scholarly journals Quantumness Measures for a System of Two Qubits Interacting with a Field in the Presence of the Time-Dependent Interaction and Kerr Medium

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 635
Author(s):  
Sayed Abdel-Khalek ◽  
Kamal Berrada ◽  
Eied M. Khalil ◽  
Abdel-Shafy F. Obada ◽  
Esraa Reda ◽  
...  
Keyword(s):  
Single Mode ◽  
Dynamical Behaviour ◽  
Time Dependent ◽  
Von Neumann Entropy ◽  
Kerr Medium ◽  
Von Neumann ◽  
Mode Field ◽  
Mandel’S Parameter ◽  
Qubit System ◽  
Dependent Interaction

In this work, we introduce the standard Tavis-Cummings model to describe two-qubit system interacting with a single-mode field associated to power-law (PL) potentials. We explore the effect of the time-dependent interaction and the Kerr-like medium. We solve the Schrödinger equation to obtain the density operator that allows us to investigate the dynamical behaviour of some quantumness measures, such as von Neumann entropy, negativity and Mandel’s parameter. We provide how these entanglement measures depend on the system parameters, which paves the way towards better control of entanglement generation in two-qubit systems. We find that the enhancement and preservation of the atoms-field entanglement and atom-atom entanglement can be achieved by a proper choice of the initial parameters of the field in the absence and presence of the time-dependent interaction and Kerr medium. We examine the photons distribution of the field and determine the situations for which the field exhibits super-poissonian, poissonian or sub-poissonian distribution.

scholarly journals Tavis–Cummings Model with Moving Atoms

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 452
Author(s):  
Sayed Abdel-Khalek ◽  
Kamal Berrada ◽  
Eied M. Khalil ◽  
Hichem Eleuch ◽  
Abdel-Shafy F. Obada ◽  
...  
Keyword(s):  
Power Law ◽  
Coupling Parameter ◽  
Dynamical Behavior ◽  
Single Mode ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Mode Field ◽  
Nonlinear Version ◽  
Power Law Exponent ◽  
Potential Applications

In this work, we examine a nonlinear version of the Tavis–Cummings model for two two-level atoms interacting with a single-mode field within a cavity in the context of power-law potentials. We consider the effect of the particle position that depends on the velocity and acceleration, and the coupling parameter is supposed to be time-dependent. We examine the effect of velocity and acceleration on the dynamical behavior of some quantumness measures, namely as von Neumann entropy, concurrence and Mandel parameter. We have found that the entanglement of subsystem states and the photon statistics are largely dependent on the choice of the qubit motion and power-law exponent. The obtained results present potential applications for quantum information and optics with optimal conditions.

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.

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.

Entanglement in composite systems due to external influences

2018 ◽  
Vol 33 (21) ◽  
pp. 1850128
Author(s):  
D. M. Gitman ◽  
M. S. Meireles ◽  
A. D. Levin ◽  
A. A. Shishmarev ◽  
R. A. Castro
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Density Operator ◽  
Time Dependent ◽  
Von Neumann Entropy ◽  
Entanglement Measure ◽  
Photon Beams ◽  
Von Neumann ◽  
Electron Positron ◽  
In The Beginning

In this paper, we consider two examples of an entanglement in two-qubit systems and an example of entanglement in quantum field theory (QFT). In the beginning, we study the entanglement of two spin states by a magnetic field. A nonzero entanglement appears for interacting spins. When the coupling between the spins is constant, we study the entanglement by several types of time-dependent magnetic fields. In the case of a constant difference between [Formula: see text] components of magnetic fields acting on each spin, we find several time-dependent coupling functions [Formula: see text] that also allow us to analyze analytically and numerically the entanglement measure. Considering two photons moving in an electron medium, we demonstrate that they can be entangled in a controlled way by applying an external magnetic field. The magnetic field affecting electrons of the medium affects photons and, thus, causes an entanglement of the photon beams. The third example is related to the effect of production of electron–positron pairs from the vacuum by a strong external electric field. Here, we have used a general nonperturbative expression for the density operator of the system under consideration. Applying a reduction procedure to this density operator, we construct mixed states of electron and positron subsystems. Calculating the von Neumann entropy of such states, we obtain the loss of information due to the reduction and, at the same time, the entanglement measure of electron and positron subsystems. This entanglement can be considered as an example of an entanglement in QFT.

scholarly journals Entanglement Dynamics of Three and Four Level Atomic System under Stark Effect and Kerr-Like Medium

2019 ◽  
Vol 1 (1) ◽  
pp. 23-36
Author(s):  
S. Jamal Anwar ◽  
M. Ramzan ◽  
M. Usman ◽  
M. Khalid Khan
Keyword(s):  
Quantum Entanglement ◽  
Stark Effect ◽  
Quantum Fisher Information ◽  
Local Maximum ◽  
Stark Shift ◽  
Von Neumann Entropy ◽  
Kerr Medium ◽  
Von Neumann ◽  
Atomic Systems ◽  
Non Linear

We investigated numerically the dynamics of quantum Fisher information (QFI) and entanglement for three- and four-level atomic systems interacting with a coherent field under the effect of Stark shift and Kerr medium. It was observed that the Stark shift and Kerr-like medium play a prominent role during the time evolution of the quantum systems. The non-linear Kerr medium has a stronger effect on the dynamics of QFI as compared to the quantum entanglement (QE). QFI is heavily suppressed by increasing the value of Kerr parameter. This behavior was found comparable in the cases of three- and four-level atomic systems coupled with a non-linear Kerr medium. However, QFI and quantum entanglement (QE) maintain their periodic nature under atomic motion. On the other hand, the local maximum value of QFI and von Neumann entropy (VNE) decrease gradually under the Stark effect. Moreover, no prominent difference in the behavior of QFI and QE was observed for three- and four-level atoms while increasing the value of Stark parameter. However, three- and four-level atomic systems were found equally prone to the non-linear Kerr medium and Stark effect. Furthermore, three- and four-level atomic systems were found fully prone to the Kerr-like medium and Stark effect.

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.

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