Coherent States and Classical Limit of Quantum Electrodynamics

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Electromagnetic Field ◽  
Quantum Optics ◽  
Coherent State ◽  
Quantum Electrodynamics ◽  
Classical Limit ◽  
Coherent States ◽  
Quantum Fluctuations ◽  
Squeezed States ◽  
Quantum Theories

The coherent state formalism is used in order to study the classical limit of quantum theories and, in particular, quantum electrodynamics. It is shown that we can construct states for which the quantum fluctuations are negligible. Interesting cases include the electromagnetic field in a cavity, or ‘squeezed’ states used in quantum optics.

SU(1,1) SQUEEZED STATES AS DAMPED OSCILLATORS

1989 ◽  
Vol 03 (16) ◽  
pp. 1213-1220 ◽  
Author(s):  
E. CELEGHINI ◽  
M. RASETTI ◽  
M. TARLINI ◽  
G. VITIELLO
Keyword(s):  
Quantum Optics ◽  
Coherent States ◽  
Single Mode ◽  
Explicit Construction ◽  
Squeezed States ◽  
Two Photon ◽  
Generalized Coherent States ◽  
Photon Process ◽  
Damped Oscillators ◽  
Damped Oscillator

The conventional squeezed states of quantum optics, which can be thought of as generalized coherent states for the algebra SU(1,1), are dynamically generated by single-mode hamiltonians characterized by two-photon process interactions. By the explicit construction of a (highly non-linear) faithful realization of the group [Formula: see text] of automorphisms of SU(1,1), such hamiltonians are shown to be equivalent — up just to elements of [Formula: see text] — to that describing quantum mechanically a damped oscillator.

The influence of excitation number of photon-added coherent state field on the entanglement swapping process

2017 ◽  
Vol 31 (27) ◽  
pp. 1750198 ◽  
Author(s):  
M. Soltani ◽  
M. K. Tavassoly ◽  
R. Pakniat
Keyword(s):  
Coherent State ◽  
Quantum Electrodynamics ◽  
Coherent States ◽  
Success Probability ◽  
Entanglement Swapping ◽  
Cavity Quantum Electrodynamics ◽  
Linear Entropy ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Coherent Field

In this paper, we outline a scheme for the entanglement swapping procedure based on cavity quantum electrodynamics using the Jaynes–Cummings model consisting of the coherent and photon-added coherent states. In particular, utilizing the photon-added coherent states ([Formula: see text][Formula: see text][Formula: see text][Formula: see text], where [Formula: see text] is the Glauber coherent state) in the scheme, enables us to investigate the effect of [Formula: see text], i.e., the number of excitations corresponding to the photon-added coherent field on the entanglement swapping process. In the scheme, two two-level atoms [Formula: see text] and [Formula: see text] are initially entangled together, and distinctly two exploited cavity fields [Formula: see text] and [Formula: see text] are prepared in an entangled state (a combination of coherent and photon-added coherent states). Interacting the atom [Formula: see text] with field [Formula: see text] (via the Jaynes–Cummings model) and then making detection on them, transfers the entanglement from the two atoms [Formula: see text], [Formula: see text] and the two fields [Formula: see text], [Formula: see text] to the atom-field “[Formula: see text]-[Formula: see text]”, i.e., entanglement swapping occurs. In the continuation, we pay our attention to the evaluation of the fidelity of the swapped entangled state relative to a suitable maximally entangled state, success probability of the performed detections and linear entropy as the degree of entanglement of the swapped entangled state. It is demonstrated that, an increase in the number of excitations, [Formula: see text], leads to the increment of fidelity as well as the amount of entanglement. According to our numerical results, the maximum values of fidelity (linear entropy) 0.98 (0.46) is obtained for [Formula: see text], however, the maximum value of success probability does not significantly change by increasing [Formula: see text].

