scholarly journals Non-Gaussianity of Four-Photon Superpositions of Fock States

2021 ◽  
Author(s):  
Viktor V. Dodonov ◽  
Miguel de Freitas Citeli
Keyword(s):  
Coherent States ◽  
Squeezed States ◽  
Fock States

We compare several different measures of non-Gaussianity for two families of four-photon superpositions of the Fock states: even vacuum squeezed states and orthogonal-even coherent states.

scholarly journals Non-Gaussianity of Four-Photon Superpositions of Fock States

2021 ◽  
Vol 3 (3) ◽  
pp. 350-365
Author(s):  
Miguel Citeli de Freitas ◽  
Viktor V. Dodonov
Keyword(s):  
Fourth Order ◽  
Effective Temperature ◽  
Coherent States ◽  
Squeezed States ◽  
Gaussian States ◽  
Fock States ◽  
The Past ◽  
Fidelity Measure ◽  
Non Gaussian ◽  
Thermal States

We study two families of four-photon superpositions of the Fock states: even vacuum squeezed states (EVSS) and orthogonal-even coherent states (OECS). These families are distinguished due to several properties: for certain values of parameters, they give the fourth-order uncertainty products close to the known minimal value (which is lower than for the Gaussian states); they have equal dimensionless values of the second- and fouth-order moments of the coordinate and momentum for all values of parameters; they possess zero covariances for all values of parameters. Since these states are obviously non-Gaussian, we consider them as good candidates to compare several different measures of non-Gaussianity proposed by different authors for the past fifteen years. The reference Gaussian states in all examples are thermal states dependent on a single parameter (an effective temperature or the coordinate variance). We analyze the measures based on the normalized Hilbert–Schmidt distance and the relative entropy (introduced by Genoni–Paris–Banaszek), the fidelity measure (Ghiu–Marian–Marian) and its logarithmic analog (Baek–Nha), as well as the Mandilara–Karpov–Cerf “Gaussianity parameter”. These measures are compared with the kurtosis of the coordinate probability density and with the non-Gaussian behavior of the Wigner function.

scholarly journals Minimal Products of Coordinate and Momentum Uncertainties of High Orders: Significant and Weak High-Order Squeezing

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 980
Author(s):  
Miguel Citeli de Freitas ◽  
Vitor Dantas Meireles ◽  
Viktor V. Dodonov
Keyword(s):  
Lower Bounds ◽  
Coherent States ◽  
High Order ◽  
Point Of View ◽  
Squeezed States ◽  
Mean Values ◽  
Fock States

We consider the problem of minimization of products of mean values of the high powers of operators x and p. From this point of view, we study several two-term superpositions of the Fock states, as well as three popular families of infinite superpositions: squeezed states, even/odd coherent states, and orthogonal even coherent states (or compass states). The new element is the analysis of products of the corresponding (co)variances and the related generalized (Robertson–Schrödinger) intelligent states (RSIS). In particular, we show that both Fock and pure Gaussian homogeneous states are RSIS for the fourth powers (but not for the sixth ones). We show that lower bounds of the high-order uncertainty products can be significantly below the vacuum values. In this connection, the concept of significant and weak high-order squeezing is introduced.

Thermal Coherent States and Thermal Squeezed States

1991 ◽  
Vol 38 (12) ◽  
pp. 2339-2347 ◽  
Author(s):  
J. Oz-Vogt ◽  
A. Mann ◽  
M. Revzen
Keyword(s):  
Coherent States ◽  
Squeezed States

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.

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