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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Realization of lasing without inversion in the system with lower-level coherence

Zhenfei Luo, Zhizhan Xu

Published Sep 10, 1993• 0 citations
Publisher

Abstract

It is shown that the ladder system with lower-level coherence may be used to obtain lasing without inversion. The present model system has several important features. (1) No requirement is placed on atomic decay rates. (2) The Rabi frequency of coherence-driving field must exceed a lower threshold. (3) An unidirectional pumping is indispensable. (4) A dressed-state-coherence origin of gain is proved without strong coherence-driving field approximation.

DOI
10.1117/12.155782

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Physical Review A•Jul 15, 2003•28 citations
It is shown that the ladder system with lower-level coherence may be used to obtain lasing without inversion. The present model system has several important features. (1) No requirement is placed on atomic decay rates. (2) The Rabi frequency of coherence-driving field must exceed a lower threshold. (3) An unidirectional pumping is indispensable. (4) A dressed-state-coherence origin of gain is proved without strong coherence-driving field approximation.
We study the operational properties of the lasing field generated from strongly driven two-level atoms in a ring cavity by including the field saturation to all orders. Lasing without inversion between bare atomic states can occur for both off-resonant-- and resonant-pump fields. In the case of an off-resonant--pump field, lasing occurs at one of the Rabi sidebands, for which there exists population inversion between the relevant dressed-atom--field states. In the case of a resonant-pump field, lasing can occur near either of two Rabi sidebands, for which there is no population inversion between the dressed states; here the gain is due to the atomic coherence between the dressed states. While the operation of the off-resonantly--pumped dressed-state laser is similar to that of an ordinary laser, the operation of the resonantly pumped dressed-state laser exhibits some interesting features, such as (1) mode pushing and (2) larger laser intensity coming from smaller linear gain as the detuning is changed. In order to show such features, the calculations have to go beyond the secular approximation.
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.
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.
A scheme for obtaining laser in the deep x-ray regime is proposed based on the principle of gain without inversion. A ladder scheme is proposed in Ar+8{\mathrm{Ar}}^{+8}Ar+8 system. In this system, conventional lasing with population inversion has been obtained in a neonlike fashion. This lasing field is proposed for the drive field on the higher transition of the ladder. A coherent field obtained in the high harmonics ultrashort laser provides the probe field to be amplified. This will be selected to best match the frequency needed for the transition from lower level of the present x-ray lasing to the ground state. Numerical calculations in the bare state picture exhibit possible gain at resonance, and at the Rabi side bands, for appropriate choice of system parameters, i.e., the strength of the driving field, the strength of the incoherent pump that provides the required energy needed for the inversionless amplification and the deexcitation rate. The latter rate is detrimental to lasing as it increases. It is quite interesting to note that the system exhibits surprisingly high stability for gain without inversion even for quite high rate of the incoherent deexcitation processes. Real and imaginary parts of the coherences were also obtained for detuned drive and probe fields. These provide insight into the role played by the quantum interference. The present theoretical calculations give high confidence in the quantum interference process as a candidate for realizing very short wavelength laser.