34,399 research outputs found
Noncanonical quantum optics
Modification of the right-hand-side of canonical commutation relations (CCR)
naturally occurs if one considers a harmonic oscillator with indefinite
frequency. Quantization of electromagnetic field by means of such a non-CCR
algebra naturally removes the infinite energy of vacuum but still results in a
theory which is very similar to quantum electrodynamics. An analysis of
perturbation theory shows that the non-canonical theory has an automatically
built-in cut-off but requires charge/mass renormalization already at the
nonrelativistic level. A simple rule allowing to compare perturbative
predictions of canonical and non-canonical theories is given. The notion of a
unique vacuum state is replaced by a set of different vacua. Multi-photon
states are defined in the standard way but depend on the choice of vacuum.
Making a simplified choice of the vacuum state we estimate corrections to
atomic lifetimes, probabilities of multiphoton spontaneous and stimulated
emission, and the Planck law. The results are practically identical to the
standard ones. Two different candidates for a free-field Hamiltonian are
compared.Comment: Completely rewritten version of quant-ph/0002003v2. There are
overlaps between the papers, but sections on perturbative calculations show
the same problem from different sides, therefore quant-ph/0002003v2 is not
replace
Introduction to Quantum Optics
The theory of quantum propagator and time--dependent integrals of motion in
quantum optics is reviewed as well as the properties of Wigner function,
Q--function, and coherent state representation. Propagators and wave functions
of a free particle, harmonic oscillator, and the oscillator with varying
frequency are studied using time--dependent linear in position and momentum
integrals of motion. Such nonclassical states of light (of quantum systems) as
squeezed states, correlated states, even and odd coherent states (Schr\"odinger
cat states) are considered. Photon distribution functions of Schr\"odinger cat
male and female states are given, and the photon distribution function of
squeezed vacuum is derived using the theory of the oscillator with varying
parameters. Properties of multivariable Hermite polynomials used for the
description of the multimode squeezed and correlated light and polymode
Schr\"odinger cats are studied.Comment: Latex,35 pages,Lectures in Latin America Scool of Physics 199
Continuous phase-space representations for finite-dimensional quantum states and their tomography
Continuous phase spaces have become a powerful tool for describing,
analyzing, and tomographically reconstructing quantum states in quantum optics
and beyond. A plethora of these phase-space techniques are known, however a
thorough understanding of their relations was still lacking for
finite-dimensional quantum states. We present a unified approach to continuous
phase-space representations which highlights their relations and tomography.
The infinite-dimensional case from quantum optics is then recovered in the
large-spin limit.Comment: 15 pages, 9 figures, v4: extended tomography analysis, added
references and figure
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