Coherent states in a laser cavity K. M. Priyashanka, K. A. I. L Wijewardena Gamalath

A mathematical model was developed to obtain the population inversion of the atoms in laser field in a laser cavity by considering the electric field in the optical cavity and the atomic states of the medium to be quantized. The master equation of the density operator of the laser field was studied analytically and numerically. Using coherent states, the Fokker-Plank equation for the phase space density for the laser field was solved analytically for the time dependent and steady state situations. The laser field above the threshold can be represented by a randomly phased mixture of coherent states. As the pump parameter increases in the laser process, the phase density becomes narrower, tending toward a delta function, creating a coherence laser field.A mathematical model was developed to obtain the population inversion of the atoms in laser field in a laser cavity by considering the electric field in the optical cavity and the atomic states of the medium to be quantized. The master equation of the density operator of the laser field was studied analytically and numerically. Using coherent states, the Fokker-Plank equation for the phase space density for the laser field was solved analytically for the time dependent and steady state situations. The laser field above the threshold can be represented by a randomly phased mixture of coherent states. As the pump parameter increases in the laser process, the phase density becomes narrower, tending toward a delta function, creating a coherence laser field.

International Letters of Chemistry Physics and AstronomyJul 1, 20151 citation

A semiclassical model for a laser field inside an optical cavity

K.M. Priyashanka, K.A.I.L. Wijewardena Gamalath

Treating the laser medium quantum mechanically and the laser electric field classically, a mathematical model was developed to study a laser field inside a single mode optical cavity by numerical and analytical techniques. The simulations for threshold population, population inversion and average population with electric field frequency for 500 kHz resonance frequency of the atom are presented. The gain coefficient and the pump parameter with the frequency of the cavity electric field for 1000 kHz resonance frequency of the atom were simulated. The threshold population is a minimum when the frequency of electric field is equal to the resonance frequency of the atom. The population inversion varies sinusoidal with time and the frequency of the electric field and is a maximum at the threshold frequency of the atom. The saturated laser intensity at steady state increases linearly with the pump parameter and for larger values of the pump parameter, a smaller time is needed to reach the saturation of the laser field.Treating the laser medium quantum mechanically and the laser electric field classically, a mathematical model was developed to study a laser field inside a single mode optical cavity by numerical and analytical techniques. The simulations for threshold population, population inversion and average population with electric field frequency for 500 kHz resonance frequency of the atom are presented. The gain coefficient and the pump parameter with the frequency of the cavity electric field for 1000 kHz resonance frequency of the atom were simulated. The threshold population is a minimum when the frequency of electric field is equal to the resonance frequency of the atom. The population inversion varies sinusoidal with time and the frequency of the electric field and is a maximum at the threshold frequency of the atom. The saturated laser intensity at steady state increases linearly with the pump parameter and for larger values of the pump parameter, a smaller time is needed to reach the saturation of the laser field.

World Scientific NewsJan 1, 20150 citations

Quantum theory of a laser with injected atomic coherence: Quantum noise quenching via nonlinear processes

Ning Lü, János A. Bergou

A quantum theory of a two-level single-mode laser with injected atomic coherence is developed by generalizing the Scully-Lamb laser theory to a form appropriate for the analysis of a coherently pumped laser. We assume that the active atoms are prepared initially in a coherent superposition of the upper and lower levels, and we derive the master equation for the field density operator by treating the interaction of the laser field with many active atoms simultaneously. It is shown that the photon-number distribution can be exactly Poissonian. The laser operation is analyzed in terms of the Fokker-Planck equation for the laser field. Both the intensity and phase diffusion coefficients are phase sensitive and, for stable laser operation, become much smaller than those of an ordinary laser. Consequently, the injected atomic coherence reduces both the photon-number noise and phase noise simultaneously. The intensity diffusion coefficient can vanish exactly, and at the same time the phase diffusion coefficient can become very small. This leads to spontaneous-emission noise quenching in the photon-number distribution, and the laser field can become very close to a coherent state. A scheme to generate the proper form of the initial atomic coherence necessary for the quantum noise quenching is proposed and analyzed.A quantum theory of a two-level single-mode laser with injected atomic coherence is developed by generalizing the Scully-Lamb laser theory to a form appropriate for the analysis of a coherently pumped laser. We assume that the active atoms are prepared initially in a coherent superposition of the upper and lower levels, and we derive the master equation for the field density operator by treating the interaction of the laser field with many active atoms simultaneously. It is shown that the photon-number distribution can be exactly Poissonian. The laser operation is analyzed in terms of the Fokker-Planck equation for the laser field. Both the intensity and phase diffusion coefficients are phase sensitive and, for stable laser operation, become much smaller than those of an ordinary laser. Consequently, the injected atomic coherence reduces both the photon-number noise and phase noise simultaneously. The intensity diffusion coefficient can vanish exactly, and at the same time the phase diffusion coefficient can become very small. This leads to spontaneous-emission noise quenching in the photon-number distribution, and the laser field can become very close to a coherent state. A scheme to generate the proper form of the initial atomic coherence necessary for the quantum noise quenching is proposed and analyzed.

