Coherent States and Fock States at Very High Average Photon Numbers

1981 ◽  
Vol 34 (4) ◽  
pp. 357
Author(s):  
GJ Troup ◽  
HS Perlman
Keyword(s):  
Coherent State ◽  
Field Intensity ◽  
Laser Field ◽  
Coherent States ◽  
Photon Number ◽  
Constant Field ◽  
Fock States ◽  
Fock State ◽  
Very High ◽  
Average Photon Number

A laser field may be idealized as a coherent state, but it is often more convenient to use Fock states fQr quantum electrodynamical calculations. A Fock state implies fluctuations in the field intensity, aptl a constant field intensity (coherent state) implies fluctuations in the photon number. Both these effects are discussed rigorously. When the average photon number tends to infinity, these different states become asymptotically indistinguishable.

Experimental resources needed to implement photon number splitting attack in quantum cryptography

2022 ◽  
Vol 19 (2) ◽  
pp. 025203
Author(s):  
S P Kulik ◽  
K S Kravtsov ◽  
S N Molotkov
Keyword(s):  
Coherent State ◽  
Quantum Key Distribution ◽  
Distribution Systems ◽  
Communication Channel ◽  
Random Phase ◽  
Photon Number ◽  
Fock States ◽  
Fock State ◽  
Experimental Parameters ◽  
Photon Number Splitting Attack

Abstract The analysis of the security of quantum key distribution systems with respect to an attack with nondemolishing measurement of the number of photons (photon number splitting—PNS attack) is carried out under the assumption that in the communication channel in each parcel there is a pure Fock state with a different number of photons, and the distribution of states by number of photons has Poisson statistics. In reality, in the communication channel in each parcel there are not individual Fock states, but a pure coherent state with a random phase—a superposition of Fock states with different numbers of photons. The paper analyzes the necessary experimental resources necessary to prepare individual Fock states with a certain number of photons from the superposition of Fock states for a PNS attack. Optical schemes for implementing such an attack are given, and estimates of experimental parameters at which a PNS attack is possible are made.

On the Squeezing and Displacement of nth-Order

1997 ◽  
Vol 11 (09n10) ◽  
pp. 399-406
Author(s):  
Norton G. de Almeida ◽  
Célia M. A. Dantas
Keyword(s):  
Coherent State ◽  
Coherent States ◽  
Photon Number ◽  
Natural Generalization ◽  
Statistical Properties ◽  
Number Distribution ◽  
Quantum Statistical ◽  
Photon Number Distribution

The norder expressions for the squeezed and coherent states are derived as a natural generalization of the usual squeezed coherent and coherent states. The photon number distribution of n order of squeezed coherent states that are eigenstates of the operators [Formula: see text] is derived. The n order coherent state is a particular case of the states that we are now deriving. Some mathematical and quantum statistical properties of these states are discussed.

Photon-catalyzed optical coherent states generated via a non-degenerate parametric amplifier with quantum-optical catalysis

2020 ◽  
Vol 98 (2) ◽  
pp. 119-124 ◽  
Author(s):  
Hong-Chun Yuan ◽  
Xue-Xiang Xu ◽  
Heng-Mei Li ◽  
Ye-Jun Xu ◽  
Xiang-Guo Meng
Keyword(s):  
Coherent State ◽  
Wigner Function ◽  
Coherent States ◽  
Laguerre Polynomial ◽  
Photon Number ◽  
Parametric Amplifier ◽  
Normalization Factor ◽  
Nonclassical Properties ◽  
Quadrature Squeezing ◽  
Quantum Optical

We theoretically generate a kind of photon-catalyzed optical coherent states (PCOCSs) by heralded interference between any photons and coherent state via a non-degenerate parametric amplifier, which is also just a Laguerre polynomial excited coherent state. Based on obtaining the probability of successfully detecting them (also the normalization factor), the nonclassical properties of the PCOCSs are analytically investigated according to autocorrelation function, quadrature squeezing, and the negativity of the Wigner function. It is found that the nonclassicality depends on the amplitude of the coherent state, the catalysis photon number, and amplifier parameter. The negative volume of their Wigner function can be enlarged by increasing the catalysis photon number. These parameters may be effectively used to improve and enhance the nonclassical characteristics.

scholarly journals DYNAMICS OF STATES IN THE NONLINEAR INTERACTION REGIME BETWEEN A THREE-LEVEL ATOM AND GENERALIZED COHERENT STATES AND THEIR NON-CLASSICAL FEATURES

2012 ◽  
Vol 26 (05) ◽  
pp. 1250027 ◽  
Author(s):  
M. K. TAVASSOLY ◽  
F. YADOLLAHI
Keyword(s):  
Coherent State ◽  
Coherent States ◽  
Exact Analytical Solution ◽  
Photon Number ◽  
Single Mode ◽  
Level Atom ◽  
Special Cases ◽  
Interaction Regime ◽  
Atomic Population Inversion ◽  
Poissonian Statistics

