Phase coherence quantum definition

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. 

By definition, quantum control relies upon the unique quantum properties of light and matter, principally the wavelilce nature of both. As such, maintenance of the phase information contained in both the matter and light is central to the success of the control scenarios. Chapter 5 deals with decoherence, that is, the loss of phase information due to the influence of the external environment in reducing the system coherence. Methods of countering decoherence are also discussed. 

Whilst the above is perfectly adequate for the description of processes observed with continuous-wave (cw) input, proper representation of the optical response to pulsed laser radiation requires one further modification to the theory. It is commonly thought difficult to represent pulses of light using quantum field theory indeed, it is impossible if a number state basis is employed. However by expressing the radiation as a product of coherent states with a definite phase relationship, it is relatively simple to construct a wavepacket to model pulsed laser radiation [39]. The physical basis for this approach is that pulses necessarily have a finite linewidth and therefore in fact entail a large number of radiation modes, so that for the pump radiation, it is appropriate to construct a coherent superposition... 

Within the density-matrix formalism (Vol. 1, Sect. 2.9) the coherent techniques measure the off-diagonal elements pab of the density matrix, called the coherences, while incoherent spectroscopy only yields information about the diagonal elements, representing the time-dependent population densities. The off-diagonal elements describe the atomic dipoles induced by the radiation field, which oscillate at the field frequency radiation sources with the field amplitude Ak(r, t). Under coherent excitation the dipoles oscillate with definite phase relations, and the phase-sensitive superposition of the radiation amplitudes Ak results in measurable interference phenomena (quantum beats, photon echoes, free induction decay, etc.). 

This is the operative technical term. It is equivalent to our earlier condition that there is a definite initial state and not an ensemble. The optically prepared state is then a pure state in the quantum mechanical sense, namely, it can be expressed as a superposition of states, each with its own phase, hence coherent. ... 

Coherence in materials Due to the uncertainty principle, the energy distribution of photons in apulse laser shows a finite bandwidth. Thus, a pulse laser can excite several quantum states of materials within the bandwidth at the same time. Such an excited state can be expressed in terms of a linear combination of these states and develops in time with a definite phase if there is no disturbance from the environments. 

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