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Physical Review A

Lasing without inversion in the absence of a coherent coupling field

Gautam Vemuri, Kashyap V. Vasavada, G. S. Agarwal

Published Oct 1, 1995• 40 citations
Publisher

Abstract

We analyze the inversionless gain in a three-level ladder system by replacing the usual coherent coupling field with an incoherent field. Surprisingly, it is found that one can obtain inversionless amplification of a weak probe even in the absence of a coherent field in the model. We conclude that gain is determined by the ensemble average of the product of the two-photon coherence and the ``effective Rabi frequency'' of the field. Thus, even though the incoherent pump reduces the two-photon coherence, gain can be restored by choosing sufficiently high strengths of the incoherent field.

DOI
10.1103/physreva.52.3228

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Journal of Natural Science of Heilongjiang University•Jan 1, 2007•0 citations
We analyze the inversionless gain in a three-level ladder system by replacing the usual coherent coupling field with an incoherent field. Surprisingly, it is found that one can obtain inversionless amplification of a weak probe even in the absence of a coherent field in the model. We conclude that gain is determined by the ensemble average of the product of the two-photon coherence and the ``effective Rabi frequency'' of the field. Thus, even though the incoherent pump reduces the two-photon coherence, gain can be restored by choosing sufficiently high strengths of the incoherent field.
We explore the possibility of enhancing the gain in lasing without inversion schemes by replacing the usual incoherent pump with a finite bandwidth (spectrally coloured) pump. Three level atoms in the ladder and lambda configuration are modelled and we find that replacing the incoherent pump with a partially coherent pump amplifies the gain by as much as a factor of 4. The results are obtained via Monte-Carlo simulations of the density matrix equations, which, for a coloured pump, have the form of Langevin equations. We find that for a given set of atom-field parameters, the gain for coherent pumping is larger than for incoherent pumping, and that maximum gain is obtained for a partially coherent pump. The frequency of the coloured pump plays an important role in determining the optimum gain that can be obtained.
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.
Recently it was reported that replacing an incoherent pumping mechanism by a spectrally colored (partially coherent) pump can lead to significant gain enhancement in lasing without inversion schemes [Phys. Rev. A 48, R4055 (1993)]. We extend that study further by considering the effects of the noise parameters (strength and bandwidth) of the pump on the gain in two types of three-level atomic energy-level schemes---the ladder and the \ensuremath{\Lambda} models. The calculations presented in this paper show a way to continuously ``tune'' the bandwidth of the pump and make a direct comparison between the gain obtained for coherent, incoherent, and partially coherent pumping. We find that for a given set of atom-field parameters, the gain for coherent pumping is larger than for incoherent pumping, and that maximum gain is obtained for a partially coherent pump. Increasing the strength of the noise also leads to an increase in the gain. The frequency of the colored pump plays a critical role in determining the maximum gain that can be obtained.
Most models of lasing without inversion utilize incoherent pumping of the upper state of the transition on which lasing occurs. We suggest replacing incoherent pumping by a color pump (i.e. laser with a finite bandwidth) for selective pumping of the upper state, where one can also take advantage of the tunability of the laser. A three-level ladder system is considered with the upper two levels providing the lasing transition. We reduce the density matrix equations for this system to a set of eight coupled Langevin equations with multiplicative noise. These equations are solved using Monte-Carlo methods to obtain the gain as a function of various atom and field parameters. The use of the color pump leads to a significant enhancement in gain. Using a dressed states formalism, an explanation of the possible physical mechanism behind this gain enhancement is provided.
A scheme for obtaining a laser without inversion in the deep X-ray regime is proposed based on the principle of gain without inversion. A ladder scheme is proposed in the Ar 8+ system. In this system, conventional lasing with population inversion in a neonlike scheme is used. 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. The ground level is incoherently pumped into the highest level, while the latter is incoherently depumped into the ground level, at a different adjustable rate. A detailed density matrix calculation of the ladder configuration is performed [3], and the conditions under which the system exhibits inversionless gain, as well as regular gain, are derived. Numerical calculations in the bare state picture exhibits gain without inversion both at resonance and at the generalized Rabi side bands. The probe lineshape is shown to be constructed of two symmetrical dispersionlike features each centered at the generalized Rabi side bands. This is evidence of the quantum interference occurring at these locations and the basis for the gain without inversion.
A four-level system driven by two coherent fields is considered. the probe gain at a short wavelength can be achieved due to the quantum interference in the presence of an incoherent pump. The density matrix calculation provides the conditions for probe amplification from different origin, including gain without population inversion in any state basis, gain with population inversion in the dressed-state basis, and gain with population inversion in the bare-state basis. Also, by controlling Rabi frequency of the coupling field a totally changing from non-inversion to inversion can be achieved which does not depend on the intensity of the incoherent pump.