scholarly journals Quantum oscillations between weakly coupled Bose–Einstein condensates: Evolution in a non-degenerate double well

2021 ◽  
Author(s):  
John D. Andersen ◽  
Srikanth Raghavan ◽  
V. M. Kenkre
Keyword(s):  
Elliptic Function ◽  
Initial Phase ◽  
Weak Link ◽  
Energy Difference ◽  
Pitaevskii Equation ◽  
Jacobian Elliptic Function ◽  
Quantum Oscillations ◽  
Initial Phase Difference ◽  
Weakly Coupled ◽  
Bose Einstein

In this paper, we discuss coherent atomic oscillations between two weakly coupled Bose–Einstein condensates that are energetically different. The weak link is notionally provided by a laser barrier in a (possibly asymmetric) multi-well trap or by Raman coupling between condensates in different hyperfine levels. The resultant boson Josephson junction dynamics is described by a double-well nonlinear Gross–Pitaevskii equation. On the basis of a new set of Jacobian elliptic function solutions, we describe the period of the oscillations as well as associated quantities and predict novel observable consequences of the interplay of the energy difference and initial phase difference between the two condensate populations.

MODULATIONAL INSTABILITY AND EXACT SOLITON AND PERIODIC SOLUTIONS FOR TWO WEAKLY COUPLED EFFECTIVELY 1D CONDENSATES TRAPPED IN A DOUBLE-WELL POTENTIAL

2010 ◽  
Vol 24 (14) ◽  
pp. 2211-2227 ◽  
Author(s):  
E. KENGNE ◽  
R. VAILLANCOURT ◽  
B. A. MALOMED
Keyword(s):  
Periodic Solutions ◽  
Modulational Instability ◽  
Wave Number ◽  
Pitaevskii Equation ◽  
Nonlinear Dispersion ◽  
Nonlinear Dispersion Relation ◽  
Weakly Coupled ◽  
Modulational Stability ◽  
Bose Einstein ◽  
Double Well Potential

The modulational instability of the coupled Gross–Pitaevskii equation (alias nonlinear Schrödinger equation), which describes two Bose–Einstein condensates trapped in an asymmetric double-well potential, is investigated. The nonlinear dispersion relation that relates the frequency and wave number of the modulating perturbations is found and its analysis shows several possibilities for the modulational stability region. Exact soliton and periodic solutions are constructed via elliptic ordinary differential equations.

BOSON JOSEPHSON JUNCTION WITH TRAPPED ATOMS

1999 ◽  
Vol 13 (05n06) ◽  
pp. 633-641
Author(s):  
S. RAGHAVAN ◽  
A. SMERZI ◽  
S. FANTONI ◽  
S. R. SHENOY
Keyword(s):  
Josephson Junction ◽  
Elliptic Function ◽  
Critical Ratio ◽  
Parameter Ratio ◽  
Weakly Coupled ◽  
Condensate Phase ◽  
Population Imbalance ◽  
Tunneling Matrix Element ◽  
Bose Einstein ◽  
Zero Time

We consider coherent atomic tunneling between two weakly coupled Bose-Einstein condensates at T =0 in a double-well trap. The condensate dynamics of the macroscopic amplitudes in the two wells is modeled by two Gross-Pitaevskii equations (GPE) coupled by a tunneling matrix element. Analytic elliptic function solutions are obtained for the time evolution of the inter-well fractional population imbalance z(t) (related to the condensate phase difference) of the Boson Josephson junction (BJJ). Surprisingly, the neutral-atom BJJ shows (non-sinusoidal generalizations of) effects seen in charged-electron superconductor Josephson junctions (SJJ). The BJJ elliptic-function behavior has a singular dependence on a GPE parameter ratio Λ at a critical ratio Λ=Λc, beyond which a novel 'macroscopic quantum self-trapping' effect sets in with a non-zero time-averaged imbalance <z>≠0.

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

scholarly journals Vortices in a toroidal Bose-Einstein condensate with a rotating weak link

2015 ◽  
Vol 91 (3) ◽  
Author(s):  
A. I. Yakimenko ◽  
Y. M. Bidasyuk ◽  
M. Weyrauch ◽  
Y. I. Kuriatnikov ◽  
S. I. Vilchinskii
Keyword(s):  
Weak Link ◽  
Einstein Condensate ◽  
Bose Einstein Condensate ◽  
Bose Einstein

Bose–Einstein condensates: Analytical methods for the Gross–Pitaevskii equation

2006 ◽  
Vol 354 (1-2) ◽  
pp. 115-118 ◽  
Author(s):  
Carlos Trallero-Giner ◽  
J. Drake ◽  
V. Lopez-Richard ◽  
C. Trallero-Herrero ◽  
Joseph L. Birman
Keyword(s):  
Analytical Methods ◽  
Pitaevskii Equation ◽  
Bose Einstein

ANALYTICAL STUDY ON NONLINEAR DIFFERENTIAL–DIFFERENCE EQUATIONS VIA A NEW METHOD

2010 ◽  
Vol 24 (08) ◽  
pp. 761-773
Author(s):  
HONG ZHAO
Keyword(s):  
Difference Equations ◽  
Elliptic Function ◽  
Analytical Study ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Jacobian Elliptic Function ◽  
Jacobian Elliptic Functions ◽  
Periodic Wave Solutions ◽  
Trigonometric Function Solutions

Based on the computerized symbolic computation, a new rational expansion method using the Jacobian elliptic function was presented by means of a new general ansätz and the relations among the Jacobian elliptic functions. The results demonstrated an effective direction in terms of a uniformed construction of the new exact periodic solutions for nonlinear differential–difference equations, where two representative examples were chosen to illustrate the applications. Various periodic wave solutions, including Jacobian elliptic sine function, Jacobian elliptic cosine function and the third elliptic function solutions, were obtained. Furthermore, the solitonic solutions and trigonometric function solutions were also obtained within the limit conditions in this paper.

BOSE-EINSTEIN CONDENSATION OF ATOMS WITH ATTRACTIVE INTERACTION

1999 ◽  
Vol 13 (05n06) ◽  
pp. 625-631 ◽  
Author(s):  
N. AKHMEDIEV ◽  
M. P. DAS ◽  
A. V. VAGOV
Keyword(s):  
Statistical Physics ◽  
Scattering Length ◽  
Stationary Solutions ◽  
Attractive Potential ◽  
Einstein Condensation ◽  
Pitaevskii Equation ◽  
Bose Einstein Condensation ◽  
Three Body ◽  
Negative Scattering Length ◽  
Bose Einstein

We suggest that crucial effect on Bose-Einstein condensation in systems with attractive potential is three-body interaction. We investigate stationary solutions of the Gross-Pitaevskii equation with negative scattering length and a higher-order stabilising term in presence of an external parabolic potential. Stability properties of the condensate are similar to those for thermodynamic systems in statistical physics which have first order phase transitions. We have shown that there are three possible type of stationary solutions corresponding to stable, metastable and unstable phases. Results are discussed in relation to recently observed 7 Li condensate.

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