Dynamics of Bloch vector in thermal Jaynes-Cummings model

Abstract

In this paper, we investigate the dynamics of the Bloch vector of a single two-level atom which interacts with a single quantized electromagnetic field mode according to the Jaynes-Cummings model, where the field is initially prepared in a thermal state. The time evolution of the Bloch vector S(t) seems to be in complete disorder because of the thermal distribution of the initial state of the field. Both the norm and the direction of S(t) oscillate hard and their periods seem infinite. We observe that the trajectory of the time evolution of S(t) in the two- or three-dimensional space does not form a closed path. To remove the fast frequency oscillation from the trajectory, we take the time-average of the Bloch vector S(t). We examine the histogram of {S_{z}(nΔt)|n=0,1,...,N} for small Δt and large N. It represents an absolute value of a derivative of the inverse function of S_{z}(t). (When the inverse function of y=S_{z}(t) is a multi-valued function, the histogram represents a summation of the absolute values of its derivatives at points whose real parts are equal to y on the Riemann surface.) We examine the dependence of the variance of the histogram on the temperature of the field. We estimate the lower bound of the entanglement between the atom and the field.

16 pages, 8 eps figures, latex2e; v2: a new section and references added

References in corpus (12)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Finite-Time Disentanglement via Spontaneous Emission
• Quantum Open System Theory: Bipartite Aspects
• Entanglement induced by a single-mode heat environment
• Sudden Death of Entanglement of Two Jaynes-Cummings Atoms
• Subsystem Purity as an Enforcer of Entanglement
• Entanglement invariant for the double Jaynes-Cummings model
• Revivals and entanglement from initially entangled mixed states of a damped Jaynes-Cummings model
• Hot entanglement in a simple dynamical model
• Evolution of the superposition of displaced number states with the two-atom multiphoton Jaynes-Cummings model: interference and entanglement
• Scheme for generating entangled states of two field modes in a cavity
• Entanglement enhancement and postselection for two atoms interacting with thermal light

Cited by in corpus (6)

• Complexity of Pure and Mixed Qubit Geodesic Paths on Curved Manifolds
• Application of Abel-Plana formula for collapse and revival of Rabi oscillations in Jaynes-Cummings model
• Revisiting the Jaynes-Cummings model with time-dependent coupling
• Quasiperiodicity in time evolution of the Bloch vector under the thermal Jaynes-Cummings model
• Thermal effects in Jaynes-Cummings model derived with low-temperature expansion
• Equivalence of a compressible inviscid flow and the Bloch vector under the thermal Jaynes-Cummings model