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Journal of Experimental and Theoretical Physics Letters

Generation of sub-Poisson light by a single-mode two-level laser with incoherent pumping

A. V. Kozlovskiĭ, А. Н. Ораевский

Published May 1, 1998• 1 citation
Publisher

Abstract

It is found that the steady-state radiation of a single-mode two-level laser with incoherent pumping can be in a nonclassical (sub-Poisson) state if the spontaneous decay rate is less than the cavity loss rate and the pumping rate. The optimal conditions of squeezing are found. Multiple squeezing of the radiation intensity is possible in a transient lasing regime.

DOI
10.1134/1.567751

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It is found that the steady-state radiation of a single-mode two-level laser with incoherent pumping can be in a nonclassical (sub-Poisson) state if the spontaneous decay rate is less than the cavity loss rate and the pumping rate. The optimal conditions of squeezing are found. Multiple squeezing of the radiation intensity is possible in a transient lasing regime.
The quantum statistical properties of the radiation of a one-atom two-level laser with incoherent pumping are analyzed. Solution of the Liouville equation for the density operator in the basis of Fock states shows that stationary radiation from a single-mode laser with incoherent pumping can be in a squeezed (sub-Poissonian) stationary state if the rate of spontaneous decay is lower than the rate of cavity losses and the pump rate. Inside the cavity the Fano factor reaches F =0.85 (15% squeezing). Multiple squeezing ( F =0.19) is possible in the transient lasing regime. Significant squeezing obtains at the cavity output; the spectral Fano factor at zero frequency is 0.36 under optimal conditions.
The problem of the creation of a sub-Poissonian radiation source on the basis of a semiconductor laser with an external cavity is considered, which operates, from the viewpoint of quantum optics, in the single-mode regime. The conditions of the generation of sub-Poissonian radiation, under which the whole set of sub-threshold modes, including the nearest modes of the external (long) cavity, is completely suppressed at room temperature, were experimentally revealed and theoretically studied. Single-frequency low-noise lasing is of interest not only for the creation of nonclassical light sources, but also for sensitive spectroscopic applications in the classical domain.
We theoretically consider a three-level laser with an incoherent one-way pump from a ground state into an intermediate excited state and a coherent drive into the upper laser state. The possibilities of inversionless lasing are studied. It is demonstrated that, in the case of a strong coupling with the drive laser (when its generation depends essentially on the three-level medium), the quantum properties of laser radiation can be improved by using m-quantum coherent excitation or by applying a sub-Poissonian coherent pump.
The reduced density matrix method is used to calculate the quantum-statistical properties of the radiation of a quantum-dot laser operating on the whispering gallery mode of a dielectric microsphere. It is shown that under the conditions of strong coupling between the quantum dot and an electromagnetic field the radiation of such a laser can be in a nonclassical (sub-Poissonian) state. The laser scheme considered is characterized by an extremely low lasing threshold and a small number of saturation photons, as result of which lasing is possible with close to zero population inversion of the working levels, if g ≫ P ≫ γ ≫ Γ, where g is the field-matter interaction constant, P is the pumping rate, γ is the loss rate of the resonator, and Γ is the spontaneous emission rate. The largest squeezing inside the resonator-microsphere (the Fano factor F = 0.75) obtains for g ≫ P ≫ γ ≫ Γ, and the greatest squeezing in the fluctuation spectrum outside the resonator [V(ω = 0) ≈ 0.25] occurs for g ∼ P ∼ γ ≫ Γ, and in this case a substantial deviation of the photon number statistics of the radiation leaving the resonator from the Poissonian statistics is observed.
A quantitative analysis is made of quantum fluctuations in the number of photons in the resonator of a single-mode laser considered in a quasi-linear approximation. An expression is obtained for a general four-level system, which is exact above the lasing threshold, but can also be used to calculate the fluctuations in the case of three- and two-level lasers. Above the threshold when certain relationships between the spontaneous decay constants are satisfied, the photon statistics are of the sub-Poisson type in four- and three-level systems. However, for other relationships between the decay constants, pumping rate, and average number of photons, fluctuations in the resonator obey both the Poisson and super-Poisson statistics with variances much greater than the average number of photons. Both Poisson and super-Poisson statistics with large values of the variance are found for a two-level system. The results of calculations indicate that, in general, there is no coherent Glauber state of the field in a laser resonator when the threshold is significantly exceeded.
The problem of the two-level laser is studied analytically. The steady-state solution is expressed as a continued fraction and allows for accurate approximation by rational functions. Moreover, we show that the abrupt change observed in the pump dependence of the steady-state population is directly connected to the transition to the lasing regime. The condition for a sharp transition to Poissonian statistics is expressed as a scaling limit of vanishing cavity loss and light-matter coupling, $\ensuremath{\kappa}\ensuremath{\rightarrow}0$, $g\ensuremath{\rightarrow}0$, such that ${g}^{2}/\ensuremath{\kappa}$ stays finite and ${g}^{2}/\ensuremath{\kappa}>2\ensuremath{\gamma}$, where $\ensuremath{\gamma}$ is the rate of nonradiative losses. The same scaling procedure is also shown to describe a similar change to the Poisson distribution in the Scully-Lamb laser model, suggesting that the low-$\ensuremath{\kappa}$, low-ggg asymptotics is of more general significance for the laser transition.