The dependence of the multiphoton absorption probability for an atomic system on the statistical properties of the incident light is investigated. It is shown, by means of
nth-order time-dependent perturbation theory, that the multiphoton absorption probability depends on the
(n,n)th normally ordered correlation functions of the electromagnetic field. For stationary fields, the transition probability per unit time is constant and is directly related to the reduced cross-spectral correlation function of the electromagnetic field. This expression for the transition probability is then analyzed under various conditions of coherence. Explicit calculations are carried out for thermal light and for laser light, and the transition rates are compared when each has a Lorentzian spectrum. In particular, when the width of the final atomic level is much larger than the bandwidth of the field, the transition rate for thermal light is
n! times higher than with laser light of the same mean intensity. The other extreme case, i.e., when the width of the final atomic level is much smaller than the bandwidth of the field, is also considered in detail. An equation for the density operator of the field is derived; this equation governs the change in the statistical properties of the photon system in
n-photon absorption processes. On the basis of this equation, the time-dependent properties of the photon system are then studied and some physical consequences of these equations are discussed. Some numerical solutions relating to the time dependence of the factorial moments in two-photon absorption processes are presented.
Abstract In order to continue and generalize the studies of the density matrix of a light field undergoing k‐photon absorption, in this paper we put the emphasis on the off‐diagonal elements. The solution obtained earlier for the diagonal elements describing the photon statistics can be found as a special case but will not be discussed again. The general solution calculated by recursion shows an asymptotic behaviour if the initial photon number is sufficiently high. Only the initial phase information survives. Illustrating the solution we start with coherent light and a generalized coherent state.
The effects of two-photon absorption from a single beam of light on the statistical properties of the beam are considered. Simple expressions are obtained for the initial rates of change and limiting steady-state values of the mean photon number and degree of second-order coherence of the beam. The general time dependences of these properties of the light and of the complete photon probability distribution are evaluated for several initial types of beam. The physical significance of the results is described, and their relationship to calculations which use a classical representation of the light is discussed.
Squeezing in both intracavity and travelling-wave multiphoton absorption is investigated theoretically for incident intense nearly coherent light. It is shown that after sufficiently strong travelling-wave k-photon absorption (k=2,3...) a squeezed state of the radiation field is reached that is not a minimum uncertainty state. In this state the inphase and quadrature variances of the normalized electric field strength approach the asymptotic values k/(4(2k-1)) and k/4, respectively. With the help of an approximate Heisenberg picture treatment of a continuous mode field travelling through a broad-band k-photon absorber an analytical expression is obtained for the evolution of the squeezing spectrum in dependence on the degree of absorption. For intracavity multiphoton absorption the spectrum of output squeezing is investigated with the help of the usual Langevin equation approach. It turns out that the squeezing bandwidth in intracavity and travelling-wave multiphoton absorption is determined by the cavity bandwidth and the absorber linewidth, respectively.
We consider steady states of the one-mode quantized field interacting with two independent baths, each characterized by the one- and two-photon absorption and emission processes. In the absense of two-photon emission, using an exact analytical solution to the master equation for the diagonal elements of the density matrix in the Fock basis in terms of the confluent hypergeometric function, we obtain simple explicit expressions for the photon distribution function and for the factorial moments in the limiting cases of weak and strong two-photon absorption. If the two-photon absorption is strong enough, the steady state exhibits a sub-Poissonian photon statistics characterizing nonclassical behaviour, but Mandel's -parameter cannot be less . However, the distribution depends essentially on the temperature of the `one-photon bath'. For weak two-photon absorption, the stationary distribution is Gaussian, provided that the temperature of the `one-photon' bath is high enough. For an inversely populated `one-photon' bath, the -parameter is close to . In a generic case of nonzero two-photon emission probability, approximate asymptotic expressions for the factorial moments are found.