Observation of disorder-induced superfluidity

TL;DR

This work demonstrates disorder-induced superfluidity in a 2D Bose-Hubbard system realized with a transmon-based quantum processor. By independently tuning hopping and on-site disorder and employing a qutrit encoding to enable resonant tunneling, the authors observe a MI to BG to SF sequence and provide evidence for a globally coherent phase via condensate formation, nonzero compressibility, a long-range SPDM, and a linearly dispersing phonon mode measured through the dynamical structure factor. They combine direct measurements with Gutzwiller theory and extensive MPS simulations, including an effective device Hamiltonian that captures higher-order couplings, to map the phase diagram and assess adiabatic state preparation. The results establish disorder-induced superfluidity in a programmable quantum platform and illuminate rare-region effects and glassy dynamics relevant to granular superconductors, porous media, and cold-atom systems, with implications for understanding anomalous metals and Bose metals in disordered bosonic systems.

Abstract

The emergence of states with long-range correlations in a disordered landscape is rare, as disorder typically suppresses the particle mobility required for long-range coherence. But when more than two energy levels are available per site, disorder can induce resonances that locally enhance mobility. Here we explore phases arising from the interplay between disorder, kinetic energy, and interactions on a superconducting processor with qutrit readout and control. Compressibility measurements distinguish an incompressible Mott insulator from surrounding compressible phases and reveal signatures of glassiness, reflected in non-ergodic behavior. Spatially-resolved two-point correlator measurements identify regions of the phase diagram with a non-vanishing condensate fraction. We also visualize the spectrum by measuring the dynamical structure factor. A linearly-dispersing phonon mode materializes in the superfluid, appearing even when disorder is introduced to the clean Mott insulator. Our results provide strong experimental evidence for disorder-induced superfluidity.

Figures (17)

• Figure 1: Phases of interacting bosons in a disordered landscape. (A) Heuristic phase diagram as a function of hopping ($J$) and disorder strength ($W$), with $U$ the on-site interaction. Theory and numerics Prokofev_PRB2009Prokofev_PRL_2011 point to a 're-entrant' disorder-mediated superfluid phase above the Mott insulator; however, no evidence for this has been observed experimentally. (B) For $W=0$, once $J$ exceeds a critical value $J_\text{c}$, bosons hop freely between sites and form a coherent superfluid. Although disorder localizes single-particle states, particles may undergo short-range resonant tunneling---which could, in principle, promote superfluidity.
• Figure 2: Formation of particle-hole excitations. (A) Typical single-shot density measurements, showing doublon ($n_i=2$) and holon ($n_i=0$) formation at four different points in the $J$-$W$ phase diagram using a 2D grid of qutrits at fixed interaction strength $U/(2\pi)=190$ MHz. As $J/U$ is increased, more particle-hole pairs are formed. Data is post-selected to enforce number conservation, yielding matched holon and doublon counts.(B) Measured doublon fraction in the $J$-$W$ parameter plane, averaged over 10,000 measurement instances and 10 disorder realizations over a $4 \times 9$ grid of qutrits. Since $\langle n \rangle = 1$, the spatially averaged excitation number variance, $\langle n^2 \rangle - \langle n \rangle^2$, can be directly obtained by multiplying the measured doublon fraction by 2.
• Figure 3: Mapping the compressibility in the $J-W$ plane (A) Annealing ramp protocols, analogous to 'field-cooling' (FC) and 'zero-field-cooling' (ZFC) experiments in glasses. In the ZFC case, the potential gradient is applied after the state has been adiabatically prepared; for the FC ramps, the gradient is applied during state preparation, with $t_\text{ramp}=100\text{ ns}$ and $t_\text{field}=250 \text{ ns}$. In a $N_x=9$ by $N_y=4$ grid, the on-site potentials are ramped to $\Delta \cos( \pi x/8)$, with perturbation strength $\Delta/(2\pi) = 30 \text{ MHz}$. (B) Compressibility as a function of $J$ at zero disorder, measured using both the ZFC (brown) and FC (blue) protocols. The inset shows $\langle n_i \rangle$ at $J/U=0.1$ and $W=0$ for a state prepared with the FC protocol. (C) Compressibility in the $J$-$W$ plane, displaying transition to a compressible state as $W$ and $J$ are increased, measured using both the ZFC (left) and FC (right) protocols. 150 disorder realizations were taken. (D) Difference in compressibility, $\Delta \kappa$, between FC and ZFC protocols, revealing a non-ergodic corner of the phase diagram ($\Delta \kappa\neq 0$, shaded blue).
• Figure 4: Characterizing the condensate (A) $C_{ij}$ is measured relative to a fixed qubit $i$ for two values of $J/U$ with zero disorder. The qubit grid has dimension $4\times 9$. (B) $C_{ij}$ averaged over all pairs as a function of Manhattan distance, $|i-j|$. We take a cut at $W=0$ (left) and $J=0.0625U$ (right). For the latter measurement, 10 disorder realizations are taken. The insets show the same data in grayscale. (C) Condensate wavefunction for four different combinations of $J$ and $W$. (D) The condensate fraction, extracted from the largest eigenvalue of $C_{ij}$, in the $J$-$W$ plane. When $W \neq 0$, 10 disorder realizations are averaged.
• Figure 5: Direct measurement of dynamical structure factor. (A) After preparing the desired state on a $4\times 9$ grid of qubits, we apply a spatiotemporal potential modulation pattern and then measure $\langle n_i \rangle$ at each site (see Supp.). We show a typical drive (left) and response (right) with momentum $k=2\pi/8$ and frequency $\omega/(2\pi)=40$ MHz. The drive is spatially uniform over the shorter dimension and sinusoidal in the other dimension. The response shown here has subtracted from it the response with no drive and is averaged over the smaller spatial dimension. (B) Reactive part of the space- and time-resolved $\langle n \rangle$, after averaging over the shorter dimension ($L=4$). 10 disorder realizations are taken for experiments where $W\neq 0$. The locations of the zeros (where the system is maximally absorptive, corresponding to its fundamental modes) are indicated by brown dots. Theory prediction using the Gutzwiller ansatz (see Supp.) is plotted in black for the disorder-free experiments. (C) Phase boundaries were identified by binarization of the compressibility, the difference between ZFC and FC (Fig. 3), and the condensation fraction measurements (Fig. 4). The 4 parameter points used in Fig. 5 B are shown with encircled numbers.