Collisions of solitary waves in condensates beyond mean-field theory

Abstract

Bright solitary waves in a Bose-Einstein condensate contain thousands of identical atoms held together despite their only weakly attractive contact interactions. They nonetheless behave like a compound object, staying whole in collisions, with their collision properties strongly affected by intersoliton quantum coherence. We show that separate solitary waves decohere due to phase diffusion, dependent on their effective ambient temperature, after which their initial mean-field relative phases are no longer well defined or relevant for collisions. In this situation, collisions occur predominantly repulsively and can no longer be described within mean-field theory. When considering the timescales involved in recent solitary wave experiments where nonequilibrium phenomena play an important role, these features could explain the predominantly repulsive collision dynamics observed in most condensate soliton train experiments.

Field moment expansion method for interacting Bosonic systems

“…For large M or n tot an exact quantum treatment is infeasible. Rather than try and implement an exact quantum solver it is simpler to extend the classical theory using correction terms that capture quantum effects on the classical physics [13][14][15][16][17][18][19].…”

“…When occupation numbers are large and interactions weak the MFT is known to accurately describe the dynamics of these systems [3,8,[20][21][22]. However, any interacting system with a nonlinearity will exhibit quantum corrections on some time scale [18,[23][24][25][26][27][28]. The MFT, tracking only the mean value of the field operator, cannot account for these quantum terms [13].…”

“…The MFT, tracking only the mean value of the field operator, cannot account for these quantum terms [13]. This means that effects like phase diffusion, quantum squeez-ing, and fragmentation inherently require beyond MFT approach [11,13,18,23]. The effect of these corrections on MFT is a current topic of interest [7,12,13,18,19,26,[28][29][30][31].…”

“…This means that effects like phase diffusion, quantum squeez-ing, and fragmentation inherently require beyond MFT approach [11,13,18,23]. The effect of these corrections on MFT is a current topic of interest [7,12,13,18,19,26,[28][29][30][31]. This motivates the development of numerical methods which can capture beyond MFT physics [13][14][15][16][17][18][19].…”

“…The effect of these corrections on MFT is a current topic of interest [7,12,13,18,19,26,[28][29][30][31]. This motivates the development of numerical methods which can capture beyond MFT physics [13][14][15][16][17][18][19]. We will refer to the time at which MFT can no longer accurately approximate the evolution of the underlying system as the "quantum breaktime".…”