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arXiv:2506.16466

Compressibility measurement of the thermal MI--BG transition in an optical lattice

Russ, Phil, Yan, Mi, Kowalski, Nicholas, Wadleigh, Laura, V. W. Scarola, DeMarco, Brian

Published Jun 19, 2025• 0 citations
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Abstract

Disorder can be applied to transform conducting to insulating states by localizing individual quantum particles. The interplay between disorder and interactions in many-particle systems leads to a richer tapestry of quantum phase transitions. Here, we report the measurement in an ultracold lattice gas of a disorder-induced transition from a state with small disorder-independent compressibility to a state for which compressibility increases with disorder. At zero temperature this is the transition from a Mott insulator (MI) to a Bose glass (BG), both of which are insulating states. This transformation is observed using measurements of core compressibility. By determining how double occupancy changes with atom number, we identify the threshold disorder strength required to switch from disorder-independent MI-like to disorder-dependent BG-like compressible behavior.

DOI
10.48550/arxiv.2506.16466

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Disorder can be applied to transform conducting to insulating states by localizing individual quantum particles. The interplay between disorder and interactions in many-particle systems leads to a richer tapestry of quantum phase transitions. Here, we report the measurement in an ultracold lattice gas of a disorder-induced transition from a state with small disorder-independent compressibility to a state for which compressibility increases with disorder. At zero temperature this is the transition from a Mott insulator (MI) to a Bose glass (BG), both of which are insulating states. This transformation is observed using measurements of core compressibility. By determining how double occupancy changes with atom number, we identify the threshold disorder strength required to switch from disorder-independent MI-like to disorder-dependent BG-like compressible behavior.
In recent years ultracold atoms in optical lattices have been extensively employed as quantum simulators to study the physics of conventional solid state systems. Due to the possibility of introducing controlled disorder, it appears now a straightforward progression to use ultracold atoms in optical potentials to also study the physics of complex systems. We experimentally study a system of bosonic 87Rb atoms in a 3D optical lattice, where disorder is introduced on the length scale of the lattice sites by using an auxiliary optical lattice with a non‐commensurate wavelength. Increasing the amount of disorder, we observe the transition from a Mott Insulator state to a novel gapless insulating phase induced by the cooperation of interactions and disorder, which could be identified with a Bose Glass phase. We discuss the experimental results as well as possible additional techniques for a better diagnostic of the system and future implementations of the two‐color lattices in the study of different disorder‐induced phenomena.
We use a bichromatic optical lattice to experimentally realize a disordered system of ultracold strongly interacting 87Rb bosons. In the absence of disorder, the atoms are pinned by repulsive interactions in the sites of an ideal optical crystal, forming one-dimensional Mott-insulator states. We measure the excitation spectrum of the system as a function of disorder strength and characterize its phase-coherence properties with a time-of-flight technique. Increasing disorder, we observe a broadening of the Mott-insulator resonances and the transition to a state with vanishing long-range phase coherence and a flat density of excitations, which suggest the formation of a Bose-glass phase.
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We investigate the instabilities of the Mott-insulating phase of the weakly disordered Bose-Hubbard model within a renormalization group analysis of the replica field theory obtained by a strong-coupling expansion around the atomic limit. We identify an order parameter and associated correlation length scale that are capable of capturing the transition from a state with zero compressibility, the Mott insulator, to one in which the compressibility is finite, the Bose glass. The order parameter is the relative variance of the disorder-induced mass distribution. In the Mott insulator, the relative variance renormalizes to zero, whereas it diverges in the Bose glass. The divergence of the relative variance signals the breakdown of self-averaging. The length scale governing the breakdown of self-averaging is the distance between rare regions. This length scale is finite in the Bose glass but diverges at the transition to the Mott insulator with an exponent of $\ensuremath{\nu}=1/D$ for incommensurate fillings. Likewise, the compressibility vanishes with an exponent of $\ensuremath{\gamma}=4/D\ensuremath{-}1$ at the transition. At commensurate fillings, the transition is controlled by a different fixed point at which both the disorder and interaction vertices are relevant.