trapped ions: condensed matter from the bottom up

Trapped Ions: Condensed Matter

ChrisMonroe

From The Bottom Up

University of Maryland

Trapped Ion Spin Hamiltonian Engineering

Ground states and Adiabatic Protocols

Dynamics

Many-Body SpectroscopyPropagation of Excitations: Lieb-RobinsonPrethermalizationMany-Body Localization

Spin-1

Extending to N~100 spins and beyond

Trapped Atomic Ions: Spin Models

Porras and Cirac, PRL 92, 207901 (2004)

Deng, Porras, Cirac, PRA 72, 063407 (2005)

Taylor and Calarco, PRA 78, 062331 (2008)

A. Friedenauer et al., Nat. Phys. 4, 757 (2008)

K. Kim et al., PRL 102, 250502 (2009)

K. Kim et al., Nature 465, 590 (2010)

E. Edwards et al., PRB 82, 060412 (2010)

J. Barreiro et al., Nature 470 , 486-491 (2011)

R. Islam et al., Nature Comm. 2, 377 (2011)

B. Lanyon et al., Science 334, 57 (2011)

J. Britton et al., Nature 484, 489 (2012)

A. Khromova et al., PRL 108, 220502 (2012)

R. Islam et al., Science 340, 583 (2013)

P. Richerme et al., PRL 111, 100506 (2013)

P. Richerme et al., PRA 88, 012334 (2013)

P. Richerme et. al., Nature 511, 198 (2014)

P. Jurcevic et al., Nature 511, 202 (2014)

C. Senko et. al., Science 345, 430 (2014)

P. Jurcevic et al., ArXiv 1505.02066 (2015)

J. Smith et al., ArXiv 1508.07026 (2015)

2S1/2(600 Hz/G @ 1 G)

wHF/2p = 12 642 812 118 + 311B2 Hz

| = |0,0

| = |1,0

171Yb+ hyperfine spin

2S1/2

2P1/2

369 nm

2.1 GHz

g/2p = 20 MHz

|

|

171Yb+ spin detection

(600 Hz/G @ 1 G)

wHF/2p = 12 642 812 118 + 311B2 Hz

# photons collected in 500 ms

0 5 10 15 20 250

1

Pro

babilit

y

|z

2S1/2

2P1/2

369 nm

g/2p = 20 MHz

|

|

2.1 GHz

171Yb+ spin detection

>99% detectionefficiency

# photons collected in 500 ms

0 5 10 15 20 250

1

Pro

babilit

y

|z

(600 Hz/G @ 1 G)

wHF/2p = 12 642 812 118 + 311B2 Hz

(600 Hz/G @ 1 G)

wHF/2p = 12 642 812 118 + 311B2 Hz2S1/2

2P1/2

|

|

171Yb+ spin manipulation

D = 33 THz

355 nm (10 psec @ 100 MHz)

2P3/2

g/2p = 20 MHz

~5 mm

d

r

Entangling Trapped Ion Spins

Cirac and Zoller (1995)

Mølmer & Sørensen (1999)

Solano, de Matos Filho, Zagury (1999)

Milburn, Schneider, James (2000)

d ~ 10 nmed ~ 500 Debye

“dipole-dipole coupling”

for full entanglement

Gates within a single crystal

Dk

355nm pulsed laser

Diffractive optic (х10)

Harris Corp32channel AOMFocusing optics

10 focused beams

2μm pixels

T. Choi, et al., PRL 112, 19502 (2014)

S. Debnath, et al., in preparation (2015)

F=0.983(4)(excluding SPAM errors)

Ising (XX) gate [1,2]

T. Choi, et al., PRL 112, 19502 (2014)




T. Choi, et al., PRL 112, 19502 (2014)


Many ions: phonon modes

transverse modes

frequency

axial modes

N ions in a line transverse trap frequency wx = high as you can go

axial trap frequency

gate speedslows with N

laser

m

Ramanbeatnotes:

wHF m

uppersidebands

frequencywHF+m

carrierlowersidebands

wHF -m

Resonant spin-dependent force

wHF (Df=p/2)wHF

normal mode eigenvectorsion i mode m

Control of interaction range

Theory

Pow

er L

aw E

xponen

t a

w

wm

D

- COM

uppersidebands

frequencywHF

carrier

lowersidebands

Dw

m-wCOM

tunelaserhere

tunelaserhere



Dynamics


Spin-1


Equilibrium: Adiabatic Quantum Simulation

Initialization:spins along y

Detection:

measure spins along x

Time (<10 msec)

from S. Lloyd, Science 319, 1209 (2008)

