Trapped Atomic Ions IIScaling the Ion TrapQuantum Computer
Christopher MonroeFOCUS Center & Department of PhysicsUniversity of Michigan
Universal Quantum Logic Gateswith Trapped Ions
Step 1 Laser cool collective motion to rest
Cirac and Zoller, Phys. Rev. Lett. 74, 4091 (1995)
n=0
Universal Quantum Logic Gateswith Trapped Ions
laser
j k
Step 2 Map jth qubit to collective motion
Cirac and Zoller, Phys. Rev. Lett. 74, 4091 (1995)
Universal Quantum Logic Gateswith Trapped Ions
laser
j k
Step 3 Flip kth qubit depending upon motion
Cirac and Zoller, Phys. Rev. Lett. 74, 4091 (1995)
Universal Quantum Logic Gateswith Trapped Ions
laser
j k
Step 4 Remap collective motion to jth qubit (reverse of Step 1)
Cirac and Zoller, Phys. Rev. Lett. 74, 4091 (1995)
Net result: [|j + |j] |k |j |k + |j|k
n=0
Four-qubit quantum logic gate
Sackett, et al., Nature 404, 256 (2000)
| | + ei|
= m + m
During the gate (at some point), the state of an ion qubit and motional bus state is:
Decoherence Kills the Cat
Anomalous heating in ion traps
Q. Turchette, et. al., Phys. Rev. A 61, 063418-8 (2000)L. Deslauriers et al., Phys. Rev. A 70, 043408 (2004)
Heating due tofluctuating patch potentials (?)
~ 1/d 4
)(4
2
ES
m
qn
d
0.04 0.1 0.2 0.3 0.610-2
10-1
100
101
102
SE() 10-12 (V/m)2/Hz
40Ca+
199Hg+111Cd+
137Ba+9Be+
1/d4 guide-to-eye
Electric Field Noise History in 3-6 MHz traps
est. thermal noise
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)
137Ba+ IBM-Almaden (2002)
40Ca+ Innsbruck (1999)
199Hg+ NIST (1989)9Be+ NIST (1995-)
111Cd+ Michigan (2003)
0.3 mm J. Bergquist, NIST
ion loading?ion lifetime?
Photoionization-loading of Cd+ into trap
Cd+ loading rate (sec-1)
laser center wavelength (nm)
Cd 1S0 1P1
transition
(a) Off-resonant 266nm 10Hz nsec YAG
(b) Resonant 229nm 80 MHz psec Ti:Saph (Pavg1 mW)
228.4 228.6 228.8 229.0 229.2 229.4
0
1
2
3
laserbandwidth
1S0
1P1
continuum
229nm
229nm
NeutralCd
+
E(r) ?
Ion Trap Tricks to “get around” E :
(1) Apply magnetic field along z; evB Lorentz force confines in xy planePENNING TRAP large capacity (1-108) ions rotate around z confinement limited by eB/mc
+
E(r)
NO! E quadrupole: E(r) = (x + y 2z)
z
~few 1000Be+ ions ina Penning Trap
J. Bollinger, NIST
QuantumHard-drive?
+
E(r) ?
Ion Trap Tricks to “get around” E :
(1) Apply magnetic field along z; evB Lorentz force confines in xy planePENNING TRAP large capacity (1-108) ions rotate around z confinement limited by eB/mc
+
E(r)
NO! E quadrupole: E(r) = (x + y 2z)
z
W. PaulH. Dehmelt
(2) Apply sinusoidal electric quadrupole fieldRF (PAUL) TRAP ions stationery (on average) strong confinement
sint
x + [2 cost]x = 0
Dynamics of a single ion in a rf trap
timepos
itio
n x
“secular” motionat frequency trap
“micromotion”at frequency
Mathieu Equation: x(t) bounded for <<
2 = eV0/md2
Vac
3D ion trap geometry
ring
endcap
endcap
d
rf
dc
0.3 mm
ions
Desirable properties for quantum computing:
simple crystal structure- anisotropic linear rf trap
tight confinement (high trap)
- high rf voltage- small electrodes
vs
Linear RF Ion Trap
rf gnd
rfgnd
V0cost
transverse confinement:2D rf ponderomotive potential
Linear RF Ion Trap axial confinement:static “endcaps”
+U
+U
+U
+U
+U
+U
+U
+U0
0
0
0
dc
rf
dc
dc
rf
dc
dc
rf
dc
dc
rf
dc
3-layer geometry:•allows 3D offset compensation•scalable to larger structures
dc
dc dc
dc
rf
dc
rf
dc
Cd+
Scale up?
