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Theoretical and Mathematical Physics

Nonequilibrium statistical operator method in the theory of a single-mode laser based on two-level atoms

L. A. Pokrovskii

Published Oct 1, 1978• 7 citations
Publisher
DOI
10.1007/bf01036291

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The quantum theory of two-level atom single-mode laser system of Sargent, Scully and Lamb is extended to two-mode laser in a three-level atomic system with common lower level, and master equation is obtained for the system with all the three levels being pumped. There appear four terms in the master equation that are absent in the single-mode case and those interpreted as 2-photon processes play an especial role in the present case. The master equation is represented by a probability flow diagram in two-dimensions with the photon numbers n1 and n2 of the two-mode as variables. The probability flow diagram can be extended to infinity, and each arrow of it represents a term of the right hand side of master equation. By taking sum over one of the variables n1 or n2, the master equation is reduced to two equations, each of them can be represented by an one-dimensional probability flow diagram. The equation of motion under steady state is obtained by considering the correspondence between the macroscopic balance and the microscopic balance.A parameter H is introduced to reduce the equation of motion and to facilitate the mathematical procedure and a formal solution is thus obtained. Using the equation of motion and its formal solution various operation characteristics are discussed. Among them are: the threshold condition for each mode; the condition of only one mode operation; the variation of photon statistics between single-mode operation and two-mode operation and the variation of photon statistics with lower level being pumped and not pumped.

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We have studied the statistical and squeezing properties of the cavity light generated by a two-level laser. This optical system contains N two-level atoms available in a cavity coupled to a single-mode vacuum reservoir. They are pumped to the top level from the bottom level by means of the electron bombardment. Applying the steady-state solutions of the equations of evolution of the expectation values of the atomic operators and the quantum Langevin equation, we obtained the global and local photon statistics of the single-mode light beam. We have found that, for the two-level laser operating well above the threshold, the uncertainties in the plus and minus quadratures are equal and satisfy the minimum uncertainty relation. In view of this, we have identified the light generated by the laser operating well above threshold to be coherent. On the other hand, the light generated by the laser operating at threshold is found to be chaotic. From the obtained results, we have also observed that a large part of the local mean photon number, the local photon number variance, and the local quadrature variance are confined in a relatively narrow frequency interval.

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Fluctuations in a single-mode laser using three-level atoms

L. A. Pokrovskii, Alexander M. Khazanov

Russian Physics Journal•Feb 1, 1984•0 citations
The density operator theory and method are used to extend the fully quantum-mechanical theory of the two-level single-mode laser advanced by Sargent, Scully and Lamb (1974) to the homogeneously broadened four-level atomic system so that the master equation of the three-mode laser operation for this system is obtained. The steady-state operation characteristics of the laser in different cases are discussed and compared. Especially, pictorial comparison and discussion of the quantum-statistical properties of the laser are carried out by means of numerical computation. Meanwhile some experimental results obtained by Otsuka (1978) are qualitatively explained.
The quantum theory of two-level atom single-mode laser system of Sargent, Scully and Lamb is extended to two-mode laser in a three-level atomic system with common lower level, and master equation is obtained for the system with all the three levels being pumped. There appear four terms in the master equation that are absent in the single-mode case and those interpreted as 2-photon processes play an especial role in the present case. The master equation is represented by a probability flow diagram in two-dimensions with the photon numbers n1 and n2 of the two-mode as variables. The probability flow diagram can be extended to infinity, and each arrow of it represents a term of the right hand side of master equation. By taking sum over one of the variables n1 or n2, the master equation is reduced to two equations, each of them can be represented by an one-dimensional probability flow diagram. The equation of motion under steady state is obtained by considering the correspondence between the macroscopic balance and the microscopic balance.A parameter H is introduced to reduce the equation of motion and to facilitate the mathematical procedure and a formal solution is thus obtained. Using the equation of motion and its formal solution various operation characteristics are discussed. Among them are: the threshold condition for each mode; the condition of only one mode operation; the variation of photon statistics between single-mode operation and two-mode operation and the variation of photon statistics with lower level being pumped and not pumped.
We have studied the statistical and squeezing properties of the cavity light generated by a two-level laser. This optical system contains N two-level atoms available in a cavity coupled to a single-mode vacuum reservoir. They are pumped to the top level from the bottom level by means of the electron bombardment. Applying the steady-state solutions of the equations of evolution of the expectation values of the atomic operators and the quantum Langevin equation, we obtained the global and local photon statistics of the single-mode light beam. We have found that, for the two-level laser operating well above the threshold, the uncertainties in the plus and minus quadratures are equal and satisfy the minimum uncertainty relation. In view of this, we have identified the light generated by the laser operating well above threshold to be coherent. On the other hand, the light generated by the laser operating at threshold is found to be chaotic. From the obtained results, we have also observed that a large part of the local mean photon number, the local photon number variance, and the local quadrature variance are confined in a relatively narrow frequency interval.