Antiferromagnetic Néel order of N=10 spins

All in state 2600 runs, a=1.12

AFM ground state order 222 events

441 events out of 2600 = 17%Prob of any state at random =2 x (1/210) = 0.2%

219 events

R. Islam et al., Science

340, 583 (2013)

All in state

First Excited States

(Pop. ~2% each)

Second Excited States

(Pop. ~1% each)

Distribution of all 210 = 1024 states

Pro

bab

ility

0 341 682 1023

NominalAFMstate

B << J0

0101010101 1010101010

Pro

bab

ility

0.10

0.08

0.06

0.04

0.02

Initialy-polarized

state

B >> J0


340, 583 (2013)

0 341 682 1023

Distribution of states ordered by energy (N=10)

Energy/J0

a = 1.12a = 0.86


340, 583 (2013)

AFM order of N=14 spins (16,384 configurations)



Dynamics


Spin-1


w1

Coherent Imaging Spectroscopy (N=5 spins)


w1

w2


multiple frequencies


w1

w2

w3


multiple frequencies


theory



Initial statedistribution

Final statedistr.



Ground state population

Particular excited state population

Probe frequency (kHz)

binary index

binary index

(nom. initial state)

excitedstates

Rescaled population

B0 = 1.4 kHz

B0 = 0.4 kHz

Coherent Imaging Spectroscopy: Critical Gap


(N=8 spins)

aji

JJ ji

-= 0

,

“Global Quench”(a) Prepare (↓x+↑x)

N “kT = ”(b) Turn on interactions(c) Measure correlations

M. Cheneau, et al., Nature 481, 484 (2012)

P. Hauke, et al., PRL 111, 207202 (2013)

M. Knap, et al., PRL 111, 147205 (2013)

Z.-X. Gong, et al., PRL 113, 030602 (2014)

Dynamics: quantum quenchE.H. Lieb and D.W. Robinson, “The finite group velocity of quantum spin systems,”

Commun. Math. Phys. 28, 251–257 (1972).

a=2.5N=41 N=41 N=41 a=1.5 a=0.5C20,20+j C20,20+jC20,20+j

ExperimentTheory



Long range “Light Cones” (Ising: N=11 spins)



Long range “Light Cones” (XY: N=25 spins)

a = 1.3

“Global Quench”(a) Prepare (↓z+↑z)

N

(b) Turn on interactions(c) Measure correlations in spacetime

Braunstein and Caves Phys. Rev. Lett. 72, 3439 (1994)

Hauke, Heyl, Tagliacozzo, Zoller, arXiv:1509.01739 (2015)

Quantum Fisher Information: characterizes system entanglement

is an entanglement witness operator

Thermalization/Localization

How can quantum systems thermalize? Eigenstate Thermalization Hypothesis (Rigol et al., Nature 2008)

How can quantum systems fail to thermalize?

Prethermalization

Ord

er

pa

ram

ete

r

XY Model with inhomogeneous couplings

Z. Gong and L.-M. Duan, NJP 15, 113051 (2013)

Step 2: Evolve under variable-range XY model

Step 1: Initialize with localized excitation

Step 3: Measure spinsafter time t

Prethermalization

a = 1.3

a = 0.55

B. Neyenhuis et al., in preparation (2015)

Track “center” of spin excitation


Short Range: a = 1.3 Long Range: a = 0.55

N=22 spins

initial state at t=0state measured at J0t = 36

a = 0.6


Thermalization/Localization

How can quantum systems thermalize? Eigenstate Thermalization Hypothesis (Rigol et al., Nature 2008)

How can quantum systems fail to thermalize?

Many-Body Localization • Ising Model with random disorder

A. Polkovnikov et al., Rev. Mod. Phys. 83, 863 (2011)

P. Hauke and M. Heyl, arXiv:1410.1491 (2014)

Exp: W. R. McGehee, et al., PRL 111, 145303 (2014)

Exp: M. Schreiber, et al., Science 349, 842 (2015)

wHF/2p = 12.6 GHz2S1/2

2P1/2

|

|

171Yb+ site-resolved field sz

D = 33 THz

355 nm

2P3/2

g/2p = 20 MHz

s+

s+

p

d = 10 MHz

Step 2: Quench to transverse Ising model with random disorder

Step 1: Initialize spins staggeredalong z (“kT=”)

Step 3: Measure each spin along zafter time t

Step 4: Repeat for many different disorder instances and strengths

Many Body Localization (N=10)

J. Smith et al., ArXiv

1508.07026 (2015)

(no disorder)


1508.07026 (2015)

No disorder


1508.07026 (2015)

Some disorder


1508.07026 (2015)

Hamming distance from initial state:

thermalized value

shorter-rangeinteraction

more localized!

