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