Scale-Invariant Townes Solitons

Cheng-An Chen

Cheng-An Chen, Chen-Lung Hung

We report near-deterministic generation of two-dimensional (2D) matter-wave Townes solitons and a precision test on scale invariance in attractive 2D Bose gases. We induce a shape-controlled modulational instability in an elongated 2D matter wave to create an array of isolated solitary waves of various sizes and peak densities. We confirm scale invariance by observing the collapse of solitary-wave density profiles onto a single curve in a dimensionless coordinate rescaled according to their peak densities and observe that the scale-invariant profiles measured at different coupling constants g can further collapse onto the universal profile of Townes solitons. The reported scaling behavior is tested with a nearly 60-fold difference in soliton interaction energies and allows us to discuss the impact of a non-negligible magnetic dipole-dipole interaction (MDDI) on 2D scale invariance. We confirm that the effect of MDDI in our alkali cesium quasi-2D samples effectively conforms to the same scaling law governed by a contact interaction to well within our experiment uncertainty.

Lincoln D. Carr, J. Brand

Brice Bakkali-Hassani, C. Maury, Y.-Q. Zou +6 more

Most experimental observations of solitons are limited to one-dimensional (1D) situations, where they are naturally stable. For instance, in 1D cold Bose gases, they exist for any attractive interaction strength g and particle number N. By contrast, in two dimensions, solitons appear only for discrete values of gN, the so-called Townes soliton being the most celebrated example. Here, we use a two-component Bose gas to prepare deterministically such a soliton: Starting from a uniform bath of atoms in a given internal state, we imprint the soliton wave function using an optical transfer to another state. We explore various interaction strengths, atom numbers, and sizes and confirm the existence of a solitonic behavior for a specific value of gN and arbitrary sizes, a hallmark of scale invariance.

Brice Bakkali-Hassani

At a sufficiently large phase-space density, a Bose gas can be described by a macroscopic wave function subject to nonlinear dynamics. Degenerate Bose gases now constitute a major platform in the study of self-trapped nonlinear fields known as solitons or solitary waves. Up to now, most experimental observations of solitons have been restricted to one-dimensional situations, where they are generically stable. On the contrary, multidimensional solitary waves are more prone to instabilities and thus more challenging to observe experimentally. In this thesis, we produce solitary waves in a two-dimensional ultracold bosonic system. After presenting our experimental setup, we demonstrate our ability to produce deterministically a Townes soliton, a celebrated solution of the nonlinear Schrödinger equation in two dimensions. Our novel approach is based on a two-component mixture: starting from a uniform bath of atoms in a given internal state, we imprint the soliton wave function using an optical transfer to another state. We show that the soliton can exist with various sizes, a hallmark of the scale invariance present in the underlying model. We then confirm the relation linking the soliton atom number to the interaction strength. Our experimental observations are supported by further numerical and theoretical considerations. These studies also allow us to go beyond the simplest model sustaining a Townes soliton, by considering effects beyond the mean-field description. Finally, we propose a few experiments aimed at characterizing excited, moving, as well as colliding solitons.

Demetrios N. Christodoulides