A quantum model of lasing without inversion

Abstract

Starting from a quantum description of multiple Λ-type three-level atoms driven with a coherent microwave field and incoherent optical pumping, we derive a microscopic model of lasing from which we move towards a consistent macroscopic picture. Our analysis applies across the range of system sizes from nanolaser to the thermodynamic limit of conventional lasing. We explore the necessary conditions to achieve lasing without inversion by calculating the non- equilibrium steady state solutions of the model at, and between, its microscopic and macroscopic limits. For the macroscopic picture, we use mean field theory to present a thorough analysis of the lasing phase transition. In the microscopic case, we exploit the underlying permutation symmetry of the density matrix to calculate exact solutions for N 3-level systems. This allows us to show that the steady state solutions approach the thermodynamic limit as N increases, restoring the sharp non-equilibrium phase transition seen in this limit. We demonstrate how the lasing phase transition and degree of population inversion can be adjusted by simply varying the phase of the coherent driving field. The high level of quantum control presented by this microscopic model and the framework outlined here have clear applications to further understanding and developing nanophotonic technology.

Goos–Hänchen shifts in a V-type three-level atomic system interacting with squeezed vacuum

“…A plethora of investigations has been dedicated to elucidating these phenomena. Notable instances encompass electromagnetically induced transparency (EIT) [6,7], Stimulated Raman adiabatic passage [8], coherent population trapping [9], multi-wave mixing [7,10], giant Kerr nonlinearity [11,12], optical soliton [13,15], lasing without inversion [16][17][18], optical bistability/multistability [19][20][21], and controlled Goos-Hänchen (GH) shift [22,23]. These exemplify a spectrum of intriguing quantum optical effects that have been * Author to whom any correspondence should be addressed.…”