The present study investigates the interaction of an equidistant three-level atom and a single-mode cavity field that has been initially prepared in a generalized coherent state. The atom–field interaction is considered to be, in general, intensity-dependent. We suppose that the nonlinearity of the initial generalized coherent state of the field and the intensity-dependent coupling between atom and field are distinctly chosen. Interestingly, an exact analytical solution for the time evolution of the state of atom–field system can be found in this general regime in terms of the nonlinearity functions. Finally, the presented formalism has been applied to a few known physical systems such as Gilmore–Perelomov and Barut–Girardello coherent states of SU(1,1) group, as well as a few special cases of interest. Mean photon number and atomic population inversion will be calculated, in addition to investigating particular non-classicality features such as revivals, sub-Poissonian statistics and quadratures squeezing of the obtained states of the entire system. Also, our results will be compared with some of the earlier works in this particular subject.

Exchange of nonclassical properties between two interacting modes of light and mutual conversion of the Fock and coherent states

1999 ◽  
Vol 77 (3) ◽  
pp. 211-220 ◽  
Author(s):  
J Fu ◽  
X -C Gao ◽  
J -B Xu ◽  
X -B Zou
Keyword(s):  
Coherent State ◽  
Numerical Computation ◽  
Coherent States ◽  
Unitary Transformation ◽  
Transformation Method ◽  
Nonclassical Properties ◽  
Fock State ◽  
Mutual Conversion ◽  
03.65 Ge

The invariant-related unitary transformation method is used to study the exchange of nonclassical properties between two interacting modes of light. With the aid of numerical computation, it is of interest to find that the mutual conversion of the Fock state and the coherent state is attained when the interaction is chosen appropriately.PACS Nos.: 03.65.Ge, 42.50.Ar

MINIMUM UNCERTAINTY SU(1,1) COHERENT STATES FOR NUMBER DIFFERENCE — TWO-MODE PHASE SQUEEZING

2000 ◽  
Vol 14 (05) ◽  
pp. 157-166 ◽  
Author(s):  
HONG-YI FAN ◽  
ZHI-HU SUN
Keyword(s):  
Coherent State ◽  
Coherent States ◽  
Difference Operator ◽  
Fock Space ◽  
Photon Number ◽  
Phase Operator ◽  
Complete Representation ◽  
Minimum Uncertainty ◽  
Operational Phase

For the two-mode photon number-difference operator D = a†a -b†b and the Noh, Fougers and Mandel (NFM) operational phase operator [Formula: see text], we introduce the concept of number-difference-phase squeezing. We then find a new minimum-uncertainty state for number-difference-phase squeezing, which turns out to be a special combination of generalized SU(1,1) coherent state. As a by-product, a new orthonormal and complete representation in two-mode Fock space made up of R†n|m, m> is found.

NONLINEAR DISPLACED FOCK STATE REPRESENTATION

2001 ◽  
Vol 15 (04n05) ◽  
pp. 163-173 ◽  
Author(s):  
HONGYI FAN ◽  
HAILING CHENG
Keyword(s):  
Coherent States ◽  
Completeness Relation ◽  
State Representation ◽  
Fock States ◽  
Fock State

As a generalization of the nonlinear coherent states we construct nonlinear displaced Fock states (NLDFS). In contrast to the ordinary displaced Fock state, two kinds of NLDFS are introduced, which are composed by nonlinear displacing operator on the nonlinear Fock states Df(α)| n>f and [Formula: see text]. The over-completeness relation for NLDFS is obtained by virtue of the generalized technique of integration within an ordered product of operators. Generation of some kind of NLDFS is briefly discussed.

DYNAMICS OF A NONDEGENERATE TWO-PHOTON JAYNES–CUMMINGS MODEL

1995 ◽  
Vol 09 (11n12) ◽  
pp. 665-683 ◽  
Author(s):  
RICHARD D'SOUZA ◽  
ARUNDHATI S. JAYARAO
Keyword(s):  
Coherent States ◽  
Coherence Function ◽  
Dynamical Behavior ◽  
Photon Number ◽  
Stark Shift ◽  
Atomic Inversion ◽  
Two Photon ◽  
Different Types ◽  
Atomic Squeezing ◽  
Average Photon Number

A generalized Jaynes–Cummings model including the Stark shifts is investigated where the transition is mediated by two different modes of photons. For two different types of correlated field states, the pair coherent states and two-mode SU(1, 1) coherent states, the effect of including the Stark shift on the dynamical behavior of atomic inversion, atomic squeezing parameters, second order coherence function, and photon number distribution is investigated. Our results indicate significant changes in the behavior of these quantities for large and small average photon number <n> in the presence and absence of Stark shift and depending on the type of correlated field involved.

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