Quantum optics function

For the weak coupling case with Eq. (32), our master equation reduces to the well-known quantum master equation, obtained through the approximation, widely used in quantum optics. This equation describes, among other things, quantum decoherence due to Brownian motion. Hence, we have derived an exact quantum master equation for the transformed density operator p that describes exact decoherence. Furthermore, our master equation cannot keep the purity of the transformed density matrix. Indeed, one can show that if p(t) is factorized into a product of transformed wave functions at t = 0, it will not be factorized into their product for t > 0. This is consistent the nondistributivity of the nonunitary transformation (18). 

A suitable choice of the variational wave functions for various electron-phonon two-level systems is a long-standing problem in solid state physics as well as in quantum optics. For two-level reflection symmetric systems with intralevel electron-phonon interaction the approach with a variational two-center squeezed coherent phonon wave function was found to yield the lowest ground state energy. The two-center wave function was constructed as a linear combination of the phonon wave functions related to both levels introducing new VP. 

We perform concrete calculations in the complex P-representation [Drummond 1980 McNeil 1983] in the frame of both probability distribution functions and stochastic equations for the complex c-number variables. We follow the standard procedures of quantum optics to eliminate the reservoir operators and to obtain a master equation for the density operator of the modes. The master equation is then transformed into a Fokker-Planck equation for the P-quasiprobability distribution function. In particular, for an ordinary NOPO and in the case of high cavity losses for the pump mode (73 7), if in the operational regime the pump depletion effects are involved, this approach yields... 

This work is intended as an attempt to present two essentially different constructions of harmonic oscillator states in a FD Hilbert space. We propose some new definitions of the states and find their explicit forms in the Fock representation. For the convenience of the reader, we also bring together several known FD quantum-optical states, thus making our exposition more self-contained. We shall discuss FD coherent states, FD phase coherent states, FD displaced number states, FD Schrodinger cats, and FD squeezed vacuum. We shall show some intriguing properties of the states with the help of the discrete Wigner function. 

One aim of this chapter is to show graphs of the discrete W functions for FD quantum-optical states. Because of the discreteness of the arguments, the W-function graph should be a histogram. However, two-dimensional projections of such three-dimensional histograms could be very confusing. Therefore, for... 

There is considerable current interest in systems with optical functionality, such as optical switches, logic gates, or sensors. The utility of such devices depend critically on rather subtle balances of a range of influences, each of which ultimately needs to be addressed from a fundamental quantum mechanical perspective. 

Figure 2. The frequency dependence of propagation phase for optical waves (a) and quantum wave function (b) [Eq. (3)].

In this context, it is worthwhile to recall the quantum jump approach developed in the quantum optics community. In this approach, an emission of a photon corresponds to a quantum jump from the excited to the ground state. For a molecule with two levels, this means that right after each emission event, = 0 (i.e., the system is in the ground state). Within the classical approach this type of wave function collapse never occurs. Instead, the emission event is described with the probability of emission per unit time being Fp (t), where Pee(0 is described by the stochastic Bloch equation. At least in principle, the quantum jump approach, also known as the Monte Carlo wave function approach [98-103], can be adapted to calculate the photon statistics of a SM in the presence of spectral diffusion. 

The optical phase of the carrier wave in a linearly polarized femtosecond pulse can be measured by the photoelectron rate (Fig. 6.59). If the electrons are produced by the nth harmonic of the visible femtosecond pulse, the rate is proportional to the 2nth power of the visible field amplimde. The amplitude depends strongly on the phase of the optical wave relative to the envelope maximum of the pulse. Measurements of this photo-electron rate as a function of the phase shift of the field amplitude against the pulse maximum allows the determination of the phase and the pulse width of the high-harmonic attosecond pulse [754]. There are many more applications of attosecond pulses these can be found, for example, in the publications of the groups of P. Corkum at the NRC in Ottawa [753] and F. Krausz at the MPI for Quantum Optics in Garching, who have pioneered this field [754]. 

Most of the important applications of polymer-based nanocomposites have been realized in the optical area by the interesting association of the organic and inorganic components. Usually, optical composites are seen to be mixtures of a functional material and a processable matrix [49]. Optically functional parts include quantum-confined semiconductors, inorganic oxides, organic materials (small molecules), and polymers. The processable matrix materials are usually polymers but can also be copolymers, polymer blends, glass, or ceramics. 

As is to be expected, inherent disorder has an effect on electronic and optical properties of amorphous semiconductors providing for distinct differences between them and the crystalline semiconductors. The inherent disorder provides for localized as well as nonlocalized states within the same band such that a critical energy, can be defined by distinguishing the two types of states (4). At E = E, the mean free path of the electron is on the order of the interatomic distance and the wave function fluctuates randomly such that the quantum number, k, is no longer vaHd. For E < E the wave functions are localized and for E > E they are nonlocalized. For E > E the motion of the electron is diffusive and the extended state mobiHty is approximately 10 cm /sV. For U <, conduction takes place by hopping from one localized site to the next. Hence, at U =, )J. goes through a... 

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