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

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.

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

Thermal Science ◽

10.2298/tsci20s1237h ◽

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.

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

Thermal Science ◽

10.2298/tsci20237h ◽

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.

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GEOMETRIC PHASE AND DISENTANGLEMENT OF A MOVING FOUR-LEVEL ATOM IN THE PRESENCE OF NONLINEAR MEDIUM

International Journal of Quantum Information ◽

10.1142/s0219749912500074 ◽

2012 ◽

Vol 10 (01) ◽

pp. 1250007 ◽

Cited By ~ 3

Author(s):

NOUR ZIDAN ◽

S. ABDEL-KHALEK ◽

M. ABDEL-ATY

Keyword(s):

System Dynamics ◽

Geometric Phase ◽

Nonlinear Medium ◽

Atomic Motion ◽

Kerr Medium ◽

Mode Structure ◽

Field Mode ◽

Level Atom

In this paper, we investigate the geometric phase of the field interacting with a moving four-level atom in the presence of Kerr medium. The results show that the atomic motion, the field-mode structure and Kerr medium play important roles in the evolution of the system dynamics. As illustration, we examine the behavior of the geometric phase and entanglement with experimentally accessible parameters. Some new aspects are observed and discussed.

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Cosmic flows and the expansion of the local Universe from non-linear phase–space reconstructions

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stv2928 ◽

2016 ◽

Vol 456 (4) ◽

pp. 4247-4255 ◽

Cited By ~ 10

Author(s):

Steffen Heß ◽

Francisco-Shu Kitaura

Keyword(s):

Phase Space ◽

Cold Dark Matter ◽

Initial Conditions ◽

Hubble Constant ◽

Linear Phase ◽

Local Universe ◽

Non Linear ◽

Galaxy Sample ◽

Fisher Relation ◽

The Impact

Abstract In this work, we investigate the impact of cosmic flows and density perturbations on Hubble constant H0 measurements using non-linear phase–space reconstructions of the Local Universe (LU). In particular, we rely on a set of 25 precise constrained N-body simulations based on Bayesian initial conditions reconstructions of the LU using the Two-Micron Redshift Survey galaxy sample within distances of about 90 h−1 Mpc. These have been randomly extended up to volumes enclosing distances of 360 h−1 Mpc with augmented Lagrangian perturbation theory (750 simulations in total), accounting in this way for gravitational mode coupling from larger scales, correcting for periodic boundary effects, and estimating systematics of missing attractors (σlarge = 134 s−1 km). We report on Local Group (LG) speed reconstructions, which for the first time are compatible with those derived from cosmic microwave background-dipole measurements: |vLG| = 685 ± 137 s−1 km. The direction (l, b) = (260$_{.}^{\circ}$5 ± 13$_{.}^{\circ}$3, 39$_{.}^{\circ}$1 ± 10$_{.}^{\circ}$4) is found to be compatible with the observations after considering the variance of large scales. Considering this effect of large scales, our local bulk flow estimations assuming a Λ cold dark matter model are compatible with the most recent estimates based on velocity data derived from the Tully–Fisher relation. We focus on low-redshift supernova measurements out to 0.01 < z < 0.025, which have been found to disagree with probes at larger distances. Our analysis indicates that there are two effects related to cosmic variance contributing to this tension. The first one is caused by the anisotropic distribution of supernovae, which aligns with the velocity dipole and hence induces a systematic boost in H0. The second one is due to the inhomogeneous matter fluctuations in the LU. In particular, a divergent region surrounding the Virgo Supercluster is responsible for an additional positive bias in H0. Taking these effects into account yields a correction of ΔH0 = -1.76 ± 0.21 s− 1 km Mpc− 1, thereby reducing the tension between local probes and more distant probes. Effectively H0 is lower by about 2 per cent.

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Quantum Entanglement and Geometric Phase of Two Moving Two-Level Atoms

Open Systems & Information Dynamics ◽

10.1142/s1230161215500158 ◽

2015 ◽

Vol 22 (03) ◽

pp. 1550015 ◽

Cited By ~ 22

Author(s):

S. Abdel-Khalek

Keyword(s):

Geometric Phase ◽

Essential Role ◽

Coupling Parameter ◽

Atomic Motion ◽

Von Neumann Entropy ◽

Field Mode ◽

Von Neumann ◽

Nonlocal Correlations ◽

Interesting Correlation ◽

Important Kind

An important kind of interaction between two moving two-level atoms and a field mode, where the coupling parameter is taken to be time-dependent, is presented in this paper. Nonlocal correlations between the atoms and the field have been investigated by means of concurrence and von Neumann entropy in terms of the involved parameters of the system. The results show that the atomic motion plays an essential role in the evolution of system dynamics, its nonlocal correlations and geometric phase. Moreover, an interesting correlation between the entanglement and the geometric phase during the evolution was observed. The presented system can be very useful for generating and maintaining high amount of entanglement by means of controlling the parameters of atomic motion.

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

Quantum Reports ◽

10.3390/quantum1010004 ◽

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.

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Primordial non-Gaussianity without tails – how to measure fNL with the bulk of the density PDF

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa2160 ◽

2020 ◽

Vol 498 (1) ◽

pp. 464-483 ◽

Cited By ~ 2

Author(s):

Oliver Friedrich ◽

Cora Uhlemann ◽

Francisco Villaescusa-Navarro ◽

Tobias Baldauf ◽

Marc Manera ◽

...

