The Mixed Coherent State Representation of the Density Operator in Thermo-Field Dynamics

Abstract

In the framework of thermo-field dynamics, invented by Umezawa et al., we construct a mixed coherent state representation of density operator ρ. This new representation is useful because it provides an approach to retrieve ρ from its c-number solution of master equations in the entangled state representation.

Solving quantum trajectories for systems with linear Heisenberg-picture dynamics and Gaussian measurement noise

“…The final method that will be mentioned here is that of the thermo-entangled state representation (sometimes called non-equilibrium thermo-field dynamics). This key technique transforms the superoperators of the standard formulation of the SME into operators acting in a larger Hilbert space [77][78][79][80][81][82][83][84]. We can then utilize powerful group theoretic tools to re-organize the infinite string of time slice evolutions.…”

“…This representation is based on prior work by Takahashi and Umezawa, relating to thermo field dynamics [82,83], in which a fictitious field is introduced in order to convert ensemble average calculations into equivalent pure state expressions. Here, we focus on just the results that we require, and the interested reader is referred to the available literature for more detail [77][78][79][80][81][82][83][84]88].…”

Evolution of the photon-added coherent state in a laser channel

“…In Sect. 2, we review simply the thermoentangled state (TES) [16,17] representation defined in a two-mode Fock space, in which one mode is a fictitious one representing the effect of environment, and it can arrange master equations of density operators in quantum statistics as state-vector evolution equations. In Sect.…”

New Approach for Solving the Lindblad Equation of the Density Operator for a Harmonic Oscillator Interacting with an Electromagnetic Field

“…Usually, solving master equations needs to use either the Langevin equation or the Fokker-Planck equation [10] after recasting the density operators into some definite representations, e.g., particle number representation (Q-function), coherent state representation (P-representation) [11], or the Wigner representation [12][13][14][15]. In this work, instead of using these conventional techniques we solve the master equation by virtue of the newly developed thermo entangled state (TES) [16,17] defined in a two-mode Fock space, in which one mode is a fictitious one representing the effect of environment. It is Takahashi-Umezawa [18,19] who first introduced the fictitious Fock space to treat ensemble average as a pure state average, this pure state (thermo vacuum state) is also a two-mode squeezed state.…”