scholarly journals On the Open Dicke-Type Model Generated by an Infinite-Component Vector Spin

2020 ◽  
Vol 27 (03) ◽  
pp. 2050012
Author(s):  
Ryota Kyokawa ◽  
Hajime Moriya ◽  
Hiroshi Tamura
Keyword(s):  
Harmonic Oscillator ◽  
Time Evolution ◽  
Single Mode ◽  
Type Model ◽  
Quantum Model ◽  
Asymptotic Equivalence ◽  
Completely Positive ◽  
Type Interaction ◽  
Dicke Model ◽  
Infinite Component

We consider an open Dicke model comprising a single infinite-component vector spin and a single-mode harmonic oscillator which are connected by Jaynes–Cummings-type interaction between them. This open quantum model is referred to as the OISD (Open Infinite-component Spin Dicke) model. The algebraic structure of the OISD Liouvillian is studied in terms of superoperators acting on the space of density matrices. An explicit invertible superoperator (precisely, a completely positive trace-preserving map) is obtained that transforms the OISD Liouvillian into a sum of two independent Liouvillians, one generated by a dressed spin only, the other generated by a dressed harmonic oscillator only. The time evolution generated by the OISD Liouvillian is shown to be asymptotically equivalent to that generated by an adjusted decoupled Liouvillian with some synchronized frequencies of the spin and the harmonic oscillator. This asymptotic equivalence implies that the time evolution of the OISD model dissipates completely in the presence of any (tiny) dissipation.

(ANTI)COMMUTATIVITY OF THE HARMONIC CREATION AND ANNIHILATION OPERATORS

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1808-1818
Author(s):  
S. KUWATA ◽  
A. MARUMOTO
Keyword(s):  
Irreducible Representation ◽  
Harmonic Oscillator ◽  
Linear Algebra ◽  
Commutation Relation ◽  
Complex Number ◽  
Single Mode ◽  
Equation Of Motion ◽  
Sufficient Condition ◽  
Special Linear ◽  
Creation And Annihilation Operators

It is known that para-particles, together with fermions and bosons, of a single mode can be described as an irreducible representation of the Lie (super) algebra 𝔰𝔩2(ℂ) (2-dimensional special linear algebra over the complex number ℂ), that is, they satisfy the equation of motion of a harmonic oscillator. Under the equation of motion of a harmonic oscillator, we obtain the set of the commutation relations which is isomorphic to the irreducible representation, to find that the equation of motion, conversely, can be derived from the commutation relation only for the case of either fermion or boson. If Nature admits of the existence of such a sufficient condition for the equation of motion of a harmonic oscillator, no para-particle can be allowed.

scholarly journals A discrete quantum model of the harmonic oscillator

2008 ◽  
Vol 41 (8) ◽  
pp. 085201 ◽  
Author(s):  
Natig M Atakishiyev ◽  
Anatoliy U Klimyk ◽  
Kurt Bernardo Wolf
Keyword(s):  
Harmonic Oscillator ◽  
Quantum Model

scholarly journals Statistical Study of the Entanglement for Qubit Interacting with an Electromagnetic Field

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Neveen Sayed-Ahmed ◽  
M. M. Amein ◽  
Taghreed M. Jawa ◽  
Tahani A. Aloafi ◽  
F. S. Bayones ◽  
...  
Keyword(s):  
Binomial Distribution ◽  
Numerical Study ◽  
Single Mode ◽  
Simulation Method ◽  
Von Neumann Entropy ◽  
Quantum Model ◽  
Wigner Functions ◽  
Von Neumann ◽  
Proposed Model ◽  
Distribution State

A statistical method is applied to predict the behaviour of a quantum model consisting of a qubit interacting with a single-mode cavity field. The qubit is prepared in excited state while the field starts from the binomial distribution state. The wave function of the proposed model is obtained. A von Neumann entropy is used to investigate the behaviour of the entanglement between the field and the qubits. Moreover, the atomic Q and Wigner functions are used to identify the behaviour of the distribution in a phase space. The simulation method is used to estimate the parameters of the proposed model to reach the best results. A numerical study is performed to estimate the specific dependency of the binomial distribution state. The results of entanglement were compared with the atomic Q and Wigner functions. The results showed that there are many maximum values of entanglement periodically. The results also confirmed a correlation between von Neumann entropy, the atomic Q , and Wigner functions.

scholarly journals Quantum Weak Invariants: Dynamical Evolution of Fluctuations and Correlations

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1219
Author(s):  
Zeyi Shi ◽  
Sumiyoshi Abe
Keyword(s):  
Time Evolution ◽  
Open Quantum System ◽  
Dynamical Evolution ◽  
Time Dependent ◽  
Von Neumann Entropy ◽  
Completely Positive Map ◽  
Expectation Values ◽  
Completely Positive ◽  
Temporal Asymmetry ◽  
Von Neumann

Weak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of a completely positive map, the fluctuations monotonically grow even if the map is not unital, in contrast to the fact that monotonic increases of both the von Neumann entropy and Rényi entropy require the map to be unital. In this way, the weak invariants describe temporal asymmetry in a manner different from the entropies. A formula is presented for time evolution of the covariance matrix associated with the weak invariants in cases where the system density matrix obeys the Gorini–Kossakowski–Lindblad–Sudarshan equation.

A FOUR-LEVEL ATOM INTERACTING WITH A SINGLE-MODE CAVITY FIELD: DOUBLE Ξ-CONFIGURATION

2008 ◽  
Vol 22 (26) ◽  
pp. 2587-2599 ◽  
Author(s):  
N. H. ABDEL-WAHAB
Keyword(s):  
Coherent State ◽  
Time Evolution ◽  
Single Mode ◽  
Cavity Field ◽  
Field System ◽  
Input Field ◽  
Level Atom ◽  
Constants Of Motion ◽  
Q Function ◽  
Single Mode Cavity

In this article, the problem of a double Ξ-type four-level atom interacting with a single-mode cavity field is considered. The considered model describes several distinct configurations of a four-level atom. Also, this model includes the detuning parameters of the atom-field system. We obtain the constants of motion and the wavefunction is derived when the atom is initially prepared in the upper state. We used this model for computing a number of the field aspects for the considered system. As an illustration, the model is used for studying the time evolution of the Mandel Q-parameter, amplitude-squared squeezing phenomenon and Q-function when the input field is considered in a coherent state. The results show that these phenomena are affected by the presence of detuning parameters.

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