Entangled Photon Electron Following Thermo Field Dynamics Method

Abstract

Thermo-field dynamics (TFD) is a method linking quantum information to statistical thermodynamics, focus directly on the state because the states in the tilde space in TFD play a role of tracer of the initial states by defining an extended density matrix described on the double Hilbert space. The study of quantum entanglement is more complicated, so the TFD method makes it easier, this is the subject of this paper. We use Thermo-field Dynamics method to study entanglement entropies and transition probability of a Photon-electron system between equilibrium with heat bath, and non-equilibrium, based on the dissipative von Neumann equation. Numerically, at the equilibrium and by controlling the system through temperature, we show that entanglement entropies verify the Nernst’s theorem. By increasing the quantization of a single-mode electromagnetic field, entanglement and transition probability decrease. At non-equilibrium, we show that entanglement entropies obey the second law of thermodynamics, and the emission of a photon decrease the probability of detecting the electron at a quantum level.