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 Quantum Fisher Information and Entanglement of Moving Two Two-Level Atoms under the Influence of Environmental Effects

Physics ◽  
2019 ◽  
Vol 1 (1) ◽  
pp. 131-146
Author(s):  
Syed Jamal Anwar ◽  
M. Usman ◽  
M. Ramzan ◽  
M. Khalid Khan
Keyword(s):  
Time Evolution ◽  
Fisher Information ◽  
Environmental Effects ◽  
Stark Effect ◽  
Thermal Environment ◽  
Quantum Fisher Information ◽  
Atomic Motion ◽  
Kerr Medium ◽  
Stark Effects ◽  
Non Linear

We have investigated numerically the dynamics of quantum Fisher information (QFI) and quantum entanglement (QE) of a two moving two-level atomic systems interacting with a coherent and thermal field in the presence of intrinsic decoherence (ID) and Kerr (non-linear medium) and Stark effects. The state of the entire system interacting with coherent and thermal fields is evaluated numerically under the influence of ID and Kerr (nonlinear) and Stark effects. QFI and von Neumann entropy (VNE) decrease in the presence of ID when the atomic motion is neglected. QFI and QE show an opposite response during its time evolution in the presence of a thermal environment. QFI is found to be more susceptible to ID as compared to QE in the presence of a thermal environment. The decay of QE is further damped at greater time-scales, which confirms the fact that ID heavily influences the system’s dynamics in a thermal environment. However, a periodic behavior of entanglement is observed due to atomic motion, which becomes modest under environmental effects. It is found that a non-linear Kerr medium has a prominent effect on the VNE but not on the QFI. Furthermore, it has been observed that QFI and QE decay soon under the influence of the Stark effect in the absence of atomic motion. The periodic response of QFI and VNE is observed for both the non-linear Kerr medium and the Stark effect in the presence of atomic motion. It is observed that the Stark, Kerr, ID, and thermal environment have significant effects during the time evolution of the quantum system.

scholarly journals Entanglement and geometric phase of the coherent field interacting with a three two-level atoms in the presence of non-linear terms

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 237-245
Author(s):  
Eman Hilal ◽  
Sadah Alkhateeb ◽  
Sayed Abel-Khalek ◽  
Eied Khalil ◽  
Amjaad Almowalled
Keyword(s):  
Coherent State ◽  
Geometric Phase ◽  
Initial Conditions ◽  
Von Neumann Entropy ◽  
Field Mode ◽  
Von Neumann ◽  
Coherent Field ◽  
Non Linear ◽  
Atomic States ◽  
The Impact

We study the interaction of a three two-level atoms with a one-mode optical coherent field in coherent state in the presence of non-linear Kerr medim. The three atoms are initially prepared in upper and entangled states while the field mode is in a coherent state. The constants of motion, three two-level atoms and field density matrix are obtained. The analytic results are employed to perform some investigations of the temporal evolution of the von Neumann entropy as measure of the degree of entanglement between the three two-level atoms and optical coherent field. The effect of the detuning and the initial atomic states on the evolution of geometric phase and entanglement is analyzed. Also, we demonstrate the link between the geometric phase and non-classical properties during the evolution time. Additionally the effect of detuning and initial conditions on the Mandel parameter is studied. The obtained results are emphasize the impact of the detuning and the initial atomic states of the feature of the entanglement, geometric phase and photon statistics of the optical coherent field.

scholarly journals Entanglement and geometric phase of the coherent field interacting with a three two-level atoms in the presence of non-linear terms

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 39-48
Author(s):  
Eman Hilal ◽  
Sadah Alkhateeb ◽  
Sayed Abdel-Khalek ◽  
Eied Khalil ◽  
Amjaad Almowalled
Keyword(s):  
Coherent State ◽  
Geometric Phase ◽  
Initial Conditions ◽  
Von Neumann Entropy ◽  
Kerr Medium ◽  
Field Mode ◽  
Coherent Field ◽  
Non Linear ◽  
Atomic States ◽  
The Impact

