Nonstationary equation for the one-particle wave function of the Bose–Einstein condensate

2021 ◽  
Vol 47 (4) ◽  
pp. 347-350
Author(s):  
V. B. Bobrov ◽  
S. A. Trigger ◽  
A. G. Zagorodny
Keyword(s):  
Wave Function ◽  
Einstein Condensate ◽  
Nonstationary Equation ◽  
Bose Einstein Condensate ◽  
Particle Wave Function ◽  
The One ◽  
Bose Einstein

A CLASS OF CLOSED SOLUTIONS FOR THE BOGOLIUBOV EXCITATIONS ON SMOOTH GROUND STATE OF A TRAPPED BOSE–EINSTEIN CONDENSATE

2005 ◽  
Vol 19 (15) ◽  
pp. 713-720
Author(s):  
YONG-LI MA ◽  
HAICHEN ZHU
Keyword(s):  
Ground State ◽  
Einstein Condensate ◽  
Zero Energy ◽  
Ground State Wavefunction ◽  
New Class ◽  
Bose Einstein Condensate ◽  
Energy Mode ◽  
The One ◽  
Bose Einstein ◽  
Bogoliubov Excitations

Bogoliubov–de Gennes equations (BdGEs) for collective excitations from a trapped Bose–Einstein condensate described by a spatially smooth ground-state wavefunction can be treated analytically. A new class of closed solutions for the BdGEs is obtained for the one-dimensional (1D) and 3D spherically harmonic traps. The solutions of zero-energy mode of the BdGEs are also provided. The eigenfunctions of the excitations consist of zero-energy mode, zero-quantum-number mode and entire excitation modes when the approximate ground state is a background Bose gas sea.

scholarly journals Unearthing wave-function renormalization effects in the time evolution of a Bose–Einstein condensate

2013 ◽  
Vol T153 ◽  
pp. 014024
Author(s):  
Paolo Facchi ◽  
Saverio Pascazio ◽  
Francesco V Pepe ◽  
Ennio Arimondo ◽  
Donatella Ciampini ◽  
...  
Keyword(s):  
Wave Function ◽  
Time Evolution ◽  
Einstein Condensate ◽  
Wave Function Renormalization ◽  
Bose Einstein Condensate ◽  
Bose Einstein

EXCITON-PHONON PACKETS WITH BOSE–EINSTEIN CONDENSATE

2003 ◽  
Vol 17 (28) ◽  
pp. 5289-5293
Author(s):  
D. ROUBTSOV ◽  
Y. LÉPINE
Keyword(s):  
Wave Function ◽  
Coherent State ◽  
Einstein Condensate ◽  
Einstein Condensation ◽  
Inhomogeneous State ◽  
Bose Einstein Condensation ◽  
Bose Einstein Condensate ◽  
Bose Einstein

We discuss the possibility for a moving droplet of excitons and phonons to form a coherent state inside the packet. We describe such an inhomogeneous state in terms of Bose–Einstein condensation and prescribe it a macroscopic wave function. Existence and, thus, coherency of such a Bose-core inside the droplet can be checked experimentally if two moving packets are allowed to interact.

scholarly journals TWO-PHOTON NONLINEAR SPECTROSCOPY OF PERIODICALLY TRAPPED ULTRACOLD ATOMS IN A CAVITY

2011 ◽  
Vol 25 (13) ◽  
pp. 1737-1746
Author(s):  
TARUN KUMAR ◽  
ARANYA B. BHATTACHERJEE ◽  
MANMOHAN
Keyword(s):  
Ultracold Atoms ◽  
Einstein Condensate ◽  
Nonlinear Spectroscopy ◽  
Transmission Spectra ◽  
Two Photon ◽  
Photon Transition ◽  
Cavity Transmission ◽  
Bose Einstein Condensate ◽  
The One ◽  
Bose Einstein

We study the transmission spectra of a Bose Einstein condensate (BEC) confined in an optical lattice interacting with two modes of a cavity via nonlinear two-photon transition. In particular, we show that the one-photon and two-photon cavity transmission spectra of a BEC are different. We found that when the BEC is in the Mott state, the usual normal mode splitting present in the one-photon transition is missing in the two-photon interaction. When the BEC is in the superfluid state, the transmission spectrum shows the usual multiple lorentzian structure. However the separation between the lorentzians for the two-photon case is much larger than that for the one-photon case. This study could form the basis for nondestructive high resolution Rydberg spectroscopy of ultracold atoms or two-photon spectroscopy of a gas of ultracold atomic hydrogen.

scholarly journals Soliton Solutions and Collisions for the Multicomponent Gross–Pitaevskii Equation in Spinor Bose–Einstein Condensates

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Ming Wang ◽  
Guo-Liang He
Keyword(s):  
Soliton Solutions ◽  
Auxiliary Function ◽  
Einstein Condensate ◽  
Polarization Parameter ◽  
One Dimension ◽  
Pitaevskii Equation ◽  
Bose Einstein Condensate ◽  
The One ◽  
Bose Einstein ◽  
Two Peaks

In this paper, we investigate a five-component Gross–Pitaevskii equation, which is demonstrated to describe the dynamics of an F=2 spinor Bose–Einstein condensate in one dimension. By employing the Hirota method with an auxiliary function, we obtain the explicit bright one- and two-soliton solutions for the equation via symbolic computation. With the choice of polarization parameter and spin density, the one-soliton solutions are divided into four types: one-peak solitons in the ferromagnetic and cyclic states and one- and two-peak solitons in the polar states. For the former two, solitons share the similar shape of one peak in all components. Solitons in the polar states have the one- or two-peak profiles, and the separated distance between two peaks is inversely proportional to the value of polarization parameter. Based on the asymptotic analysis, we analyze the collisions between two solitons in the same and different states.

