Abstract

An unraveling of master equation for a set of fields interfering with one another is developed and conditions are found under which decoherence can be avoided for conditional and unconditional evolution of one of this fields.

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References

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  1. W. H. Zurek, "Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse?," Phys. Rev. D 24, 1516 (1981).
    [CrossRef]
  2. W. H. Zurek, "Environment-induced superselection rules," Phys. Rev. D 26, 1862 (1982).
    [CrossRef]
  3. W. H. Zurek, "Decoherence and transition from quantum to classical," Phys. Today 44, 36 (1991).
    [CrossRef]
  4. S. M. Barnett and S. J. D. Phoenix, "The principles of quantum cryptography," Phil. Trans. R. Soc. Lond. A 354, 793 (1996).
    [CrossRef]
  5. D. P. DiVincenzo, "Quantum computation," Science 270, 255 (1995).
    [CrossRef]
  6. M. D. Srinivas and E. B. Davies, "Photon counting probabilities in quantum optics," Opt. Acta 28, 981 (1981).
    [CrossRef]
  7. H. Carmichael, An Open System Approach to Quantum Optics (Springer-Verlag, Berlin, 1993).
  8. S. Ya. Kilin Quantum Optics. Fields and Their Detection (Minsk, 1990).
  9. S. Ya. Kilin, D. B. Horoshko, and V. N. Shatokhin, "Quantum instabilities and decoherence problem," Acta Phys. Pol. A93, 97 (1998).
  10. V. Buzek and P. L. Knight, "Quantum interference, superposition states of light, and nonclassical effects," Prog. Opt. 36 3(1995).
    [CrossRef]
  11. B. M. Garraway and P. L. Knight, "Evolution of quantum superpositions in open environments: Quantum trajectories, jumps, and localization in phase space," Phys. Rev. A 50, 2548 (1994).
    [CrossRef] [PubMed]
  12. D. B. Horoshko and S. Ya. Kilin, "Direct detection feedback for preserving quantum coherence in an open cavity," Phys. Rev. Lett. 78, 840 (1997).
    [CrossRef]
  13. H. Mabuchi and P. Zoller, "Inversion of quantum jumps in quantum optical systems under continuos observation," Phys. Rev. Lett. 76, 3108 (1996).
    [CrossRef] [PubMed]

Other (13)

W. H. Zurek, "Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse?," Phys. Rev. D 24, 1516 (1981).
[CrossRef]

W. H. Zurek, "Environment-induced superselection rules," Phys. Rev. D 26, 1862 (1982).
[CrossRef]

W. H. Zurek, "Decoherence and transition from quantum to classical," Phys. Today 44, 36 (1991).
[CrossRef]

S. M. Barnett and S. J. D. Phoenix, "The principles of quantum cryptography," Phil. Trans. R. Soc. Lond. A 354, 793 (1996).
[CrossRef]

D. P. DiVincenzo, "Quantum computation," Science 270, 255 (1995).
[CrossRef]

M. D. Srinivas and E. B. Davies, "Photon counting probabilities in quantum optics," Opt. Acta 28, 981 (1981).
[CrossRef]

H. Carmichael, An Open System Approach to Quantum Optics (Springer-Verlag, Berlin, 1993).

S. Ya. Kilin Quantum Optics. Fields and Their Detection (Minsk, 1990).

S. Ya. Kilin, D. B. Horoshko, and V. N. Shatokhin, "Quantum instabilities and decoherence problem," Acta Phys. Pol. A93, 97 (1998).

V. Buzek and P. L. Knight, "Quantum interference, superposition states of light, and nonclassical effects," Prog. Opt. 36 3(1995).
[CrossRef]

B. M. Garraway and P. L. Knight, "Evolution of quantum superpositions in open environments: Quantum trajectories, jumps, and localization in phase space," Phys. Rev. A 50, 2548 (1994).
[CrossRef] [PubMed]

D. B. Horoshko and S. Ya. Kilin, "Direct detection feedback for preserving quantum coherence in an open cavity," Phys. Rev. Lett. 78, 840 (1997).
[CrossRef]

H. Mabuchi and P. Zoller, "Inversion of quantum jumps in quantum optical systems under continuos observation," Phys. Rev. Lett. 76, 3108 (1996).
[CrossRef] [PubMed]

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Equations (50)

