A quantum model of lasing without inversion

TL;DR

This paper develops a comprehensive quantum model for lasing without inversion, analyzing conditions for phase transition and quantum control across system sizes from nanolasers to bulk lasers.

Contribution

It introduces a microscopic quantum model for lasing without inversion, connecting it to macroscopic mean-field theory and exact solutions for finite systems.

Findings

Lasing without inversion can be achieved by tuning the phase of the coherent drive.

The steady state approaches the thermodynamic limit as the number of atoms increases.

The model enables quantum control of the lasing phase transition.

Abstract

Starting from a quantum description of multiple Lambda-type 3-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 nanolasers 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 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 applications to further understanding and developing nanophotonic technology.