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Journal of Physics B Atomic Molecular and Optical Physics

Quantum noise reduction in a laser by cascade coherent excitation

Xiangming Hu, Zhizhan Xu

Published Feb 20, 2001• 2 citations
Publisher

Abstract

We study the statistical properties of a three-level laser where cascade coherent excitation as a two-step process is used as a coherent pump and a laser field is generated on the upper transition. It is shown that the laser intensity fluctuations are suppressed up to 50% below the shot noise limit and that the laser linewidth is reduced below the Schawlow-Townes formula by more than one order of magnitude of the laser intensity. By transforming to the picture dressed by the coherent field on the upper transition, we identify a transfer of the lower coherent excitation to be responsible for the quantum noise reduction. Cascade coherent excitation turns out to be a new way in which one can create a pathway for recycling of active electrons and regularization of laser excitation process. The conditions for the physical realization of the Raman scheme (Ritsch et al 1992 Europhys. Lett. 19 7) as a limiting case is discussed.

DOI
10.1088/0953-4075/34/5/308

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We study the statistical properties of a three-level laser where cascade coherent excitation as a two-step process is used as a coherent pump and a laser field is generated on the upper transition. It is shown that the laser intensity fluctuations are suppressed up to 50% below the shot noise limit and that the laser linewidth is reduced below the Schawlow-Townes formula by more than one order of magnitude of the laser intensity. By transforming to the picture dressed by the coherent field on the upper transition, we identify a transfer of the lower coherent excitation to be responsible for the quantum noise reduction. Cascade coherent excitation turns out to be a new way in which one can create a pathway for recycling of active electrons and regularization of laser excitation process. The conditions for the physical realization of the Raman scheme (Ritsch et al 1992 Europhys. Lett. 19 7) as a limiting case is discussed.
We demonstrate that the intensity fluctuations of a laser with a Raman gain medium, described by a large number of independent 3-level atoms, can drop well below the shot noise level. In the limit of a good cavity, where one can adiabatically eliminate the atoms, we find an optimum Mandel Q parameter of Q ≈ −1/2 over a large range of parameters, when the laser is operated well above threshold. This leads to a strong suppression of the low-frequency quantum fluctuations in the laser output. In addition we find that due to suppression of spontaneous emission into the lasing mode, the spectral linewidth of the emitted light can be reduced below the Schawlow-Townes limit by more than one order of magnitude.
Based on the standard laser model of a large number N of model atoms resonantly coupled to a single lasing mode, we show that the nonlinear dynamics of the active atoms of the laser can lead to output-intensity fluctuations significantly reduced below the shot-noise level. We identify the multiple recycling of the active electron from the lower lasing level to the upper level through the pumping as the key process leading to this dynamic-pump-noise reduction. This process has been neglected in most of the standard treatments of the laser so far. We find that the results are closely related to recent calculations based on the assumption of an external regular pump. For the widely used four-level model of the active atoms, the intensity noise can be reduced 50% below the shot-noise level. Generalizing the model to an m-level system, we find a quantum-noise reduction by a factor of 1/2m/(m-1)(m\ensuremath{\ge}3), leading to perfect output-intensity noise reduction in the limit of a large number of intermediate steps in the recycling process of the active atoms. Finally, we demonstrate that the bandwidth of the noise reduction can be significantly enhanced using a nonlinear absorber in the cavity.
We show that the nonlinear dynamics of the active atoms in conventionally pumped multilevel laser systems can lead to output intensity fluctuations significantly below the shot noise level1,2 (see also Refs, 3-5). Our calculations are based on the standard model of the laser which assumes a large number of atoms resonantly coupled to a single lasing mode. We identify the multiple recycling of the active electron from the lower lasing level to the upper level through pumping as the key process leading to this dynamic pump noise reduction. It is required that (i) the pump rates be comparable to the decay rates of the atom, and (ii) we have a closed repumping cycle, and a constant number of atoms. We find that the results are closely related to recent calculations based on the assumption of an external regular pump6 (for noise reduction in semiconductor lasers, see Ref. 7).
We consider the problem of reducing the contributions of pump and spontaneous-emission noise to the output noise of a laser field. We consider two models based on an atomic medium, one analytic, the other involving numerical simulation of a sequence of pump cycles. The predictions of both models are shown to agree. For regular pump excitation the intensity fluctuations of a laser well above threshold may be reduced to zero at the cavity resonance frequency if the ratio of the lifetimes of the upper and lower lasing levels is sufficiently large that spontaneous emission is suppressed. When the atomic lifetimes are comparable, spontaneous emission reduces the amount of noise reduction. For example, for equal atomic lifetimes regular pump excitation will result in a maximum noise reduction in the output field of one-half the shot-noise limit.
In this paper we investigate the quantum statistical properties in a cascade laser system with the lower transition being in a quantum-beat configuration. It is shown that a type of three-mode squeezing may be generated. The fluctuations of the intensity difference between the sum-mode from the quantum-beat and the cascade single mode may be reduced below the shot-noise limit. The best achievable noise reduction is up to 50%. Good squeezing occurs when the sum mode and the cascade single mode have normalized intensities much larger than unity and the intensity difference is much smaller than the respective intensity.
We present a general theory that connects the pump process in multilevel lasers with the statistics of the laser field. The key ingredient in our approach is the derivation of an effective master equation that involves only the two laser levels and that contains a non-Markovian pump term. This pump term gives rise to a narrowing of the photon-number distribution in steady state. The qualitative features of this dynamic noise reduction can be inferred from the eigenvalues of the pump term, which are known analytically. As the mechanism that is responsible for the noise reduction, we identify a correlated excitation process in which the effective excitation rate from the lower to the upper laser level depends on the photon number. This correlated excitation process is very different from an excitation at equidistant times, such as in lasers with periodic external injection. We stress that our approach is general and the treatment nonlinear because we do not resort to approximations such as an adiabatic elimination of atomic variables or the linearization of a Fokker-Planck equation. It is therefore particularly relevant for the description of systems where the active medium consists of a few atoms only and where the field losses are not negligible on the time scale of the atomic relaxations. This would be the case in an ion-trap laser. For such a situation our results are substantially different from those obtained by a linearized treatment. \textcopyright{} 1996 The American Physical Society.