The experimental work on solitons in BECs during the past decade has been extremely important in two respects. First, experiments have shown unam-biguously that solitons and related nonlinear waves do exist in BECs. This was disputed at the time when the first experiments were performed in 1999 [1,2] and may still be found surprising given that we are dealing with a quan-tum many-body system driven towards strongly non-equilibrium dynamics. Second, the experiments have inspired theoretical work in many directions. A particular example is the work on solitary waves in dimensional crossovers induced by trapping potentials that restrict the geometry, as discussed in Chap. 7. A ubiquitous feature in all of the experimental realizations of solitons so far is the three-dimensional nature of experimental set-ups, which can never be completely neglected in the interpretation of the results obtained. In this respect almost all of the experimental work discussed in this book falls into the wider area of “multidimensional solitons. ” In order to avoid the duplication of discussions led in other chapters, we chose to narrow the scope of this chapter to discuss mainly solitary waves with a genuinely multidimensional structure. We therefore restrict the discussion to experimental studies of the creation and dynamics of vortex rings in experiments at JILA [3] and Harvard [4, 5]. In particular, we completely omit the vast body of experimental work on line vortices and the related baby-skyrmions, i.e., vortices with filled cores [6, 7]), as these will be covered in Part VI. We also completely omit the experiments on bright solitons, and the first planar dark soliton experiments [1,2] that were primarily concerned with soli-ton observation and propagation in BECs rather than dynamical instabilities and soliton decay. Detailed reviews of these experiments can be found in
The experimental work on solitons in BECs during the past decade has been extremely important in two respects. First, experiments have shown unam-biguously that solitons and related nonlinear waves do exist in BECs. This was disputed at the time when the first experiments were performed in 1999 [1,2] and may still be found surprising given that we are dealing with a quan-tum many-body system driven towards strongly non-equilibrium dynamics. Second, the experiments have inspired theoretical work in many directions. A particular example is the work on solitary waves in dimensional crossovers induced by trapping potentials that restrict the geometry, as discussed in Chap. 7. A ubiquitous feature in all of the experimental realizations of solitons so far is the three-dimensional nature of experimental set-ups, which can never be completely neglected in the interpretation of the results obtained. In this respect almost all of the experimental work discussed in this book falls into the wider area of “multidimensional solitons. ” In order to avoid the duplication of discussions led in other chapters, we chose to narrow the scope of this chapter to discuss mainly solitary waves with a genuinely multidimensional structure. We therefore restrict the discussion to experimental studies of the creation and dynamics of vortex rings in experiments at JILA [3] and Harvard [4, 5]. In particular, we completely omit the vast body of experimental work on line vortices and the related baby-skyrmions, i.e., vortices with filled cores [6, 7]), as these will be covered in Part VI. We also completely omit the experiments on bright solitons, and the first planar dark soliton experiments [1,2] that were primarily concerned with soli-ton observation and propagation in BECs rather than dynamical instabilities and soliton decay. Detailed reviews of these experiments can be found in
A briefly formulated update of the recently published review [B.A. Malomed, Multidimensional soliton systems. Adv. Phys. 9(1) (2024), pp. 2301592] on the topic of multidimensional solitons (chiefly, in nonlinear optics and atomic Bose–Einstein condensates (BECs)) is presented. The update briefly summarizes some notable results on this topic that have been reported very recently, and offers a compact outline of the directions of the current experiment and theoretical work in this and related fields. In particular, as concerns newest experimental findings, included are the creation of multiple quantum droplets in prolate BEC, and the observation of expanding toroidal light structures in linear optics. The update of theoretical results includes the analysis of 2D solitons in the optical system with the quadratic nonlinearity and fractional diffraction, and the prediction of stable 3D vortex solitons in various BEC schemes with long-range interactions.
A briefly formulated update of the recently published review [1] on the topic of multidimensional solitons (chiefly, in nonlinear optics and atomic Bose-Einstein condensates (BECs)) is presented. The update briefly summarizes some notable results on this topic that have been reported very recently, and offers a compact outline of the directions of the current experiment and theoretical work in this and related fields. In particular, as concerns newest experimental findings, included are the creation of multiple _quantum droplets_ in prolate BEC, and the observation of expanding toroidal light structures in linear optics. The update of theoretical results includes the analysis of 2D solitons in the optical system with the quadratic nonlinearity and _fractional diffraction_, and the prediction of stable 3D _vortex solitons_ in various BEC schemes with long-range interactions.
