Decoherence and Classical dynamics in Markovian Quantum Open Systems
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Transcript of Decoherence and Classical dynamics in Markovian Quantum Open Systems
Decoherence and Classical dynamics in Markovian
Quantum Open Systems
O. Brodier(1) A. M. Ozorio de Almeida(2)
(1)M.P.I.P.K.S. Dresden, ALLEMAGNE
(2)C.B.P.F. Rio de Janeiro, BRASIL
Phase Space Representation
x
p
Classical propagation
Quantum propagation
dQQ
qpQi
qp tt 2ˆ
2exp,W
,P,P 0 ttt qpqp Liouville propagation:
Wigner function:
S. Habib, K. Shizume, W. H. ZurekPhys.Rev.Lett. 80 (1998) 4361-4365
Separation time
Z. P. Karkuszewski, J. Zakrzewski, W. H. ZurekPhys. Rev. A 65, 042113 (2002)
texpp
p
tH ln1
Decoherence due to coupling to environment:
effect on separation time?
Characteristic function
xxx di
tqpt Wexp,
xxξxξξ dSi
tqpt 0W,exp,
01q̂p̂
ξξξ nq
mp
tmnmn
nmn
i
Momenta:
Semiclassical analysis:
LLLLLLH
i
tˆˆˆ
2
1ˆˆˆ
2
1ˆˆˆˆ,ˆˆ
Markovian Quantum Open System:
ξξlξξξ St
SH
t
S 2,
Hamilton Jacobi:
Result
xxxxxx dtbdtq 00
22 W,W,q̂
texp, tb x
qvm
pqpH
2,
2
m
v with
Conclusion
• analysis of decoherence of a Markovian Quantum Open System
• Dynamical dependence of decoherence
A. M. Ozorio de Almeida, O. Brodier in press Ann. Phys. (2006)
W.K.B.
qSq
i
exp
qdq
dSp
q
qqSqq ,
iexp
q
q
qqqq
Spp
,,2
Entanglement dynamics
A
B
A
B
tc k
Measuring environment → Pure entanglement
Entanglement of a mixture
tc ̂
k
kk ttN
t 1ˆ
tctcN
tck
k ˆ1
Setup 1
01 cttc
A
B
0
011
10
A
0
0
11
01
B
11
10
01
00
:1 21 tpp
:1 tp
:2 tp t1
Setup 2
22
BAi
A
B
i
22
BAi
22
BA
22
BA
11
10
01
00
tctctttc ˆ2021 211
22
tt2
21
Conclusion
• For this example there exists an optimal experimental setup which gives the exact entanglement measure.
• General Prescription for Measuring Environment?