An Introduction to Quantum Optics and Quantum Fluctuations

2019 ◽  
Author(s):  
Peter W. Milonni
Keyword(s):  
Quantum Optics ◽  
Spontaneous Emission ◽  
Quantum Electrodynamics ◽  
Planck Equation ◽  
Quantum Fluctuations ◽  
Van Der Waals Interactions ◽  
Vacuum Field ◽  
Langevin Equations ◽  
Uncertainty Relations ◽  
Point Energy

This book is an introduction to quantum optics for students who have studied electromagnetism and quantum mechanics at an advanced undergraduate or graduate level. It provides detailed expositions of theory with emphasis on general physical principles. Foundational topics in classical and quantum electrodynamics, including the semiclassical theory of atom-field interactions, the quantization of the electromagnetic field in dispersive and dissipative media, uncertainty relations, and spontaneous emission, are addressed in the first half of the book. The second half begins with a chapter on the Jaynes-Cummings model, dressed states, and some distinctly quantum-mechanical features of atom-field interactions, and includes discussion of entanglement, the no-cloning theorem, von Neumann’s proof concerning hidden variable theories, Bell’s theorem, and tests of Bell inequalities. The last two chapters focus on quantum fluctuations and fluctuation-dissipation relations, beginning with Brownian motion, the Fokker-Planck equation, and classical and quantum Langevin equations. Detailed calculations are presented for the laser linewidth, spontaneous emission noise, photon statistics of linear amplifiers and attenuators, and other phenomena. Van der Waals interactions, Casimir forces, the Lifshitz theory of molecular forces between macroscopic media, and the many-body theory of such forces based on dyadic Green functions are analyzed from the perspective of Langevin noise, vacuum field fluctuations, and zero-point energy. There are numerous historical sidelights throughout the book, and approximately seventy exercises.

QUANTUM OPTICS: GROUP AND NON-GROUP METHODS

1999 ◽  
Vol 13 (24n25) ◽  
pp. 3021-3038 ◽  
Author(s):  
ALLAN I. SOLOMON
Keyword(s):  
Quantum Optics ◽  
Coherent State ◽  
Quantum Group ◽  
Squeezed States ◽  
Theoretical Methods ◽  
Group Methods ◽  
Photon States

We give a brief review of some group and quantum group theoretical methods used for the construction of photon states, generalisations of coherent and squeezed states. We finally describe a more general approach, exemplified by a new generalized coherent state, a generalization of the Kerr state.

THE DEPENDENCY ON THE SQUEEZING PARAMETER FOR THE UNCERTAINTY RELATION IN THE SQUEEZED STATES OF THE TIME-DEPENDENT OSCILLATOR

2004 ◽  
Vol 18 (16) ◽  
pp. 2307-2324 ◽  
Author(s):  
JEONG RYEOL CHOI
Keyword(s):  
Quantum Mechanics ◽  
Coherent State ◽  
Coherent States ◽  
Uncertainty Relation ◽  
Time Dependent ◽  
Squeezed States ◽  
Time Dependency ◽  
Minimum Value ◽  
Number State

We obtained the uncertainty relation in squeezed states for a time-dependent oscillator. The uncertainty relation in coherent states is same as that of the number states with n=0. However, the uncertainty relation in squeezed states does not satisfy this property and depends on squeezing parameter c. For instance, the uncertainty relation is ℏ/2 which is the minimum value as far as quantum mechanics permits for c=1, same as that in coherent state for c=±∞, and infinity for c=-1. If the time-dependency of the Hamiltonian for the system vanishes, the uncertainty relation in squeezed states will no longer depend on c and becomes the same as that in number state with n=0, like the uncertainty relation in coherent states.

Effect of the oscillations in the photon distribution of a squeezed field on the fluorescence spectrum of the Jaynes–Cummings model

2020 ◽  
pp. 2050426
Author(s):  
L. Villanueva-Vergara ◽  
F. Soto-Eguibar ◽  
H. M. Moya-Cessa
Keyword(s):  
Electromagnetic Field ◽  
Coherent State ◽  
Fluorescence Spectrum ◽  
Squeezed States ◽  
Level System ◽  
Photon Distribution ◽  
Atomic Inversion ◽  
Squeezed Coherent State ◽  
Physical Spectrum

Following the scheme proposed by Eberly and Wodkiewicz for the physical spectrum, we calculate the fluorescence spectrum of the Jaynes–Cummings model when the two-level system interacts with an electromagnetic field that initially is in a squeezed coherent state. We show the appearing of “ringing lines” in the fluorescence spectrum that are echoes of the oscillations in the photon distribution of the compressed field. These ringing lines may be a similar effect as the ringing revivals of the atomic inversion that are a signature of squeezed states.