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.

Dark–dark solitons for the coupled spatially modulated Gross–Pitaevskii system in the Bose–Einstein condensation

2020 ◽  
Vol 34 (26) ◽  
pp. 2050282 ◽  
Author(s):  
Xin Zhao ◽  
Bo Tian ◽  
Qi-Xing Qu ◽  
Yu-Qiang Yuan ◽  
Xia-Xia Du ◽  
...  
Keyword(s):  
Soliton Solutions ◽  
Dark Soliton ◽  
Einstein Condensate ◽  
Einstein Condensation ◽  
Time Coordinate ◽  
Elastic Interactions ◽  
Bose Einstein Condensate ◽  
The One ◽  
Bose Einstein ◽  
Spatially Varying

Investigation in this paper is the spatially modulated two-component GP system with Rabi coupling in a Bose–Einstein condensate consisting of the two hyperfine states. Based on the Kadomtsev–Petviashvili hierarchy reduction, we derive the Gramian expression of the one- and two-dark–dark soliton solutions. The nonlinearity coefficients [Formula: see text] and the external spatially varying trapping potential [Formula: see text] can be constrained as the functions of [Formula: see text], where [Formula: see text] is the spatial coordinate, [Formula: see text] is the time coordinate, [Formula: see text] is the dispersion parameter. With the Rabi coupling coefficient [Formula: see text] increasing, period along [Formula: see text] decreases. When [Formula: see text] is a constant, soliton propagates stably with the amplitude and velocity unvarying; When [Formula: see text] is a function of [Formula: see text], background is periodic and velocity of the soliton varies with [Formula: see text] increasing. Head-on and overtaking elastic interactions between the two solitons are presented analytically and graphically.

scholarly journals A Convergent Three-Step Numerical Method to Solve a Double-Fractional Two-Component Bose–Einstein Condensate

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1412
Author(s):  
Adán J. Serna-Reyes ◽  
Jorge E. Macías-Díaz ◽  
Nuria Reguera
Keyword(s):  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Einstein Condensate ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
Nonlinear Parabolic ◽  
Complex Functions ◽  
Two Component ◽  
The One ◽  
Bose Einstein

This manuscript introduces a discrete technique to estimate the solution of a double-fractional two-component Bose–Einstein condensate. The system consists of two coupled nonlinear parabolic partial differential equations whose solutions are two complex functions, and the spatial fractional derivatives are interpreted in the Riesz sense. Initial and homogeneous Dirichlet boundary data are imposed on a multidimensional spatial domain. To approximate the solutions, we employ a finite difference methodology. We rigorously establish the existence of numerical solutions along with the main numerical properties. Concretely, we show that the scheme is consistent in both space and time as well as stable and convergent. Numerical simulations in the one-dimensional scenario are presented in order to show the performance of the scheme. For the sake of convenience, A MATLAB code of the numerical model is provided in the appendix at the end of this work.

scholarly journals Intrinsic Decoherence and Recurrences in a Large Ferromagnetic F = 1 Spinor Bose–Einstein Condensate

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 67
Author(s):  
Juan Carlos Sandoval-Santana ◽  
Roberto Zamora-Zamora ◽  
Rosario Paredes ◽  
Victor Romero-Rochín
Keyword(s):  
Density Matrix ◽  
Coherent States ◽  
Rotational Symmetry ◽  
Einstein Condensate ◽  
Body Density ◽  
Intrinsic Decoherence ◽  
Bose Einstein Condensate ◽  
Spin Interactions ◽  
The One ◽  
Bose Einstein

Decoherence with recurrences appear in the dynamics of the one-body density matrix of an F=1 spinor Bose–Einstein condensate, initially prepared in coherent states, in the presence of an external uniform magnetic field and within the single mode approximation. The phenomenon emerges as a many-body effect of the interplay of the quadratic Zeeman effect, which breaks the rotational symmetry, and the spin-spin interactions. By performing full quantum diagonalizations, a very accurate time evolution of large condensates is analyzed, leading to heuristic analytic expressions for the time dependence of the one-body density matrix, in the weak and strong interacting regimes, for initial coherent states. We are able to find accurate analytical expressions for both the decoherence and the recurrence times, in terms of the number of atoms and strength parameters, which show remarkable differences depending on the strength of the spin-spin interactions. The features of the stationary states in both regimes are also investigated. We discuss the nature of these limits in light of the thermodynamic limit.

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

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