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

The kinetic of the two-photon lasing with one and two quanta cavity losses

N. A. Enaki, Marina Ţurcan

Published Dec 18, 2008• 2 citations
Publisher

Abstract

The be-quanta generation and the coherent process of the light at two-photon emission it's a new type of the coherence which can be realized between pairs of the particles [14]. This possibility of the emission can be realized in the two-photon laser and maser. The first experiments demonstrate this realization [10]. In this paper it is propose a new system of the kinetic equations which describes the non-coherent and be-quanta coherent emission which take into account emissions and the transition from spontaneous to induced emissions in the system. It is studied the rate of the emission as function of this parameters [17]. It is demonstrate mono-photonics losses from the resonator drastically destroy the coherence between the be-photons.

DOI
10.1117/12.823643

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The be-quanta generation and the coherent process of the light at two-photon emission it's a new type of the coherence which can be realized between pairs of the particles [14]. This possibility of the emission can be realized in the two-photon laser and maser. The first experiments demonstrate this realization [10]. In this paper it is propose a new system of the kinetic equations which describes the non-coherent and be-quanta coherent emission which take into account emissions and the transition from spontaneous to induced emissions in the system. It is studied the rate of the emission as function of this parameters [17]. It is demonstrate mono-photonics losses from the resonator drastically destroy the coherence between the be-photons.
The two-photon generator of coherent light formed from entangled photon pairs is proposed. Considering the multi-mode field of micro-cavity in the processes of generation of photon pairs the two-photon resonator losses are proposed. The master equation for cavity biphotons is obtained from quantum treatment of problem. The analytical and numerical stationary solutions for master equation are presented. Also is found that the lasing of light is started from vacuum fluctuations of cavity field. The comparison of proposed model with other two-photon laser models is discussed.
Multi-photon lasing has been realized in systems with strong nonlinear interactions between emitters and cavity modes, where single-photon processes are suppressed. Coherence between the internal states of a quantum emitter, or among multiple emitters, plays a key role. Such continuous nonclassical sources of light can find applications in quantum computation, quantum sensing, quantum metrology, and quantum communication. This thesis explores the multi-photon lasing phenomena in various quantum dot-photonic crystal cavity quantum electrodynamic (QED) setups. Exciton-phonon interactions are inevitable in such systems and are incorporated using the polaron-transformed master equation. The Born-Markov approximation is employed to obtain the reduced density matrix rate equation. Using quantum laser theory, we derived the Scully-Lamb laser rate equations and evaluated the single- and multi-photon excess emission rates defined as the difference between emission and absorption rates into the cavity mode without mean-field approximations. We investigated cooperative two-photon lasing, correlated emission lasing, hyperradiant lasing, non-degenerate two-mode two-photon lasing, and continuous variable entanglement in open quantum systems with single or multiple semiconductor quantum dots (two-level, three-level, and four-level) driven coherently/incoherently and coupled to single/ bimodal cavities.
Considering the resonator losses in photon pairs the coherence between the photon pairs as the function of number of bimodes is studied. Taking into account the big number of resonator bimodes in which the photon pairs with fixed energy and phase are generated, it is demonstrated that the coherence between the pairs of photons remains larger than the coherence between individual photons. It is shown that the ignition of two-photon lasing from vacuum fluctuations increases with the increase in the number of resonator modes. This effect can be regarded as a collective phenomenon between the resonator bimodes in which the pairs of entangled photons are generated.
The two types of cooperative effects between the converted photons in the multiple steps of Raman lasing are proposed. The first type involves the cooperative process between the photons of one of the steps of Raman conversion. The second cooperative effect appears between the photons belonging to different steps of multiple conversions. This new type of generated coherent state is proposed by novel bimodal entangled sources, which take into consideration both the coherence and collective phenomena between the photons belonging to the system of the bimodal field obtained in multiple Raman emissions. For this, the creation and annihilation operators of the new resonator quasi-particle ware introduced taking into consideration the Hilbert space of field vectors at frequency differences, ωp+1−ωp between the anti-Stokes components of multiple Raman lasing. The application of higher-order multiple Roman bimodal coherent field quantum information is described in accordance with the definition of quantum amplitude and phase of such entangled states of light. The cooperative properties of the bimodal field in the multiple scattering processes of Raman lasing in the cavity/fiber and its interaction with ensemble of atoms prepared in coherent state are proposed. We introduced the new characteristics of bi-modes field in which the multiple Raman scattering takes into consideration the interaction with coherent excitation and non-stationary quantum fluctuations of the generation rate of the introduced quasi particles. Here, we represent the rate moments through the annihilation and generation operators of the cavity quasi-parties.
A quantum theory of two-photon correlated-spontaneous-emission lasers (CEL's) is developed, starting from the exact atom-field interaction Hamiltonian for cascade three-level atoms interacting with a single-mode radiation field. We consider the situation where the active atoms are prepared initially in a coherent superposition of three atomic levels and derive a master equation for the field-density operator by using a quantum theory for coherently pumped lasers. The master equation is transformed into a Fokker-Planck equation for the antinormal-ordering Q function. The drift coefficients of the Fokker-Planck equation enable us to study the steady-state operation of the two-photon CEL's analytically. We have studied both resonant two-photon CEL for which there is no threshold, and off-resonant two-photon CEL for which there exists a threshold. In both cases the initial atomic coherences provide phase locking, and squeezing in the phase quadrature of the field is found. The off-resonant two-photon CEL can build up from a vacuum when its linear gain is larger than the cavity loss (even without population inversion). Maximum squeezing is found in the no-population-inversion region with the laser intensities far below saturation in both cases, which are more than 90% for the resonant two-photon CEL and nearly 50% for the off-resonant one. Approximate steady-state Q functions are obtained for the resonant two-photon CEL and, in certain circumstances, for the off-resonant one.
In a recent article1to which we shall refer as [S&B], a two-photon laser was proposed and analyzed. This device consists of a cavity resonant at frequency vAand containing ions of type B with an inverted population NB/V between levels separated by an energy difference hvBsuch that vB= 2vA; it is necessary that the system not lase at vB, which criterion can be satisfied by low reflectivity of the cavity at frequency vB, by strong parasitic absorption in the laser material near frequency vB, or preferably by a choice of ion such that the transition vBis highly forbidden to a single-quantum process. The authors of [S&B] thus show that a certain priming density of photons of frequency vAwill provoke the simultaneous emission from the inverted population NBof pairs of photons vAat a rate exceeding the cavity loss,t he process diverging until the population inversion is eliminated.