Detecting a logarithmic nonlinearity in the Schrödinger equation using Bose-Einstein condensates

Abstract

We study the effect of a logarithmic nonlinearity in the Schrödinger equation (SE) on the dynamics of a freely expanding Bose-Einstein condensate (BEC). The logarithmic nonlinearity was one of the first proposed nonlinear extensions to the SE which emphasized the conservation of important physical properties of the linear theory, e.g.: the separability of noninteracting states. Using this separability, we incorporate it into the description of a BEC obeying a logarithmic Gross-Pittaevskii equation. We investigate the dynamics of such BECs using variational and numerical methods and find that, using experimental techniques like delta kick collimation, experiments with extended freefall times as available on microgravity platforms could be able to lower the bound on the strength of the logarithmic nonlinearity by at least one order of magnitude.

Oscillating Quantum Droplets from the free expansion of Logarithmic One-Dimensional Bose Gases

“…In other words, we recover the three-dimensional behavior for α 3 and β reported in Ref. [33]. Consequently, the upper bound for β ≤ 3.3 × 10 −15 eV obtained in Ref.…”

“…i.e., the dilute BEC properties in three-dimensions with logarithmic interactions are governed by the later energy functional as in Ref. [33].…”

“…where the ratio r = l/a ⊥ measures the BEC's size and λ = ω z /ω ⊥ . Since the constant α is positive but arbitrary and has no physical relevance [33], we choose α = a ⊥ /N , so the contributions of the term ln(αN/a ⊥ ) that arises in Eq. ( 23) can be neglected for all practical purposes.…”

Collective-Mode Enhanced Matter-Wave Optics

“…When focusing at infinity, we achieve a total internal kinetic energy in three dimensions of as low as 3 /2 k B • 38 +6 −7 pK. Such atomic ensembles allow for placing better experimental constraints on proposed modifications of quantum theory [13][14][15]. Moreover, they fulfill the strict re-quirements concerning the atomic expansion for experiments, where BECs fall freely during tens of seconds in an atom interferometer [16][17][18] as needed e. g. for a stringent quantum test of the equivalence principle [19][20][21], gravitational wave detection [22,23] or the determination of the gravitational constant [24] and the photon recoil [25].…”

The Conservative and Efficient Numerical Method of 2-D and 3-D Fractional Nonlinear Schrödinger Equation Using Fast Cosine Transform

“…The Nonlinear Schrödinger Equation (NLSE) is a nonlinear partial differential equation that describes the evolution of wave functions in quantum mechanics. It finds extensive applications across various fields of physics, including optics [1], cold atomic physics [2], and plasma physics [3]. In nonlinear optics, the NLSE serves as a fundamental mathematical model to depict the behavior of light waves in nonlinear media.…”