Von Neumann entropy and entropy squeezing of a two-level atom and the superposition of squeezed displaced fock states

2008 ◽  
Vol 29 (4) ◽  
pp. 398-407
Author(s):  
G. M. Abd Al-Kader ◽  
A.-S. F. Obada
Keyword(s):  
Von Neumann Entropy ◽  
Entropy Squeezing ◽  
Von Neumann ◽  
Fock States ◽  
Level Atom

Aspects of Entropy Squeezing and Entanglement for Moving Two-Level Atom in Presence of Finite Trio Coherent State

2016 ◽  
Vol 13 (10) ◽  
pp. 7455-7459
Author(s):  
S. I Ali ◽  
A. M Mosallem ◽  
T Emam
Keyword(s):  
Entanglement Entropy ◽  
Photon Number ◽  
Atomic Motion ◽  
Von Neumann Entropy ◽  
Wehrl Entropy ◽  
Entropy Squeezing ◽  
Von Neumann ◽  
Special Values ◽  
Level Atom ◽  
Motion Parameters

In this paper, we investigate the entanglement of the interaction of three modes of radiation field with moving and unmoving two-level atom. The time evolution of the von Neumann entropy, entropy squeezing and marginal atomic Wehrl entropy is investigated. The marginal atomic Wehrl entropy as squeezing indicator of the entanglement of the system is suggested. The results beacon the important roles played by both the atomic motion parameters in the evolution of entanglement, entropy squeezing and marginal atomic Wehrl entropy. Using special values of the photon number of transition and atomic motion parameter, the entanglement phenomena of sudden death and long living entanglenment can be appeared. The results show that there is atomic motion monotonic harmonization atomic Wehrl entropy (WE). It is illustrated that the amount of the above-mentioned phenomena can be tuned by controlling the evolved parameters appropriately.

On the interaction between a time-dependent field and a two-level atom

2019 ◽  
Vol 34 (10) ◽  
pp. 1950081 ◽  
Author(s):  
N. H. Abdel-Wahab ◽  
Ahmed Salah
Keyword(s):  
Quantum Electrodynamics ◽  
Initial Conditions ◽  
Coupling Parameter ◽  
Quantum Systems ◽  
Trapped Ions ◽  
Time Dependent ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Level Atom ◽  
Dependent Field

In this paper, we study the interaction between the time-dependent field and a two-level atom with one mode electromagnetic field. We consider that the field of photons is assumed to be coupled with modulated coupling parameter which depends explicitly on time. It is shown that the considered model can be reduced to a well-known form of the time-dependent generalized Jaynes–Cummings model. Under special initial conditions, in which the atom and the field are prepared in the excited and the coherent states, respectively, the explicit time evolution of the wave function of the entire system is analytically obtained. Our proposal has many advantages over the previous optical schemes and can be realized in several multiple experiments, such as trapped ions and quantum electrodynamics cavity. The influence of the time-dependent field parameter on the collapses-revivals, the normal squeezing of the radiation, the anti-bunching of photons and the entanglement phenomena for the considered atomic system is examined. The linear entropy, the von Neumann entropy are used to quantify entanglement in the quantum systems. We noticed that these phenomena are affected by the existence of both the time-dependent coupling field and detuning parameters.

scholarly journals Entanglement of Pseudo-Hermitian Random States

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1109
Author(s):  
Cleverson Andrade Goulart ◽  
Mauricio Porto Pato
Keyword(s):  
Density Matrix ◽  
Random Matrices ◽  
Bell States ◽  
Von Neumann Entropy ◽  
Abstract Model ◽  
Von Neumann ◽  
Fock States ◽  
Bosonic System ◽  
Random States

In a recent paper (A. Fring and T. Frith, Phys. Rev A 100, 101102 (2019)), a Dyson scheme to deal with density matrix of non-Hermitian Hamiltonians has been used to investigate the entanglement of states of a PT-symmetric bosonic system. They found that von Neumann entropy can show a different behavior in the broken and unbroken regime. We show that their results can be recast in terms of an abstract model of pseudo-Hermitian random matrices. It is found however that although the formalism is practically the same, the entanglement is not of Fock states but of Bell states.