We study the interaction of a three two-level atoms (3-2LA) with a one-mode op?tical coherent field in coherent state in the presence of non-linear Kerr medium. The three atoms are initially prepared in upper and entangled states while the field mode is in a coherent state. The constants of motion, 3-2LA and field density matrix are obtained. The analytic results are employed to perform some investigations of the temporal evolution of the von Neumann entropy as measure of the degree of entanglement between the 3-2LA and optical coherent field. The effect of the detuning and the initial atomic states on the evolution of geometric phase and en?tanglement is analyzed. Also, we demonstrate the link between the geometric phase and non-classical properties during the evolution time. Additionally the effect of detuning and initial conditions on the Mandel parameter is studied. The obtained results are emphasize the impact of the detuning and the initial atomic states of the feature of the entanglement, geometric phase and photon statistics of theoptical coherent field.

Generalized Nonadditive Information Theory and Quantum Entanglement

2004 ◽  
Author(s):  
Sumiyoshi Abe
Keyword(s):  
Information Theory ◽  
Quantum Theory ◽  
Statistical Mechanics ◽  
Quantum Entanglement ◽  
Theory Of Measurement ◽  
Conditional Entropy ◽  
Tsallis Entropy ◽  
Von Neumann Entropy ◽  
Additive Theory ◽  
Von Neumann

Nonadditive classical information theory is developed in the axiomatic framework and then translated into quantum theory. The nonadditive conditional entropy associated with the Tsallis entropy indexed by q is given in accordance with the formalism of nonextensive statistical mechanics. The theory is applied to the problems of quantum entanglement and separability of the Werner-Popescu-type mixed state of a multipartite system, in order to examine if it has any points superior to the additive theory with the von Neumann entropy realized in the limit q → 1. It is shown that the nonadditive theory can lead to the necessary and sufficient condition for separability of the Werner-Popescu-type state, whereas the von Neumann theory can give only a much weaker condition…. Tsallis' nonextensive generalization of Boltzmann-Gibbs statistical mechanics [3, 15, 16] and its success in describing behaviors of a large class of complex systems naturally lead to the question of whether information theory can also admit an analogous generalization. If the answer is affirmative, then that will be of particular importance in connection with the problem of quantum entanglement and quantum theory of measurement [6, 8], in which necessities of a nonadditive information measure and an information content are suggested. One should also remember that there exists a conceptual similarity between a complex system and an entangled quantum system. In these systems, a "part" is indivisibly connected with the rest. An external operation on any part drastically influences the whole system, in general. Thus, the traditional reductionistic approach to an understanding of the nature of such a system may not work efficiently. In this chapter, we report a recent development in nonadditive quantum information theory based on the Tsallis entropy indexed by q [15] and its associated nonadditive conditional entropy [1]. This theory includes the ordinary additive theory with the von Neumann entropy in a special limiting case: q → To see if it has points superior to the additive theory, we apply it to the problems of separability and quantum entanglement.

scholarly journals Quantum thermodynamics and quantum entanglement entropies in an expanding universe

2017 ◽  
Vol 32 (15) ◽  
pp. 1750066 ◽  
Author(s):  
Mehrnoosh Farahmand ◽  
Hosein Mohammadzadeh ◽  
Hossein Mehri-Dehnavi
Keyword(s):  
Scalar Field ◽  
Quantum Entanglement ◽  
Particle Creation ◽  
Space Time ◽  
Von Neumann Entropy ◽  
Quantum Thermodynamics ◽  
Entanglement Generation ◽  
Von Neumann ◽  
Underlying Space ◽  
The Universe

We investigate an asymptotically spatially flat Robertson–Walker space–time from two different perspectives. First, using von Neumann entropy, we evaluate the entanglement generation due to the encoded information in space–time. Then, we work out the entropy of particle creation based on the quantum thermodynamics of the scalar field on the underlying space–time. We show that the general behavior of both entropies are the same. Therefore, the entanglement can be applied to the customary quantum thermodynamics of the universe. Also, using these entropies, we can recover some information about the parameters of space–time.