Keyword(s):

Power Spectrum ◽

Initial Conditions ◽

Density Fluctuations ◽

Joint Analysis ◽

Late Time ◽

Non Linear ◽

Free Parameters ◽

Non Gaussian ◽

The Impact ◽

Time Density

ABSTRACT We investigate the possibility to detect primordial non-Gaussianity by analysing the bulk of the probability distribution function (PDF) of late-time cosmic density fluctuations. For this purpose, we devise a new method to predict the impact of general non-Gaussian initial conditions on the late-time density PDF. At redshift z = 1 and for a smoothing scale of 30 Mpc h−1 our predictions agree with the high-resolution Quijote N-body simulations to $\sim 0.2{{\ \rm per\ cent}}$ precision. This is within cosmic variance of a ∼100(Gpc h−1)3 survey volume. When restricting to this 30 Mpc h−1 smoothing scale and to mildly non-linear densities (δ[30 Mpc h−1] ∈ [−0.3, 0.4]) and also marginalizing over potential ignorance of the amplitude of the non-linear power spectrum an analysis of the PDF for such a survey volume can still measure the amplitude of different primordial bispectrum shapes to an accuracy of $\Delta f_{\mathrm{NL}}^{\mathrm{loc}} = \pm 7.4\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{equi}} = \pm 22.0\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{ortho}} = \pm 46.0$. When pushing to smaller scales and assuming a joint analysis of the PDF with smoothing radii of 30 and 15 Mpc h−1 (δ[15 Mpc h−1] ∈ [−0.4, 0.5]) this improves to $\Delta f_{\mathrm{NL}}^{\mathrm{loc}} = \pm 3.3\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{equi}} = \pm 11.0\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{ortho}} = \pm 17.0$ – even when marginalizing over the non-linear variances at both scales as two free parameters. Especially, such an analysis could simultaneously measure fNL and the amplitude and slope of the non-linear power spectrum. However, at 15 Mpc h−1 our predictions are only accurate to $\lesssim 0.8{{\ \rm per\ cent}}$ for the considered density range. We discuss how this has to be improved in order to push to these small scales and make full use of upcoming surveys with a PDF-based analysis.

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Corrigendum : Entanglement and geometric phase of the coherent field interacting with a three two-level atoms in the presence of non-linear terms by Eman Hilal, Sadah Alkhateeb, Sayed Abdel-Khalek, Eied M. Khalil, and Amjaad Almowalled

Thermal Science ◽

10.2298/tsci210729242e ◽

2021 ◽

pp. 242-242

Author(s):

E Editorial

Keyword(s):

Guest Editor ◽

Geometric Phase ◽

Coherent Field ◽

Non Linear ◽

Retracted Article ◽

Font Color

Simeon Oka, Editor-in-Chief Emeritus of the journal Thermal Science request that due to mistake of the Guest Editor in the issue Thermal Science 2020 Volume 24, Issue Suppl. 1, have been published two versions of the same papers, one version before revision and other version after correction according to reviewers comments. Link to the retracted article <a href="https://doi.org/10.2298/TSCI20S1039H">10.2298/TSCI20S1039H</a>

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On Kaufmann's theory of the impact of the pianoforte hammer

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

10.1098/rspa.1920.0016 ◽

1920 ◽

Vol 97 (682) ◽

pp. 99-110 ◽

Cited By ~ 12

Keyword(s):

Initial Conditions ◽

Practical Importance ◽

Prima Facie ◽

Point Of View ◽

Infinite Length ◽

Modes Of Vibration ◽

Rigorous Treatment ◽

The Subject ◽

Set Up ◽

The Impact

The theory of the vibrations of the pianoforte string put forward by Kaufmann in a well-known paper has figured prominently in recent discussions on the acoustics of this instrument. It proceeds on lines radically different from those adopted by Helmholtz in his classical treatment of the subject. While recognising that the elasticity of the pianoforte hammer is not a negligible factor, Kaufmann set out to simplify the mathematical analysis by ignoring its effect altogether, and treating the hammer as a particle possessing only inertia without spring. The motion of the string following the impact of the hammer is found from the initial conditions and from the functional solutions of the equation of wave-propagation on the string. On this basis he gave a rigorous treatment of two cases: (1) a particle impinging on a stretched string of infinite length, and (2) a particle impinging on the centre of a finite string, neither of which cases is of much interest from an acoustical point of view. The case of practical importance treated by him is that in which a particle impinges on the string near one end. For this case, he gave only an approximate theory from which the duration of contact, the motion of the point struck, and the form of the vibration-curves for various points of the string could be found. There can be no doubt of the importance of Kaufmann’s work, and it naturally becomes necessary to extend and revise his theory in various directions. In several respects, the theory awaits fuller development, especially as regards the harmonic analysis of the modes of vibration set up by impact, and the detailed discussion of the influence of the elasticity of the hammer and of varying velocities of impact. Apart from these points, the question arises whether the approximate method used by Kaufmann is sufficiently accurate for practical purposes, and whether it may be regarded as applicable when, as in the pianoforte, the point struck is distant one-eighth or one-ninth of the length of the string from one end. Kaufmann’s treatment is practically based on the assumption that the part of the string between the end and the point struck remains straight as long as the hammer and string remain in contact. Primâ facie , it is clear that this assumption would introduce error when the part of the string under reference is an appreciable fraction of the whole. For the effect of the impact would obviously be to excite the vibrations of this portion of the string, which continue so long as the hammer is in contact, and would also influence the mode of vibration of the string as a whole when the hammer loses contact. A mathematical theory which is not subject to this error, and which is applicable for any position of the striking point, thus seems called for.

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