MAXIMUM ENTANGLEMENT IN A JAYNES-CUMMINGS SYSTEM WITH STRONGLY DRIVEN ATOMS

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1613-1620 ◽  
Author(s):  
F. CASAGRANDE ◽  
A. LULLI
Keyword(s):  
Cavity Mode ◽  
Resonant Cavity ◽  
Vacuum State ◽  
Interaction Time ◽  
Von Neumann Entropy ◽  
Lower State ◽  
Von Neumann ◽  
Level Atom ◽  
Maximum Value ◽  
Coherent Field

We describe the entanglement of a Jaynes-Cummings system, where a two-level atom is also strongly driven by an external coherent field while it crosses a resonant cavity prepared in a coherent state. First we consider the atom-cavity field entanglement, described by the Von Neumann entropy. We find that it depends only on the interaction time and the initial atomic state. The entropy vanishes in the case of maximally polarized atom, independent of the interaction time, whereas it reaches its maximum value for atom in the upper or lower state and for long enough interaction times. Then we investigate the entanglement between two consecutive strongly driven atoms interacting with the cavity mode assumed in the vacuum state, showing that they never entangle in spite of the existence of atom-atom correlations.

WEHRL ENTROPY OF A MIXED STATE THREE-LEVEL ATOM INTERACTING WITH A CAVITY FIELD

2010 ◽  
Vol 09 (06) ◽  
pp. 623-630
Author(s):  
S. ABDEL-KHALEK ◽  
Y. HASSOUNI ◽  
M. ABDEL-ATY
Keyword(s):  
Mixed State ◽  
Von Neumann Entropy ◽  
Entangled State ◽  
Cavity Field ◽  
Wehrl Entropy ◽  
Von Neumann ◽  
Level Atom ◽  
Total Correlation ◽  
State Case ◽  
Mutual Entropy

In this paper, the Wehrl entropy approach is discussed and compared with the quantum entanglement using a mixed-state three-level atom interacting with a cavity field. In the pure state case, the behavior of the atomic Wehrl entropy shows the same behavior of the entanglement due to the von-Neumann entropy, while the mixed state case gives the total correlation due to quantum mutual entropy. If the system is in an entangled state, the formalism can be used to quantify the entanglement as well as the total correlations.

Nonclassical properties of asymmetric two two-level atoms interacting with multi-photon quantized field

2018 ◽  
Vol 32 (23) ◽  
pp. 1850250 ◽  
Author(s):  
Abdallah A. Nahla ◽  
M. M. A. Ahmed
Keyword(s):  
Electromagnetic Field ◽  
Analytical Formula ◽  
Von Neumann Entropy ◽  
Quantum Model ◽  
Entropy Squeezing ◽  
Von Neumann ◽  
Proposed Model ◽  
Atom Interaction ◽  
Quantized Field ◽  
Atomic Population Inversion

A quantum model for the interaction between asymmetric two two-level atoms and an electromagnetic field is presented. The [Formula: see text]-photon processes and atom–atom interaction are considered in this quantum model. The wavefunction for asymmetric case of the proposed model is obtained analytically. While, the explicit analytical formula of the wavefunction for symmetric case was calculated in previous works. Initially, the electromagnetic field is in the coherent state and two two-level atoms are identical in the excited states. For the proposed model, some statistical aspects are obtained, such as the linear entropy, atomic population inversion, entropy squeezing, atomic variance and von Neumann entropy. The evaluations of these statistical properties are discussed for the variation in the detuning parameters. Moreover, the nonclassical effects for atom–atom interaction are observed.

