Glauber coherent states

Using the standard representation of Glauber coherent states in terms of the number states of photons [14,81]... 

In conclusion, the following should be noted. For the harmonic oscillator, the Glauber coherent states are introduced... 

R J Glauber, in Coherent States in Quantum Theory, Mir, Moscow, 1972, p 26... 

Negative values of this parameter indicate sub-Poissonian photon statistics, namely, nonclassical character of the field. One obvious example of the nonclassical field is a field in a number state n) for which the photon number variance is zero, and we have g 2 (0) = 1 — 1 /n and q = — 1. For coherent states, g (0) = 1 and q = 0. In this context, coherent states draw a somewhat arbitrary line between the quantum states that have classical analogs and the states that do not have them. The coherent states belong to the former category, while the states for which g (0) < 1 or q < 0 belong to the latter category. This distinction is better understood when the Glauber-Sudarshan quasidistribution function P(ct) is used to describe the field. 

Glauber [8] constructed coherent states in the ID Hilbert space by applying the displacement operator D a, a ) = exp(afit — a a) on vacuum state 0). Analogously, one can define the generalized coherent state [16]... 

It would be interesting to compare Eqs. (26) and (27) with the Glauber definition of the coherent state [37]... 

The classical light is usually defined [35,36] to be one for which the Glauber-Sudarshan P function, namely, the weight factor in the coherent state representation of the density matrix... 

If the initial modes are in a superposition of coherent states (with amplitudes Oyo, where j = a, b) and chaotic fields (with intensities (n j)), then the evolution of the frequency converter is described by the following Glauber-Sudarshan P function... 

In order to gain a deeper insight into the nature of these quantum fluctuations, let us regard them from a different point of view the EM field of a well-stabilized single-mode laser can be described by a coherent state (called a Glauber state [1334])... 

The ordinary photoeffect was discovered by Hertz in 1887 and explained in terms of the absorption of a single quantum of light by Einstein in his now famous work published in 1905 [7.17], It was not until 1959, however, that the relationship between the statistics of an arbitrary incident radiation field and the emitted photoelectrons was firmly established by Mandel [7.18]. Consideration of the general photodetection process in terms of quantum-electrodynamic coherent states of the radiation field was undertaken by Glauber [7.19] in 1963, and by Kelley and Kleiner [7.20] in 1964, and provides a convenient starting point for calculations involving multiple-photon as well as single-photon absorptions. 

R. Glauber Coherent and incoherent states of the electromagnetic field. Phys. Rev. 131, 2766 (1963)... 

The basic difference between an atomic beam from a BEG (an atom laser) and an atomic beam from a thermal atomic oven is the same as the difference between a laser beam and a spectrally filtered and collimated light beam from a thermal light source. According to quantum theory (Glauber 1963), a laser field is a coherent state of light with minimal fluctuations in its amplitude and phase. In other words, the essence of an atomic beam from a BEG, as well as a laser beam, lies in its statistical properties. 

This duration is known as the coherence time of the photon states (Bom and Wolf, 1970 Glauber, 1965). Considering more explicitly the example of the Lorentzian form (56), one gets for expression (72)... 

In the case of coherent laser light, the pulses are characterized by well-defined phase relationships and slowly varying amplitudes (Haken, 1970). Such quasi-classical light pulses have spectral and temporal distributions that are also strictly related by a Fourier transformation, and are hence usually refered to as Fourier-transform-limited. They are required in the typical experiments of coherent optical spectroscopy, such as optical nutation, free induction decay, or photon echoes (Brewer, 1977). Here, the theoretical treatments generally adopt a semiclassical procedure, using a density matrix or Bloch formalism to describe the molecular system subject to a pulsed or continuous classical optical field, which generates a macroscopic sample polarization. In principle, a fully quantal description is possible if one represents the state of the field by the coherent or quasi-classical state vectors (Glauber, 1965 Freed and Villaeys, 1978). For our purpose, however. 

Glauber, R. J. (19636). Coherent and incoherent states of the radiation field. Physical Review, 131, 2766-2788. 

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