Electronic phase coherence measurements

Measurements of electronic phase coherence and its decay are discussed in the next section. Pump-probe experiments with two incident laser pulses and... 

The terms elastic and inelastic scattering of electrons describe that which results in no loss of energy and some measureable loss of energy respectively. If the incident electron beam is coherent (i.e. the electrons are in phase) and of a fixed wavelength, then elastically scattered electrons remain coherent and inelastic electrons are usually incoherent. 

In order to obtain estimates of quantum transport at the molecular scale [105], electronic structure calculations must be plugged into a formalism which would eventually lead to observables such as the linear conductance (equilibrium transport) or the current-voltage characteristics (nonequilibrium transport). The directly measurable transport quantities in mesoscopic (and a fortiori molecular) systems, such as the linear conductance, are characterized by a predominance of quantum effects—e.g., phase coherence and confinement in the measured sample. This was first realized by Landauer [81] for a so-called two-terminal configuration, where the sample is sandwiched between two metalhc electrodes energetically biased to have a measurable current. Landauer s great intuition was to relate the conductance to an elastic scattering problem and thus to quantum transmission probabilities. 

In contrast to XRD methods that may introduce sample preparation artifacts (see Jiang et al. 1997 Li et al. 1998), TEM integrated with selected-area electron diffraction (SAED) and energy dispersive spectrometry (analytical electron microscopy, AEM) measurements, provides direct, in situ observations on rock microtextures, crystallite size distributions, lattice imperfections of crystallites and interstratification (see the extensive reviews by Peacor 1992 and Merriman and Peacor 1999). TEM observations on selected portions of thinned (ion-milled) whole rock samples contradict the fundamental particle theory of Nadeau et al. (1984a,b,c summarized recently by Nadeau 1998). The observations show that phyllosilicate domains with interstratified structures form coherent boundaries, and therefore, MacEwan-type crystallites do exist in quasi-undisturbed rocks (Peacor 1998). In addition, AEM studies may provide reliable mineral-chemical data on the phases devoid of any external or internal impurities. 

Another situation occurs for various space tests of general relativity and related experiments for 9G/dt. The accumulation time and the reading-data time is essentially the same. Even if we try, similarly to atomic physics, to perform brief, say, one-day measurements every year, even that would not help. The problem is that when looking for a rotation of an electron we cannot measure the phase of the rotation and deal with something related in sense of classical physics to average parameters of the orbital motion. The planetary motion allows us to look for the phase of the rotation and thus the coherence time is equal to many periods of evolution. In a sense that is similar to the Ramsey method with two coherent space-separated short measurements. As a result, the effects of the gradients are of the same importance as effects of the time dependence of conventional terms. Any interpretation of the data in such a case is indeed strongly model-dependent. 

Volume 11/19 brings the spectroscopic data on diamagnetic and paramagnetic molecules as well as on molecular ions up to date considering the publications up to and partly including 1990. The spectroscopic information collected in this volume has been obtained principally from gas phase microwave measurements. In addition, gas phase data have been included derived from methods related to microwave spectroscopy by employing a coherent radiation source. These are molecular beam techniques, radio frequency spectroscopy, electron resonance spectroscopy, laser spectroscopy, and double resonance techniques. Some other methods are considered if the accuracy of the derived molecular parameters is comparable to that of micro-wave spectroscopy and no microwave data are available. Examples would be Fourier infirared spectroscopy or electric deflection method. 

Fig. 2. Electronics block diagram for pulse-echo-method sound-velocity measurements. Frequency divider is used to provide phase-coherent pulses for a pulse-superposition method for sound-velocity-change measurements, due to changing temperature in the present case.

In larger molecules the phase-coherence time of excited levels may be shorter than the population lifetime because of perturbations between closely spaced levels of different electronic states, which cause a dephasing of the excited-level wave functions. One example is the NO2 molecule, where the width of the Hanle signal turns out to be more than one order of magnitude larger than expected from independent measurements of population lifetime and Landd factors [851, 852]. This discrepancy is explained by a short intramolecular decay time (dephasing time), but a much larger radiative lifetime [853]. 

A term that is nearly synonymous with complex numbers or functions is their phase. The rising preoccupation with the wave function phase in the last few decades is beyond doubt, to the extent that the importance of phases has of late become comparable to that of the moduli. (We use Dirac s terminology [7], which writes a wave function by a set of coefficients, the amplitudes, each expressible in terms of its absolute value, its modulus, and its phase. ) There is a related growth of literature on interference effects, associated with Aharonov-Bohm and Berry phases [8-14]. In parallel, one has witnessed in recent years a trend to construct selectively and to manipulate wave functions. The necessary techniques to achieve these are also anchored in the phases of the wave function components. This trend is manifest in such diverse areas as coherent or squeezed states [15,16], electron transport in mesoscopic systems [17], sculpting of Rydberg-atom wavepackets [18,19], repeated and nondemolition quantum measurements [20], wavepacket collapse [21], and quantum computations [22,23]. Experimentally, the determination of phases frequently utilizes measurement of Ramsey fringes [24] or similar methods [25],... 

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