The fluctuations of the constituent populations in a multi-level system are considered as applied to a three and four level semiconductor model. It is shown that under certain conditions the fluctuations of the electron numbers in the conduction band can be super-poisson, defined as having a variance greater than the mean number. The general autocorrelation function for a three level system is obtained. For certain limits, this correlation function is the sum of two damped sinusoidal terms. This would indicate there is an oscillatory interaction between the population numbers. The photon distribution as a function of position within a one-dimensional active medium is derived. When two partially reflecting mirrors are situated at both ends of the medium, the stationary photon distribution obtained is a function of the cavity amplification and the mirror reflectivities. The distribution of photo-electrons emitted from a detector of area A and resolving time T when illuminated by an incident light beam is derived. By using a binomial rather tha a deterministic quantum efficiency an additional term is obtained in the autocorrelation function. The resulting spectral density of the photo-current fluctuations is shown to be the sum of a Poisson particle noise and wave interference term. Several examples of different spectral line shapes are discussed. Also considered is an intensity modulated light beam.
The fluctuations of the constituent populations in a multi-level system are considered as applied to a three and four level semiconductor model. It is shown that under certain conditions the fluctuations of the electron numbers in the conduction band can be super-poisson, defined as having a variance greater than the mean number. The general autocorrelation function for a three level system is obtained. For certain limits, this correlation function is the sum of two damped sinusoidal terms. This would indicate there is an oscillatory interaction between the population numbers. The photon distribution as a function of position within a one-dimensional active medium is derived. When two partially reflecting mirrors are situated at both ends of the medium, the stationary photon distribution obtained is a function of the cavity amplification and the mirror reflectivities. The distribution of photo-electrons emitted from a detector of area A and resolving time T when illuminated by an incident light beam is derived. By using a binomial rather tha a deterministic quantum efficiency an additional term is obtained in the autocorrelation function. The resulting spectral density of the photo-current fluctuations is shown to be the sum of a Poisson particle noise and wave interference term. Several examples of different spectral line shapes are discussed. Also considered is an intensity modulated light beam.
The probability distribution p ( n , T ) of the number of counts n from a photoelectric detector illuminated by coherent light for a time T is studied, by associating photons stochastically with Gaussian random waves. The cumulants of the distribution are derived and it is shown to be of the expected form for a boson assembly in a limited volume of phase space. The distribution depends strongly on the degeneracy of the light beam. It approaches the Poisson form for classical particles at low degeneracies and the distribution characteristic of classical waves at high degeneracies. The analysis leads, incidentally, to an expression for the extent of the unit cell of phase space in the direction of the beam. It is argued that this should be adopted as the measure of coherence length.
In this tutorial, Langevin stochastic equations and Markov probability equations are used to model electron- and photon-number fluctuations in three- and four-level lasers. Equations are derived for the moments of the electron and photon numbers (means, variances and correlations). Both approaches produce the same moment equations. In the Langevin approach, the moments of the noise terms must be specified by other means, whereas in the Markov approach, they are determined self-consistently and satisfy the shot-noise rule: For each process that is modeled by the rate equations, the driving terms in the variance equations equal the moduli of the associated terms in the mean equations. The driving terms in the correlation equations have the same magnitudes as the variance terms, but can be positive or negative, depending on whether the changes in the electron and photon numbers are correlated or anti-correlated, respectively. Formulas are derived for the relative intensity noise and its spectrum. The consequences of these results for three- and four-level lasers are discussed.
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.
We examine the coherence properties of stationary light obtained by the superposition of nonstationary independent emissions occurring at random space–time points. The positions of the points are independent and uniformly distributed over the volume of the source. The emission times fluctuate in accordance with a stationary renewal point process. This process admits of super-Poisson, sub-Poisson, or Poisson behavior. The individual emissions are assumed to be in a coherent, chaotic, or n state. The statistical nature of the random-emission space–time points plays an important role in determining the coherence properties and photon statistics of the total field. This is manifested in the normalized second-order correlation function, which turns out to have the usual form for chaotic light with two additional terms. The first of these is determined by the statistical nature of the individual emissions (it is positive for coherent or chaotic, but zero for single-photon, emissions). The second term is governed by the statistics of the primary excitations (it is positive for super-Poisson, zero for Poisson, and negative for sub-Poisson excitations). Both additional terms become small for light with a high degeneracy parameter (many total photons per emission lifetime). The behavior of the light is then asymptotically chaotic. In the opposite limit, when the degeneracy parameter is small (or the emissions are instantaneous), the correlation properties of the primary excitations are directly transferred to the correlation properties of the photons. The first-order spatial-coherence properties of the field turn out to be identical with those of chaotic light (i.e., the van Cittert–Zernike theorem is obeyed), although the second-order properties differ. The photon-counting distribution reflects the character of the correlation function. Thus sub-Poisson primary excitations, together with n-state emissions, can lead to sub-Poisson photon counts under certain conditions. Such nonclassical light may be made arbitrarily intense if interference effects are eliminated by detecting many spatial modes. As an example of our theory, we cite a Franck–Hertz experiment excited by a space-charge-limited electron beam. If the electron excitations are represented as a sub-Poisson renewal point process, and the photon emissions as one-photon states, the light generated should be antibunched and sub-Poisson.
This dissertation considers multi-wave interactions in bulk semiconductors. Non-equilibrium Green's functions are used to derive an appropriate set of equations describing the interaction of a light field with a semiconductor. Many-body effects lead to the screening of the Coulomb potential in these equations, as well as, carrier-carrier scattering. The carrier-carrier scattering is studied within the context of the carrier Boltzmann equation which contains the dynamically screened Coulomb potential. The relation between carrier scattering and optical dephasing is also made. The carrier scattering rates are then used in the equations describing a two beam pump-probe experiment. The resulting equations are solved numerically for both passive and active systems, and effects such as spectral hole burning, coherent light scattering, and light induced band splitting are studied. Considering three CW beams (pump and two probes) allows for the study of four-wave mixing in semiconductors. By considering CW fields, the semiconductor may be treated in the quasi-equilibrium approximation allowing for greater detail in the treatment of the light field. The resulting probe absorption yields asymmetries which result in an asymmetric four-wave mixing spectrum. The four-wave mixing spectrum is then used to study the amount of squeezing in the light field exiting the cavity in a four-wave mixing experiment.
We theoretically investigate the quantum statistical properties of a two-mode cavity light generated by a ∨ -type three-level atom interacting with nondegenerate subharmonic light and coupled to a two-mode squeezed vacuum reservoir. Using the master equation, we obtain steady-state expectation values for the atomic and cavity-mode operators. Based on these results, we analyze the global and local photon number variances, intensity fluctuation spectrum, joint photon number distribution, and photon count statistics. Our results reveal that squeezing parameter and subharmonic generation significantly enhance intensity fluctuations, as well as the mean and variance of photon counts, whereas atom-field coupling and cavity decay suppress them. The system exhibits super-Poissonian photon statistics, indicating that photon number fluctuations exceed the mean photon number. Furthermore, the photon count variance, which incorporates intracavity transmission and input noise, increases with detector efficiency. These results provide a comprehensive picture of photon statistics in atom-photon systems and guide the design of advanced quantum optical devices.