Generalized Dynamical Duality of Quantum Particles in One Dimension

Abstract

We prove a generalized dynamical duality for identical particles in one dimension (1D). Namely, 1D systems with arbitrary statistics -- including bosons, fermions and anyons -- approach the same momentum distribution after long-time expansion from a trap, provided they share the same scattering length for short-range interactions. This momentum distribution is uniquely given by the rapidities, or quasi-momenta, of the initial trapped state. Our results can be readily detected in quasi-1D ultracold gases with tunable s- and p-wave interactions.

Figures (2)

• Figure 1: (Color online). Momentum distributions of two (upper panel) and three (lower panel) identical particles at different expansion times after released from a harmonic trap. Here we take different statistics $\alpha=0$ (boson), $\pi/2$ (anyon) and $\pi$ (fermion), and the scattering length is fixed at $l=-l_{T}$, with $l_T=\sqrt{2/(m\omega)}$ the trap length and $\omega$ the harmonic frequency. Gray lines with dots at the longest time ($t=10$) show quasi-momentum distributions of initial states. The units of $k$, $n(k)$ and $t$ are respectively $1/l_T$, $l_T$ and $1/\omega$.
• Figure 2: (Color online). Quasi-momentum distribution ($n_{\rm q}(k)$) of harmonically trapped two (a) and three (b) identical fermions at a fixed p-wave scattering length $l=-l_T$ and tunable effective range $r_p$. Here $l_T$ is the harmonic length, and the units of $k$, $n_{\rm q}$ and $r_p$ are respectively $1/l_T$, $l_T$ and $l_T$.