Quantum Theory of Spectral Modulation

1974 ◽  
Vol 52 (17) ◽  
pp. 1694-1702 ◽  
Author(s):  
Andrzej Zardecki ◽  
Claude Delisle
Keyword(s):  
Quantum Theory ◽  
Time Delay ◽  
Density Operator ◽  
Michelson Interferometer ◽  
Coherence Time ◽  
Path Difference ◽  
Intensity Modulation ◽  
Quantum Mechanical ◽  
Spectral Modulation ◽  
Thermal Light

Recent experiments of Delisle and Brochu, in which spectral modulation at a large path difference was observed, are analyzed in quantum mechanical terms. Starting with a stationary density operator for thermal light, a two beam superposition such as taking place in a Michelson interferometer, is investigated. It is shown that a simple interference law holds separately for each mode of radiation. Consequently, a coherent superposition of light should be observed for a time delay arbitrarily large compared to the coherence time. The latter determines merely the range of intensity modulation. Analysis of the Michelson interferometer accounting for the energy returned to the source is also presented.

Operators and meaning of wave function

2016 ◽  
pp. 4039-4042
Author(s):  
Viliam Malcher
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
State Vector ◽  
The State ◽  
Physical Significance ◽  
Central Problem ◽  
Quantum Mechanical ◽  
Mechanical Description ◽  
Quantum Mechanical Description ◽  
Interpretation Of Quantum Theory

The interpretation problems of quantum theory are considered. In the formalism of quantum theory the possible states of a system are described by a state vector. The state vector, which will be represented as |ψ> in Dirac notation, is the most general form of the quantum mechanical description. The central problem of the interpretation of quantum theory is to explain the physical significance of the |ψ>. In this paper we have shown that one of the best way to make of interpretation of wave function is to take the wave function as an operator.

scholarly journals On individuality in quantum theory

2015 ◽  
Vol 13 (1) ◽  
pp. 29-38
Author(s):  
Jasmina Jeknic-Dugic
Keyword(s):  
Quantum Theory ◽  
Structural Realism ◽  
Mechanical Analysis ◽  
Quantum Systems ◽  
Quantum Mechanical ◽  
Ontic Structural Realism

A quantum mechanical analysis of the decomposability of quantum systems into subsystems provides support for the so-called "attenuated Eliminative Ontic Structural Realism" within Categorical Structuralism studies in physics. Quantum subsystems are recognized as non-individual, relationally defined objects that deflate or relax some standard objections against Eliminative Ontic Structural Realism. Our considerations assume the universally valid quantum theory without tackling interpretational issues.

scholarly journals On the electromagnetic fields due to variable electric charges and the intensities of spectrum lines according to the quantum theory

1935 ◽  
Vol 150 (870) ◽  
pp. 416-421 ◽  
Keyword(s):  
Quantum Theory ◽  
Wave Functions ◽  
Spectral Lines ◽  
Quantum Mechanical ◽  
Final States ◽  
Electric Moment ◽  
Mechanical Method ◽  
Quantum Mechanical Method ◽  
Consistent Method ◽  
Time Average

In a recent paper Schott has criticized the quantum mechanical method of finding the intensities of spectral lines, and in particular the assumption that the intensity may be derived by treating the atom as a dipole, radiating classically. The electric moment of this dipole is taken as p = e -2 πivt ∫ Ψ* f rΨ i d τ + Conjugate complex, (1A) where Ψ i and Ψ f are the wave functions of the initial and final states of the atom respectively, and in the Quantum Theory the usual assumption is that the energy radiated per unit time is given by R = 2 |p¨ ¯ | 2 /3 c 2 , (1B) where p¨ ¯ is the time average of p¨. A more consistent method is suggested in which the electric density ρ and the current j, corresponding to the transition, are found, and the electromagnetic field due to these two is examined.

scholarly journals Development of a Compact Three-Degree-of-Freedom Laser Measurement System with Self-Wavelength Correction for Displacement Feedback of a Nanopositioning Stage

2018 ◽  
Vol 8 (11) ◽  
pp. 2209 ◽  
Author(s):  
Yindi Cai ◽  
Zhifeng Lou ◽  
Siying Ling ◽  
Bo-syun Liao ◽  
Kuang-chao Fan
Keyword(s):  
Laser Diode ◽  
Low Cost ◽  
Michelson Interferometer ◽  
Optical Path Difference ◽  
Path Difference ◽  
Degree Of Freedom ◽  
Laser Source ◽  
Laser Measurement ◽  
Length Unit ◽  
Three Degree Of Freedom

