The formalism of collective (Dicke-like) states and operators is used to describe the relaxation of the initially prepared state of a material in the presence of a laser field. The material states are shown to be expressible as minimum uncertainty wave packets formed from those special collective states that couple with the radiation field. It is shown that these coherent states of matter exhibit all the features that are usually attributed to ensemble averages of two-level molecules in a conventional statistical picture. However, there are new features in the quantum mechanical model when there are correlations among the molecules in the ensemble. The loss of minimum uncertainty characteristics of the wave packet correspnds to the transverse (T2) relaxation of the statistical model. Different types of T2 processes can be defined corresponding to the decay of different orders of coherence of the wave packet. Only for the case that the system decays in all orders of coherence do the quantum and statistical results coincide. There is expected to be a transverse relaxation that preserves one or more orders of coherence. Experiments are suggested that can test these ideas. A particular case of the formalism of collective states applies to molecular crystals and it provides a quantum mechanical picture of the dephasing of molecular excitons in terms of orders of coherence analogous to the usual manner of describing states of the radiation field.
The formalism of collective (Dicke-like) states and operators is used to describe the relaxation of the initially prepared state of a material in the presence of a laser field. The material states are shown to be expressible as minimum uncertainty wave packets formed from those special collective states that couple with the radiation field. It is shown that these coherent states of matter exhibit all the features that are usually attributed to ensemble averages of two-level molecules in a conventional statistical picture. However, there are new features in the quantum mechanical model when there are correlations among the molecules in the ensemble. The loss of minimum uncertainty characteristics of the wave packet correspnds to the transverse (T2) relaxation of the statistical model. Different types of T2 processes can be defined corresponding to the decay of different orders of coherence of the wave packet. Only for the case that the system decays in all orders of coherence do the quantum and statistical results coincide. There is expected to be a transverse relaxation that preserves one or more orders of coherence. Experiments are suggested that can test these ideas. A particular case of the formalism of collective states applies to molecular crystals and it provides a quantum mechanical picture of the dephasing of molecular excitons in terms of orders of coherence analogous to the usual manner of describing states of the radiation field.
Conceptual problems in quantum optics are investigated by a study of the physical significance of various types of description of the field of a single mode. The descriptions are examined through the effect of the field on matter. Both undamped and damped modes are considered, the descriptions being those of various degrees of precision in classical and quantum-mechanical formalisms. The matter consists of a large number of "molecules," and the interaction is studied by means of low-order perturbation theory. Formal expressions are obtained for the energy interchange between field and molecules in terms of the zeroth-order (uncoupled) operators, with the effect of the commutation properties of the field variables explicitly separated from that of the excitation of the field, in second order. The significance of taking expectation values of the operator results is discussed, and it is concluded that this procedure is justified only when the experiment under consideration involves an averaging process; thus, the molecular variables should be averaged, but not necessarily those of the field. Conditions under which the averaging process is justified are considered, and it is reasoned that, when such a process is not justified, a statistical description of the field can result only in a statistical description of the interaction process. Results of various field descriptions are compared, and it is shown that for induced emission and for spontaneous emission from coherently oscillating molecules, classical and quantum-mechanical fields are equivalent. However, for a self-consistent theory of spontaneous emission from molecules that are not oscillating coherently, the quantum-mechanical commutation properties of the field are essential if the molecules are treated quantum-mecahnically, and the field must be treated classically if the molecules are treated classically; the type of description used for the excitation of the field is inconsequential. Photoelectric emission is examined, and, within the approximation framework used, shown to be accurately described by a classical treatment of the field. It is pointed out that there does not necessarily exist a connection between "photon statistics," that is, the statistics associated with an ensemble of fields, and photocurrent fluctuations in one or more detectors coupled to the same field.
