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