Quasimomentum distribution and expansion of an anyonic gas

Abstract

We point out that the momentum distribution is not a proper observable for a system of anyons in two-dimensions. In view of anyons as Wilczek's composite charged flux-tubes, this is a consequence of the fact that the orthogonal components of the kinetic momentum operator do not commute at the position of a flux tube, and thus cannot be diagonalized in the same basis. As a substitute for the momentum distribution of an anyonic (spatially localized) state, we propose to use the asymptotic single-particle density after expansion of anyons in free space from the state. This definition is identical with the standard one when the statistical parameter approaches that for bosons or fermions. Exact examples of expansion dynamics, which underpin our proposal, and observables that can be used to measure anyonic statistics, are shown.PACS numbers: 05.30. Pr, Anyons are quantum particles residing in two dimensions (2D), obeying fractional statistics interpolating between bosons and fermions [1,2]. The only physical realization of anyons so far is found in the fractional quantum Hall effect (FQHE) [3,4], where localized quasiparticle excitations have a fractional elementary charge [4] and statistics [5,6]. While fundamental motivation for exploring anyons is self-evident, the so-called non-Abelian anyonic excitations hold potential for technological advances, as they could be used for robust topological quantum computation [7] (for review see Ref.[8]).Some of the intriguing quantum mechanical implications of fractional statistics were pointed out decades ago [1,2]. Experiments with ultracold atomic gases seem to be a perfect playground for exploring anyonic physics, because of the quality in preparation, manipulation, and detection of numerous intriguing quantum states [9], and because of the possibility to explore 2D systems [10], with synthetic magnetic fields [11], which could be used to tinker with statistics. In an early paper, Paredes et al., inspired by the FQHE, proposed the realization of a 1/2-Laughlin state in a bulk rotating gas [12]. Different schemes were later proposed with atoms in optical lattices [13][14][15]. Ultracold atoms with two hyperfine levels in non-Abelian potentials could yield ground states with non-Abelian anyonic excitations [16], while bosons in Floquet-driven optical lattices may effectively exhibit fermionic statistics [17]. The one-dimensional (1D) version of anyons [18][19][20][21][22][23][24][25][26] has also aroused interest, especially in 1D optical lattices [23][24][25][26]. Such particles were proposed to emerge from occupation dependent hopping amplitudes, which could be realized with laser-assisted tunneling [23,25], or Floquet modulations [26]. Other proposals include lattices of polar molecules [27], photonics lattices [28] and circuit-QED systems [29]. An undoubtedly important ingredient that needs to be investigated in this context is the detection of the anyonic quantum state. The studied detection schemes rely on braiding [12,14,30,31], the pair-correlation function [15], and...

Time-of-Flight Measurements as a Possible Method to Observe Anyonic Statistics

“…Different, yet related aspects of the anyonic character of quasiholes have been addressed in recent works: the fractionalization of angular momentum has been discussed in [31] for test particles immersed in an ultracold atomic FQH system and, very recently, in [32] for impurities interacting with a bosonic bath. Signatures of anyonic statistics in the correlation functions of an expanding gas of anyons have been suggested in [33].…”

Anyon optics with time-of-flight two-particle interference of double-well-trapped interacting ultracold atoms

“…In this context, the properties and probable detection of synthetic particles, proposed initially in two dimensions and referred to as anyons [20,21], that obey nontrivial particle-exchange statistics interpolating between the familiar bosonic and fermionic ones, continues to be an intensely active field of theoretical and experimental research across several disciplines of physics; see, e.g., in the context of quantum computing [22,23], currentcurrent correlations of fractional-quantum-Hall anyons in high magnetic fields [24], noninteracting ultracold anyonic atoms in harmonic traps [25], and quasiholes in a fractional quantum Hall state of ultracold atoms [26]. We also note theoretical [16,17] and experimental [18] studies for simulating anyonic NOON states with photons in waveguide lattices.…”