scholarly journals Time-varying Bose–Einstein condensates

2021 ◽  
Vol 477 (2254) ◽  
Author(s):  
Robert A. Van Gorder
Keyword(s):  
Scattering Length ◽  
Potential Scattering ◽  
Variational Approximation ◽  
Control Mechanisms ◽  
Time Varying ◽  
Theoretical Formulation ◽  
Experimental Physics ◽  
Advanced Control ◽  
Bounded Space ◽  
Bose Einstein

Bose–Einstein condensates (BECs), a state of matter formed when a low-density gas of bosons is cooled to near absolute zero, continue to motivate novel work in theoretical and experimental physics. Although BECs are most commonly studied in stationary ground states, time-varying BECs arise when some aspect of the physics governing the condensate varies as a function of time. We study the evolution of time-varying BECs under non-autonomous Gross–Pitaevskii equations (GPEs) through a mix of theory and numerical experiments. We separately derive a perturbation theory (in the small-parameter limit) and a variational approximation for non-autonomous GPEs on generic bounded space domains. We then explore various routes to obtain time-varying BECs, starting with the more standard techniques of varying the potential, scattering length, or dispersion, and then moving on to more advanced control mechanisms such as moving the external potential well over time to move or even split the BEC cloud. We also describe how to modify a BEC cloud through evolution of the size or curvature of the space domain. Our results highlight a variety of interesting theoretical routes for studying and controlling time-varying BECs, lending a stronger theoretical formulation for existing experiments and suggesting new directions for future investigation.

Perturbation theory for Bose–Einstein condensates on bounded space domains

2020 ◽  
Vol 476 (2243) ◽  
pp. 20200674
Author(s):  
Robert A. Van Gorder
Keyword(s):  
Perturbation Theory ◽  
Unbounded Domains ◽  
External Potential ◽  
Pitaevskii Equation ◽  
Bounded Domains ◽  
Control Mechanisms ◽  
Space Domain ◽  
Bounded Space ◽  
Bose Einstein ◽  
Analytical Approaches

Bose–Einstein condensates (BECs), first predicted theoretically by Bose and Einstein and finally discovered experimentally in the 1990s, continue to motivate theoretical and experimental physics work. Although experiments on BECs are carried out in bounded space domains, theoretical work in the modelling of BECs often involves solving the Gross–Pitaevskii equation on unbounded domains, as the combination of bounded domains and spatial heterogeneity render most existing analytical approaches ineffective. Motivated by a lack of theory for BECs on bounded domains, we first derive a perturbation theory for both ground and excited stationary states on a given bounded space domain, allowing us to explore the role various forms of the self-interaction, external potential and space domain have on BECs. We are able to show that the shape and curvature of a space domain strongly influence BEC structure, and may be used as control mechanisms in experiments. We next derive a non-autonomous perturbation theory to predict BEC response to temporal changes in an external potential. In certain cases, our approach can be extended to unbounded domains, and we conclude by constructing a perturbation theory for bright solitons within external potentials on unbounded domains.

scholarly journals Compensation Process and Generation of Chirped Femtosecond Solitons and Double-kink Solitons in Bose-Einstein Condensates with Time-dependent Atomic Scattering Length in a Time-varying Complex Potential

2021 ◽  
Author(s):  
Emmanuel Kengne ◽  
Ahmed Lakhssassi
Keyword(s):  
Scattering Length ◽  
Einstein Condensate ◽  
Trapping Potential ◽  
Matter Wave ◽  
Time Varying ◽  
Frequency Chirp ◽  
S Wave ◽  
Nls Equation ◽  
Double Kink ◽  
Bose Einstein

Abstract We consider the one-dimensional (1D) cubic-quintic Gross--Pitaevskii (GP)nequation, which governs the dynamics of Bose--Einstein condensate (BEC) matter waves with time-varying scattering length and loss/gain of atoms in a harmonic trapping potential. We derive the integrability conditions and the compensation condition for the 1D GP equation and obtain, with the help of a cubic-quintic nonlinear Schr\"{o}dinger (NLS) equation with self-steepening and self-frequency shift, exact analytical solitonlike solutions with the corresponding frequency chirp which describe the dynamics of femtosecond solitons and double-kink solitons propagating on a vanishing background. Our investigation shows that under the compensation condition, the matter wave solitons maintain a constant amplitude, the amplitude of the frequency chirp depends on the scattering length, while the motion of both the matter wave solitons and the corresponding chirp depend on the external trapping potential. More interesting, the frequency chirps are localized and their feature depends on the sign of the self-steepening parameter. Our study also shows that our exact solutions can be used to describe the compression of matter wave solitons when the absolute value of the s-wave scattering length increases with time.

EXACT SOLUTIONS IN ONE-DIMENSIONAL BOSE–EINSTEIN GAS IN A TIME-VARYING TRAP POTENTIAL AND ATOMIC SCATTERING LENGTH

2007 ◽  
Vol 21 (07) ◽  
pp. 1043-1050 ◽  
Author(s):  
E. KENGNE ◽  
S. T. CHUI
Keyword(s):  
Scattering Length ◽  
Elliptic Functions ◽  
Variable Coefficients ◽  
Einstein Condensate ◽  
Time Varying ◽  
Jacobian Elliptic Functions ◽  
One Dimensional ◽  
Atomic Scattering ◽  
Cubic Nonlinear Schrödinger Equation ◽  
Bose Einstein

In this paper we discuss the solutions of the cubic nonlinear Schrödinger equation with variable coefficients that model a trapped, quasi-one-dimensional Bose–Einstein condensate with time-varying potential and time-varying atomic scattering length. By applying the theory of Jacobian elliptic functions, we propose a new ansatz to find two new families of solutions. We also obtained regions in the parameters space in which the found families of solutions exist.

scholarly journals Scattering Length Instability in Dipolar Bose-Einstein Condensates

2006 ◽  
Vol 97 (16) ◽  
Author(s):  
D. C. E. Bortolotti ◽  
S. Ronen ◽  
J. L. Bohn ◽  
D. Blume
Keyword(s):  
Scattering Length ◽  
Bose Einstein

scholarly journals Effective Potential for Ultracold Atoms at the Zero Crossing of a Feshbach Resonance

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
N. T. Zinner
Keyword(s):  
Effective Potential ◽  
Feshbach Resonance ◽  
Cold Atoms ◽  
Particle Number ◽  
Scattering Length ◽  
Order Effect ◽  
Effective Range ◽  
Effective Range Expansion ◽  
Zero Crossing ◽  
Bose Einstein

We consider finite-range effects when the scattering length goes to zero near a magnetically controlled Feshbach resonance. The traditional effective-range expansion is badly behaved at this point, and we therefore introduce an effective potential that reproduces the full T-matrix. To lowest order the effective potential goes as momentum squared times a factor that is well defined as the scattering length goes to zero. The potential turns out to be proportional to the background scattering length squared times the background effective range for the resonance. We proceed to estimate the applicability and relative importance of this potential for Bose-Einstein condensates and for two-component Fermi gases where the attractive nature of the effective potential can lead to collapse above a critical particle number or induce instability toward pairing and superfluidity. For broad Feshbach resonances the higher order effect is completely negligible. However, for narrow resonances in tightly confined samples signatures might be experimentally accessible. This could be relevant for suboptical wavelength microstructured traps at the interface of cold atoms and solid-state surfaces.

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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