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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)
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Steady State Entanglement
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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!
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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
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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
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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!
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Motivation:
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Motivation:
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Motivation:
New approaches
Use the interaction of the system with the environment
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Motivation:
New approaches
Use the interaction of the system with the environment
Dissipation drives the system into the desired state
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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
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Motivation:
Procedure:
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Motivation:
Procedure:
Engineer the coupling
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Motivation:
Procedure:
Engineer the coupling
Steady state = desired state
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Motivation:
Procedure:
Engineer the coupling
Steady state = desired state
Arbitrary initial state
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Motivation:
Procedure:
Engineer the coupling
Steady state = desired state
Arbitrary initial state
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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
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Motivation:
Procedure:
Engineer the coupling
Steady state = desired state
Arbitrary initial state
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Setup:
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Main idea:
HamiltonianHamiltonian::
usls
kkkkaBBakdaAAakdH
)()( III JJA
III JJB
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Main idea:
HamiltonianHamiltonian::
usls
kkkkaBBakdaAAakdH
)()(
Master equationMaster equation::
III JJA III JJB
..)()( CHBBBBAAAAdtdt
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Main idea:
HamiltonianHamiltonian::
usls
kkkkaBBakdaAAakdH
)()(
Master equationMaster equation::
III JJA III JJB
..)()( CHBBBBAAAAdtdt
Unique Steady StateUnique Steady State::
0 EPREPR BA
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Setup:
laser
magneticfields
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Setup:
Reservoir: common modes of the electromagnetic field.Control: Laser and magnetic fields
laser
magneticfields
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Setup:
laser
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Setup:
laser
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Setup:
laser
212121011011
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Setup:
laser
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Setup:
laser
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)2()2( BBBBBBdAAAAAAddt
d
+undesired processes
Masterequation:
Entanglement:
IIxIx
IIzIzIIyIy
JJ
JJJJ
,,
,,,, varvar
Theory:
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Entanglement: ideal case
2,,
,,,, varvar
IIxIx
IIyIyIIzIz
JJ
JJJJ
Theory:
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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
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Experimental realization of purely dissipation based entanglement:
Theory: Two-level model
Experiment: Multi-level structure
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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
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Experimental results:
Ia)
0 5 10 15 20 25
1
0.9
0.8
Tim e in m s
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Experimental results:
Ia)
0 5 10 15 20 25
1
0.9
0.8
Tim e in m s
EPR variance
)()( zy JJ
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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
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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
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Conclusions and Outlook:
First observation of entanglement generated by dissipation
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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.
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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.
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Conclusions and Outlook:
Realization of Steady State Entanglement:
Atoms with two-level atomic ground states, e.g. Yb171
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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
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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
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Proposal for long-lived entanglement
Other systems, e.g.optomechanical oscillators
Summary:
Dissipatively driven entanglement
Future
General theoretical model for quadratic Hamiltonians
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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
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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)(
~)(
~
)(
)(
)()(