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

Abstract

We propose a standard time-of-flight experiment as a method for observing the anyonic statistics of quasiholes in a fractional quantum Hall state of ultracold atoms. The quasihole states can be stably prepared by pinning the quasiholes with localized potentials and a measurement of the mean square radius of the freely expanding cloud, which is related to the average total angular momentum of the initial state, offers direct signatures of the statistical phase. Our proposed method is validated by Monte Carlo calculations for ν=1/2 and 1/3 fractional quantum Hall liquids containing a realistic number of particles. Extensions to quantum Hall liquids of light and to non-Abelian anyons are briefly discussed.

Charge and statistics of lattice quasiholes from density measurements: A tree tensor network study

“…We now consider FQH and FCI states of N particles, in the presence of some localized QH excitations. We start by reviewing a recent proposal to characterize the braiding phase of these excitations through density profile measurements in the continuum [59,68], and we then conjecture on its generalization to the lattice case.…”

“…In Refs. [59,68], some of the current authors developed a scheme to access the anyonic statistics for QH excitations of FQH states. In contrast to other proposals based on interferometric experiments [see for instance Ref.…”

“…For FQH states in the LLL, the correspondence between L z and the mean square radius r 2 [79] simplifies our scheme even further, since it implies that one can obtain the braiding phase simply by measuring the density profile in the presence of QHs. More precisely, L z / + N = N r 2 /2l 2 B and the QH braiding phase reads [68]…”

“…(5) and (7) by a Monte Carlo study of two paradigmatic FQH states. We considered the Laughlin [68] and Moore-Read [59] wave functions, and for the latter we focused on the case of two non-Abelian QHs [7,11]. Nevertheless, the procedure is totally general, and it could be applied to any state in the LLL.…”

“…III we review the main findings of Refs. [59,68] and, in particular, the relation connecting the QH braiding phase to the depletions that these excitations create in the density profile of continuum systems. This relation is then generalized to the case of lattice systems in Sec.…”