Quantum state manipulationof trapped ions
D. J. Wineland, NIST, Boulder, Colorado
Time magazineArticle about D-Wavequantum computerFebruary 17, 2014
Summary: ion qubits Spectroscopy & atomic clocks quantum limited measurements & quantum information
elements of quantum computing quantum simulation
Mostly NIST examples, but many people & many groups worldwide
199Hg+1 mm
“trap” electrodes
= 282 nm
Mercury ion “qubit”, 1981 →
|2S1/2 |0
|2D5/2 |1 ( 0.1 s)
superpositions |0 + |1
ultraviolet light
1 mm
0 +1
|1
|0
Qubit measurement
2P1/2 ( 2 ns)
1 mm
2P1/2
194 nm
Hg+
photomultiplier
0 +1 0
|1
|0
1 mm
2P1/2
194 nm
Hg+
photomultiplier
|1
|0
0 +1 1
trapping first-order Doppler shift 0 laser cooling time dilation small trapping in high vacuum at 4 K small environmental perturbations (collisions, black body shifts, etc.)
Single 199Hg+ ions for (optical) clocks:J. C. Bergquist et al., (NIST)1981
first clock with systematic uncertainly (7x10-17) below Cesium- W. H. Oskay et al., Phys. Rev. Lett. 97, 020801 (2006)
Jim Bergquist2S1/2
2D5/2
2P1/2
Hg+
trapping first-order Doppler shift 0 laser cooling time dilation small trapping in high vacuum at 4 K environmental perturbations (collisions, black body shifts, etc.) small
Jim Bergquist
first clock with systematic uncertainly (7x10-17) below Cesium- W. H. Oskay et al., Phys. Rev. Lett. 97, 020801 (2006)
2S1/2
2D5/2
2P1/2
Hg+
Single 199Hg+ ions for (optical) clocks:J. C. Bergquist et al., (NIST)1981
Plus several other ion species:88Sr+, 171Yb+, 27Al+, 40Ca+, 115In+
review: P. Gill, Phil. Trans. R. Soc. A 369, 4109 (2011)
229Th3+
(PTB, UCLAKuzmich group)
199Hg+1 mm
2S1/2 = |0
2D5/2 = |1
2S1/2
2D5/2
…
m=0
m=2m=1
…
m=0
m=2m=1
motion quantumstates
fine-scale energy structure:
Transition frequency 1 x 1015 Hz m = 1 transition
Frequency 106 – 107 Hz
P
rob
. (S
1/2)
J. C. Bergquist, W. M. Itano, D. J. Wineland, Phys. Rev. A36, 428 (1987).
2S1/2
2D5/2
2P1/2
Hg+ 282 nm
alternatelyapplySingle-ion spectroscopy:
2S1/2
2D5/2
…
m=0
m=2m=1
…
m=0
m=2m=1
m = 0
P
rob
. (S
1/2)
J. C. Bergquist, W. M. Itano, D. J. Wineland, Phys. Rev. A36, 428 (1987).
2S1/2
2D5/2
…
m=0
m=2m=1
…
m=0
m=2m=1
m = -1
2S1/2
2D5/2
…
m=0
m=2m=1
…
m=0
m=2m=1
m = +1
2S1/2
2D5/2
2P1/2
Hg+ 282 nm
alternatelyapply
P
rob
. (S
1/2)
F. Diedrich et al., PRL 62, 403 (1989)
2S1/2
2D5/2
…
m=0
m=2m=1
…
m=0
m=2m=1
m = -1m = 0
2S1/2
2D5/2
…
m=0
m=2m=1
…
m=0
m=2m=1
m = -1m = 0
2S1/2
2D5/2
…
m=0
m=2m=1
…
m=0
m=2m=1
m = -1
Ground-state cooling (put atom in m=0 motion state)
INTERNAL STATE “SPIN” QUBIT
MOTION “DATA BUS”(e.g., center-of-mass mode)
Motion qubit states•
• •
•
|m = 3|m = 2|m = 1|m = 0
Atomic ion quantum computation:J. I. Cirac, P. Zoller, Phys. Rev. Lett. 74, 4091 (1995)
(emerged from 1994 ICAP, Boulder, CO)
2. SPIN MOTION MAP3. SPIN MOTION GATE
Ignacio Cirac Peter Zoller
|
|
“m” formotion
• •
• •
1. START MOTION IN GROUND STATE
SPIN MOTION MAP
“ - pulse”●
●●
●
●●
quantized motion levels
m = 0
m = 3
m = 1m = 2
m = 4
m = 0
m = 3
m = 1m = 2
m = 4
|1
|0
(|0 + |1) |m=0 |0 (|m=0 + |m=1)
initial state transfer information onto motion
aux m=1
m=0
1 m=1
m=0
m=1
m=0
SPIN-MOTION GATE:
(Chris Monroe et al. PRL, ’95)
|0
Atomic ion experimental groupspursuing QIP:
MITNISTNorthwesternNPLOsakaOxfordParis (Université Paris)Pretoria, S. AfricaPTBSaarlandSandia National LabSiegenSimon FraserSingaporeSK Telecom, S. KoreaSussexSydney U. Washington Weizmann Institute
AarhusAmherst The CitadelTsinghua (Bejing)U.C. BerkeleyU.C.L.A. DukeETH (Zürich)FreiburgGarching (MPQ)Georgia Tech GriffithsHannoverInnsbruck JQI (U. Maryland)Lincoln LabsImperial (London)Mainz
+ many other platforms:neutral atoms, Josephson junctions,
quantum dots, NV centers in diamond,single photons, …
● small electrodes: use lithographic techniques● move ions in multi-zone arrays for scaling
1 mm
Jason Amini et al.(NIST)
microfab at: GTRI, Sandia, NIST, Berkeley, Innsbruck, Mainz, ….
