Dark soliton collisions in superfluid Fermi gases

Abstract

In this work dark soliton collisions in a one-dimensional superfluid Fermi gas are studied across the BEC-BCS crossover by means of a recently developed finite-temperature effective field theory (2015 Eur. Phys. J. B 88 122). The evolution of two counter-propagating solitons is simulated numerically based on the theory's nonlinear equation of motion for the pair field. The resulting collisions are observed to introduce a spatial shift into the trajectories of the solitons. The magnitude of this shift is calculated and studied in different conditions of temperature and spin-imbalance. When moving away from the BEC-regime, the collisions are found to become inelastic, emitting the lost energy in the form of small-amplitude density oscillations. This inelasticity is quantified and its behavior analyzed and compared to the results of other works. The dispersion relation of the density oscillations is calculated and is demonstrated to show a good agreement with the spectrum of collective excitations of the superfluid.

The Variational Reduction for Low-Dimensional Fermi Gases and Bose–Fermi Mixtures: A Brief Review

“…Other features of the two-soliton interaction can be found in Ref. [32]. Figure 5 shows the spatiotemporal diagrams for the 1D density, n 1D , for different numbers of dark solitons N s = (6, 10, 14, 18).…”

“…In addition, we have presented results for dark solitons, obtained in the framework of the 1D approximation. We have verified that the interaction is repulsive [32] and strongly depends on the initial distance between the dark solitons.…”

“…Since Eqs. (13) and (14) produce results which agree well with the full 3D simulations [21], one can use the effective 1D equations to study more complex dynamical behavior, such as that of dark solitons [29,32].…”

Crossover between snake instability and Josephson instability of dark solitons in superfluid Fermi gases

“…If we now know the values Ψ l,m,n and φ l,m,n at a certain time step t n for all positions x l and y m , the explicit RK4 method allows us to calculate for every position the values Ψ l,m,n+1 and φ l,m,n+1 of the next time step by using the following algorithm [35]: p 1 l,m,n = f (φ l,m,n ) (A.10) p 2 l,m,n = g(Ψ l,m,n , φ l,m,n ) (A.11) q 1 l,m,n = f (φ l,m,n + p 2 l,m,n /2) (A.12) q 2 l,m,n = g(Ψ l,m,n + p 1 l,m,n /2, φ l,m,n + p 2 l,m,n /2) (A.13) r 1 l,m,n = f (φ l,m,n + q 2 l,m,n /2) (A.14) r 2 l,m,n = g(Ψ l,m,n + q 1 l,m,n /2, φ l,m,n + q 2 l,m,n /2) (A.15) s 1 l,m,n = f (φ l,m,n + r 2 l,m,n ) (A.16) s 2 l,m,n = g(Ψ l,m,n + r 1 l,m,n , φ l,m,n + r 2 l,m,n ) (A.17) Ψ l,m,n+1 = Ψ l,m,n + ∆t 6 (p 1 l,m,n + 2 q 1 l,m,n + 2 r 1 l,m,n + s 1 l,m,n ) (A.18) φ l,m,n+1 = φ l,m,n + ∆t 6 (p 2 l,m,n + 2 q 2 l,m,n + 2 r 2 l,m,n + s 2 l,m,n ) (A. 19) This scheme can be repeated until the solution has been evolved up to the desired point in time. In order to study explicitly the character of amplitude and phase modes, we introduce the fields P ± (r, t) = [δΨ(r, t) ± δΨ * (r, t)] /2 (A.4)…”

Dark Solitons in the Unitary Bose Gas

“…The realizability of black and gray solitons in ultracold gases is well documented in the weak-coupling limit [13,14] and in a unitary Fermi gas [15]. Moreover, the properties of black solitons have been theoretically investigated for superfluid fermions also in the BCS-BEC crossover [16][17][18][19]. It is then a natural question to ask, whether black and gray solitons can be realized also in the case of Bose gases at unitarity, and what their specific properties are.…”