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Nature Communications

Observation of Bloch oscillations dominated by effective anyonic particle statistics

Weixuan Zhang, Hao Yuan, Haiteng Wang, Fengxiao Di, Na Sun, Xingen Zheng, Houjun Sun, Xiangdong Zhang

Published May 2, 2022• 40 citations
Publisher

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 [Formula: see text] 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.

DOI
10.1038/s41467-022-29895-0

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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 [Formula: see text] 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.
Bloch oscillations are exotic phenomena describing the periodic motion of a wave packet subjected to the external force in a lattice, where the system possessing single- or multipleparticles could exhibit distinct oscillation behaviors. In particular, it has been pointed out that quantum statistics could dramatically affected the Bloch oscillation even in the absence of particle interactions, where the oscillation frequency of two pseudofermions with the anyonic statistical angle being pi becomes half of that for two bosons. However, these statisticdependent Bloch oscillations have never been observed in experiments up to now. Here, we report the first experimental simulation of anyonic Bloch oscillations using electric circuits. By mapping eigenstates of two anyons to modes of designed circuit simulators, the Bloch oscillation of two bosons and two pseudofermions are verified by measuring the voltage dynamics. It is found that the oscillation period in the two-boson simulator is almost twice of that in the two-pseudofermion simulator, which 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 novelty signal control.
The onset of Bloch oscillations (BOs) for two correlated anyons hopping on a one-dimensional lattice is theoretically investigated in the framework of the anyon-Hubbard model. It is shown that, even in the absence of on-site particle interaction, BOs are degraded for a nonvanishing statistical phase exchange owing to the nonlocal quasiparticle nature of anyons. A remarkable exception is found for pseudofermions, i.e., particles that, although they are bosons on site, behave as fermions off site. In this case, if the ratio of forcing to the hopping rate is smaller than $\ensuremath{\sim}$0.50.50.5, in the absence of on-site interaction long-lived BOs are observed at a frequency which is half the BO frequency of single particles. This is notably distinct from results for previously investigated BOs of two strongly correlated bosons or fermions, in which particle correlation leads to a doubling of the BO frequency.
Non-Abelian anyons, which correspond to collective excitations possessing multiple fusion channels and noncommuting braiding statistics, serve as the fundamental constituents for topological quantum computation. Here, we reveal the exotic Bloch oscillations (BOs) induced by non-Abelian fusion of Fibonacci anyons. It is shown that the interplay between fusion-dependent internal energy levels and external forces can induce BOs and Bloch-Zener oscillations (BZOs) of coupled fusion degrees with varying periods. In this case, the golden ratio of the fusion matrix can be determined by the period of BOs or BZOs in conjunction with external forces, giving rise to an effective way to unravel non-Abelian fusion. Furthermore, we experimentally simulate non-Abelian fusion BOs by mapping the Schr\"odinger equation of two Fibonacci anyons onto the dynamical equation of electric circuits. Through the measurement of impedance spectra and voltage evolution, both fusion-dependent BZOs and BOs are simulated. Our findings establish a connection between BOs and non-Abelian fusion, providing a versatile platform for simulating numerous intriguing phenomena associated with non-Abelian physics.
Bloch oscillations of quantum particles manifest themselves as periodic spreading and relocalization of the associated wave functions when traversing lattice potentials subject to external gradient forces. Albeit this phenomenon is deeply rooted into the very foundations of quantum mechanics, all experimental observations so far have only contemplated dynamics of one and two particles initially prepared in separable local states. Evidently, a more general description of genuinely quantum Bloch oscillations will be achieved on excitation of a Bloch oscillator by nonlocal states. Here we report the observation of Bloch oscillations of two-particle N00N states, and discuss the nonlocality on the ground of Bell-like inequalities. The time evolution of two-photon N00N states in Bloch oscillators, whether symmetric, antisymmetric or partially symmetric, reveals transitions from particle antibunching to bunching. Consequently, the initial states can be tailored to produce spatial correlations akin to those of bosons, fermions and anyons, presenting potential applications in photonic quantum simulation.
Abstract Few-body physics for anyons has been intensively studied within the anyon-Hubbard model, including the quantum walk and Bloch oscillations of two-anyon states. Recently, theoretical and experimental simulations of two-anyon states in a one-dimensional lattice have been carried out by expanding the wavefunction in terms of non-orthogonal basis vectors, resulting in non-physical degrees of freedom. In the present work, we deduce finite difference equations for the two-anyon state in a one-dimensional lattice by solving the Schrödinger equation with orthogonal and complete basis vectors. Such an orthogonal scheme gives all the orthogonal physical eigenstates, while the conventional (non-orthogonal) method produces many non-physical redundant eigensolutions whose components violate the anyonic commutation relations. The dynamical property of the two-anyon states in a sufficiently large lattice is investigated and compared in both the orthogonal and conventional schemes. For initial states with two anyons at the same site or two (next-)neighboring sites, we observe the same dynamical behavior in both schemes, including the revival probability, probability density function and two-body correlation. For other initial states, the conventional scheme produces erroneous states that no longer obey the anyonic relations. The period of Bloch oscillations in the pseudo-fermionic limit has been found to be twice that in the bosonic limit, while these oscillations disappear at other statistical parameters. Our findings are vital for quantum simulations of few-body anyonic physics in lattice models.
Bloch oscillations (BOs) are oscillations of electrons under external constant forces in a lattice, revealing the wavelike behavior of electrons. BOs lead to the localization of the wave packet that is called Wannier-Stark localization (WSL), resulting in the inhibition of conductivity. We simulate BOs experimentally in a one-dimensional superconducting circuit with nine qubits. The nine qubits form a one-dimensional lattice and an electron is mapped to a photon. We experimentally realize the coherent control of BOs by applying a well-controlled driving force with a frequency close to BOs. We observe the competition between localization and delocalization of the wave pocket by changing the drive parameters. Our study demonstrates the visualized wave behavior of electrons and proves a way to modulate electron transport in a perfect lattice. Published by the American Physical Society 2024