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Acta Physica Sinica

Laser without inversion in a Δ -configuration three-level system with cyclic transition

Qiang Gao, Song Tong-Qiang

Published Jan 1, 2012• 0 citations
Publisher

Abstract

In the case of incoherent pumping, laser without population inversion in a resonant three-level Δ -configuration system is investigated. By taking the strong coupling field limit, we obtain the approximate steady-state analytical solution of populations and imaginary part of coherences within the dressed-state regime, and discuss the condition of the generating of laser without inversion and the dependences of population distribution and system gain on Rabi frequency of the probe and coherence fields. The results show that the resonant three-level Δ-configuration system is always in the state of no population inversion, and laser without inversion occurs if one of the two fields is strong. When one of the two fields is much stronger than the other one, the gain without inversion is independent of the two Rabi frequencies.

DOI
10.7498/aps.61.144205

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In the case of incoherent pumping, laser without population inversion in a resonant three-level Δ -configuration system is investigated. By taking the strong coupling field limit, we obtain the approximate steady-state analytical solution of populations and imaginary part of coherences within the dressed-state regime, and discuss the condition of the generating of laser without inversion and the dependences of population distribution and system gain on Rabi frequency of the probe and coherence fields. The results show that the resonant three-level Δ-configuration system is always in the state of no population inversion, and laser without inversion occurs if one of the two fields is strong. When one of the two fields is much stronger than the other one, the gain without inversion is independent of the two Rabi frequencies.
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.
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.
Summary form only given.A three-level atom in the V-configuration is treated under two coherent laser fields at resonance with the two allowed transitions. The master equation for the system and full quantum mechanical Hamiltonian are derived, and equations of motion for the elements of the density matrix are obtained by projecting into the bare- and dressed-states schemes. Analysis of light amplification without population inversion in this V-type system is accomplished within the framework of the dressed-state basis. The physical content of the equations of motion for the density matrix elements, namely the coherences and the populations is provided by identifying effective decay and relaxation rates and gain/absorption constants with the appropriate composite coefficients. These depend on the Rabi frequencies of both the drive and probe coherent fields. Time-dependent solutions for both the coherences and the populations are obtained both numerically and analytically under the secular approximation. We have shown how to construct these analytical approximate time-dependent solutions for dressed-state populations and coherences. These approximate solutions, as well as the full numerical calculation quantities, exhibit oscillations at the generalized Rabi frequency.
Light-induced absorption with population inversion and amplification without population inversion in a coherently prepared closed three level V-type system are investigated. This study is performed from the point of view of a two color dressed-state basis. Both of these processes are possible due to atomic coherence and quantum interference contrary to simple intuitive predictions. Merely on a physical basis, one would expect a complementary process to the amplification without inversion. We believe that absorption in the presence of population inversion found in the dressed-state picture utilized in this study, constitutes such a process. We derive approximate analytic time-dependent solutions, for coherences and populations that are compared with full numerical solutions exhibiting good agreement. Steady-state quantities are also calculated, and the conditions under which the system exhibits absorption and gain with and without inversion, in the dressed-state representation are derived. It is found that for weak input probe-laser field absorption with inversion and amplification without inversion may occur, for a range of system parameters. These take place at resonance and the generalized Rabi ac Stark-shifted frequencies, in agreement with exprimental investigations, and at beat frequencies, depending on the relevant parameters.
Summary form only given. We study a model for an incoherently pumped laser operating with a Doppler-broadened three-level system placed in a doubly resonant cavity and producing two laser fields, one of them without population inversion. Each laser field couples to only one of the transitions of the three-level medium. We have studied our model for parameters appropriate to two real atomic systems (i) a cascade scheme in atomic /sup 138/Ba looking for lasing with (without) inversion at /spl lambda//sub /spl beta//=554 nm (/spl lambda//sub /spl alpha//=821 nm), and (ii) a V-scheme in atomic /sup 85/Rb with ordinary lasing at /spl lambda//sub /spl alpha//=780 nm and lasing without inversion (LWI) at /spl lambda//sub /spl alpha//=4216 nm. These two cases are qualitatively different in that two-photon processes are responsible for inversionless gain in case (i) while LWI in case (ii) arises from one-photon processes. Moreover, the frequency up-conversion ratio is R=0.67 for the case of /sup 138/Ba and it is R=1.88 for the case of /sup 85/Rb. In spite of the fact that the frequencies of the two laser fields are relatively different, our results show that dual-wavelength lasing extends up to Doppler broadening values typical for optical transitions of atoms in a vapor cell. In case (i) /spl alpha/-lasing occurs without two-photon inversion only for approximately the lower half of the domain of Doppler-broadening values. However, in case (ii) one has LWI in all the domains. Some considerations for a practical realization of the dual-wavelength inversionless-conventional laser are discussed.