Physical Review AJul 1, 198945 citations

Quantum theory of non-degenerate inversionless laser: Effects of initial partial coherence

Nadeem A. Ansari, A. H. Toor

In this paper, we have included the effects of initial partial coherence in the quantum theory of a non-degenerate inversionless laser. A three-level atomic system in open A-configuration is considered. The atoms are initially prepared in the partial coherent superposition of the lower two atomic levels with some incoherent population in the excited state. The master equation for the cavity field modes is derived and converted into a Fokker-Planck equation to determine the phase locking and stability conditions. The effects of initial partial coherence on the gain of two modes are studied under these conditions. The range of values of the initial partial coherence for which the action of lasing without inversion can take place are shown. Our results show that under certain conditions the two modes can amplify with equal gain below threshold.In this paper, we have included the effects of initial partial coherence in the quantum theory of a non-degenerate inversionless laser. A three-level atomic system in open A-configuration is considered. The atoms are initially prepared in the partial coherent superposition of the lower two atomic levels with some incoherent population in the excited state. The master equation for the cavity field modes is derived and converted into a Fokker-Planck equation to determine the phase locking and stability conditions. The effects of initial partial coherence on the gain of two modes are studied under these conditions. The range of values of the initial partial coherence for which the action of lasing without inversion can take place are shown. Our results show that under certain conditions the two modes can amplify with equal gain below threshold.

Journal of Modern OpticsDec 1, 19968 citations

Quantum Theory of Laser Radiation. II. Statistical Aspects of Laser Light

J. A. Fleck

We have solved a master equation to obtain the diagonal elements of the density matrix for laser light. The master equation represents a generalization of a master equation derived earlier for a single radiation mode interacting with $N$ stationary two-level atoms. The generalization takes into account the pumping scheme which characterizes a three-level laser. For positive temperatures and a lossless cavity, the equilibrium solution of the master equation gives the correct statistical-mechanical description of the atoms and radiation. For negative temperatures, the distribution function for the number of photons in the mode is either exponential or peaked, depending on whether the laser is operating below or above threshold. The calculated intensity fluctuations are in good agreement with semiclassical results for lasers operating slightly above threshold.We have solved a master equation to obtain the diagonal elements of the density matrix for laser light. The master equation represents a generalization of a master equation derived earlier for a single radiation mode interacting with $N$ stationary two-level atoms. The generalization takes into account the pumping scheme which characterizes a three-level laser. For positive temperatures and a lossless cavity, the equilibrium solution of the master equation gives the correct statistical-mechanical description of the atoms and radiation. For negative temperatures, the distribution function for the number of photons in the mode is either exponential or peaked, depending on whether the laser is operating below or above threshold. The calculated intensity fluctuations are in good agreement with semiclassical results for lasers operating slightly above threshold.

Physical ReviewSep 9, 196626 citations

Decoherence of the Laser Field in Energy Steady-State Operation

Mikio Fujii

The rate at which pure initial states satisfying the detailed balance condition on the photon number states deteriorate into mixtures in the decoherence process is computed for a laser field above threshold in the Scully-Lamb laser model. In steady-state laser operation, the field state suggested by Scully and Lamb is shown to be the least increase of the error area in the complex amplitude plane, thus becoming the most stable field state among the squeezed states characterized by the phase order parameter Δ.The rate at which pure initial states satisfying the detailed balance condition on the photon number states deteriorate into mixtures in the decoherence process is computed for a laser field above threshold in the Scully-Lamb laser model. In steady-state laser operation, the field state suggested by Scully and Lamb is shown to be the least increase of the error area in the complex amplitude plane, thus becoming the most stable field state among the squeezed states characterized by the phase order parameter Δ.

Journal of the Physical Society of JapanDec 15, 19990 citations

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stationary two-level atoms. The generalization takes into account the pumping scheme which characterizes a three-level laser. For positive temperatures and a lossless cavity, the equilibrium solution of the master equation gives the correct statistical-mechanical description of the atoms and radiation. For negative temperatures, the distribution function for the number of photons in the mode is either exponential or peaked, depending on whether the laser is operating below or above threshold. The calculated intensity fluctuations are in good agreement with semiclassical results for lasers operating slightly above threshold.