Application of a non-linear thermodynamic master equation to three-level quantum systems

by Παναγιώτης Αλατάς

Institution: University of Patras
Year: 2014
Keywords: Open quantum systems; Thermodynamics; Three-level system; Master equation; Electromagnetically induced transparency; Density matrix; Qutrit; Non-linear; Generic; 530.42; Ανοικτά κβαντικά συστήματα; Θερμοδυναμική; Σύστημα τριών καταστάσεων; Εξίσωση master; Ηλεκτρομαγνητικά επαγόμενη διαφάνεια; Μήτρα πυκνότητας πιθανότητας; Μη-γραμμική
Record ID: 1153354
Full text PDF: http://hdl.handle.net/10889/7534


In this Master’s thesis, we have focused on the description of three-level quantum systems through master equations for their density matrix, involving a recently proposed non-linear thermodynamic one. The first part is focused on a three-level system interacting with two heat baths, a hot and a cold one. We investigated the rate of heat flow from the hot to the cold bath through the quantum system, and how the steady-state is approached. Additional calculations here refer to the rate of entropy production and the evolution of all elements of the density matrix of the system from an arbitrary initial state to their equilibrium or steady-state value. The results are compared against those of a linear, Lindblad-type master equation designed so that for a quantum system interacting with only one heat bath, the same final Gibbs steady state is attained. In the second part of this thesis, we focus on the electromagnetically induced transparency (EIT), a phenomenon typically achievable only in atoms with specific energy structures. For a three level system (to which the present study has focused), for example, EIT requires two dipole allowed transitions (the 1-3 and the 2-3) and one forbidden (the 1-2). The phenomenon is observed when a strong laser (termed the control laser) is tuned to the resonant frequency of the upper two levels. Then, as a weak probe laser is scanned in frequency across the other transition, the medium is observed to exhibit both: a) transparency at what was the maximal absorption in the absence of the coupling field, and b) large dispersion effects at the atomic resonance. We discuss the Hamiltonian describing the phenomenon and we present results from two types of master equations: a) an empirically modified Von-Neumann one allowing for decays from each energy state, and b) a typical Lindblad one, with time-dependent operators. In the first case, an analytical solution is possible, which has been confirmed through a direct solution of the full master equation. In the second case, only numerical results can be obtained. We present and compare results from the two master equations for the susceptibility of the system with respect to the probe field, and we discuss them in light also of available experimental data for this very important phenomenon.