Intense Wave Formation from Multiple Soliton Fusion and the Role of Extra Dimensions Feifei Xin , 1,2,* Ludovica Falsi, 1 Davide Pierangeli, 1,3 Fabrizio Fusella, 1 Galina Perepelitsa, 4 Yehudit Garcia, 4 Aharon J. Agranat, 4 and Eugenio DelRe 1,3 1 Dipartimento di Fisica, Universit` a di Roma “La Sapienza,” 00185 Rome, Italy 2 College of Physics and Materials Science, Tianjin Normal University, 300387, Tianjin, China 3 ISC-CNR, Universit ` a di Roma “La Sapienza,” 00185 Rome, Italy 4 The Brojde Center for Innovative Engineering and Computer Science, The Hebrew University, Jerusalem 91904, Israel (Received 14 February 2022; revised 2 May 2022; accepted 27 June 2022; published 18 July 2022) We experimentally and numerically explore the role of dimensionality in multiple (three or more) soliton fusion supported by nonreciprocal energy exchange. Three-soliton fusion into an intense wave is found when an extra dimension, with no broken inversion symmetry, is involved. The phenomenon is observed for 2 þ 1D spatial waves in photorefractive crystals, where solitons are supported by a spatially local saturated Kerr-like self-focusing and fusion is driven by the leading nonlocal correction, the spatial analog of the nonlinear Raman effect. DOI: 10.1103/PhysRevLett.129.043901 One of the underlying themes of present scientific endeavor is identifying the basic laws that govern systems in which multiple bodies interact and complexity arises [1]. In wave systems, particlelike dynamics emerge when non- linearity supports solitons, localized waves that bounce, spiral, and interact [2–12]. As their mechanical counterparts, strongly interacting solitons also give rise to complexity- driven phenomena, such as the transition to turbulence [13–18] in soliton gases [19,20], replica symmetry breaking in systems dominated by disorder [21,22], and the formation of rogue waves, a still unsolved puzzle in many-body wave physics. Rogue waves are statistically rare extreme amplitude perturbations that emerge from an otherwise randomly fluctuating environment. At present, there is no consensus on their origin, the commonly accepted view being that they form through a variety of mechanisms, these including spectral filtering and wave condensation [23,24]. In systems dominated by interacting solitons, rogue waves appear to be the product of complex dynamics resulting from collisions [13–15,24–32]. How this occurs at the microscopic level is unclear. Intuitively, high-amplitude waves may form as multiple solitons fuse through nonreciprocal energy transfer, a scenario that fits well numerical studies and available output waveforms [13,25,33–35]. In nonlinear systems like water, optical fibers, and photorefractive crystals, nonreciprocal energy exchange occurs through the so-called nonlinear Raman effect, the leading nonlocal correction to the standard self-phase- modulation Kerr-like nonlinearity [36–40]. In distinction to the Kerr-like component, the Raman interaction is intrinsically insensitive to the relative phase between the mutually coherent colliding solitons, transferring energy from one soliton to the other only on the basis of their relative velocity with respect to an externally fixed direc- tion in time or space. It is this underlying broken inversion symmetry that can cause Raman soliton coupling to act as a microscopic rectifier, an optical Maxwell demon that drives the formation of rogue waves with long-tail statistics [41,42]. For water waves and optical pulses, the Raman effect is the consequence of the broken inversion symmetry associated with the nonreciprocal built-in causality along propagation. In photorefractive crystals, rogue waves are observed forming out of interacting spatial solitons, non- linear waves in a transverse plane (say, the x, y plane) that evolve along the beam propagation axis (the z axis), obeying a 2 þ 1D nonlinear Schrödinger equation [32]. Here, the nonreciprocal Raman effect occurs in space and is associated with an applied electric field. In comparison, other soliton-soliton energy exchanging mechanisms, such as Kerr-like effects, are sensitive both to the relative phase and relative intensity of the single interacting solitons, meaning that they can play a role in causing wave condensation and fusion, but not in driving long-tailed statistics through rectification [43,44]. Interestingly, while nonreciprocal energy exchange leads to soliton amplification for two colliding solitons [41,42], it leads to soliton chaos when the colliding solitons are three or more [45]. Since chaos washes out the statistical effects of rectification, it follows that nonreciprocity does not appear to be scalable in the number of colliding solitons, unable hence to offer a microscopic explanation of the extreme and fluctuating amplitudes of rogue waves. In fact, the dynamics of interacting solitons strongly depends on the dimension- ality of the system. Since nonreciprocity implies a broken inversion symmetry along one axis (say x axis), multi- ple soliton collisions in both x and a subspace orthogonal to x, an extra dimension along which they have no Raman PHYSICAL REVIEW LETTERS 129, 043901 (2022) 0031-9007=22=129(4)=043901(6) 043901-1 © 2022 American Physical Society