scholarly journals Spectral Structure and Many-Body Dynamics of Ultracold Bosons in a Double-Well

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 382
Author(s):  
Frank Schäfer ◽  
Miguel A. Bastarrachea-Magnani ◽  
Axel U. J. Lode ◽  
Laurent de Forges de Parny ◽  
Andreas Buchleitner
Keyword(s):  
Initial Conditions ◽  
Dynamical Behavior ◽  
Particle Interaction ◽  
Interaction Strength ◽  
Von Neumann Entropy ◽  
Spectral Structure ◽  
Many Body ◽  
Point Energy ◽  
Von Neumann ◽  
Body Dynamics

We examine the spectral structure and many-body dynamics of two and three repulsively interacting bosons trapped in a one-dimensional double-well, for variable barrier height, inter-particle interaction strength, and initial conditions. By exact diagonalization of the many-particle Hamiltonian, we specifically explore the dynamical behavior of the particles launched either at the single-particle ground state or saddle-point energy, in a time-independent potential. We complement these results by a characterization of the cross-over from diabatic to quasi-adiabatic evolution under finite-time switching of the potential barrier, via the associated time evolution of a single particle’s von Neumann entropy. This is achieved with the help of the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X)—which also allows us to extrapolate our results for increasing particle numbers.

scholarly journals Fast control of interactions in an ultracold two atom system: Managing correlations and irreversibility

2019 ◽  
Vol 6 (2) ◽  
Author(s):  
Thomas Fogarty ◽  
Lewis Ruks ◽  
Jing Li ◽  
Thomas Busch
Keyword(s):  
Particle Interaction ◽  
Interaction Strength ◽  
Von Neumann Entropy ◽  
Particle State ◽  
Particle Interactions ◽  
Interacting Particles ◽  
Von Neumann ◽  
Trapped Bosons ◽  
Fast Control ◽  
Atom System

We design and explore a shortcut to adiabaticity (STA) for changing the interaction strength between two ultracold, harmonically trapped bosons. Starting from initially uncorrelated, non-interacting particles, we assume a time-dependent tuning of the inter-particle interaction through a Feshbach resonance, such that the two particles are strongly interacting at the end of the driving. The efficiency of the STA is then quantified by examining the thermodynamic properties of the system, such as the irreversible work, which is related to the out-of-equilibrium excitations in the system. We also quantify the entanglement of the two-particle state through the von Neumann entropy and show that the entanglement produced in the STA process matches that of the desired target state. Given the fundamental nature of the two-atom problem in ultracold atomic physics, the presented shortcut can be expected to have significant impact on many processes that rely on inter-particle interactions.

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 PROPERTIES OF QUANTUM MANY-BODY WAVE FUNCTIONS

2009 ◽  
Vol 23 (20n21) ◽  
pp. 4041-4057
Author(s):  
J. W. CLARK ◽  
A. MANDILARA ◽  
M. L. RISTIG ◽  
K. E. KÜRTEN
Keyword(s):  
Quantum Phase Transitions ◽  
Body Wave ◽  
Wave Functions ◽  
Von Neumann Entropy ◽  
Many Body ◽  
Lattice Systems ◽  
Bipartite Entanglement ◽  
Von Neumann ◽  
Many Body Systems ◽  
The One

The entanglement properties of correlated wave functions commonly employed in theories of strongly correlated many-body systems are studied. The variational treatment of the transverse Ising model within correlated-basis theory is reviewed, and existing calculations of the one- and two-body reduced density matrices are used to evaluate or estimate established measures of bipartite entanglement, including the Von Neumann entropy, the concurrence, and localizable entanglement, for square, cubic, and hypercubic lattice systems. The results discussed in relation to the findings of previous studies that explore the relationship of entanglement behaviors to quantum critical phenomena and quantum phase transitions. It is emphasized that Jastrow-correlated wave functions and their extensions contain multipartite entanglement to all orders.

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 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 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.

Locating the Many-Body transition via the von Neumann entropy

2014 ◽  
Author(s):  
M. Pino ◽  
M. Ortuño ◽  
A. M. Somoza ◽  
J. Prior
Keyword(s):  
Von Neumann Entropy ◽  
Many Body ◽  
Von Neumann ◽  
The Many

scholarly journals Many-Body Systems and Quantum Chaos: The Multiparticle Quantum Arnol’d Cat

2019 ◽  
Vol 4 (3) ◽  
pp. 72
Author(s):  
Giorgio Mantica
Keyword(s):  
Hamiltonian System ◽  
Density Matrix ◽  
Quantum Chaos ◽  
Reduced Density Matrix ◽  
Von Neumann Entropy ◽  
Physical Parameters ◽  
Many Body ◽  
Von Neumann ◽  
Many Body Systems ◽  
Reduced Density

A multi-particle extension of the Arnol’d cat Hamiltonian system is presented, which can serve as a fully dynamical model of decoherence. The behavior of the von Neumann entropy of the reduced density matrix is studied, in time and as a function of the physical parameters, with special regard to increasing the mass of the cat particle.

ASYMPTOTIC ENTANGLEMENT IN THE PARAMETRIZED HADAMARD WALK

2012 ◽  
Vol 10 (06) ◽  
pp. 1250066 ◽  
Author(s):  
CLEMENT AMPADU
Keyword(s):  
Density Operator ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Fourier Representation ◽  
Asymptotic Entropy ◽  
Reduced Density

We study asymptotic entanglement properties of the Hadamard walk with phase parameters on the line using the Fourier representation. We use the von Neumann entropy of the reduced density operator to quantify entanglement between the coin and position degrees of freedom. We investigate obtaining exact expressions for the asymptotic entropy of entanglement, for different classes of initial conditions. We also determine under which conditions the asymptotic entropy of entanglement can be characterized as full, intermediate, or minimum.

The influence of atomic dipole–dipole interaction on the dynamics of the population inversion and entanglement of two atoms interacting non-resonantly with two coupled modes field

2017 ◽  
Vol 31 (05) ◽  
pp. 1750038 ◽  
Author(s):  
Elham Faraji ◽  
Hamid Reza Baghshahi ◽  
Mohammad Kazem Tavassoly
Keyword(s):  
Population Inversion ◽  
Initial Conditions ◽  
Resonance Condition ◽  
Dipole Interaction ◽  
Resonant Interaction ◽  
Von Neumann Entropy ◽  
Coupled Modes ◽  
Von Neumann ◽  
Atomic Dipole ◽  
Down Conversion

In this paper, the non-resonant interaction of two two-level atoms with two quantized cavity fields is studied by considering the dipole–dipole interaction between the two atoms. The correlation between the fields has been taken into account and the parametric down conversion is considered. Under certain initial conditions which is determined for the atoms and the fields, the analytical solution for the time-dependent Schrödinger equation is obtained. Employing this solution, we are able to discuss about some physical properties such as atomic population inversion and entanglement between various subsystems, i.e. “atoms–fields” and “atom–atom” by using respectively von Neumann entropy and negativity. It is deduced from the numerical results that, the mentioned quantities can be controlled by the atomic dipole–dipole interaction and detuning parameter, appropriately. The results show that the degree of entanglement between the two atoms is increased due to the presence of dipole–dipole coupling of the atoms at the beginning of atom–field interaction. Furthermore, it is found that, in the non-resonance condition, the so-called entanglement sudden death occurs in the presence of dipole–dipole interaction.

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