scholarly journals Stationary and Dynamical Solutions of the Gross-Pitaevskii Equation for a Bose-Einstein Condensate in a PT symmetric Double Well

10.14311/1797 ◽  
2013 ◽  
Vol 53 (3) ◽  
Author(s):  
Holger Cartarius ◽  
Dennis Dast ◽  
Daniel Haag ◽  
Günter Wunner ◽  
Rüdiger Eichler ◽  
...  
Keyword(s):  
Wave Function ◽  
Three Dimensional ◽  
Stationary Solutions ◽  
Einstein Condensate ◽  
Time Dependent ◽  
Pitaevskii Equation ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Double Well Potential

We investigate the Gross-Pitaevskii equation for a Bose-Einstein condensate in a PT symmetric double-well potential by means of the time-dependent variational principle and numerically exact solutions. A one-dimensional and a fully three-dimensional setup are used. Stationary states are determined and the propagation of wave function is investigated using the time-dependent Gross-Pitaevskii equation. Due to the nonlinearity of the Gross-Pitaevskii equation the potential dependson the wave function and its solutions decide whether or not the Hamiltonian itself is PT symmetric. Stationary solutions with real energy eigenvalues fulfilling exact PT symmetry are found as well as PT broken eigenstates with complex energies. The latter describe decaying or growing probability amplitudes and are not true stationary solutions of the time-dependent Gross-Pitaevskii equation. However, they still provide qualitative information about the time evolution of the wave functions.

Exact Chirped Soliton Solutions for the One-Dimensional Gross– Pitaevskii Equation with Time-Dependent Parameters

2012 ◽  
Vol 67 (3-4) ◽  
pp. 141-146 ◽  
Author(s):  
Zhenyun Qina ◽  
Gui Mu
Keyword(s):  
Soliton Solution ◽  
Soliton Solutions ◽  
Einstein Condensate ◽  
Time Dependent ◽  
Pitaevskii Equation ◽  
Zero Temperature ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
The One ◽  
Bose Einstein

The Gross-Pitaevskii equation (GPE) describing the dynamics of a Bose-Einstein condensate at absolute zero temperature, is a generalized form of the nonlinear Schr¨odinger equation. In this work, the exact bright one-soliton solution of the one-dimensional GPE with time-dependent parameters is directly obtained by using the well-known Hirota method under the same conditions as in S. Rajendran et al., Physica D 239, 366 (2010). In addition, the two-soliton solution is also constructed effectively

scholarly journals Stability analysis of three-dimensional breather solitons in a Bose–Einstein condensate

2005 ◽  
Vol 461 (2063) ◽  
pp. 3561-3574 ◽  
Author(s):  
M Matuszewski ◽  
E Infeld ◽  
G Rowlands ◽  
M Trippenbach
Keyword(s):  
Three Dimensional ◽  
Einstein Condensate ◽  
Dimensional Case ◽  
Two Dimensional ◽  
One Dimensional ◽  
Stability Properties ◽  
Bose Einstein Condensate ◽  
The Stability ◽  
Bose Einstein ◽  
Dimensional Soliton

We investigated the stability properties of breather soliton trains in a three-dimensional Bose–Einstein condensate (BEC) with Feshbach-resonance management of the scattering length. This is done so as to generate both attractive and repulsive interaction. The condensate is confined only by a one-dimensional optical lattice and we consider strong, moderate and weak confinement. By strong confinement we mean a situation in which a quasi two-dimensional soliton is created. Moderate confinement admits a fully three-dimensional soliton. Weak confinement allows individual solitons to interact. Stability properties are investigated by several theoretical methods such as a variational analysis, treatment of motion in effective potential wells, and collapse dynamics. Armed with all the information forthcoming from these methods, we then undertake a numerical calculation. Our theoretical predictions are fully confirmed, perhaps to a higher degree than expected. We compare regions of stability in parameter space obtained from a fully three-dimensional analysis with those from a quasi two-dimensional treatment, when the dynamics in one direction are frozen. We find that in the three-dimensional case the stability region splits into two parts. However, as we tighten the confinement, one of the islands of stability moves toward higher frequencies and the lower frequency region becomes more and more like that for the quasi two-dimensional case. We demonstrate these solutions in direct numerical simulations and, importantly, suggest a way of creating robust three-dimensional solitons in experiments in a BEC in a one-dimensional lattice.

scholarly journals Symmetry breaking and tunneling dynamics of a dipolar Bose–Einstein condensate in a double-well potential

2018 ◽  
Vol 96 (6) ◽  
pp. 622-626 ◽  
Author(s):  
Yuan Sheng Wang ◽  
Ping Long ◽  
Bo Zhang ◽  
Hong Zhang
Keyword(s):  
Symmetry Breaking ◽  
Long Range ◽  
Three Dimensional ◽  
Dipolar Interaction ◽  
Einstein Condensate ◽  
Bose Einstein Condensate ◽  
Symmetry Properties ◽  
Tunneling Dynamics ◽  
Bose Einstein ◽  
Double Well Potential

We investigate the properties of a three-dimensional (3D) dipolar Bose–Einstein condensate (BEC) in a double-well potential (DWP). Symmetry breaking and tunneling dynamics phenomena are demonstrated for 164Dy atoms in the 3D DWP using an effective two-mode model. The results show that the symmetry properties of the dynamics are affected markedly by the long-range nature and anisotropy of the dipolar interaction and the isotropic contact interaction.

