clean, fast and scalable quantum logic with trapped...
TRANSCRIPT
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