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ρ ˙ = i [ H a , ρ ] + γ a 2 ( 2 a + a + ρ a + a ) ,
ρ ( t ) = n = 0 + 0 t d t n 0 t 2 d t 1 ρ ( t | t 1 , t n ) ,
ρ ( t | t 1 , , t n ) = S ( t t n ) J a S ( t n t n 1 ) J a J a S ( t 1 ) ρ ,
J a ρ = γ a a + ,
S ( t ) ρ = e ( iH γ a a + a 2 ) t ρ e ( iH γ a a + a 2 ) t .
ρ ˙ = ,
ρ ( t ) = n = 0 + 0 t d t n 0 t n d t 1 e ( L J ) ( t t n ) J e ( L J ) ( t n t n 1 ) J J e ( L J ) t 1 ρ ,
ρ ( t | t 1 , , t n ) = | ψ a cond ( t ) ψ a cond ( t ) | ,
| ψ a cond = ( γ a ) n / 2 e ( iH γ a a + a / 2 ) ( t t n ) a a e ( iH γ a a + a 2 ) t 1 | ψ a ( 0 ) .
ρ ˙ = i [ H a , ρ ] i [ H a , ρ ] + γ a 2 ( 2 a + a + ρ a + a ) + γ b 2 ( 2 b + b + ρ b + b ) ,
E a = γ a 2 a + γ b 2 b ,
E b = γ a 2 a - γ b 2 b .
ρ E a ρ E a + = J a ρ ,
ρ E b ρ E b + = J b ρ .
S ˙ ρ = ( L J a J b ) ρ = i [ H a + H b , ρ ] γ a 2 ( a + + ρ a + a ) γ b 2 ( b + + ρ b + b ) ,
S ( t ) ρ = e Kt ρ e K + t ,
K = i H a + i H b + γ a 2 a + a + γ b 2 b + b .
| ψ ab cond ( t | t 1 ; t 2 ) = e K ( t t 2 ) ( γ a 2 a γ b 2 b ) e K ( t 2 t 1 ) ( γ a 2 a + γ b 2 b )
× e K t 1 | ψ a ( 0 ) | ψ b ( 0 ) .
ψ ab cond ( t t 1 ; t 2 ) = γ a 2 e K ( t t 2 ) a e K ( t 2 t 1 ) a e K t 1 ψ a ( 0 ) ψ b ( 0 )
+ γ a γ b 4 e K ( t t 2 ) a e K ( t 2 t 1 ) b e K t 1 ψ a ( 0 ) ψ b ( 0 )
γ a γ b 4 e K ( t t 2 ) b e K ( t 2 t 1 ) a e K t 1 ψ a ( 0 ) ψ b ( 0 )
γ b 2 e K ( t t 2 ) b e K ( t 2 t 1 ) b e K t 1 ψ a ( 0 ) ψ b ( 0 ) ,
| ψ ab cond ( t ) | ψ a ( t ) | ψ b ( t ) .
S ( t ) ρ a ρ b = e ( i H a γ a a + a 2 ) t ρ a e ( i H a γ a a + a 2 ) t e ( i H b γ b b + b 2 ) t ρ b e ( i H b γ b b + b 2 ) t .
( γ a 2 a + γ b 2 b ) | ψ a | ψ b | ψ a | ψ b .
ρ ˙ = i ( i [ H i , ρ ] + γ i 2 ( 2 a i ρ a i + a i + a i ρ ρ a i + a i ) ) ,
E i out = j U ij E j in ,
E j in = γ i a i ,
i γ i a i ρ a i + = i E i in ρ E i in + = ijk U ij U ki * E j out ρ E k out +
= jk δ jk E j out ρ E k out = k E k out ρ E k out +
ρ ˙ = i [ i H i , ρ ] + i E i out ρ E i out + i γ i 2 a i + a i ρ ρ i γ i 2 a i + a i .
S ( t ) = exp { ( i i H i i γ i 2 a i + a i ) t } ρ exp { ( i i H i i γ i 2 a i + a i ) t } .
| ψ a ( 0 ) = N ( | α + e | α ) ,
| ψ a cond ( t ) = ( γ a α ) n N ( | α e γ a t / 2 iωt + ( 1 ) n e | α e γ a t / 2 iωt ) ,
e a + a 1 2 ( | α + i | α ) = 1 2 ( α + i α ) = i 2 ( α i α ) .
ψ a cond ( t ) = ( γ a ) n 2 e ( iH γ a a + a 2 ) ( t t n ) e a + a a e a + a a e ( iH γ a a + a 2 ) t 1 | ψ a ( 0 ) ,
ψ a cond ( t ) = ( γ a α ) n 1 2 ( | α e γ a t 2 iωt + i | α e γ a t 2 iωt ) .
ψ a ( t ) = 1 2 ( α e γ a t 2 iωt + i α e γ a t 2 iωt )
ψ a cond ( t ) = ( γ a ) n 2 e ( iH γ a a + a 2 ) ( t t n ) Ua Ua e ( iH γ a a + a 2 ) t 1 ψ a ( 0 )
ψ a cond ( t n , t 1 , t n ) = c ( t n , t 1 , t n ) | ψ a ( t ) ,
ψ a ( t ) = e ( iH γ a a + a 2 ) t ψ a ( 0 ) .
Ua | ψ a ( t ) = c ( t ) ψ a ( t ) ,
( γ a 2 a + γ b 2 b ) | ψ a ψ b = | ψ a ψ b ,
( γ a 2 a γ b 2 b ) | ψ a ψ b = | ψ a ψ b
γ a 2 φ a a ψ a | ψ b = φ a | ψ a | ψ b .
| ψ b = c | ψ b ,
φ a a ψ a = φ a | ψ a = 0 .
( γ a 2 a + γ b 2 b ) ψ a ψ b = c | ψ a ψ b ,
γ b 2 b | ψ b = ( c ψ a | ψ a γ a 2 ψ a a ψ a ) | ψ b ,

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