scholarly journals A method to create disordered vortex arrays in atomic Bose–Einstein condensates

2009 ◽  
Vol 87 (9) ◽  
pp. 1013-1019 ◽  
Author(s):  
Enikö J.M. Madarassy
Keyword(s):  
Wave Function ◽  
Quantum Turbulence ◽  
Einstein Condensate ◽  
Complex Conjugate ◽  
Pitaevskii Equation ◽  
Two Dimensional ◽  
Bose Einstein Condensate ◽  
Phase Profile ◽  
Bose Einstein

We suggest a method to create quantum turbulence (QT) in a trapped atomic Bose–Einstein condensate (BEC). By replacing in the upper half of our box the wave function, Ψ, with its complex conjugate, Ψ*, new negative vortices are introduced into the system. The simulations are performed by solving the two-dimensional Gross–Pitaevskii equation (2D GPE). We study the successive dynamics of the wave function by monitoring the evolution of density and phase profile.

scholarly journals JOSEPHSON DYNAMICS OF A BOSE–EINSTEIN CONDENSATE IN AN ACCELERATED DOUBLE-WELL POTENTIAL

2007 ◽  
Vol 21 (07) ◽  
pp. 1067-1075
Author(s):  
ARANYA B. BHATTACHERJEE
Keyword(s):  
Recent Experiment ◽  
Optical Lattices ◽  
Einstein Condensate ◽  
Time Dependent ◽  
Experimental Result ◽  
Coupling Energy ◽  
Bose Einstein Condensate ◽  
Dissipative Mechanism ◽  
Bose Einstein ◽  
Double Well Potential

Motivated by a recent experiment on Bloch oscillation of Bose–Einstein condensates (BEC) in accelerated optical lattices, we consider the Josephson dynamics of a BEC in an accelerated double-well potential. We show that acceleration suppresses coherent population / phase oscillation between the two wells. Accelerating the double-well renders the Josephson coupling energy EJ time-dependent and this emerges as a source of dissipation. This dissipative mechanism helps to stabilize the system. The results are used to interpret a recent experimental result (M. Jona-Lasinio, O. Morsh, M. Cristiani E. Arimonod and C. Menotti, cond-mat / 0501572).

Sonic horizon formation for coupled one-dimensional Bose–Einstein condensate in an elongated harmonic potential

2018 ◽  
Vol 32 (29) ◽  
pp. 1850352
Author(s):  
Ying Wang ◽  
Shuyu Zhou
Keyword(s):  
Expansion Method ◽  
Einstein Condensate ◽  
Wave Functions ◽  
Harmonic Potential ◽  
Pitaevskii Equation ◽  
Two Component System ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
Two Component ◽  
Bose Einstein

We theoretically studied the sonic horizon formation problem for coupled one-dimensional Bose–Einstein condensate trapped in an external elongated harmonic potential. Based on the coupled (1[Formula: see text]+[Formula: see text]1)-dimensional Gross–Pitaevskii equation and F-expansion method under Thomas–Fermi formulation, we derived analytical wave functions of a two-component system, from which the sonic horizon’s occurrence criteria and location were derived and graphically demonstrated. The theoretically derived results of sonic horizon formation agree pretty well with that from the numerically calculated values.

scholarly journals Parafermionic behavior of Bose-Einstein condensates

2019 ◽  
Vol 21 ◽  
pp. 71
Author(s):  
A. Martinou ◽  
D. Bonatsos
Keyword(s):  
Optical Potential ◽  
Optical Trap ◽  
Einstein Condensate ◽  
Pitaevskii Equation ◽  
One Dimensional ◽  
Bright Solitons ◽  
Bose Einstein Condensate ◽  
Repulsive Interactions ◽  
Bose Einstein

Bright solitons of 7Li atoms in a quasi one-dimensional optical trap, formed in a stable Bose–Einstein condensate in which the interactions have been magnetically tuned from repulsive to attractive, have been seen to exhibit repulsive interactions among them when set in motion by offsetting the optical potential. Solving first the Gross–Pitaevskii equation for the special conditions corresponding to the experiment, we show then that this system can be described in terms of generalized parafermionic oscillators, the order of the parafermions being related to the strength of the interaction among the atoms and being a measure of the bosonic behavior vs. the fermionic behavior of the system.

scholarly journals Emission of Solitons From an Obstacle Moving in the Bose-Einstein Condensate

2021 ◽  
Vol 9 ◽  
Author(s):  
Yu Song ◽  
Yu Mo ◽  
Shiping Feng ◽  
Shi-Jie Yang
Keyword(s):  
Numerical Simulations ◽  
Einstein Condensate ◽  
Pitaevskii Equation ◽  
Nonlinear Interactions ◽  
One Dimensional ◽  
System Parameters ◽  
Dark Solitons ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Moving Obstacle

Dark solitons dynamically generated from a potential moving in a one-dimensional Bose-Einstein condensate are displayed. Based on numerical simulations of the Gross-Pitaevskii equation, we find that the moving obstacle successively emits a series of solitons which propagate at constant speeds. The dependence of soliton emission on the system parameters is examined. The formation mechanism of solitons is interpreted as interference between a diffusing wavepacket and the condensate background, enhanced by the nonlinear interactions.PACS numbers: 03.75.Mn, 03.75.Lm, 05.30.Jp

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