Coherent state properties

Note that this dynamics is classical-like, as the coherent state properties density operator. 

Note that, as above, this classical-like dynamics is not without relation to the quasiclassical coherent state properties of the density operator involved in this average. 

The use of the rotational coherent state is then analogous to the use of the vibrational coherent state and can be used to study rotational state resolved properties. We note that the resolution of the identity applies here as well, that is. 

It is possible to improve the error term in (54) to any desired order hN/2 by replacing (45) with its N-th iterate. That way the state that is propagated along classical trajectories is no longer given by the coherent state (52), but by a suitably squeezed version of it. These states possess the same localisation properties as (52), however, their explicit form looks considerably more awkward. 

Some Properties of Coherent States Expansion of the Coherent State on the Eigenvectors of the Quantum Harmonic Oscillator Hamiltonian... 

This appendix deals with some properties of coherent states that are playing an important physical role in the physics of weak H-bond species. 

This property is quite remarkable In the large photon number regime the coherent quantum average on a number state gives the same result as the incoherent statistical average over coherent states. 

Furthermore, using the well-known properties of the expectation values of Nm on coherent states, we obtain... 

The choice of the value of the coherent state width 7 is arbitrary, since this parameter does not affect the mathematical properties of the Gaussian basis set which determine the form of the semi-classical propagator. In fact, the value of this quantity is usually chosen in practical implementations so as to facilitate the numerical convergence. In the following, we shall set 7 = 1/2 since with this choice (25) simplifies considerably and becomes... 

Now let us be more quantitative. The interaction (16a) mapping the atomic operators PAi out on fight is very useful for a strong n and useless if k coherent states of the atomic spins and performing the first measurement pulse with outcomes A and B1, we may deduce the statistical properties of the measurement outcomes. Theoretically we expect from Eq. (16a)... 

Quantum coherence is extremely sensitive to environmental interactions. This is a main stumbling block in the attempts to build quantum computers, and in spite of the fact that such devices are planned to be based on very weakly interacting systems (entanglement of photons or atoms well isolated in cavities) it is extremely difficult to preserve coherence over a sufficiently large number of basic operations steps. Coherent states in molecules are still more perturbed, as displayed for instance by the difference between the spectra of NHs and AsHs gases [Omnes 1994], Here, the H-atom in NH3 is delocalized in a quantum superposition, being on both sides of the //.rplane, while the spatial coherence of the heavier As-atom disappears during the time of observation which results in quite different optical properties. 

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. 

Let us now calculate the probability to have a given value of the radiation phase in the coherent state under consideration. Consider, for example, the eigenvalue of the radiation phase

states corresponding to this radiation phase ... 

In turn, the variances of the corresponding Stokes operators describing the phase properties of plane waves of photons in the two-mode coherent state (85) have the form... 

In this section we have studied the cascaded quadratic processes with an input two-mode coherent state in order to characterize the quantum phase shift. We have assumed the steady-state fields and illustrated this situation by the Deutsch-Garrison technique. To fit in the framework of such a technique, we perform a linearization around a classical solution. Further we have adopted the traditional approach to the propagation. We have determined a -dependent unitary progression operator of the two-mode system in the Schrbdinger picture by direct integration. We have compared the results in the large-mismatch limit with a model of an ideal Kerr-like medium, whose properties are effectively those of the cascaded quadratic nonlinearities. 

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