Observation of Bloch oscillations dominated by effective anyonic particle statistics

Abstract

Bloch oscillations are exotic phenomena describing the periodic motion of a wave packet subjected to an external force in a lattice, where a system possessing single or multiple particles could exhibit distinct oscillation behaviors. In particular, it has been pointed out that quantum statistics could dramatically affect the Bloch oscillation even in the absence of particle interactions, where the oscillation frequency of two pseudofermions with an anyonic statistical angle of $${{{\boldsymbol{\pi }}}}$$ π becomes half of that for two bosons. However, these statistically dependent Bloch oscillations have never been observed in experiments until now. Here, we report the experimental simulation of anyonic Bloch oscillations using electric circuits. By mapping the eigenstates of two anyons to the modes of the designed circuit simulators, the Bloch oscillations of two bosons and two pseudofermions are verified by measuring the voltage dynamics. The oscillation period in the two-boson simulator is almost twice of that in the two-pseudofermion simulator, that is consistent with the theoretical prediction. Our proposal provides a flexible platform to investigate and visualize many interesting phenomena related to particle statistics and could have potential applications in the field of the signal control.

Three-dimensional non-Abelian Bloch oscillations and novel higher-order topological states

“…Recently, based on the similarity between circuit Laplacian and lattice Hamiltonian, simulating topological states with electric circuits has attracted lots of interest [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61]. Compared with other classical platforms, circuit networks possess remarkable advantages of being versatile and reconfigurable.…”

Hyperbolic band topology with non-trivial second Chern numbers

“…Motivated by recent experimental breakthroughs in realizing various quantum phases by electric circuits [43][44][45][46][47][48][49][50][51][52] , in the following, we design hyperbolic circuit networks to observe the above proposed hyperbolic band topology with second Chern numbers. Figure 3a illustrates the photograph image of the fabricated circuit sample, which corresponds to the periodic hyperbolic cluster with twelve units (as illustrated in Fig.…”

A New Type of Classical Logic Circuit with Exponential Speedup

“…packet moves to the right of runway by a distance of L at t ¼ L/2, then completely to right side of the runway. At this time there is frjϕðtÞg ¼ T ð0Þfr À 2tjϕð0Þg (35) Thus, after a period of t ¼ L/2, an approximation of the transmittance can be obtained by measuring the voltage distribution on the nodes at the right side of the runway X right jfrjϕðtÞgj 2 ¼ jT ð0Þj 2 (36) In this way, the output value of the binary tree is obtained. Since the value of L is chosen as…”

“…Consequently, many extremely complex physical phenomena are also fulfilled in circuit networks. [33][34][35][36][37][38][39][40] The question is whether a classical circuit can be constructed to realize the balanced NAND-Tree algorithm and the logical operation with exponential speedup.…”