N. Yao, et al., PRL 113, 243002 (2014)

P. Hauke & M. Heyl, ArXiv:1410.1491 (2015)

therm-alized

MBL

memory retention

P. HaukeM. Heyl(Innsbruck)


1508.07026 (2015)

Quantum Fisher Information: characterizes system entanglement

Braunstein and Caves Phys. Rev. Lett. 72, 3439 (1994)

Hauke, Heyl, Tagliacozzo, Zoller, arXiv:1509.01739 (2015)

MBL: expect logarithmic growth with time



Dynamics


Spin-1


Quantum simulations with Spin-½

2S1/2|z = |0,0

|z = |1,0|1,1

|1,-1

qubit

rsb+bsb on both transitions

rsb |0 |+

bsb |0 |-

Work in subspace: states

2S1/2|0

|1,0|-

qutrit

|+

1

I. Cohen and A. Retzker, PRL 112, 040503 (2014)

C. Senko, et al., Phys. Rev. X 5, 021026 (2015)



Dynamics


Spin-1


Scaling Up: 4K to get lower pressure

4 K Shield

40 K Shield

300 K

To camera

Ion trap

P. RichermeP. Hess

50-100 spins SOON

Quantum Computation in Small Quantum Registers• Linear ion chain with 20-100 ions (Elementary Logic Unit, or ELU)

• Arbitrary quantum logic operation among the qubits in the chain

Interconnect of Multiple Such Registers via Photonic Channel• Reconfigurable interconnect using optical crossconnect switches

• Efficient optical interface for remote entanglement generation

100 qubits / module

1000 modules

100,000 qubit quantum computer?

Modular Scaling to 106 qubits?

Single Module

Single Module ~100 spins on 2 × 19” Racks

Superconducting Circuits

Leading Quantum Computer Hardware Candidates

CHALLENGES• short (10-6 sec) memory• 0.05K cryogenics• all qubits different • not reconfigurable

Superconducting qubit: right or left current

FEATURES & STATE-OF-ART• connected with wires• fast gates• 5-10 qubits demonstrated• printable circuits and VLSI

Atomic qubits connected through laser forces on motion or photons

individual atoms

lasersphoton

Trapped Atomic Ions

Others: still exploratory

FEATURES & STATE-OF-ART• very long (>>1 sec) memory• 5-20 qubits demonstrated• atomic qubits all identical• connections reconfigurable

CHALLENGES• lasers & optics• high vacuum • 4K cryogenics• engineering needed

• NV-Diamond• Semiconductor quantum dots• Atoms in optical lattices

Investments:IARPA LockheedGTRI UK Gov’tSandia

LARGEInvestments:

Google/UCSB IBMLincoln Labs Intel/Delft

Univ. ofMaryland

Boulder

http://www.lps.umd.edu/index.html

Grad StudentsDavid CamposClay CrockerShantanu DebnathCaroline FiggattDavid Hucul (UCLA)Volkan InlekKevn LandsmanAaron LeeKale JohnsonHarvey KaplanLexi ParsagianChris RickerdCrystal Senko ( Harvard)Ksenia SosnovaJake SmithKen Wright

UndergradsEric BirklebawKate CollinsMicah Hernandez

AROLPS/NSA

PostdocsPaul HessMarty LichtmanNorbert LinkeBrian Neyenhuis ( Lockheed)Guido PaganoPhil Richerme ( Indiana)Grahame Vittorini ( Honeywell)Jiehang Zhang

Res. ScientistJonathan Mizrahi

T1Q1 Trapped Ion Quantum Informationwww.iontrap.umd.edu

CollaboratorsLuming Duan (Michigan)Philip Hauke (Innsbruck)David Huse (Princeton)Alexey Gorshkov (JQI/NIST)Alex Retzker (Hebrew U)

trapped ions: condensed matter from the bottom up

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