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Optics Letters

Field-driven super/subradiant lasing without inversion in three-level ladder scheme

Gennady A. Koganov, Boris Shif, R. Shuker

Published Jul 19, 2011• 5 citations
Publisher

Abstract

A model of a superradiant laser comprising of N three-level systems driven by two pumping lasers is considered in semiclassical approximation. Steady-state equations for density matrix elements are solved both analytically and numerically. Various properties of generated light are investigated. It is found that such a laser can exhibit both superradiance, when the intensity scales as N(2), and subradiance when the intensity does not depend on N. The phase of the laser field is locked to the relative phase of the pumping lasers.

DOI
10.1364/ol.36.002779

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A model of a superradiant laser comprising of N three-level systems driven by two pumping lasers is considered in semiclassical approximation. Steady-state equations for density matrix elements are solved both analytically and numerically. Various properties of generated light are investigated. It is found that such a laser can exhibit both superradiance, when the intensity scales as N(2), and subradiance when the intensity does not depend on N. The phase of the laser field is locked to the relative phase of the pumping lasers.
Abstract A scheme for active second harmonics generation is suggested. The system comprises N three-level atoms in ladder configuration, situated into a resonant cavity. The system generates the field whose frequency is twice the frequency of the pumping laser, and the field phase is locked to the phase of the pumping field. It is found that the system can lase in either superradiant or subradiant regime, depending on the number of atoms N . When N passes some critical value the transition from the super to subradiance occurs in a phase-transition-like manner. Stability study of the steady state supports this conclusion. For experimental realization of the super/subradiant second harmonics generation we propose semiconductor quantum well structures, superconducting quantum circuits, and evanescently coupled waveguides in which equally spaced levels relevant to this study exist.
A scheme for active frequency doubling is suggested. The system comprises N semiconductor quantum wells situated into resonant cavity. Theoretical model for such systems is based on three-level virtual atoms in ladder configuration. It is found that the system can lase in either superradiant or subradiant regime, depending on the number of atoms N. When N passes some critical value the transition from the super to subradiance occurs in a phase-transition-like manner. Stability study of the steady state supports this conclusion.
Abstract We show that it is possible to get gain without inversion at high frequency in a three-level ladder type scheme driven by a single driving laser. The transition from the ground state to first excited state is driven by a low-frequency resonant laser field. The next excited state lies far above the first one; therefore its resonant frequency can be much higher than that of the lower transition, and hence one should go beyond the most commonly used rotating wave approximation consisting of retaining only resonant terms (slowly oscillating) in the Hamiltonian. We solve the master equation, both analytically (under proper approximations) and numerically, with the full Hamiltonian keeping counter-rotating highly non-resonant terms. We show a dressed state picture explaining spectral features of gain-absorption profiles. Also we present a kind of phase diagram in the plane γ –Λ, where γ and Λ are spontaneous emission rate and incoherent pumping rate, respectively. The whole γ –Λ plane is divided into four areas: gain-inversion, absorption-no inversion, gain without inversion and absorption with inversion. The first two are usual regimes of incoherently pumped lasers, while the last two stem from the quantum interference phenomena. We analyse the parameter areas where such quantum regimes are possible. The exact numerical solution of the time-dependent master equation shows that keeping counter-rotating terms (no rotating wave approximation) gives rise to new spectral features in the form of additional peaks at combination frequencies. Actually the considered system works as a coherent frequency up-converter.
We have studied an incoherently pumped laser operating with a Doppler-broadened three-level system placed in a doubly resonant cavity. This system generates two laser fields, one of them without population inversion. Both ladder and V-type three-level schemes are considered with a ratio $R={\ensuremath{\omega}}_{\ensuremath{\alpha}}/{\ensuremath{\omega}}_{\ensuremath{\beta}}$ of inversionless laser frequency ${\ensuremath{\omega}}_{\ensuremath{\alpha}}$ to ordinary laser frequency ${\ensuremath{\omega}}_{\ensuremath{\beta}}$ of R=0.67R=0.67R=0.67 and R=1.88,R=1.88,R=1.88, respectively. Dual-wavelength lasing extends up to Doppler-broadening values for optical transitions of atoms in a vapor cell. Some considerations for the practical realization of this dual-wavelength laser are discussed.
A dressed-state study of lasing without population inversion from a three-level atom interacting with a bi-chromatic laser field in the ladder configuration is presented. In our model we allow the atom to be dressed by both of the coupling and probe fields. The system under consideration is explored both analytically and numerically within the steady-state regime. A parameter study is performed in which we explore the influence of the change of control parameters (Rabi frequencies and incoherent pump rates, etc) on the system behaviour. The parameter study also applies to situations where both coherent fields have comparable intensities. Expressions for steady-state populations and coherences are derived, from which the constraints on the system control parameters allowing gain or absorption of various types, are calculated. The system is demonstrated to possess gain without inversion (GWI), as well as regular gain with inversion, for the appropriate choice of system control parameters. Inversion without lasing (IWL) is also found. The dressed-state approach offers a different insight into the system dynamics in which Rabi oscillations and spectral features appear natural. We believe that the dressed-state approach provides a more adequate description of the system dynamics than that provided by the bare state basis.
A dressed-state study of lasing without population inversion from a three-level atom interacting with a bichromatic laser field in the ladder configuration is being formulated. The system is allowed to be dressed by both laser-field photons (double dressing). The temporal behavior of the system under consideration is being explored numerically. Although the use of dressed-basis density matrix equations introduces major complexity into the equations, this procedure has crucial importance to the understanding of the atomic spectrum and the underlying physics of the processes involved. The system is found to possess a gain without population inversion, as well as a regular gain with inversion for various transitions, both in the transient and steady-state regimes. Enhancement of the refractive index accompanied by vanishingly small absorption was also found. The frequency response of various transitions is explored via numerical Fourier analysis. Some transitions are found to exhibit a dispersion-like line shape, clear evidence of a quantum-coherent interference effect. The spectrum consists of two distinct quintets centered about the coupling and probe-laser frequencies. The spectral features consisting of each quintet are located symmetrically (at resonance conditions only) around the line center at positions shifted from the center by the generalized Rabi and double Rabi frequencies.