quantum simulations: from ground to excited states

Quantum Simulations: From Ground to Excited States

Phil RichermeMonroe Group

University of Maryland and NIST

iQsim WorkshopBrighton, UK

December 18, 2013

?AFM

AFM AFM

AFM AFM?

AFM

From Ground to Excited States

Current System: Fully-connected Ising model with d20 spins, for study of:• Ground-state phase diagrams [1]• Quantum phase transitions [2]• Studies of frustration [3,4]

[1] E. E. Edwards et. al., PRB 82, 060412 (2010)[2] R. Islam et. al., Nat. Comm. 2, 377 (2011)[3] K. Kim et. al., Nature 465, 590 (2010)

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


Current System: Fully-connected Ising model with d20 spins, for study of:• Ground-state phase diagrams [1]• Quantum phase transitions [2]• Studies of frustration [3,4]• Quantum fluctuations in a classical system [5]• Many-body Hamiltonian spectroscopy• Correlation propagation after global quenches

This Talk

[4] R. Islam et. al., Science 340, 583 (2013)[5] P. Richerme et. al., PRL 111, 100506 (2013)



Current System: Fully-connected Ising model with d20 spins, for study of:• Ground-state phase diagrams [1]• Quantum phase transitions [2]• Studies of frustration [3,4]• Quantum fluctuations in a classical system [5]• Many-body Hamiltonian spectroscopy• Correlation propagation after global quenches• Scaling up the number of interacting spins• Non-equilibrium phase transitions• Studies of dynamics and thermalization

Future Work


[4] R. Islam et. al., Science 340, 583 (2013)[5] P. Richerme et. al., PRL 111, 100506 (2013)

200m

2S1/2

nHF = 12 642 812 118 Hz + 311B2 Hz/G2

|z = |0,0

|z = |1,0 |1,1|1,-1

171Yb+

2 m

2S1/2

2P1/2

370 nm

12.6 GHz|z

g/2p = 20 MHz

F=1

F=0

F=1

F=0

|z

2.1 GHz

HF

200m

2S1/2

nHF = 12 642 812 118 Hz + 311B2 Hz/G2

|z = |0,0

|z = |1,0 |1,1|1,-1

171Yb+

2 m

2.1 GHz

12.6 GHz2S1/2

2P1/2

370 nm

|z

g/2p = 20 MHz

F=0

F=1

F=0

|zF=1

HF

Generating Spin-Spin Couplings

+HF

Beatnote frequency

Axialmodes

HF

Transversemodes

Axialmodes

Transversemodes

Carrier

μμ

)()(, ˆˆ jx

ix

ji

jieff JH

+HF

||2)( 0

22

2,

jiJbb

mk

Jk k

kj

kijiji

12.6 GHz2S1/2

2P1/2

|z

|z

33 THz

HF

+HF

K. Mølmer and A. Sørensen, PRL 82, 1835 (1999)

+i

itB )(ˆ)(

Studying Frustrated Ground States

+ i

iyy

jx

ix

ji

jixeff tBJH )()()(, ˆ)(ˆˆ

Step 1: Initialize all spins along yx

y

Step 2: Turn on By and Jxi,j and adiabatically lower By

time

By

Jxi,j

ampl

itude

Step 3: Measure all spins along x

>0

AFM ground state order 222 events

Antiferromagnetic Néel order of N=10 spins

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

219 events

All in state

All in state

2600 runs, =1.12

Distribution of all 210 = 1024 states

Prob

abili

ty

0 341 682 1023

NominalAFMstate

B = 0

0101010101 1010101010

Prob

abili

ty

0.10

0.08

0.06

0.04

0.02

Initialparamagnetic

state

B >> J

Distribution of all 214 = 16383 states

Prob

abili

ty

0 341 682 1023

NominalAFMstate

B = 0

0101010101 1010101010

Prob

abili

ty

0.10

0.08

0.06

0.04

0.02

Initialparamagnetic

state

B >> J

Most prevalent state should always be the ground state

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

14 ions

AFM Ising Model with a Longitudinal Field

So far:

Now:

vary strength of Bx

N/2 classical phase transitions as Bx is increased

+ i

iyy

jx

ix

ji

jix tBJH )()()(, ˆ)(ˆˆ

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

++ i

iyy

i

ixx

jx

ix

ji

jix tBBJH )()()()(, ˆ)(ˆˆˆ

Study frustrated ground states of AFM Ising Model

ramp adiabatically


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

+ i

ixx

jx

ix

ji

jix BJH )()()(, ˆˆˆ


==

Steps are only present for AFM Ising models with long-range interactions


+ i

ixx

jx

ix

ji

jix BJH )()()(, ˆˆˆ



+ i

ixx

jx

ix

ji

jix BJH )()()(, ˆˆˆ T = 0

No thermal fluctuations to drive phase transitions

System remains in the same phase



+ i

ixx

jx

ix

ji

jix BJH )()()(, ˆˆˆ T = 0

No thermal fluctuations to drive phase transitions

System remains in the same phase

Add quantum fluctuations to drive the phase transitions

Experimental Protocol

++ i

iyy

i

ixx

jx

ix

ji


Step 1: Initialize all spins along BBx

By

B

Step 2: Turn on By , Bx , and Jxi,j and adiabatically lower By

time

By

Jxi,j

ampl

itude

Bx

Step 3: Measure all spins along x


AFM Ising Model with a Longitudinal Field: 6 ions


010010

AFM Ground States

2-Bright Ground State

1-Bright Ground States


AFM Ising Model with a Longitudinal Field: 10 ions






5-Bright (AFM) Ground States

System exhibits a completedevil's staircase for N → ∞

P. Bak and R. Bruinsma, PRL 49, 249 (1982) P. Richerme et. al., PRL 111, 100506 (2013)

Quantum Fluctuations Drive Phase Transitions

++ i

iyy

i

ixx

jx

ix

ji


Ramp By

Ramp Bx

+ i

ixx

jx

ix

ji

jix tBJH )()()(, ˆ)(ˆˆ


No Thermal FluctuationsNo Quantum Fluctuations

No Thermal FluctuationsQuantum Fluctuations

From ground to excited states

• Difficult (impossible?) to calculate excited state behavior for N > 20-30

• Excited states are interesting:• Hamiltonian spectroscopy• Propagation of quantum

correlations• Non-equilibrium phase

transitions• Thermalization

Begin studying excited states of our system

From ground to excited states)()(, ˆˆ j

xix

ji

jixJH

+i

iyy tB )(ˆsin

Can drive transitions between states if:

• Matrix element couples the states

• Drive frequency matches energy splitting

01ˆ2 )( i

iy

Experimental Protocol:Step 1: Initialize in FM or AFM state

small perturbation

C. Senko et. al., in preparation


xix

ji

jixJH

+i

iyy tB )(ˆsin




01ˆ2 )( i

iy

Experimental Protocol:Step 1: Initialize in FM or AFM state

small perturbation

C. Senko et. al., in preparationAFM

FM


xix

ji

jixJH

+i

iyy tB )(ˆsin




01ˆ2 )( i

iy

Experimental Protocol:Step 1: Initialize in FM or AFM stateStep 2: Apply driving field for 3 ms

small perturbation


FM


xix

ji

jixJH

+i

iyy tB )(ˆsin




01ˆ2 )( i

iy

Experimental Protocol:Step 1: Initialize in FM or AFM stateStep 2: Apply driving field for 3 msStep 3: Scan to find resonances

small perturbation


FM


xix

ji

jixJH

+i

iyy tB )(ˆsin




01ˆ2 )( i

iy

Experimental Protocol:Step 1: Initialize in FM or AFM stateStep 2: Apply driving field for 3 msStep 3: Scan to find resonances

small perturbation

C. Senko et. al., in preparation


xix

ji

jixJH

+i

iyy tB )(ˆsin small perturbation

Start from AFM states:


xix

ji

jixJH

+i

iyy tB )(ˆsin small perturbation

Start from FM states:

From ground to excited states – 18 ions

2621430

131071

111111111111111111


2621430

131071

2621430

131071

011111111111111111


2621430

131071

2621430

131071

011111111111111111

)...

(2

,11,1

3,12,1

NN JJ

JJE

+++

++

Direct Measurement of Spin-Spin Couplings

~N2 terms in Jij matrix, need ~N2 measurements of E

Spectroscopy Method:~N levels for single scan

~N2 levels for ~N scans

)...

(2

,11,1

3,12,1

NN JJ

JJE

+++

++

Probe frequency (kHz) Probe frequency (kHz)

Direct Measurement of Spin-Spin Couplings

~N2 terms in Jij matrix, need ~N2 measurements of E

Spectroscopy Method:~N levels for single scan

~N2 levels for ~N scans

)...

(2

,11,1

3,12,1

NN JJ

JJE

+++

++

Spectroscopy at non-zero transverse field

Spectroscopy at non-zero transverse field

Spectroscopy can measure (or constrain) critical gap

From ground to excited states

Begin studying excited states of our system

• Difficult (impossible?) to calculate excited state behavior for N > 20-30

• Excited states are interesting:• Hamiltonian spectroscopy• Propagation of quantum

correlations• Non-equilibrium phase

transitions• Thermalization

Correlation Propagation with 11 ions

Step 1: Initialize all spins along z

Step 2: Quench to Ising or XY model at t = 0 and let system evolve

Step 3: Measure all spins along z

Step 4: Calculate correlation function

P. Richerme et. al., in preparation

Global Quench: Ising Model


Global Quench: Ising Model

boun

dbo

und


Global Quench: XY Model

Scaling Up

4 K Shield

40 K Shield

300 K

To camera

Ion trap

Conclusion

Recent Results:• Quantum fluctuations to drive

classical phase transitions• Spectroscopic method for

Hamiltonian verification• Propagation of correlations after a

global quenchCurrent Pursuits:• Non-equilibrium phase transitions• Thermalization• Larger numbers of ions with a

cryogenic trap

www.iontrap.umd.edu

P.I.Prof. Chris Monroe

PostdocsChenglin CaoTaeyoung ChoiBrian NeyenhuisPhil Richerme

Clayton CrockerShantanu DebnathCaroline FiggattDavid HuculVolkan InlekKale Johnson

JOINTQUANTUMINSTITUTE

Aaron LeeAndrew ManningCrystal SenkoJacob SmithDavid WongKen Wright

Graduate Students Recent AlumniWes CampbellSusan ClarkCharles ConoverEmily EdwardsDavid HayesRajibul IslamKihwan KimSimcha KorenblitJonathan Mizrahi

Theory CollaboratorsJim FreericksBryce Yoshimura

Zhe-Xuan GongMichael Foss-FeigAlexey Gorshkov

Daniel BrennanKatie Hergenreder

Geoffrey JiUndergraduate Students

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