Coherence properties

This section begins with a brief description of the basic light-molecule interaction. As already indicated, coherent light pulses excite coherent superpositions of molecular eigenstates, known as wavepackets , and we will give a description of their motion, their coherence properties, and their interplay with the light. Then we will turn to linear and nonlinear spectroscopy, and, finally, to a brief account of coherent control of molecular motion. 

The spatial coherence properties are described by the mutual intensity or equaltime coherence between these points (c.f., mutual coherence) which is defined... 

We still need to consider the coherence properties of astronomical sources. The vast majority of sources in the optical spectral regime are thermal radiators. Here, the emission processes are uncorrelated at the atomic level, and the source can be assumed incoherent, i. e., J12 = A /tt T(ri) (r2 — ri), where ()(r) denotes the Dirac distribution. In short, the general source can be decomposed into a set of incoherent point sources, each of which produces a fringe pattern in the Young s interferometer, weighted by its intensity, and shifted to a position according to its position in the sky. Since the sources are incoherent. 

The fundamental quantity for interferometry is the source s visibility function. The spatial coherence properties of the source is connected with the two-dimensional Fourier transform of the spatial intensity distribution on the ce-setial sphere by virtue of the van Cittert - Zemike theorem. The measured fringe contrast is given by the source s visibility at a spatial frequency B/X, measured in units line pairs per radian. The temporal coherence properties is determined by the spectral distribution of the detected radiation. The measured fringe contrast therefore also depends on the spectral properties of the source and the instrument. 

Single atomic ions confined in radio frequency traps and cooled by laser beams (Figure 7.4a) formed the basis for the first proposal of a CNOT quantum gate with an explicit physical system [14]. The first experimental realization of a CNOT quantum gate was in fact demonstrated on a system inspired by this scheme [37]. In this proposal, two internal electronic states of alkaline-earth or transition metal ions (e.g. Ba2+ or Yb3+) define the qubit basis. These states have excellent coherence properties, with T2 and T2 in the range of seconds [15]. Each qubit can be... 

Exploitation of these is possible in LEDs that display coherence properties, in thresholdless laser diodes, and in many other optical, opto-electronic and quantum electronic devices. 

Coherent control Control of the motion of a microscopic object by using the coherent properties of an electromagnetic held. Coherent phase control uses a pair of lasers with long pulse durations and a well-defined relative phase to excite the target by two independent paths. Wave packet control uses tailored ultrashort pulses to prepare a wave packet at a desired position at a given time. 

An inherent limitation of mode-selective methods is that Nature does not always provide a local mode that coincides with the channel of interest. One way to circumvent the natural reactive propensities of a molecule is to exploit the coherence properties of the quantum mechanical wave function that describes the motion of the particle. These properties may be imparted to a reacting molecule by building them first into a light source and then transferring them to the molecular wave function by means of a suitable excitation process. 

It is often the case that the Franck-Condon factors contained in dq(ij) vary sufficiently slowly over the range of E encompassed by the dump pulse to be regarded as constant [191], (This assumption, called the slowly varying continuum approximation is discussed in detail in Chapter 10). Under these circumstances we can use the following generalized Parseval s equality to show that P(q) is independent of the coherence properties of the dump pulse. Specifically we have... 

The question is how radiation from therapeutic lasers and LEDs works at the cellular and organism level and what the optimal light parameters are for different uses of these light sources. It has been suggested [24] that coherent properties of laser fight are not manifested at the molecular level by light interaction with biotissue. Some additional (therapeutic) effects from coherent and polarized radiation... 

New and promising developments can be seen in high-intensity (2-photon) laser photolysis, in the combination of fields and radiation (see Chap. 3), in exploitation of the coherence properties (see Chap. 2), and in the detection of more autocatalytic or autoinductive reaction systems. 

The equality sign holds if the radiation results from a transition between two pure atomic states, such as a transition. Then the radiation is said to be completely coherent. An experimental measurement of P or p allows us to obtain some information on the coherence properties of the excitation process. 

Laser micro/nano drilling and on-site nanoscale measurement utilizing a coherence property of light and the dynamic control on wave-front... 

This property has been used to measure the coherence properties of laser pulses [28]. Because it is readily obtainable by Fourier transform from the... 

Very interesting questions concern coherence properties of a coupled system consisting of a single atom and the electromagnetic field. What are the consequences of the quantum nature of the field What happens if the field contains more and more photons and its features are more classical Can one entangle and disentangle the atom and the field on demand and to which extent ... 

Let us now turn to the coherence properties of our molecular beam. In general, coherence means that there is a fixed and well-defined phase relation in space and time between two or more wavefronts. 

The conceptual framework underlying the control of the selectivity of product formation in a chemical reaction using ultrashort pulses rests on the proper choice of the time duration and the delay between the pump and the probe (or dump) step or/and their phase, which is based on the exploitation of the coherence properties of the laser radiation due to quantum mechanical interference effects [56, 57, 59, 60, 271]. During the genesis of this field. 

The second-order correlation function has coherence properties completely different from those of the hrst-order correlation function. An interference pattern can be observed in the second-order correlation function, but in contrast to the hrst-order correlation function, the interference appears between two points located at Ri and R2. Moreover, an interference pattern can be observed even if the helds are produced by two independent sources for which the phase difference completely random [15]. In this case the second-order correlation function (22) is given by... 

This constant is essentially the limit of K as gi en by Eq. (5.14), in the case where the two absorbed photons become identical however, the factor rtiniY is replaced by n (n — 1) since the photon annihilation operator acts twice on the same radiation mode. As will be seen below, this difference is ultimately reflected in a dependence on the coherence properties of the laser source, which is uniquely associated with single-beam processes. It is also worth observing that although the first two terms of Eq. (5.13) become identical if the two absorbed photons are deiived from the same beam, inclusion of a factor of 2 in Eq. (6.1) would amount to double-counting the time-ordered diagrams, and is therefore not ap])ropriate. 

Figure 45. Schematic representation of the preparation and detection of rotational coherence in a molecule. The case depicted corresponds to the linearly polarized excitation (polarization vector ,) of a symmetric top molecule in ground-state ro-vibronic level S0v0 J0K0M0) to those rotational levels of the excited vibronic state 15,1 ,) allowed by the rotational selection rules germane to a parallel-type transition moment. The excitation process creates a superposition state of three rotational levels, the coherence properties of which can be probed by time resolving the polarized fluorescence (polarization it) to the manifold of ground-state ro-vibronic levels S0vf JfKfMfy, or by probing with a second, variably time-delayed laser pulse (polarization...

The designs of the previously mentioned selectivity schemes ignore the possibility of control of the evolution of excitation energy via exploitation of the coherence properties of the coupled matter-electromagnetic field system. Several schemes that do exploit the coherence of the time evolution of a wavepacket excitation have recently been proposed. This chapter is concerned with one of these schemes, namely, the use of coherent pulse sequences to control product formation in chemical reactions. We shall see that this scheme follows naturally from an understanding of the characteristics of time-delayed coherent anti-Stokes Raman spectroscopy (CARS) and of photon echo spectroscopy. 

We now examine, as a first case of exploitation of the coherence properties of the coupled molecule-electromagnetic field system, a representation of CARS... 

The coherence properties of laser radiation provide an opportunity to exert some external control over intramolecular dynamics. Control over photofragmentation product branching ratios has been achieved in both time and frequency domain experiments. 

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