The dressed-atom approach to the fluctuation problem in lasers is described. Such an approach allows one to analyze the fluctuations in various kinds of laser models. The intensity fluctuations in a regularly pumped laser are considered in the framework of the dressed-atom approach. The Fokker-Plank equation for the field density matrix is derived from first principles without heuristic assumptions. An alternative interpretation of the noise suppression in the regularly pumped laser is given. It is based upon the nonstationary picture for atomic variables. In such a regime the statistics of the output laser field may be controlled by the input statistics of the atomic initial conditions. It is the regular pump that provides the best input statistics. In the latter case the atoms are essentially nonstationary and coherently oscillate at the Rabi frequency. They are treated in a framework of the time-dependent picture in spite of the short atomic lifetime as compared with the cavity mode lifetime. The nonstationary version of the dressed-atom approach is employed to treat the regular pump case. It is demonstrated that a coherent coupling of the Rabi oscillations in the quadratic dressed-atom terms gives rise to a survival of a linear inverse proportional dependence of the atomic correlation functions upon field intensity. This survival in turn accounts for the anomalously large dressed-atom contribution to the fluctuations. Our results are in quantitative agreement with those of other approaches.
The dressed-atom approach to the fluctuation problem in lasers is described. Such an approach allows one to analyze the fluctuations in various kinds of laser models. The intensity fluctuations in a regularly pumped laser are considered in the framework of the dressed-atom approach. The Fokker-Plank equation for the field density matrix is derived from first principles without heuristic assumptions. An alternative interpretation of the noise suppression in the regularly pumped laser is given. It is based upon the nonstationary picture for atomic variables. In such a regime the statistics of the output laser field may be controlled by the input statistics of the atomic initial conditions. It is the regular pump that provides the best input statistics. In the latter case the atoms are essentially nonstationary and coherently oscillate at the Rabi frequency. They are treated in a framework of the time-dependent picture in spite of the short atomic lifetime as compared with the cavity mode lifetime. The nonstationary version of the dressed-atom approach is employed to treat the regular pump case. It is demonstrated that a coherent coupling of the Rabi oscillations in the quadratic dressed-atom terms gives rise to a survival of a linear inverse proportional dependence of the atomic correlation functions upon field intensity. This survival in turn accounts for the anomalously large dressed-atom contribution to the fluctuations. Our results are in quantitative agreement with those of other approaches.
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.
The quantum noise properties of atomic and semiconductor lasers are compared. The intensity fluctuation spectrum of the output field is calculated for the case of regularly, i.e., sub-Poissonian, pumped lasers. The effects of spontaneous emission on the output amplitude fluctuations may be suppressed in regularly pumped atomic lasers by requiring the lifetime of the lower lasing level to be short in comparison with that of the upper laser level. The output amplitude fluctuations then tend to zero at the laser frequency. In regularly pumped semiconductor lasers, net stimulated emission of photons dominates over spontaneous emission because of the combination of pumping and rapid intraband thermalization due to Coulomb scattering.
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.
The influence of injected atomic coherence on a laser's operation is discussed by analyzing the semiclassical equations of motion of this system. Both stationary-steady-state and time-dependent regimes of operation are investigated. We present the dependence of the stationary laser intensity and phase on the external parameters (population inversion, amplitude of atomic coherence, and detuning). For small cavity-field detuning and large atomic coherence, both frequency and phase locking occurs. The laser frequency is locked to the atomic frequency, and the phase is locked to a value determined primarily by the phase of the atomic coherence. Under certain conditions, in the inverted regime, the output intensity is an ssS-shaped function of the atomic coherence, leading to the possibility of a bistable behavior. However, only a portion of the bistable curve gives stable stationary operation, and in critical points (the location of which depends crucially on the external parameters) time-dependent instabilities branch away. When the detuning is larger than a critical value there is neither phase nor frequency locking. We find that the time-dependent behavior of the laser intensity in this case is oscillatory (quasiperiodic), and show that there is a stable limit cycle in the phase plane of the quadratures. There is a small parameter region where a stationary steady state and an oscillatory state may coexist. We also consider the nonlinear quantum theory of a laser with injected atomic coherence, and include the effect of pumping statistics. We derive the Fokker-Planck equation for the P representation, and express the noise in terms of moments. We find that in the steady state the intensity noise can be suppressed below the shot-noise limit but that the phase fluctuations are not affected by pump regularity. For nonzero detuning, we find that transient squeezing of the phase fluctuations is possible.
We discuss the influence of atomic memory effects on the field fluctuations of a laser in a general context. We derive a Fokker-Planck equation for the field that takes into account the long lifetime of the lasing atoms. Using this equation, we discuss two consequences of atomic memory. First, we find that even in the presence of saturation, memory effects can lead to a reduction of spontaneous-emission noise for short measurement times. Second, we quite generally show that atomic memory effects lead to time-dependent diffusion coefficients.
The fundamental source of noise in laser and optical amplifier is spontaneous emission. However, it is possible to reduce this noise by preparing the gain medium (atoms) in coherent superposition of states. There are essentially two schemes for generating atomic coherence in optical amplifiers. \n \nFirst scheme involves the preparation of atoms in a coherent superposition of states before injecting them inside the cavity. In the other scheme atoms (initially pumped incoherently) are continuously driven by an external pump field inside the cavity. Almost all the studies concerning the quenching of spontaneous emission noise in optical amplifiers, based on the notion of atomic coherent superposition, ignore the finite bandwidth of the field that is responsible for generating coherence. In this dissertation, we have examined the effect of the finite bandwidth associated with the phase fluctuations of the driving field on a number of noise quenching schemes. \n \nIt is known that coherent preparation of atoms can, under certain conditions, lead to noise-free amplification and almost 50 percent phase squeezing in a two-photon correlated emission laser. We study the effect of phase fluctuations in the injected atoms on the phase noise of the field in these systems. We discuss the conditions under which squeezing is preserved in the two-photon linear amplifiers. We also show that, even for very large phase fluctuations in the injected atoms, almost 50 percent phase squeezing can be achieved. The corresponding gain is however significantly reduced. \n \nWe also study a system of phase-sensitive amplifier where atoms are prepared in a coherent superposition of states by a strong classical field. We study the role of pump phase fluctuations associated with the finite linewidth on the quantum statistical properties of the radiation field. A study of output field characteristics reveals that the presence of a weak pump field gives rise to equal variances in both the field quadratures which are independent of linewidth. On the other hand, the presence of strong pump field alters the output field characteristics with the generation of squeezing which is later on destroyed due to the presence of phase fluctuations