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Journal de physique

Statistical properties of photons in a three-level plus two-mode model

Nikolay N. Bogolubov, Fam Le Kien, A.S. Shumovsky

Published Jan 1, 1986• 16 citations
Publisher

Abstract

The characteristics of the photon statistical properties are studied in a soluble three-level plus two-mode model. The model consists of a single lambda-configuration three-level emitter interacting with two modes of the quantized radiation field, the emitter being initially in the lowest level. The normally ordered variances of the photon numbers and the cross-correlation function are calculated All the results are obtained without using perturbation theory and decorrelation approximations. It is shown that the states of the signal-mode field produced from its initial vacuum are sub-Poissonian for all times. For the case when both the signal-mode and pump-mode fields are initially in the Glauber coherent states the temporal behaviour of the photon statistical characteristics are described Under suitable conditions photon antibunching and anticorrelation between the modes are potentially possible in the system.

DOI
10.1051/jphys:01986004703042700

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The characteristics of the photon statistical properties are studied in a soluble three-level plus two-mode model. The model consists of a single lambda-configuration three-level emitter interacting with two modes of the quantized radiation field, the emitter being initially in the lowest level. The normally ordered variances of the photon numbers and the cross-correlation function are calculated All the results are obtained without using perturbation theory and decorrelation approximations. It is shown that the states of the signal-mode field produced from its initial vacuum are sub-Poissonian for all times. For the case when both the signal-mode and pump-mode fields are initially in the Glauber coherent states the temporal behaviour of the photon statistical characteristics are described Under suitable conditions photon antibunching and anticorrelation between the modes are potentially possible in the system.
We investigate the transient and the steady-state behaviour of the photon statistics of a single-atom laser, consisting of a three-level Λ system, driven by an incoherent external pump field and strongly coupled to a single mode of an optical cavity. For several limiting cases we are able to obtain analytical results. A comparison with standard multi-atom laser theory reveals a surprisingly good agreement down to very small intracavity photon numbers. Under appropriate operating conditions a calculation of the second-order intensity correlation function yields sub-Poissonian statistics as well as strong antibunching induced by the nonlinear dynamics of the atom.
Quantum statistical properties such as first-order coherence, antibunching, sub-Poisson distribution and the probability distribution of photon number are studied by considering the non-resonant interaction of two radiation fields with a ' Lambda ' structure three-level atom. It is found that the different detunings and the different ratios of average photon number of two radiation fields as well as the time regime have a remarkable influence on quantum statistical properties of the two radiation fields. The author also emphasises that the initial atomic state plays an important role in the non-resonant interaction and tries to explore the connections among these non-classical effects.
Statistic properties of photon in the system of a two-mode field initially in a coherent state resonantly interacting with a three-level V-type atom are investigated by means of the quantum theory and numerical calculations.The dependence of the statistic properties of photon on the total photon number of the two-mode,the partition parameter and the coupling constant are discussed for three cases:①no state-selective atomic measurement;②direct state-selective atomic measurement;③state-selective atomic measurement after the application of a classical field.The results indicate that when the direct state-selective measurement is performed on the atom,the average intensity of the sub-poisson statistic distribution of mode a is enhanced;when the partition parameter is decreased,the average intensity of the sub-poisson statistic distribution of mode a is reduced and that of mode b is enhanced;when the state-selective mesurement is performed on the atom,the Cauchy-Schwarz inequality is violated;when the total photon number of the two modes is increased or the direct state-selective measurement is performed on the atom,the anti-correlation character between the two modes is preserved,but the average intensity of the anti-correlation is reduced.
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Recently Glauber has described the properties of coherent radiation fields, and has constructed the density matrix of the field in two simple cases: (1) The radiating system is a classical radiator and no reaction is considered; (2) the central-limit theorem applies to a collection of radiators. This paper investigates other simple "almost" exactly soluble problems, in which a quantum-mechanical two-level system interacts with a quantized electromagnetic field originally in a pure coherent state in a single mode. The first-order correlation function ${G}^{(1)}=〈{E}^{\ensuremath{-}}{E}^{+}〉$ is compared with $〈{E}^{\ensuremath{-}}〉〈{E}^{+}〉$ at resonance when the stimulating field is initially a pure coherent state and the two-level system is initially in its excited state. The corresponding quantities are also computed for a field whose initial density matrix is a Gaussian superposition of coherent states (e.g., blackbody radiation), as well as for a field which is initially described as having a given number of photons.