PERELOMOV AND BARUT–GIRARDELLO SU(1, 1) COHERENT STATES FOR HARMONIC OSCILLATOR IN ONE-DIMENSIONAL HALF SPACE

2006 ◽  
Vol 21 (12) ◽  
pp. 2635-2644 ◽  
Author(s):  
Q. H. LIU ◽  
H. ZHUO
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Half Space ◽  
Ground State ◽  
Classical Limit ◽  
Coherent States ◽  
Mean Values ◽  
One Dimensional ◽  
The Mean

The Perelomov and the Barut–Girardello SU(1, 1) coherent states for harmonic oscillator in one-dimensional half space are constructed. Results show that the uncertainty products ΔxΔp for these two coherent states are bound from below [Formula: see text] that is the uncertainty for the ground state, and the mean values for position x and momentum p in classical limit go over to their classical quantities respectively. In classical limit, the uncertainty given by Perelomov coherent does not vanish, and the Barut–Girardello coherent state reveals a node structure when positioning closest to the boundary x = 0 which has not been observed in coherent states for other systems.

ON THE SEMICLASSICAL LIMIT OF LOOP QUANTUM COSMOLOGY

2012 ◽  
Vol 21 (09) ◽  
pp. 1250076 ◽  
Author(s):  
ALEJANDRO CORICHI ◽  
EDISON MONTOYA
Keyword(s):  
Coherent State ◽  
Quantum Cosmology ◽  
Coherent States ◽  
Semiclassical Limit ◽  
Loop Quantum Cosmology ◽  
Squeezed States ◽  
Gaussian States ◽  
Exactly Solvable ◽  
Spatial Topology ◽  
Frw Model

We consider a k = 0 Friedman–Robertson–Walker (FRW) model within loop quantum cosmology (LQC) and explore the issue of its semiclassical limit. The model is exactly solvable and allows us to construct analytical (Gaussian) coherent-state solutions for each point on the space of classical states. We propose physical criteria that select from these coherent states, those that display semiclassical behavior, and study their properties in the deep Planck regime. Furthermore, we consider generalized squeezed states and compare them to the Gaussian states. The issue of semiclassicality preservation across the bounce is studied and shown to be generic for all the states considered. Finally, we comment on some implications these results have, depending on the topology of the spatial slice. In particular, we consider the issue of the recovery, within our class of states, of a scaling symmetry present in the classical description of the system when the spatial topology is noncompact.

Angular momentum coherent states

1971 ◽  
Vol 321 (1546) ◽  
pp. 321-340 ◽  
Keyword(s):  
Angular Momentum ◽  
Coherent State ◽  
Harmonic Oscillator ◽  
Classical Limit ◽  
Coherent States ◽  
Uncertainty Relations ◽  
Mean Square ◽  
Expectation Values ◽  
Angular Momenta ◽  
Two Component

The work of Carruthers & Nieto on the harmonic oscillator coherent states is combined with Schwinger’s construction of angular momentum to produce the angular momentum coherent states. It is shown that these states become the vector representatives of angular momentum in the classical limit, and so are particularly useful for discussing the transition from quantum to classical angular momentum. The uncertainty relations for angle and angular momentum are described and are compatible with the classical limit. Under rotations the coherent states transform in a manner that in the classical limit is equivalent to the transformation of vectors, and in the same limit the root mean square variation of the expectation values of the components of angular momentum become negligible in comparison with the expectation values themselves. The coupling of two angular momenta in the classical limit is investigated: it is shown that although the product of two coherent states is not itself a coherent state, it does represent a packet similar to a true coherent state, and centred on the direction of the classical resultant of the two component vectors. The properties and implications of hyperbolic angular momentum space are discussed.

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