Scale up qubit numbers?
Optically entangle remote ions (Monroe et al.)
Joint qubit states
More robust entangling operations & logic gates: use state-dependent optical dipole forces
e.g., laser beamstanding waves
Early proposals:Milburn, Schneider, James (1999)Sørensen & Mølmer (1999, 2000)Solano, de Matos Filho, Zagury (1999)
| |0, | |1
Joint qubit states
Joint qubit states
Joint qubit states
Joint qubit states
E1E2
𝑒−𝑖 ∆𝐸𝑡
ℏ
𝑒−𝑖 ∆𝐸𝑡
ℏ
E1E2
AC Versions: moving standing wave excites motion near mode frequency ● D. Leibfried, et al, Nature 422, 412 (2003)●●● C. J. Balance et al., (Oxford group), arXiv:1406.5473
≡
error per gate 0.0011(7)world’s record!
e..g.,
simulates spin-spin interaction
Center-of-mass)mode
tilt mode
transverse mode spectrum (9 ions)
( force > COM)
ji
jz
izjiJH ˆˆ,
ji
JJ ji
0
, ~vary by varying detuning = 0 - ~3
i
iy
jz
iz
jiji BJH )()()(, ˆˆˆ
add magnetic field:
Transverse Ising model
Porras and Cirac, PRL 92, 207901 (2004)Porras and Cirac, PRL 96, 250501 (2006)Deng, Porras, Cirac, PRA 7782, 063407 (2005) Taylor and Calarco, PRA , 062331 (2008)Johanning et al., J. Phys. B 42, 154009 (2009)Schneider, Porras, Schätz, Rep. Prog. Phys. 75, 024401(2012)● ● ● ●
Exps: Shätz et al., Freiburg Monroe et al., U. Maryland Blatt et al., Innsbruck Bollinger et al., NIST
(Ji,j > 0, anti-ferromagnetic)
Simulation:
for force COM
ji
jz
izJH ˆˆ GHZ states
“movingstandingwave” state-dependentforces
Chris Monroe
MarylandP. Richerme et al., Nature 511, 198 (2014)
InnsbruckP. Jurcevi et al., Nature 511, 202 (2014)
Rainer Blatt Christian Roos
Entanglement propagation
800700
transverse mode spectrum (modes out of plane)
kHz kHz
COMpotato chip
tilt
J. Britton et. al., Nature 484, 489 (2012); B. Sawyer et al., PRL 108, 213003 (2012); PRA 89, 033408 (2014)
N 200
N > 100 spins “self assembled” triangular lattice
d
2-D array (Penning trap)Simulation in Wigner crystal
top view
John Bollinger, + J. Bohnet, J. Britton, B. Sawyer
Benchmarked Ising interactions with mean field theory
To do: implement new trap & laser beams to increase Ji,j
relative to spontaneous emission
control electronicsbelow surface trap
VIAS
Laser beams in plane with ions
Chiaverini and Lybarger, PRA 77, 022324 (2008)Schmied, Wesenberg, Leibfried, PRL 102, 233002 (2009)Schmied, Wesenberg, Leibfried, New J. Phys. 13 115011 (2011)
Engineered geometry for simulationsA. Wilson, D. Leibfried et al.