A quantum statistical theory of resonant optical phenomena is developed for the case when the fluctuations of the laser, used for exciting transitions, are important. The general equations describing the dynamics of a relaxing two-level atom (TLA) are solved exactly for different types of mean values and the two-time amplitude and intensity correlations. The phase-diffusion model is adopted for laser fluctuations. The exact results are used to analyze the effect of laser fluctuations on a number of optical effects-optical free-induction decay, adiabatic following, the spectrum of the scattered light from a relaxing TLA, the energy-absorption spectrum from a weak field, Hanle resonances, etc. In each case, the laser fluctuations are found to affect in an important way the characteristics of the above optical-resonance phenomena. For example, the spectrum of scattered radiation from a TLA has the usual three-peak structure for fields at resonance and with strengths $\ensuremath{\alpha}$ above the threshold and for $\ensuremath{\alpha}\ensuremath{\gg}{\ensuremath{\gamma}}_{c}$; however, now the peak heights (widths) are in the ratio 3x (3x2), $x=\frac{[{\ensuremath{\gamma}}_{c}+\frac{({T}_{1}^{\ensuremath{-}1}+{T}_{2}^{\ensuremath{-}1})}{3}]}{[2{\ensuremath{\gamma}}_{c}+{T}_{2}^{\ensuremath{-}1}]}$, where ${\ensuremath{\gamma}}_{c}^{\ensuremath{-}1}$ is the correlation time for laser phase fluctuations. For ${\ensuremath{\gamma}}_{c}\ensuremath{\gg}\ensuremath{\alpha}$, one gets a single-peak spectrum. The laser field is treated as a second-quantized field with excitation in either a coherent state or a Fock state. The results, obtained by straightforward perturbation theory, but valid for arbitrary values of the relaxation parameters, detuning, and the laser correlation time, are also presented.
The concept of a two-photon coherent state is introduced for applications in quantum optics. It is a simple generalization of the well-known minimum-uncertainty wave packets. The detailed properties of two-photon coherent states are developed and distinguished from ordinary coherent states. These two-photon coherent states are mathematically generated from coherent states through unitary operators associated with quadratic Hamiltonians. Physically they are the radiation states of ideal two-photon lasers operating far above threshold, according to the self-consistent-field approximation. The mean-square quantum noise behavior of these states, which is basically the same as those of minimum-uncertainty states, leads to applications not obtainable from coherent states or one-photon lasers. The essential behavior of two-photon coherent states is unchanged by small losses in the system. The counting rates or distributions these states generate in photocount experiments also reveal their difference from coherent states.
A system of many #we-level atoms or molecules in a collective Dieke state (1) interacting with a single resonant mode of the quantized radiation field has often been adopted as a quantum-mechanical model for a point laser (2). In a previous paper (3) we reported exact dosed-form solutions and photon statistics of coherent spontaneous emission for the model atom-field state in the l imit of infinitely large co-operation number. The purpose of this paper is to report more general results based on this modeI. We give the exact closed-form solutions and photon statistics of coherent emission in the presence of an applied field for the model atom-field state in the same limit. For an initial atomic Dicke state interacting with an applied field in a coherent (Glauber) state (a), the emitted pulse can be desoribed in terms of Glauber states only when the levels of excitation of the initial Dicke states are (~ superradiant ~ (~). For an initially highly inverted system or low excited system, the photon distributions undergo large fluctuations. The model interaction Hamil tonian is given by
Coherent excitation of a molecular ensemble coupled to a common radiation mode can lead to the collective emission of radiation known as superradiance. This collective emission only occurs if there is an entanglement between the molecules in their ground and excited state and can, therefore, serve as a macroscopic measure of coherence in the ensemble. Reported here are wave packet propagations for various pyrazine models of increasing complexity and molecular ensembles thereof. We show that ensemble coherence upon photoexcitation can prevail up to relatively long time scales although the effect can diminish quickly with increasing ensemble size. Coherence can also build up over time and even reemerge after the molecules have passed through a conical intersection. The effect of the pump pulse characteristics on the collective response of the molecular ensemble is also studied. A broadband pulse imprints a large amount of initial coherence to the system, as compared to a longer pulse with a smaller spread in the frequency domain. However, the differential effects arising from a different pulse duration and coherent bandwidth become less prominent if the emission of light from the ensemble takes place after a non-adiabatic decay process.
Over the past two decades there has been a renewed interest in the properties of light and its interactions with matter. In particular, the phenomenon of mixing on the surface of a quantum detector, first performed by Forrester and Gudmundsen, has had significant impact on the treatment of the interaction of light with matter. Mandel and Wolf have interpreted optical mixing of two fields in terms of wave-packet interactions. The wave packets of the fields were allowed to add in a classical manner, without any interaction between photons. In this paper, we consider the extension to an ensemble of statistical wave packets. This is accomplished by considering the wave-packet ensemble as a generalized shot-noise process, and generating statistical properties of the ensemble. The first-order probability density is obtained for the envelope of an ensemble in which each member has uniform and independently distributed phase. This is then used to compute the resulting photoelectron-counting distribution. The results can be shown to be somewhat different than would arise from a gaussian field, and a statistical test is derived to compare the two.