We study in detail the influence of pumping statistics on the laser dynamics. We apply the technique of quantum Langevin operators and generalize the corresponding noise operators to incorporate the statistical properties of the pump mechanism. These equations are then used to derive expressions for the phase and intensity fluctuations of lasers with various pump statistics. We find that a reduction of pump noise can lead to a significant squeezing of the photon number noise below the shot-noise limit. This is in complete agreement with our previous analysis, which used a density-operator approach.
We study in detail the influence of pumping statistics on the laser dynamics. We apply the technique of quantum Langevin operators and generalize the corresponding noise operators to incorporate the statistical properties of the pump mechanism. These equations are then used to derive expressions for the phase and intensity fluctuations of lasers with various pump statistics. We find that a reduction of pump noise can lead to a significant squeezing of the photon number noise below the shot-noise limit. This is in complete agreement with our previous analysis, which used a density-operator approach.
We discuss in detail the influence that the statistical properties of the pump source have on maser and laser dynamics. We derive a general master equation for the radiation field that is valid for a wide range of different pump mechanisms. If the pump noise is eliminated, we find that the photon number noise in a micromaser and a laser can be significantly reduced below the shot-noise level. In contrast, the phase fluctuations for both maser and laser are unaffected by the noise contribution of the pump.
The random nature of spontaneous emission leads to unavoidable fluctuations in a laser's output. This is often included through random Langevin forces in laser rate equations, but this approach falls short for nanolasers. In this paper, we show that the laser quantum noise can be quantitatively computed for a very broad class of lasers by starting from simple and intuitive rate equations and merely assuming that the number of photons and excited electrons only takes discrete values. While the approach has seen previous success, we here derive it rigorously from an open quantum system master equation, whereas it was previously introduced only on phenomenological grounds. We further show that in the many-photon limit, the model simplifies to Langevin equations. We perform an extensive comparison of different approaches for computing quantum noise in lasers, identifying the best approach for different system sizes, ranging from nanolasers to macroscopic lasers, and different levels of excitation, i.e., cavity photon number. In particular, we show that below the laser threshold, stochastic fluctuations in the numerical solution to the Langevin equations can drive populations to unphysical negative values, requiring the introduction of population bounds, which in turn skew the noise statistics, leading to inaccuracies. The Laser Markov Chain model, on the other hand, is accurate for all pump values and laser sizes when collective emitter effects are excluded.
We investigate the influence of pump bandwidth and pump intensity noise on the quantum-noise properties of lasers based on a Raman atomic-gain medium, which recently have been predicted to emit narrow-bandwidth, sub-shot-noise light. We show that, using finite-bandwidth pump light, the predicted limit to the laser bandwidth can still be well below the value given by the Shawlow-Townes formula and much smaller than the input bandwidth. The laser intensity noise is shown to be relatively insensitive to input phase noise as long as the Rabi frequency on the lasing transition is large compared to the bandwidth. On the other hand, even small amounts of pump amplitude noise tend to increase strongly the laser spectral bandwidth, especially in the high-intensity limit. Including dynamic pump-noise reduction through multilevel atomic cycling in our model leads to a Mandel Q parameter value even below Q=-1/2, together with a significant enhancement of the output intensity-noise squeezing.
Current laser systems have phase and amplitude fluctuations which are partially quantum in origin. The amplitude fluctuations of a highly stabilized laser are shot noise limited, that is they have quantum fluctuations due to the Poissonian fluctuations of photons in a coherent state. These photon number fluctuations have been shown to have an origin in the incoherent pumping mechanism used for standard lasers. It has recently been demonstrated experimentally that by suppressing the amplitude fluctuations of the pump a laser output with reduced amplitude fluctuations is possible. The phase fluctuations in a laser are due to phase diffusion and are substantially above the quantum limit. Techniques to reduce the laser phase fluctuations have been proposed making use of correlated spontaneous emission.
Quantum statistical properties of laser light have been extensively studied for the last thirty years by using an operator Langevin equation, a density operator master equation, and a quantum mechanical Fokker-Planck equation. It has been generally accepted among physicists and quantum electronics engineers that an ideal laser operating at far above the threshold generates a coherent state of light. Various experimental facts such as the Poissonian photoelectron statistics, the shot noise limited photocurrent fluctuations, and the Gaussian distributions of optical homodyne detector output seem to support this. However, recent careful studies on a semiconductor laser have revealed that a semiconductor laser does not necessarily produce a coherent state of light, but generates a number-phase squeezed state, in which the photon-number noise is smaller than the standard quantum limit (shot noise limit or Poisson limit). This paper reviews the theoretical and experimental aspects of number-phase squeezed state generation by a semiconductor laser.
We solve the problem of a laser with variable pumping statistics for any relative magnitude of the atomic- and cavity-decay constants, and obtain a different regime of sub-Poissonian light generation. We show that, even for Poissonian pumping, the noise in the amplitude quadrature outside the cavity can be reduced up to 50% below the shot-noise level when the polarization but not the populations can be adiabatically eliminated. Maximum noise reduction in this case is obtained when the lower level decays much faster than the upper one and occurs at a frequency given by the geometrical mean of the decay rates of the field and the lower-level population. Furthermore, the full consideration of atomic memory effects leads to a generalization of previous results on regularly pumped lasers. We find that, for regular pumping, maximum amplitude-noise reduction (up to complete quieting) still occurs at zero frequency in all cases. However, a long-living polarizaton leads to an increase in amplitude noise and may even eliminate the dip at zero frequency, at the same time leading to a significant quenching of the laser linewidth in the bad-cavity limit.