Building block: HI = ћgxx, g/2 = 450 Hzions in separated wells (d = 30 m)(A. Wilson et al., Nature 512, 57 (2014).
double well
Didi Leibfried
AndrewWilson
Ion heating: try to reduce with surface science techniques:collaboration with D. Hite, K. McKay, D. Pappas (NIST, Boulder)
Ar+ beam cleaning
side view,surface-electrodetrap
D. A. Hite et al., PRL 109, 103001 (2012) (Ar+ beam sputtering)
x 100 heating reduction
N. Daniilidis et al., (Häffner group) PRB 89, 245435 (2014): similar gain
Cryo cooling helps too: L. Deslauriers, S. Olmschenk, D. Stick, W. K. Hensinger,J. Sterk, and C. Monroe, Phys. Rev. Lett. 97, 103007(2006). J. Labaziewicz, Y. Ge, D. R. Leibrandt, S. X. Wang, R.Shewmon, and I. L. Chuang, Phys. Rev. Lett. 101, 180602(2008).J. Chiaverini and J. M. Sage, Phys. Rev. A 89, 012318 (2014).……
Review:M. Brownnutt, M. Kumph, P. Rabl, and R. Blatt, arXiv: 1409.6572
Recipe:- Hydrogen loading of fiber (~ 100 atm, ~ 1 week)- “cure” with UV (transmitted beam)
Input
Output - 98% overlap with Gaussian TEM00 mode
Output
Better laser beam control: UV Fibers? better position stability improve beam shape
Preliminary: sz-sz phase gatewith fibers: F > 0.995
Y. Colombe, D. H. Slichter, A. C. Wilson et al. Optics Express 22, 19783 (2014)
Hollow core crystal fibers: F. Gebert, M. H. Frosz, T. Weiss, Y. Wan, A. Ermolov, N. Y. Joly, P. O. Schmidt, and P. St. J. Russell, Opt. Express, 22, 15388-15396 (2014).
10 mm gold on AlN substrate
25Mg+ ions trapped30 mm from surface
U. Warring et al., PRA 87, 013437 (2013); PRL 110, 173002 (2013)
C. Ospelkaus et al., Nature 476, 181 (2011).
D. P. L. Aude et al., Appl. Phys. B 114, 3 (2014) (Oxford)
current lead for -wave hyperfine transitions
Get rid of lasers?
10 mm gold on AlN substrate
currents for sideband transitions
F = 0.76(3)
U. Warring et al., PRA 87, 013437 (2013); PRL 110, 173002 (2013)C. Ospelkaus et al., Nature 476, 181 (2011).
Make B(t) =0, maximize B-field gradient state-dependent magnetic forces
10 mm gold on AlN substrate
currents for sideband transitions
F = 0.76(3)
U. Warring et al., PRA 87, 013437 (2013); PRL 110, 173002 (2013)C. Ospelkaus et al., Nature 476, 181 (2011).
Make B(t) =0, maximize B-field gradientPotential benefits: better control with RF/microwaves “all electronic” integrated control no spontaneous emission ground state cooling not necessary laser overhead vastly reduced
10 mm gold on AlN substrate
currents for sideband transitions
Make B(t) =0, maximize B-field gradient
F = 0.76(3)
U. Warring et al., PRA 87, 013437 (2013); PRL 110, 173002 (2013)C. Ospelkaus et al., Nature 476, 181 (2011).
New apparatus (David Allcock, Daniel Slichter)- better optical access- shorter leads (lower RF and microwave loss)- separate loading zone- Ar+ cleaning- ability to cool (LN2)- better thermal & electrical conductivity at 80K- new power amps
Al+ “quantum-logic clock” (T. Rosenband, D. Lebrandt et al.)
Coulombinteraction
2P3/2
2S1/2
(F=2, mF = -2)
(F=3, mF = -3)
25Mg+
Al+
1S0
3P0
1P1
= 167 nm
uncertainty = 8.0 x 10-18 (time dilation shift)
Till Rosenband
|Al + |Al motion superposition |Mg + |Mg
David Leibrandt
trap at~ 300 K
= 280 nm
C. W. Chou et al., PRL 104, 070802 (2010)
Jun Ye’s group (JILA), Sr neutral atoms in optical lattice: f/f0(systematic) = 6.4 x 10-18
(B. J. Bloom et al., Nature 506, 71 (2014))T 30 mK
PTB, Braunschweig, Germany
f/f0(systematic) = 3.3 x 10-18
(unpublished)weak (octupole) transition, laser Stark shifts, …
H. Katori group (Riken) Sr neutral atoms in optical lattice
f/f0(systematic) = 7.2 x 10-18 (arXiv:1405.4071)
Moving target!
2.1
WE DO KNOW HOW IT WORKS…and why it doesn’t work
FACTORING MACHINEprobably decades away
QUANTUM SIMULATIONmaybe within next decade?
Shlomi Kotler, Dustin Hite, Katie McCormick ,Susanna Todaro, Leif Waldner, Yiheng Lin, Daniel Slichter, James Chou, David Allcock, Didi Leibfried, Jwo-Sy Chen, Sam Brewer, Kyle McKay
David Hume Ting Rei Tan
Jim Bergquist, John Bollinger, Joe Britton, Justin Bonet, Ryan Bowler, John Gaebler, Andrew Wilson, Dave Wineland, David Leibrandt, Peter Burns, Raghu Srinivas, Shon Cook, Robert Jordens
Not pictured: Brian Sawyer, Till Rosenband, Wayne Itano, Dave Pappas, Bob Drullinger
NIST “IONS” June 2014