New approach for analyzing time evolution of density operator in a dissipative channel by the entangled state representation

Abstract We analyze the time evolution of mixed state ρ 0 in a dissipative channel, characteristic of a decay constant κ , by virtue of the elegant properties of entangled state representation 〈 η | . We find that the matrix element of the mixed state ρ ( t ) at time t in 〈 η | representation is proportional to that of the initial ρ 0 in the decayed entangled state 〈 η e - κ t | representation, accompanying with a Gaussian damping factor e - 1 - e - 2 κ t 2 | η | 2 . Thus we have a new insight about the nature of the dissipative process.

[2]  B. R. Mollow.  Quantum Theory of Field Attenuation , 1968 .

[3]  ABCD rule involved in the product of general SU(1,1) squeezing operators and quantum states’ Fresnel transformation , 2008 .

[4]  Wolfgang P. Schleich,et al.  Quantum optics in phase space , 2001 .

[5]  P. Kelley,et al.  Theory of Electromagnetic Field Measurement and Photoelectron Counting , 1964 .

[6]  M. O. Scully,et al.  Quantum theory of an optical maser. III - Theory of photoelectron counting statistics. , 1969 .

[7]  M. Scully,et al.  The Quantum Theory of Light , 1974 .

[8]  H. Fan,et al.  New representation for thermo excitation and de-excitation in thermofield dynamics ? ? Work supporte , 2001 .

[9]  V. Buzek.  SU(1,1) Squeezing of SU(1,1) Generalized Coherent States , 1990 .

[10]  Klauder,et al.  Eigenvectors of two particles' relative position and total momentum. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[11]  G. S. Agarwal,et al.  A new representation for squeezed states , 1992 .

[12]  H. Fan,et al.  Newton-Leibniz integration for ket-bra operators in quantum mechanics and derivation of entangled state representations , 2006 .

[13]  Yue Fan,et al.  New representation of thermal states in thermal field dynamics , 1998 .

[14]  Hong-yi,et al.  Representations of two-mode squeezing transformations. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[15]  Hiroomi Umezawa,et al.  Advanced Field Theory: Micro, Macro, and Thermal Physics , 1993 .

[16]  V. Dodonov.  REVIEW ARTICLE: `Nonclassical' states in quantum optics: a `squeezed' review of the first 75 years , 2002 .

[17]  H. Fan,et al.  A new representation for two-mode squeezed states , 2004 .