
???
n1
n
???
n-1

• Big improvement
• no focussing required
• no n0 cooling required
• less sensitive to heating

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Can scalable to arbitrary N!
e.g., 6 ions

• Coupling H g Jx2
• flips all pairs of spins
• ? Entangling rate ? N-1/2

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Four-qubit quantum logic gate
????? ? ????? eif?????
Sackett, et al., Nature 404, 256 (2000)
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Same idea in a different basis
N1 ion Force F0???? (spin-dependent force)
p
x
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Strong Field Impulsive Gates
strong coupling WRabi gtgt w and WRabit 1

• off-resonant laser pulse differential AC Stark
  shift
• provides qubit-state-dependent impulse

0,0
1,-1
2P1/2
1,1
e.g. 111Cd
D
1,0
s
??
2S1/2
0,0
14.5 GHz
1,1
1,-1
1,0
??
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r
? ?
? ?




d
d
dipole engineering Udd m1m2/r3 (ed)2/r3
d(t)
?sub ms
t
quantum phase gate
??? ? ??? ???
??? ? eik-if/2 ??? ???
k linear shift f nonlinear shift 2Uddt/h
??? ? e-ik-if/2 ??? ???
??? ? ??? eif ???
Cirac Zoller (2000)
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(b) resonant ultrafast kicks
Poyatos, Cirac, Blatt Zoller, PRA 54, 1532
(1996) Garcia-Ripoll, Zoller, Cirac, PRL 91,
157901 (2003)
two sequential p-pulses
e?
e?
p-pulse up
p-pulse down
??
??
??
??
spin-dependent impulse
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The trajectory of a normal motional mode of two
ions in phase space under the influence of four
photon kicks. Gray curve free evolution. Black
curve four impulses kick the trajectory in phase
space, with an ultimate return to the free
trajectory after 1.08 revolutions.
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Fast version of sz phase gate does not require
Lamb-Dicke regime!
2P3/2
1/(15 fsec) FS splitting
e?
te ? 3nsec
2P1/2
e.g. 111Cd
l226.5 nm 10 psec
s
no kick
2S1/2
0,0
1,1
1,-1
1,0
??
??
require tFS ltlt tpulse ltlt te
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• Summary
• Trapped Ions satisfy all DiVincenzo
  requirements
• for quantum computing
• 1. identifiable qubits
• 2. efficient initialization
• 3. efficient measurement
• 4. universal gates
• 5. small decoherence

SO WHATS THE PROBLEM?!
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ENIAC (1946)
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Next Ion Traps and how to scale them!