This paper presents a miniature three-degree-of-freedom laser measurement (3DOFLM) system for displacement feedback and error compensation of a nanopositioning stage. The 3DOFLM system is composed of a miniature Michelson interferometer (MMI) kit, a wavelength corrector kit, and a miniature autocollimator kit. A low-cost laser diode is employed as the laser source. The motion of the stage can cause an optical path difference in the MMI kit so as to produce interference fringes. The interference signals with a phase interval of 90° due to the phase control are detected by four photodetectors. The wavelength corrector kit, based on the grating diffraction principle and the autocollimation principle, provides real-time correction of the laser diode wavelength, which is the length unit of the MMI kit. The miniature autocollimator kit based on the autocollimation principle is employed to measure angular errors and compensate induced Abbe error of the moving table. The developed 3DOFLM system was constructed with dimensions of 80 mm (x) × 90 mm (y) × 20 mm (z) so that it could be embedded into the nanopositioning stage. A series of calibration and comparison experiments were carried out to test the performance of this system.

scholarly journals Generation of families of spectra in PT -symmetric quantum mechanics and scalar bosonic field theory

2013 ◽  
Vol 371 (1989) ◽  
pp. 20120049 ◽  
Author(s):  
Steffen Schmidt ◽  
S. P. Klevansky
Keyword(s):  
Field Theory ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Complex Analysis ◽  
One Dimension ◽  
Quantum Mechanical ◽  
Bosonic Field ◽  
Symmetric Quantum ◽  
The Difference ◽  
Do So

This paper explains the systematics of the generation of families of spectra for the -symmetric quantum-mechanical Hamiltonians H = p 2 + x 2 (i x ) ϵ , H = p 2 +( x 2 ) δ and H = p 2 −( x 2 ) μ . In addition, it contrasts the results obtained with those found for a bosonic scalar field theory, in particular in one dimension, highlighting the similarities to and differences from the quantum-mechanical case. It is shown that the number of families of spectra can be deduced from the number of non-contiguous pairs of Stokes wedges that display symmetry. To do so, simple arguments that use the Wentzel–Kramers–Brillouin approximation are used, and these imply that the eigenvalues are real. However, definitive results are in most cases presently only obtainable numerically, and not all eigenvalues in each family may be real. Within the approximations used, it is illustrated that the difference between the quantum-mechanical and the field-theoretical cases lies in the number of accessible regions in which the eigenfunctions decay exponentially. This paper reviews and implements well-known techniques in complex analysis and -symmetric quantum theory.

Etude de l'Effet des Paramètres d'Appareil sur la Décroissance de la Visibilité du Spectre Cannelé

1971 ◽  
Vol 49 (17) ◽  
pp. 2237-2249 ◽  
Author(s):  
C. Delisle ◽  
M. Brochu ◽  
J. M. St-Arnaud
Keyword(s):  
Spectral Density ◽  
White Light ◽  
Michelson Interferometer ◽  
Finite Size ◽  
Path Difference ◽  
Parallel Beam ◽  
Density Modulation ◽  
Theory And Experiment

The visibility of the channelled spectrum, or in other words the visibility of the spectral density modulation at the exit of a Michelson interferometer illuminated with a parallel beam of white light, is theoretically independent of the frequency and path difference of the two beams formed in the interferometer. Up to now there has been no agreement between theory and experiment. It is shown here, theoretically and experimentally, that the decrease in visibility with increasing path difference is related to both the finite size of the slits and the limit of resolution of the apparatus.

scholarly journals The complex and quaternionic quantum bit from relativity of simultaneity on an interferometer

2017 ◽  
Vol 473 (2208) ◽  
pp. 20170596 ◽  
Author(s):  
Andrew J. P. Garner ◽  
Markus P. Müller ◽  
Oscar C. O. Dahlsten
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Limit State ◽  
Arbitrary Dimension ◽  
Path Difference ◽  
Level System ◽  
State Spaces ◽  
Classical Physics ◽  
Quantum Bit ◽  
Real Complex

The patterns of fringes produced by an interferometer have long been important testbeds for our best contemporary theories of physics. Historically, interference has been used to contrast quantum mechanics with classical physics, but recently experiments have been performed that test quantum theory against even more exotic alternatives. A physically motivated family of theories are those where the state space of a two-level system is given by a sphere of arbitrary dimension. This includes classical bits, and real, complex and quaternionic quantum theory. In this paper, we consider relativity of simultaneity (i.e. that observers may disagree about the order of events at different locations) as applied to a two-armed interferometer, and show that this forbids most interference phenomena more complicated than those of complex quantum theory. If interference must depend on some relational property of the setting (such as path difference), then relativity of simultaneity will limit state spaces to standard complex quantum theory, or a subspace thereof. If this relational assumption is relaxed, we find one additional theory compatible with relativity of simultaneity: quaternionic quantum theory. Our results have consequences for current laboratory interference experiments: they have to be designed carefully to avoid rendering beyond-quantum effects invisible by relativity of simultaneity.

Fully compensated Michelson interferometer of fixed-path difference

1985 ◽  
Vol 24 (11) ◽  
pp. 1599 ◽  
Author(s):  
G. Thuillier ◽  
Gordon G. Shepherd
Keyword(s):  
Michelson Interferometer ◽  
Path Difference ◽  
Fixed Path
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