scholarly journals Squeezed coherent states for noncommutative spaces with minimal length uncertainty relations

2012 ◽  
Vol 86 (6) ◽  
Author(s):  
Sanjib Dey ◽  
Andreas Fring
Keyword(s):  
Coherent States ◽  
Minimal Length ◽  
Uncertainty Relations ◽  
Noncommutative Spaces

Photon added coherent states of the parity deformed oscillator

2019 ◽  
Vol 34 (14) ◽  
pp. 1950104 ◽  
Author(s):  
A. Dehghani ◽  
B. Mojaveri ◽  
S. Amiri Faseghandis
Keyword(s):  
Coherent States ◽  
Uncertainty Relation ◽  
Annihilation Operator ◽  
Single Mode ◽  
Heisenberg Algebra ◽  
Uncertainty Relations ◽  
Deformed Oscillator ◽  
Cat States ◽  
Poissonian Statistics ◽  
Creation Operators

Using the parity deformed Heisenberg algebra (RDHA), we first establish associated coherent states (RDCSs) for a pseudo-harmonic oscillator (PHO) system that are defined as eigenstates of a deformed annihilation operator. Such states can be expressed as superposition of an even and odd Wigner cat states.[Formula: see text] The RDCSs minimize a corresponding uncertainty relation, and resolve an identity condition through a positive definite measure which is explicitly derived. We introduce a class of single-mode excited coherent states (PARDCS) of the PHO through “m” times application of deformed creation operators to RDCS. For the states thus constructed, we analyze their statistical properties such as squeezing and sub-Poissonian statistics as well as their uncertainty relations.

scholarly journals COHERENT STATES, SUPERPOSITIONS OF COHERENT STATES AND UNCERTAINTY RELATIONS ON A MÖBIUS STRIP

2013 ◽  
Vol 28 (15) ◽  
pp. 1350058 ◽  
Author(s):  
THIAGO PRUDÊNCIO ◽  
DIEGO JULIO CIRILO-LOMBARDO
Keyword(s):  
Angular Momentum ◽  
Coherent States ◽  
Continuous Variable ◽  
Uncertainty Relations ◽  
Topological Properties ◽  
Möbius Strip ◽  
Symmetry Properties ◽  
Potential Applications ◽  
Fermionic Fields ◽  
Mobius Strip

Since symmetry properties of coherent states (CS) on Möbius strip (MS) and fermions are closely related, CS on MS are naturally associated to the topological properties of fermionic fields. Here, we consider CS and superpositions of coherent states (SCS) on MS. We extend a recent propose of CS on MS (Cirilo-Lombardo, J. Phys. A: Math. Theor.45, 244026 (2012)), including the analysis of periodic behaviors of CS and SCS on MS and the uncertainty relations associated to angular momentum and the phase angle. The advantage of CS and SCS on MS with respect to the standard ones and potential applications in continuous variable quantum computation (CVQC) are also addressed.

Coherent states and uncertainty relations

1974 ◽  
Vol 48 (3) ◽  
pp. 165-166 ◽  
Author(s):  
D.A. Trifonov
Keyword(s):  
Coherent States ◽  
Uncertainty Relations

UNCERTAINTY RELATIONS FOR THE TIME-DEPENDENT SINGULAR OSCILLATOR

2006 ◽  
Vol 20 (10) ◽  
pp. 1211-1231 ◽  
Author(s):  
J. R. CHOI ◽  
I. H. NAHM
Keyword(s):  
Harmonic Oscillator ◽  
Excited States ◽  
Ground State ◽  
Coherent States ◽  
System Approach ◽  
Uncertainty Relation ◽  
Time Dependent ◽  
Uncertainty Relations ◽  
Number State ◽  
State Uncertainty

Uncertainty relations for the time-dependent singular oscillator in the number state and in the coherent state are investigated. We applied our developement to the Caldirola–Kanai oscillator perturbed by a singularity. For this system, the variation (Δx) decreased exponentially while (Δp) increased exponentially with time both in the number and in the coherent states. As k → 0 and χ → 0, the number state uncertainty relation in the ground state becomes 0.583216ℏ which is somewhat larger than that of the standard harmonic oscillator, ℏ/2. On the other hand, the uncertainty relation in all excited states become smaller than that of the standard harmonic oscillator with the same quantum number n. However, as k → ∞ and χ → 0, the uncertainty relations of the system approach the uncertainty relations of the standard harmonic oscillator, (n+1/2)ℏ.

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