scholarly journals Entanglement and geometric phase of the coherent field interacting with a three two-level atoms in the presence of non-linear terms

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 237-245
Author(s):  
Eman Hilal ◽  
Sadah Alkhateeb ◽  
Sayed Abel-Khalek ◽  
Eied Khalil ◽  
Amjaad Almowalled
Keyword(s):  
Coherent State ◽  
Geometric Phase ◽  
Initial Conditions ◽  
Von Neumann Entropy ◽  
Field Mode ◽  
Von Neumann ◽  
Coherent Field ◽  
Non Linear ◽  
Atomic States ◽  
The Impact

We study the interaction of a three two-level atoms with a one-mode optical coherent field in coherent state in the presence of non-linear Kerr medim. The three atoms are initially prepared in upper and entangled states while the field mode is in a coherent state. The constants of motion, three two-level atoms and field density matrix are obtained. The analytic results are employed to perform some investigations of the temporal evolution of the von Neumann entropy as measure of the degree of entanglement between the three two-level atoms and optical coherent field. The effect of the detuning and the initial atomic states on the evolution of geometric phase and entanglement is analyzed. Also, we demonstrate the link between the geometric phase and non-classical properties during the evolution time. Additionally the effect of detuning and initial conditions on the Mandel parameter is studied. The obtained results are emphasize the impact of the detuning and the initial atomic states of the feature of the entanglement, geometric phase and photon statistics of the optical coherent field.

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.

Entanglement for excited states of ultracold bosonic atoms in one-dimensional harmonic traps with contact interaction

2015 ◽  
Vol 29 (30) ◽  
pp. 1550189 ◽  
Author(s):  
Hsuan Tung Peng ◽  
Yew Kam Ho
Keyword(s):  
Quantum Entanglement ◽  
Excited States ◽  
Ground State ◽  
The Other ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
One Dimensional ◽  
Ultracold Bosonic Atoms ◽  
Bosonic Atoms ◽  
Atom System

We have investigated quantum entanglement for two interacting ultracold bosonic atoms in one-dimensional harmonic traps. The effective potential is modeled by delta interaction. For this two-atom system, we have investigated quantum entanglement properties, such as von Neumann entropy and linear entropy for its ground state and excited states. Using a computational scheme that is different from previously employed, a total of the lowest 16 states are studied. Here we show the dependencies of entanglement properties under various interacting strengths. Comparisons for the ground state entanglement are made with earlier results in the literature. New results for the other 15 excited states are reported here.

Quantum interferometric power and the role of nonclassical correlations in quantum metrology for a special class of two-qubit states

2017 ◽  
Vol 31 (08) ◽  
pp. 1750052 ◽  
Author(s):  
H. El Hadfi ◽  
Y. Ait Taleb ◽  
M. Daoud
Keyword(s):  
Quantum Fisher Information ◽  
Quantum Correlations ◽  
Von Neumann Entropy ◽  
Phase Estimation ◽  
Quantum Metrology ◽  
Von Neumann ◽  
Local Quantum ◽  
Parameter Precision ◽  
Qubit States

We analyze the effects of quantum correlations on the parameter precision in an interferometric configuration. As probe states, we consider a class of two-qubit states for which the analytical expression of the quantum interferometric power, quantifying the quantum correlations, is explicitly derived. Also, we give and analyze the local quantum Fisher information, which evaluates the sensitivity of the probe state to the phase shift, for some relevant local Hamiltonians. The discord-like quantum correlations based on the notion of quantum interferometric power are compared with the original quantum discord based on von Neumann entropy. We also examine the significance of quantum correlations in enhancing the precision of the phase estimation. Our study corroborates the recent series of investigations focusing on the role of quantum correlations other than entanglement on the efficiency of quantum metrology protocols.

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