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.

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 SCALING OF VON NEUMANN ENTROPY AT THE ANDERSON TRANSITION

2010 ◽  
Vol 24 (12n13) ◽  
pp. 1823-1840 ◽  
Author(s):  
Sudip Chakravarty
Keyword(s):  
Phase Transition ◽  
Wave Function ◽  
Phase Transitions ◽  
Ground State ◽  
Quantum Phase Transitions ◽  
Quantum Phase ◽  
Tuning Parameter ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Anderson Transition

Extensive body of work has shown that for the model of a non-interacting electron in a random potential there is a quantum critical point for dimensions greater than two — a metal–insulator transition. This model also plays an important role in the plateau-to-plateu transition in the integer quantum Hall effect, which is also correctly captured by a scaling theory. Yet, in neither of these cases the ground state energy shows any non-analyticity as a function of a suitable tuning parameter, typically considered to be a hallmark of a quantum phase transition, similar to the non-analyticity of the free energy in a classical phase transition. Here we show that von Neumann entropy (entanglement entropy) is non-analytic at these phase transitions and can track the fundamental changes in the internal correlations of the ground state wave function. In particular, it summarizes the spatially wildly fluctuating intensities of the wave function close to the criticality of the Anderson transition. It is likely that all quantum phase transitions can be similarly described.

ENTANGLEMENT IN ONE-AND TWO-DIMENSIONAL ANDERSON MODELS WITH LONG-RANGE CORRELATED-DISORDER

2009 ◽  
Vol 07 (05) ◽  
pp. 959-968
Author(s):  
Z. Z. GUO ◽  
Z. G. XUAN ◽  
Y. S. ZHANG ◽  
XIAOWEI WU
Keyword(s):  
Long Range ◽  
Ground State ◽  
Two Dimensions ◽  
Von Neumann Entropy ◽  
Two Dimensional ◽  
Correlation Effects ◽  
Von Neumann ◽  
Range Correlation ◽  
The Difference ◽  
Anderson Models

The ground state entanglement in one- and two-dimensional Anderson models are studied with consideration of the long-range correlation effects and using the measures of concurrence and von Neumann entropy. We compare the effects of the long-range power-law correlation for the on-site energies on entanglement with the uncorrelated cases. We demonstrate the existence of the band structure of the entanglement. The intraband and interband jumping phenomena of the entanglement are also reported and explained to as the localization-delocalization transition of the system. We also demonstrated the difference between the results of one- and two-dimensions. Our results show that the correlation of the on-site energies increases the 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 VON NEUMANN ENTROPY AND RELATIVE POSITION BETWEEN SUBALGEBRAS

2013 ◽  
Vol 24 (08) ◽  
pp. 1350066 ◽  
Author(s):  
MARIE CHODA
Keyword(s):  
Tensor Product ◽  
Relative Position ◽  
Von Neumann Algebra ◽  
Positive Definite ◽  
The Other ◽  
Von Neumann Entropy ◽  
Product Decomposition ◽  
Positive Definite Matrices ◽  
Von Neumann ◽  
Finite Von Neumann Algebra

In order to give numerical characterizations of the notion of "mutual orthogonality", we introduce two kinds of family of positive definite matrices for a unitary u in a finite von Neumann algebra M. They are arising from u naturally depending on the decompositions of M. One corresponds to the tensor product decomposition and the other does to the crossed product decomposition. By using the von Neumann entropy for these positive definite matrices, we characterize the notion of mutual orthogonality between subalgebras.

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.

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