Christine Muschik and J. Ignacio Cirac

Entanglement generated by Dissipation

Max-Planck-Institut für Quantenoptik

Hanna Krauter, Kasper Jensen, Jonas Meyer Petersen and Eugene Polzik

Niels Bohr Institute, Danish Research Foundation Center for Quantum Optics (QUANTOP)

Steady State Entanglement

Motivation:

Quantum entanglement

Basic ingredient in most applications in the field of quantum information

But: Lifetimes are usually very short

Therefore: Need for much longer lifetimes!

Motivation:

Quantum entanglement

Basic ingredient in most applications in the field of quantum information

But: Lifetimes are usually very short

Therefore: Need for much longer lifetimes!

Typically:

Quantum states are fragile under decoherence

Motivation:

Quantum entanglement

Basic ingredient in most applications in the field of quantum information

But: Lifetimes are usually very short

Therefore: Need for much longer lifetimes!

Typically:

Quantum states are fragile under decoherence

Avoidance of dissipation by decoupling the system from the environment

Motivation:

Quantum entanglement

Basic ingredient in most applications in the field of quantum information

But: Lifetimes are usually very short

Therefore: Need for much longer lifetimes!

Typically:

Quantum states are fragile under decoherence

Avoidance of dissipation by decoupling the system from the environment

Strict isolation!

Motivation:

Motivation:

Motivation:

New approaches

Use the interaction of the system with the environment

Motivation:

New approaches

Use the interaction of the system with the environment

Dissipation drives the system into the desired state

Motivation:

New approaches

Use the interaction of the system with the environment

Dissipation drives the system into the desired state

Robust method to create extremely long-lived and robust entanglement

Motivation:

Procedure:

Motivation:

Procedure:

Engineer the coupling

Motivation:

Procedure:

Engineer the coupling

Steady state = desired state

Motivation:

Procedure:

Engineer the coupling

Steady state = desired state

Arbitrary initial state

Motivation:

Procedure:

Engineer the coupling

Steady state = desired state

Arbitrary initial state

Motivation:

Procedure:

Engineer the coupling

Steady state = desired state

Arbitrary initial state

Single trapped ion J. F. Poyatos, J. I. Cirac and P. Zoller, Phys. Rev. Lett. 77, 4728 (1996)

Atoms in two cavitiesB. Kraus and J. I. Cirac, Phys. Rev. Lett. 92, 013602 (2004)

Many-body systemsS. Diehl, A. Micheli, A. Kantian, B. Kraus, H.P. Büchler, P. Zoller, Nature Physics 4, 878 (2008)F. Verstraete, M.M. Wolf, J.I. Cirac, Nature Physics 5, 633 (2009)

Proposals:

Quantum phase transitionsState preparationQuantum computing

Motivation:

Procedure:

Engineer the coupling

Steady state = desired state

Arbitrary initial state

Setup:

Main idea:

HamiltonianHamiltonian::

usls

kkkkaBBakdaAAakdH

)()( III JJA

III JJB

Main idea:

HamiltonianHamiltonian::

usls

kkkkaBBakdaAAakdH

)()(

Master equationMaster equation::

III JJA III JJB

..)()( CHBBBBAAAAdtdt

Main idea:

HamiltonianHamiltonian::

usls

kkkkaBBakdaAAakdH

)()(

Master equationMaster equation::

III JJA III JJB

..)()( CHBBBBAAAAdtdt

Unique Steady StateUnique Steady State::

0 EPREPR BA

Setup:

laser

magneticfields

Setup:

Reservoir: common modes of the electromagnetic field.Control: Laser and magnetic fields

laser

magneticfields

Setup:

laser

Setup:

laser

Setup:

laser

212121011011

Setup:

laser

Setup:

laser

)2()2( BBBBBBdAAAAAAddt

d

+undesired processes

Masterequation:

Entanglement:

IIxIx

IIzIzIIyIy

JJ

JJJJ

,,

,,,, varvar

Theory:

Entanglement: ideal case

2,,

,,,, varvar

IIxIx

IIyIyIIzIz

JJ

JJJJ

Theory:

Entanglement: ideal case

2,,

,,,, varvar

IIxIx

IIyIyIIzIz

JJ

JJJJ

1d

2P : polarization

12 n

~ : noise rate

Entanglement: including undesired processes

Theory:

2

2

22

2

2~

~

Pd

Pd

P

n

2

Experimental realization of purely dissipation based entanglement:

Theory: Two-level model

Experiment: Multi-level structure

Experimental realization of purely dissipation based entanglement:

Theory: Two-level model

Experiment: Multi-level structure

Cs133 (nuclear spin I=7/2)

3,3

3,44,4

3F

4F

Experimental results:

Ia)

0 5 10 15 20 25

1

0.9

0.8

Tim e in m s

Experimental results:

Ia)

0 5 10 15 20 25

1

0.9

0.8

Tim e in m s

EPR variance

)()( zy JJ

Experimental results:

Ia)

0 5 10 15 20 25

1

0.9

0.8

Tim e in m s

Longitudinal spin

xJ

EPR variance

)()( zy JJ

Experimental results:

0 5 10 15 20 25

1

0.95

1.05

Ib)

)(t

Tim e in m s

Ia)

0 5 10 15 20 25

1

0.9

0.8

Tim e in m s

IIxIx

IIzIzIIyIy

JJ

JJJJ

,,

,,,, varvar

Conclusions and Outlook:

First observation of entanglement generated by dissipation

Conclusions and Outlook:

First observation of entanglement generated by dissipation

Entanglement was produced with macroscopic atomic ensembles, and lasted much longer than in previous experiments where entanglement was generated using standard methods.

Conclusions and Outlook:

First observation of entanglement generated by dissipation

Entanglement was produced with macroscopic atomic ensembles, and lasted much longer than in previous experiments where entanglement was generated using standard methods.

This work paves the way towards the creation of long lived entanglement, potentially lasting for several minutes or longer.

Conclusions and Outlook:

Realization of Steady State Entanglement:

Atoms with two-level atomic ground states, e.g. Yb171

Conclusions and Outlook:

Realization of Steady State Entanglement:

Atoms with two-level atomic ground states, e.g. Yb171

Increased optical depth + optical pumping

0 20 40 60

Id)1.05

0.95

0.85

)( t

Tim e in m s

0 10 20

1

1.06

Conclusions and Outlook:

Realization of Steady State Entanglement:

Atoms with two-level atomic ground states, e.g. Yb171

Increased optical depth + optical pumping

Reduced spin-flip collisions

Better coatings, lower temperatures

Proposal for long-lived entanglement

Other systems, e.g.optomechanical oscillators

Summary:

Dissipatively driven entanglement

Future

General theoretical model for quadratic Hamiltonians

Main idea:

aaaaaadt ~~~2~

bbbbbb ~~~2

0,00,0~ vacSteady state:

,00,0 a ,00,0 b ,0EPRA ,0EPRB

AAAAAAdt 2

BBBBBB 2

EPREPREPR Steady state:

,UaUA UbUB

UU vacEPR

)~( UU

Effective ground state Hamiltonian:

..)(1 1

,,CHaeegkd

k

N

i

N

j

rkijII

rkik

ji

iI

ls

k

N

i

N

j

rkijII

rkiiIk aeegkdH ji

us

1 1,,)(

Master equation:

BtBdAtAdtd termfirstt )(2)(2)(

iIIiIIiIiINicool tt ,,,,1 )()(2

iIIiIIiIiINiheat tt ,,,,1 )()(2

iIIiIIiIIiIIiIiIiIiINideph tt ,,,,,,,,1 )()(2

Entanglement:

dephheatcool ~

ttPdttPd

etPd

tPd

tP

tn

tP

et )(

~2

2

222

2

2

2

)(~

22

2

1)(

~)(

~

)(

)(

)()(