Multi-Particle Quantum Walks in a Dipole-Conserving Bose-Hubbard Model

Abstract

When particles move through a crystal or optical lattice, their motion can sometimes become frozen by strong external forces -- yet collective motion may still emerge through subtle many-body effects. In this work, we explore such constrained dynamics by realizing a dipole-conserving Bose-Hubbard model, where single atoms are immobile but pairs of particles can move cooperatively while preserving the system's center of mass, i.e. the overall dipole moment of the particle distribution. Starting from a one-dimensional chain of ultracold bosonic atoms in an optical lattice, we generate localized dipole excitations consisting of a hole and a doublon using site-resolved optical potentials and characterize their quantum walks and scattering dynamics. Our study provides a bottom-up investigation of a Hamiltonian with kinetic constraints, and paves the way for exploring low-energy phases of fractonic matter in existing experimental platforms.

Figures (11)

• Figure 1: Elementary excitations of a dipole-conserving Bose-Hubbard model at unity filling. When the potential gradient $\Delta$ is much larger than the tunneling amplitude $J$ and on-site interaction $U$, the dynamics induced by the tilted Bose-Hubbard model $H_0$\ref{['eq:tBH']} effectively conserves the system's center of mass, equivalently described as the dipole moment of the particle distribution. a, While a doublon or a hole -- each representing an isolated fracton excitation -- cannot move individually along the chain, b, a dipole consisting of a hole-doublon pair can hop c, to the left or d, to the right. This is possible through second-order tunneling processes that preserve the total dipole moment. Here, the dipole is represented as a red arrow on a link between two adjacent sites, pointing in the direction of the dipole moment.
• Figure 2: Experimental protocol and preparation of a dipole state.a, We isolate a 1D chain of atoms out of a unity-filled Mott insulator in a deep optical lattice. In the presence of a linear potential, a localized optical potential $A$ is then applied onto a single site to create a hole-doublon pair. Next, nonequilibrium dynamics is initiated in a shallow lattice by abruptly switching off $A$. After a variable evolution time, we project the many-body state onto the Fock basis by counting the number of atoms at each site. b, The center panel shows the energy spectrum for a two-particle, two-site system as a function of $A$. To create a dipole configuration (0, 2) from the initial state (1, 1), we adiabatically ramp $A$ from 0 along the red arrow. Alternatively, we create an antidipole configuration (2, 0) by suddenly increasing $A$ across the first avoided crossing and then adiabatically ramping $A$ along the blue arrow. On the left and right sides, we show the populations of the three configurations for different final values of $A$, measured over a 4-site region of interest (ROI) as indicated in the third illustration of panel a. Solid lines display numerical predictions for the populations assuming perfect adiabaticity across the first (left) and last (right) avoided crossings, respectively. Error bars denote 1$\sigma$ statistical uncertainties.
• Figure 3: Quantum walk of a single dipole. Comparison between experimental data (left) and numerical simulations based on the dipole-conserving Hubbard model $H$\ref{['eq:dBH']} (right). Panels a and b show the atom-number and dipole-number densities, respectively Jd. The dipole wavepacket expands linearly in time while exhibiting density modulation indicative of quantum interference.
• Figure 4: Scattering dynamics of two dipoles.a, We initialize a dipole-dipole (DD) or a dipole-antidipole (DA) pair with a four-link spacing. b, Density of dipole excitations and polarization $\langle n_k^{\rm d} \rangle / \langle |n_k^{\rm d}| \rangle$ at each link as a function of time polarization. c, Due to the energy cost $|\pm U_{\rm d}| \gg J_{\rm d}$ of occupying nearest-neighbor (NN) links, dipole excitations behave like hardcore (HC) NN particles. d, [resp. e,] Probability of finding a DD (left) or DA (right) pair in NN [resp. next-nearest-neighbor (NNN)] configurations, compared to the results of exact diagonalization simulation with the tilted Bose-Hubbard chain $H_0$ (red), as well as for the cases of two on-site HC bosons (blue) and two NN--HC bosons (yellow), with the same initial separation and tunneling amplitudes estimated for the dipole and antidipole SM. Error bars denote $1\sigma$ statistical uncertainties.
• Figure 5: Experimental sequence. Major experimental parameters are shown as functions of time. An optical potential shaped with a DMD is projected onto a Mott insulator to isolate a unity-filled one-dimensional chain. The chain is then tilted along its axis by adiabatically ramping up a magnetic field gradient. A Gaussian potential from a second DMD is subsequently applied to prepare either a dipole or an antidipole. This pinning potential is then abruptly switched off to initiate the nonequilibrium dynamics. Finally, the atoms are expanded orthogonally to the chain and imaged individually by fluorescence.