A quantum model of lasing without inversion

Nicholas Werren, Erik M. Gauger, Peter Kirton

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1 Citation (Scopus)
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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 nanolasers to the thermodynamic limit of conventional lasing. We explore the necessary conditions to achieve lasing without inversion in certain regimes 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 three-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.
Original languageEnglish
Article number093027
JournalNew Journal of Physics
Issue number9
Early online date19 Sept 2022
Publication statusPublished - Sept 2022


  • cumulants
  • lasing without inversion
  • mean field theory
  • nanophotonics
  • permutation symmetry
  • quantum optics
  • three level systems

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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