scholarly journals The von Neumann Entropy for Mixed States

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 49 ◽  
Author(s):  
Jorge Anaya-Contreras ◽  
Héctor Moya-Cessa ◽  
Arturo Zúñiga-Segundo
Keyword(s):  
Mixed State ◽  
Infinite System ◽  
Complete System ◽  
Von Neumann Entropy ◽  
Mixed States ◽  
Field Interaction ◽  
Von Neumann ◽  
Level Atom ◽  
Quantized Field ◽  
Pure States

The Araki–Lieb inequality is commonly used to calculate the entropy of subsystems when they are initially in pure states, as this forces the entropy of the two subsystems to be equal after the complete system evolves. Then, it is easy to calculate the entropy of a large subsystem by finding the entropy of the small one. To the best of our knowledge, there does not exist a way of calculating the entropy when one of the subsystems is initially in a mixed state. For the case of a two-level atom interacting with a quantized field, we show that it is possible to use the Araki–Lieb inequality and find the von Neumann entropy for the large (infinite) system. We show this in the two-level atom-field interaction.

scholarly journals The Jaynes–Cummings model of a two-level atom in a single-mode para-Bose cavity field

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
H. Fakhri ◽  
M. Sayyah-Fard
Keyword(s):  
Coherent States ◽  
Quantum Noise ◽  
Single Mode ◽  
Von Neumann Entropy ◽  
Cavity Field ◽  
Squeezing Effect ◽  
Atomic Inversion ◽  
Von Neumann ◽  
Level Atom ◽  
Mechanical Nature

AbstractThe coherent states in the parity deformed analog of standard boson Glauber coherent states are generated, which admit a resolution of unity with a positive measure. The quantum-mechanical nature of the light field of these para-Bose states is studied, and it is found that para-Bose order plays an important role in the nonclassical behaviors including photon antibunching, sub-Poissonian statistics, signal-to-quantum noise ratio, quadrature squeezing effect, and multi-peaked number distribution. Furthermore, we consider the Jaynes-Cummings model of a two-level atom in a para-Bose cavity field with the initial states of the excited and Glauber coherent ones when the atom makes one-photon transitions, and obtain exact energy spectrum and eigenstates of the deformed model. Nonclassical properties of the time-evolved para-Bose atom-field states are exhibited through evaluating the fidelity, evolution of atomic inversion, level damping, and von Neumann entropy. It is shown that the evolution time and the para-Bose order control these properties.

scholarly journals Islands in linear dilaton black holes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Georgios K. Karananas ◽  
Alex Kehagias ◽  
John Taskas
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Entanglement Entropy ◽  
Von Neumann Entropy ◽  
Two Dimensional ◽  
Extremal Case ◽  
Von Neumann ◽  
Dimensional Black Hole ◽  
Linear Dilaton ◽  
Linear Dilaton Black Hole

Abstract We derive a novel four-dimensional black hole with planar horizon that asymptotes to the linear dilaton background. The usual growth of its entanglement entropy before Page’s time is established. After that, emergent islands modify to a large extent the entropy, which becomes finite and is saturated by its Bekenstein-Hawking value in accordance with the finiteness of the von Neumann entropy of eternal black holes. We demonstrate that viewed from the string frame, our solution is the two-dimensional Witten black hole with two additional free bosons. We generalize our findings by considering a general class of linear dilaton black hole solutions at a generic point along the σ-model renormalization group (RG) equations. For those, we observe that the entanglement entropy is “running” i.e. it is changing along the RG flow with respect to the two-dimensional worldsheet length scale. At any fixed moment before Page’s time the aforementioned entropy increases towards the infrared (IR) domain, whereas the presence of islands leads the running entropy to decrease towards the IR at later times. Finally, we present a four-dimensional charged black hole that asymptotes to the linear dilaton background as well. We compute the associated entanglement entropy for the extremal case and we find that an island is needed in order for it to follow the Page curve.

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