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Physical Review A

Lasing without inversion due to parametric instability of the laser near the exceptional point

Iliya V. Doronin, A. A. Zyablovsky, E. S. Andrianov, Alexander Pukhov, Alexey P. Vinogradov

Published Aug 26, 2019• 35 citations
Publisher

Abstract

We propose an approach to obtain lasing without inversion, which does not require preparation of the quantum superposition of states in the active medium. We demonstrate that with periodically variable pumping, lasing is achievable even in the case when the population inversion of the active medium is always negative. This is possible due to the fact that laser in strong-coupling regime is a non-Hermitian system with an exceptional point existing at negative value of population inversion. We show that due to nonorthogonality of eigenstates near the exceptional point, the time variation of pump power can result in parametric instability in the laser and excitation of the electromagnetic field self-oscillations. These oscillations take place even when the population inversion of the active medium is always negative. Our results help to pave the way for the creation of a new class of lasers operating at negative value of population inversion.

DOI
10.1103/physreva.100.021801

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We propose an approach to obtain lasing without inversion, which does not require preparation of the quantum superposition of states in the active medium. We demonstrate that with periodically variable pumping, lasing is achievable even in the case when the population inversion of the active medium is always negative. This is possible due to the fact that laser in strong-coupling regime is a non-Hermitian system with an exceptional point existing at negative value of population inversion. We show that due to nonorthogonality of eigenstates near the exceptional point, the time variation of pump power can result in parametric instability in the laser and excitation of the electromagnetic field self-oscillations. These oscillations take place even when the population inversion of the active medium is always negative. Our results help to pave the way for the creation of a new class of lasers operating at negative value of population inversion.
The most commonly used lasers operate with population inversion. This requires an incoherent pumping power (from lamps, electrical discharges, etc.) that rapidly scales with the frequency of the generated laser radiation. In practice, this is the main obstacle for the operation in the continuous-wave regime of short-wavelength lasers in the UV, X-rays, etc. But lasers can also operate without population inversion using atomic coherences excited in the laser medium by coherent pumping with another laser. We present in this paper a short review of the field of lasing without inversion (LWI). In particular, we summarize the basic physics of LWI in the framework of both semiclassical theory and quantumjump formalism to describe light-matter interaction. We also review the experimental state-of-the-art in LWI. Most proof-of-principle demonstrations of LWI have used atomic vapours, so far. But recently gain without inversion (a pre-requisite for lasing) has been observed also in a technologically relevant medium: semiconductor nanostructures that can be tailored to have “artificial atom” electron states.
Exceptional points show great prospects for applications such as imaging, sensing and designing lasers. Recently, systems with amplifying active medium exhibiting pump-induced exceptional points have attracted much attention due to possibility of controlling strong coupling between light and matter with the aid of pumping. In such structures, the interaction of active molecules with external degrees of freedom, such as phonons or impurities, leads to the destruction of the correlation between polarizations of different molecules. We study the effect of the correlations decay on a system behavior near pump-induced exceptional point. We show that strong coupling persists and eigenvectors together with eigenfrequencies coalesce at a negative value of population inversion, regardless of correlation decay magnitude. Thus, we show that exceptional points are robust to correlation decay, which is crucial for designing systems with exceptional points.
The creation of nanoscale lasers that operate above a coherent threshold is a challenging problem. We propose a way to circumvent this issue using systems in which a strong coupling regime is achieved between the light and the active medium. In the strong coupling regime, energy oscillations take place between the EM field in the cavity and the atoms. We show that by applying appropriate time modulation to the pumping, it is possible to control these energy oscillations in such a way that coherence in the laser system appears below the lasing threshold. In this approach, the radiation linewidth is two orders of magnitude smaller than the linewidth of a conventional laser for the same photon number. In addition, the second order coherence function of the output radiation is reduced from two to one before the system reaches a positive population inversion. Our results pave the way for the creation of nanoscale sources of coherent radiation that can operate below the lasing threshold.
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.
By means of numerical modeling of nonlinear and analytical solution of linearized Maxwell-Bloch equations, we find an intriguing regime of a superradiant laser with a symmetric low-Q Fabry-Perot cavity equipped with a distributed feedback of counter-propagating waves. We find that, in a wide range of parameters, there is lasing of a strongly-asymmetric self-modulated powerful polariton mode accompanied by excitation of several almost symmetric weak polariton or electromagnetic modes. The frequency of the powerful mode is approximately coincides with a center of the laser spectral line, and the frequencies of the weak modes are outside the spectral line of an active medium. We show that such a lasing takes place due to formation of a self-consistent inhomogeneous asymmetric grating of population inversion of active centers that provides undamped Rabi oscillations of the population inversion and dipole moments of centers. The grating makes the powerful ‘central’ mode strongly asymmetric, and the Rabi oscillations of active centers excite the weak ‘sideband’ modes due to the quadratic resonant nonlinearity of the two-level active medium.
Introduction We were able to show in Chapter 3 that a medium in which we can obtain a population inversion (i.e. a situation in which the population density in the excited state is greater than that in the fundamental level) allows for optical gain of an electromagnetic wave having a frequency near to the resonant frequency of the system. By introducing feedback of the amplified signal into the medium, the system can be made to oscillate naturally, resulting in laser oscillations . To obtain this population inversion, we must introduce at least a third (and perhaps even a fourth) energy level into the system. (We saw how a two-level system under the influence of an intense pump beam will saturate with no resulting population inversion.) The aim then of this chapter is to introduce the concepts necessary to extend our two-level system into a working model capable of illustrating the phenomenon of laser oscillation. We will not spend too much time discussing atomic transition lasers as they do not figure readily in our treatment of quantum electronic properties of semiconductors. An exception will be made, however; we brush upon the particular topics of a diode pumped laser in Complement 4.E and a quantum cascade laser in Complement 13.H. Population inversion and optical amplification Population inversion We will show how population inversion can be achieved by carrier transfer from higher lying levels to the upper level of a two-level subsystem of interest.