Entanglement and Pancharatnam Phase of a Four-Level Atom in Coherent States Within Generalized Heisenberg Algebra

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.

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COHERENT STATES IN GRAVITATIONAL QUANTUM MECHANICS

International Journal of Modern Physics D ◽

10.1142/s0218271813500041 ◽

2013 ◽

Vol 22 (02) ◽

pp. 1350004 ◽

Cited By ~ 9

Author(s):

POURIA PEDRAM

Keyword(s):

Quantum Gravity ◽

Coherent States ◽

Scale Effects ◽

Black Hole Physics ◽

Probability Distributions ◽

Planck Scale ◽

Experimental Tests ◽

Heisenberg Algebra ◽

Adjoint Representation ◽

Weight Functions

We present the coherent states of the harmonic oscillator in the framework of the generalized (gravitational) uncertainty principle (GUP). This form of GUP is consistent with various theories of quantum gravity such as string theory, loop quantum gravity and black-hole physics and implies a minimal measurable length. Using a recently proposed formally self-adjoint representation, we find the GUP-corrected Hamiltonian as a generator of the generalized Heisenberg algebra. Then following Klauder's approach, we construct exact coherent states and obtain the corresponding normalization coefficients, weight functions and probability distributions. We find the entropy of the system and show that it decreases in the presence of the minimal length. These results could shed light on possible detectable Planck-scale effects within recent experimental tests.

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The Pancharatnam phase of a two-level atom in the presence of another two-level atom in a cavity

Journal of Optics B Quantum and Semiclassical Optics ◽

10.1088/1464-4266/5/4/304 ◽

2003 ◽

Vol 5 (4) ◽

pp. 349-354 ◽

Cited By ~ 15

Author(s):

Mahmoud Abdel-Aty

Keyword(s):

Pancharatnam Phase ◽

Level Atom

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COHERENT STATES AND SCHWINGER MODELS FOR PSEUDO GENERALIZATION OF THE HEISENBERG ALGEBRA

Modern Physics Letters A ◽

10.1142/s0217732309030722 ◽

2009 ◽

Vol 24 (25) ◽

pp. 2039-2051 ◽

Cited By ~ 2

Author(s):

H. FAKHRI ◽

B. MOJAVERI ◽

A. DEHGHANI

Keyword(s):

Harmonic Oscillator ◽

Coherent States ◽

Heisenberg Algebra ◽

Creation And Annihilation Operators ◽

Number Of Generators ◽

Simple Harmonic Oscillator

We show that the non-Hermitian Hamiltonians of the simple harmonic oscillator with [Formula: see text] and [Formula: see text] symmetries involve a pseudo generalization of the Heisenberg algebra via two pairs of creation and annihilation operators which are [Formula: see text]-pseudo-Hermiticity and [Formula: see text]-anti-pseudo-Hermiticity of each other. The non-unitary Heisenberg algebra is represented by each of the pair of the operators in two different ways. Consequently, the coherent and the squeezed coherent states are calculated in two different approaches. Moreover, it is shown that the approach of Schwinger to construct the su(2), su(1, 1) and sp(4, ℝ) unitary algebras is promoted so that unitary algebras with more linearly dependent number of generators are made.

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