Clean, fast and scalable quantum logic with trapped ions

Boris BlinovUniversity of Michigan

Simons Conference on Quantum and Reversible Computation

29 May 2003

Michigan Ion Trap group

PI: Chris Monroe

Faculty: Jens Zorn

Postdocs: Boris Blinov, Paul Haljan, Winfried Hensinger, Chitra Rangan

Graduate students: Kathy-Anne Brickman, Louis Deslauriers, Patty Lee, Martin Madsen, David Moehring, and Daniel Stick

Undergraduate students: David Hucul, Rudy Kohn Jr., Russell Miller

1/18

Trapping ions: static E-field???

→ →∇·E = 0

2/18

RFV

photon-counting camera (or PMT)

e-

atomic beam

Pote

ntia

l

Position Position

DC

DC

RF

RF (Paul) ion trap

resonant light

3/18

Practical trap designs

rfrf

dc

dc dc

dc0.2 mm

ions

3-layer lithographic linear trap• RF nodal line (ion string)

• static voltage compensation electrodes

• 200 micron size (strong confinement)

• 3-layer geometry allows multiplexing, T-junctions, etc.

rfdc

0.4 mm

ions

Ring-and-fork quadrupole trap• easy to build and operate

• good optical access

• trapping few ions near RF null4/18

Trapped ions - as seen on TV

Two Cd+ ions in a 3 MHz trap (~2 µm separation)

Three Cd+ ions in a 3 MHz trap (~2 µm separation)

Multiple-ion helical crystal (Cd+

and possible impurity). Weak trap (~0.5 MHz, 6µm separation)

5/18

Trapped ions as qubits• Strong confinement in an RF trap (1-10 MHz) - qubits well localized• Long-lived atomic levels form extremely stable qubit (“God’s qubit”!)• Efficient qubit state detection by fast cycling transitions• Initial state preparation by optical pumping with near-perfect efficiency• Qubit rotations using microwaves or lasers• Quantum logic gates via strong Coulomb interaction between ions• Coupling to “flying qubits” (photons) using cavity QED• Sympathetic cooling to reduce decoherence

S1/214.5 GHz

P3/2

P1/2

Cycling transition(cooling/detection)

σ+

214.5 nm

226.5 nm

|1,1⟩

74 THz

σ+

Raman beams

π

111Cd+

|1,-1⟩ |1,0⟩

|0,0⟩

|2,2⟩|1,1⟩

6/18

Single qubit rotations via stimulated Raman transitions

0.0 0.5 1.0 1.5 2.0 2.50

5

10

15

Raman pulse time (ms)

Fluo

resc

ence

cou

nts

Solid state Raman beam source at 229 nm to experiment

7/18

Melles-GriotNd:YAG x 2

400 mW at 458nm

229 nm40 mW7.27 GHz

E-O PMx 2

BBOSideband-shaping

(e.g. Mach-Zehnder)

Sympathetic cooling of Cd+ isotopes

Two different Cd+ isotopes loaded in the trap.

One ion is constantly (Doppler) cooled, while the other may be heated. Extra heat from the latter is absorbed by the cooling ion.

112Cd+ ion 114Cd+ ion30%

20%

-5 -4 -3 -2 -1 0

111113110

112

114

116

108 10610%

0%

I=1/2(good qubits)

abun

danc

e

isotope shift of D2 line (GHz)

8/18

Entanglement of trapped ions

• Coulomb-force based entanglement:

- Cirac-Zoller CNOT gate (1995) - spin-state coupled to phonons of ion crystal vibrations

- MØlmer-SØrensen gate (1999) - spin-state coupled to phonons of ion crystal vibrations, but motional states never populated

- Cirac-Zoller “push” gate (2000) - phase gate through direct Coulomb repulsion of neighboring ions

• Photon-mediated entanglement:

- trapped ion-cavity QED merger – spin-state mapped onto field state inside the fight-finesse optical cavity

9/18

Cirac-Zoller CNOT gate

1. Ion string is prepared in the ground state of motion (n=0)2. Control ion’s spin state is mapped onto quantized motional state of the ion string3. Target ion’s spin is flipped conditional on the motional state of the ion string

|↓⟩

|↑⟩

control target

4. Motion of the ion string is extinguished by applying pulse #2 with negative phase to the control ion

Cirac and Zoller, Phys. Rev. Lett. 74, 4091 (1995)

10/18

Phase “push” gate • Ions prepared in Lamb-Dicke limit• Spin-dependent dipole force (edge of a Gaussian beam waist or a standing wave) is applied to both ions• The |↑⟩ part of ion is displaced; extra phase is acquired if both ions were in state |↑⟩• Ions brought back to rest

P3/2

control target

|↓⟩|↑⟩

P1/2

S1/2

Cirac and Zoller, Nature 404, 579 (2000)

11/18

Scaling up?

• Original Cirac-Zoller gate:- size determined by number of ions in a single trap -can be scaled up by making larger trap

- but : ground-state cooling of motion is required -very hard for large ion crystals!

• MØlmer-SØrensen and “push” two-ion gates:- only work for a pair of ions- no ground-state cooling requirement- could be scaled by creating arrays of interconnected

traps, each containing one ion qubit

12/18

Large-scale ion trap quantum computer architectures

ion traps

“conventional” strong coupling

applying spin-dependentforce to entangle ion pairsconnecting multiple traps, ion shuttling

between storage regions and pairwiseentanglement areas

++

d d

++

r

D. Kielpinski, C. Monroe, D. Wineland, Nature 417, 709 (2002) Cirac and Zoller, Nature 404, 579 (2000)13/18

Speeding up?

• Gate speed:Phonon-mediated gates (CZ and MS gates):

- collective motion of ions used as data bus – gate speed must be much slower than ωTrap ~ 1 MHz

“Push” gate:- entanglement through direct Coulomb interaction (ions don’t even have to be in the same trap!), so can be fast

• Gate repetition rate:Multiplexed traps:

- depends on shuttling speed and distances - smaller traps beneficial!- need efficient cooling to quench motional heating

14/18

Microfabricated trap arrays

4 mm

• ~40 micron transverse size

• good control of ions’ positions with static voltage electrodes

• qubit ions stored in individual traps

• ions shuttled between traps using static electric fields

100 µm

40 µm

15/18

Pushing ions with a pulsed laser - experiment

214.5 nm2 mW

Single qubit rotation source:

Raman beams or microwaves

Nd:YAG Pulsed Laser

Te2Reference

ion trap

x 2 Feed

back

x 2

AmplifiedDiode Laser

x 2 x 2

1 J, 10 ns 1064 nm80 mJ, 6 ns

@ 266 nm

16/18

Detecting pushing of ions

• Detecting the ion fluorescence oscillations due to Doppler shiftsSecular Frequency

Pulse# of

pho

tons

de

tect

ed

Time

• Measuring (very large) AC Stark shifts caused by strong laser field

17/18

Conclusions and outlook

• Trapped ions hold a great promise for practical quantum computation

• Large arrays of ion traps provide suitable environment for qubitstorage and manipulation

• Micro-traps would allow faster quantum logic, as well as capability ofcoupling the ions to optical fields

• Novel methods of trapped-ion entanglement using strong pulsed laser force are studied to increase the gate speeds

18/18