A briefly formulated update of the recently published review [1] on the topic of multidimensional solitons (chiefly, in nonlinear optics and atomic Bose-Einstein condensates (BECs)) is presented. The update briefly summarizes some notable results on this topic that have been reported very recently, and offers a compact outline of the directions of the current experiment and theoretical work in this and related fields. In particular, as concerns newest experimental findings, included are the creation of multiple quantum droplets in prolate BEC, and the observation of expanding toroidal light structures in linear optics. The update of theoretical results includes the analysis of 2D solitons in the optical system with the quadratic nonlinearity and fractional diffraction, and the prediction of stable 3D vortex solitons in various BEC schemes with long-range interactions.
Experiments on attractive Bose-Einstein condensates (BECs) have unlocked many intriguing out-of-equilibrium dynamics through the interplay between matter-wave dispersion and nonlinear attractive interaction. Competition between these effects leads to fascinating phenomena such as wave collapse, modulational instability, and formation of multidimensional bright solitons. This chapter reviews experimental studies on attractive condensates, with a primary focus on alkali atoms featuring two-body contact interactions. We review recent experimental advances in optical trapping and interaction control techniques, which have enabled new studies on attractive condensates in three and also in lower dimensions. Specifically, we discuss pioneering and recent experimental observations on the dynamics and stability of attractive BECs, including the formation of bright solitons, their collisions, and excitations in quasi-one-dimensional traps. Recent observations of the elusive two-dimensional Townes solitons and vortex solitons are also discussed in this Chapter. We then highlight an experimental technique revealing the nonclassical signatures of modulational instability in an attractive condensate.
The study of soliton-like states in systems with nonlocal nonlinearity is a traditional topic in optics and related areas. Some results obtained in these studies (such as solitons supported by thermal nonlinearity in optical glasses and orientational nonlinearity that affects light propagation in liquid crystals) are well known and have been properly reviewed in the literature; therefore, the respective models are outlined in the present chapter in a brief form. Some other studies such as those addressing models with fractional diffraction, which is represented by a linear nonlocal operator, have also been started more recently; therefore, it should be relevant to review them in detail when more results will be accumulated and this chapter includes a short outline of the latter topic. After providing an introduction to the general area of nonlocal nonlinearities, the chapter offers a summary of results obtained for multidimensional solitons in some specific nonlocal nonlinear models originating in studies of BEC, which are sufficiently mature but have not been reviewed previously. These are anisotropic quasi-2D solitons supported by long-range dipole–dipole interactions in a condensate of magnetic atoms [Tikhonenkov et al., Phys. Rev. Lett. 100, 090406(2008a)] and giant vortex solitons, which are stable for high values of the winding number [Qin et al., Phys. Rev. A 94, 053611 (2016)], as well as 2D vortex solitons moving with self-acceleration [Qin et al., Phys. Rev. A 99, 023610 (2019)]. These are solitons of a hybrid type, which include matter-wave and electromagnetic-wave components. They are supported, in a binary BEC composed of two different atomic states, by the resonant interaction of the two-component matter waves with a resonant microwave field which couples the two atomic states.
This is a review addressing soliton-like states in systems with nonlocal nonlinearity. The work on this topic has long history in optics and related areas. Some results produced by the work (such as solitons supported by thermal nonlinearity in optical glasses, and orientational nonlinearity, which affects light propagation in liquid crystals) are well known, and have been properly reviewed in the literature, therefore the respective models are outlined in the present review in a brief form. Some other studies, such as those addressing models with fractional diffraction, which is represented by a linear nonlocal operator, have started more recently, therefore it will be relevant to review them in detail when more results will be accumulated; for this reason, the present article provides a short outline of the latter topic. The main part of the article is a summary of results obtained for two-dimensional solitons in specific nonlocal nonlinear models originating in studies of Bose–Einstein condensates (BECs), which are sufficiently mature but have not yet been reviewed previously (some results for three-dimensional solitons are briefly mentioned too). These are, in particular, anisotropic quasi-2D solitons supported by long-range dipole-dipole interactions in a condensate of magnetic atoms and giant vortex solitons (which are stable for high values of the winding number), as well as 2D vortex solitons of the latter type moving with self-acceleration. The vortex solitons are states of a hybrid type, which include matter-wave and electromagnetic-wave components. They are supported, in a binary BEC composed of two different atomic states, by the resonant interaction of the two-component matter waves with a microwave field that couples the two atomic states. The shape, stability, and dynamics of the solitons in such systems are strongly affected by their symmetry. Some other topics are included in the review in a brief form. This review uses the “Harvard style” of referring to the bibliography.