Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. We study fast-moving bright solitons in the focusing nonlinear Schrödinger equation perturbed by a narrow Gaussian potential barrier. In particular, we present a general and comprehensive analysis of the case where two fast-moving bright solitons collide at the location of the barrier. In the limiting case of a δ-function barrier, we use an analytic method to show that the relative norms of the outgoing waves depends sinusoidally on the relative phase of the incoming waves, and to determine whether one, or both, of the outgoing waves are bright solitons. We show using numerical simulations that this analytic result is valid in the high velocity limit: outside this limit nonlinear effects introduce a skew to the phase dependence, which we quantify. Finally, we numerically explore the effects of introducing a finite-width Gaussian barrier. Our results are particularly relevant, as they can be used to describe a range of interferometry experiments using bright solitary matter-waves.

. (2015) Reprinted with permission from the American Physical Society: Physical Review Letters 114, 134101 c 2015 by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modied, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society. Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details.

Reprinted with permission from the American Physical Society: Physical Review A 93, 021604(R) c (2016) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modied, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details.

Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. We study bright solitons in the Gross-Pitaevskii equation as they are split and recombined in a low-energy system. We present analytic results determining the general region in which a soliton may not be split on a potential barrier and confirm these results numerically. Furthermore, we analyze the energetic regimes where quantum fluctuations in the initial center-of-mass position and momentum become influential on the outcome of soliton splitting and recombination events. We then use the results of this analysis to determine a parameter regime where soliton interferometry is practicable.

Solitons are long-lived wavepackets that propagate without dispersion and exist in a wide range of onedimensional (1D) nonlinear systems. A Bose-Einstein condensate trapped in a quasi-1D waveguide can support bright-solitary-matter waves (3D analogues of solitons) when interatomic interactions are sufficiently attractive that they cancel dispersion. Solitary-matter waves are excellent candidates for a new generation of highly sensitive interferometers, as their non-dispersive nature allows them to acquire phase shifts for longer times than conventional matter-waves interferometers. However, such an interferometer is yet to be realised experimentally. In this work, we demonstrate the splitting and recombination of a bright-solitary-matter wave on a narrow repulsive barrier, which brings together the fundamental components of an interferometer. We show that both interference-mediated recombination and classical velocity filtering effects are important, but for a sufficiently narrow barrier interference-mediated recombination can dominate. We reveal the extreme sensitivity of interference-mediated recombination to the experimental parameters, highlighting the potential of soliton interferometry.Bright-solitary waves, referred to as solitons in this work, are wavepackets that propagate in a quasi-1D geometry without dispersion, owing to a self-focussing nonlinearity. They are of fundamental interest in a broad range of settings due to their ubiquity in nonlinear systems, which occur prolifically in nature 1, 2 . In Bose-Einstein 1 arXiv:1906.06083v1 [cond-mat.quant-gas] 14 Jun 2019 condensates (BECs) the nonlinearity is provided by interatomic interactions governed by the s-wave scattering length, which can be tuned using a magnetic Feshbach resonance 3 . Bright solitons in BECs of 7 Li, 85 Rb, 39 K and 133 Cs have so far been experimentally demonstrated 4-10 . Understanding and probing the coherent phase carried by matter-wave solitons is an area of particular relevance for BEC physics, both because it is important in determining the stability of soliton-soliton collisions 10-14 and because there is a great interest in using solitons for atom interferometry 15-22 .Matter-wave interferometers have emerged as a means of achieving unprecedented sensitivity in interferometric measurements 23-26 . However, they have typically been limited by either interatomic collisions or dispersion of the atomic wavepackets, which cause dephasing and a reduced signal to noise, respectively 27 . Previous works have successfully reduced the impact of interatomic collisions through the control of interatomic interactions 28, 29 , or by generating squeezed states 30, 31 . However, dispersion remains a limitation. A soliton-based interferometer has the potential to overcome dispersion, allowing for much longer phase-accumulation times, albeit for an increased quantum noise 32 . To date, only one experiment has demonstrated interferometry with a soliton 8 , in which Bragg pulses were used for splitting and recombination. However, interferom...