• • • • •
frequencycom
axial modespectrum
3com
Flu
ores
cenc
e (a
rb)
Raman Detuning R (MHz)
-15 -10 -5 0 5 10 15
a b
c
d
a
bcd
2a
c-a
b-a 2b
,a+
c
b+ca+
b
2a c-a
b-a
2b,a
+c
b+c a+
b
carrier
4-ion axial mode spectrum
center-of-mass (a)
sym. breathing (b)
mode (c)
mode (d)
NIST-1999
multiplexed trap architecture
interconnected multi-zone structure subtraps decoupled
move ions with electrode potentials
qubit ions sympathetically cooled only a few normal modes to cool weak cooling in memory zone
individual optical addressingduring gates not required gates in tight trap fast
readout for error correctionin (shielded) subtrap no decoherence from fluorescence
D. Kielpinski, C. Monroe, and D. J. Wineland, Nature 417, 709 (2002).
Sympathetic Cooling
24Mg+ 9Be+
Cooling LightCooling with same species
Innsbruck group: Rohde, et al., J. Opt. B 3, S34 (2001)
40Ca+ 40Ca+
Cooling with different isotopesMichigan group: Blinov, et al.,
PRA 65, 040304 (2002) 114Cd+ 112Cd+
Cooling with different ion speciesNIST, Barrett et al.
PRA 68, 042302 (2003)
Approaches:
2 m
114Cd+ 112Cd+
114 laser beam on
112 laser beam on
100 m
(6-zone) alumina/gold trap (D. Wineland, et. al., NIST-Boulder)
200 mseparation zone
rf
rfdc
dc
view along axis:
1 mm
“Tee” junction(Michigan)
50 m
Microfabrication of Integral Trap structures(no assembly required)
• High aspect ratio• Planar
Si doped GaAs
AlGaAs
Ge:Au
~10 mm
~10 mm
GaAs Ion Trap Fabrication
~10 mm
~10 mm
100 m
(Michigan)
Si doped GaAs
AlGaAs
Ge:Au
~10 mm
~10 mm
100 m
GaAs Ion Trap Fabrication (Michigan)
Si doped GaAs
AlGaAs
Ge:Au
~10 mm
~10 mm
100 m
GaAs Ion Trap Fabrication (Michigan)
Dan StickMartin MadsenWinfried HensingerKeith Schwab (LPS/UMd)
6m
Progress…
• 2 m AlGaAs insulating gap: maximum voltage ~5V unable to load
• 4 m AlGaAs insulating gap: maximum voltage ~50 V (!) currently processing
Other concerns…• cantilever mechanical resonances
100 kHz
• RF dissipation
Pdiss V02C(RsC + tan) Rs = series resistance C = electrode capacitance = rf drive frequency tan= loss tangent of insulating gap
expect mW of dissipation for 50V trap operation
e
Q=CV
Rs
C
Using a photon as the data bus:Entangling atoms and photons
cavity-QEDENS-ParisCalTechMPQ-Garching…
no direct measurement of entanglement: not enough control of either atom or photon
optical fiber
trappedions
trappedions
Linking ideal quantum memory (trapped ion) with ideal quantum communication channel (photon)
1,11,01,-1
0,02S1/2
2P3/2F’=2
F’=1 2(50 MHz) 108/sec
Probabalistic entanglement between a single atom and single photon
1,11,01,-1
0,0
(m=0)
(m=1)
quantaxis
Given photon is emitted along quantization-axis:
| = || + || (postselected)
PBS
D1
D2
trappedion
collectionlens
polarization rotator
|H
|V
excitation beam
Schematic of Experiment
microwaves
measurement beam
1 m
Measured Correlations
atom qubit photon
qubit
P(|H) = 97%P(|H) = 3%P(|V) = 6% P(|V) = 94%
Repeat, but rotate both qubits by = /2 (relative phase ) before measurement.
• if initially in pure state
| = ||V + ||H
then R| = (||V + ||H)cos( + (||H + ||V)sin(
correlation
zero correlation
||V (p=50%)
||H (p=50%)
||V + ||H (p=50%)
||H + ||V (p=50%)
•if initially in 50-50 mixed state
| =
then R| =
Rotating each qubitBy /2 beforemeasurement:
|
|
/2
/2HV
correlations inrotated basis
P(|H) = 89%P(|H) = 11%P(|V) = 6% P(|V) = 94%
First direct observation of entanglementbetween a single atom and single photon.
B. B. Blinov, et. al., Nature 428, 153 (2004)
Entanglement Fidelity
F = ideal||ideal
> 87%
Also: Bell Ineq. violation – D. Moehring et al., Phys. Rev. Lett. 93, 090410 (2004)
Can use this technique to seed remote ion-ion entanglement…
Ann ArborColumbus
VV
1 2
D D
coincidence photon
detection
upon coincidence photon detection
Can use this technique to seed remote ion-ion entanglement…
… and form the basis for scalable QC
L.-M. Duan, et. al., Quantum Inf. Comp., 4, 165 (2004) quant-ph/0401020
VV
1 2
D D
coincidence photon
detection
upon coincidence photon detection
Ann Arbor
Columbus
DDD
D DD
quantum repeater; distributed quantum computer
two ions in separate traps imaged on the same camera
Quantum ComputerPhysical Implementations
1. Individual atoms and photonsa. ion trapsb. atoms in optical latticesc. cavity-QED
2. Superconductorsa. Cooper-pair boxes (charge qubits)b. rf-SQUIDS (flux qubits)
3. Semiconductorsa. quantum dotsb. phosphorus in silicon
4. Other condensed-mattera. electrons floating on liquid heliumb. single phosphorus atoms in silicon
scales
works