Revealing Pseudo-Fermionization and Chiral Binding of One-Dimensional Anyons using Adiabatic State Preparation

Abstract

Fractional statistics give rise to quantum behaviors that differ fundamentally from those of bosons and fermions. While two-dimensional anyons play a major role in strongly correlated systems and topological quantum computing, the nature of their one-dimensional (1D) counterparts remains the subject of intense debate, with renewed interest fueled by recent experimental progress. Theoretically, 1D anyons are predicted to host exotic many-body phases and quantum phase transitions, yet experimental signatures have remained elusive. Using ultracold atoms in an optical lattice, we prepare two-body ground states of the 1D anyon-Hubbard model by combining Hamiltonian engineering via quasiperiodic drives and adiabatic state manipulation. We uncover the effects of statistical interactions that lead to pseudo-fermionization and to the formation of chiral bound states when particles remain close together. Our results establish a link between lattice and continuum realizations of anyon models, and mark important steps towards the precise control of 1D anyons in both equilibrium and out-of-equilibrium settings.

Figures (15)

• Figure 1: Pseudo-fermionization and chiral binding of 1D anyons. (a) Two-particle AHM in position representation. Due to particle indistinguishability, only the lower right triangle of the coordinate system is relevant. Motion towards the upper right corresponds to shifts of the center of mass (COM), while motion towards the lower right corresponds to increasing the relative distance (REL) between the two particles. Double circles indicating double occupancy. 1D anyons acquire a phase $-\theta$ when tunneling to the right onto an occupied site (dark blue arrow) and $+\theta$ for the reverse process, giving rise to geometric phases around loops in configuration space (inset). The binding of particles requires a non-zero center-of-mass quasi-momentum $q \sim \theta$ due to the tunneling phase, resulting in chiral motion anyons_sm. The blue-shaded (resp. red-shaded) regions indicate the configurations most populated when the particles are bound (resp. antibunched, i.e. pseudo-fermionized). (b) Eigenenergies on an infinite lattice, for $U = 0$, with continuum states present for all $\theta$ (grey-shaded region). Bound-state branches, present for $\theta \neq 0$, are chiral when $\theta \neq \pi$ (solid lines for $\theta = \pm \pi/2$). For a system size $L$, the ground state mostly populates states in the lower part of the spectrum with quasi-momenta $q \lesssim \pi/L$.
• Figure 2: Friedel oscillations and pseudo-fermionization. (a) Adiabatic preparation of the two-particle ground state on a chain of $L = 5$ lattice sites with on-site interaction $U = 1.6(2)J$. Starting from a doubly-occupied site at the bottom of the chain (①), tunneling is increased to $J$, followed by a decrease of the tilt $\Delta$ from $4.3(2)J$ to $0$ (②). Finally, the statistical phase is ramped from $0$ to its final value $\theta$ (③). (b) Average density profiles evolve from a single central peak at $\theta = 0$ (bosons) to two side peaks at $\theta = \pi$ (pseudo-fermions). (c) The fraction of doubly-occupied states decreases as $\theta$ approaches $\pi$. (d) Density-density correlations $\Gamma_{ij}$, representing the probability of finding particles at $i$ and $j$, confirm the increasing tendency of particles to avoid one another. Theory predictions, obtained from exact diagonalization anyons_sm, are shown as dotted curves in (b) and (c) for parameter-free calculations, while dashed curves include adjusted offset potentials. In (d), only theory values with edge offsets are shown. Error bars represent the standard error of the mean (s.e.m.).
• Figure 3: Asymmetric expansion dynamics. (a) Adiabatic preparation of the two-particle ground state on a chain of $L = 3$ lattice sites, with $U = 0.0(2)J$: after isolating a doubly-occupied site at the bottom of the chain, tunneling is increased to $J$, before the tilt is decreased to $0$ at constant $\theta$ (①). The confining walls are then quenched to zero to allow free expansion of the system (②). (b) Density profile after expansion for $\theta = -\pi/2$ (resp. $\theta = +\pi/2$) shows leftward (resp. rightward) trajectory. (c) Center-of-mass position $\langle X \rangle$ as a function of time for different statistical phases. For $\theta \neq 0$ or $\pi$, the observed drift direction matches the one predicted for the bound pair (inset). (d) Density-density correlator $\Gamma_{ij}$ at time $t = 3.6\,\tau$, showing dominant correlations near the diagonal, consistent with chiral bound states induced by the statistical phase $\theta$. Theory predictions are based on exact diagonalization without free parameter anyons_sm.
• Figure 4: Reflection dynamics of two-particle bound states. (a) Following the preparation steps described in Fig. \ref{['fig:asymmetric']}(a) (①), the confining walls are quenched to zero to allow expansion in the presence of a potential barrier located four sites to the left of the initial position (②). Attractive bosons are directed towards the potential barrier through a controlled momentum transfer at $t = 0$anyons_sm. (b) Density profiles conditioned on particle pairs with relative distance $d < 3$ sites. At early times, both anyons ($\theta = -\pi/2$, $U = 0.0(2)J$, blue dots) and attractive bosons ($\theta = 0$, $U = -2.0(2) J$, grey dots) exhibit similar leftward motion. After reflection around $t = 4\tau$, the two cases show qualitatively different behavior: the density of nearby anyons decreases significantly, while bosons remain tightly bound. The green-shaded area indicates the approximate trajectory of the center of mass. (c) Density-density correlators $\Gamma_{ij}$ reveal that attractive bosons reflect while staying together (strong weight along the diagonal), whereas chiral anyons delocalize after reflection, revealing the chiral nature of the binding mechanism.
• Figure S1: Calibration of DMD wall potential. (a) Tilted lattice along $x$ together with the additional local potential created by the DMD (purple). (b) The DMD potential is increased to the resonance condition $V_{\textrm{DMD}} = E$, enabling resonant tunneling between neighboring sites. (c) Measured probability of finding the atom on the initial site (blue), on the neighboring site to the right (orange), or on other sites (green), as a function of the applied DMD laser power. The resonance condition $V_{\textrm{DMD}} = E$ is extracted from the transfer probability to the neighboring site.