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arXiv:2310.04495 · Physical review. B./Physical review. B

Observable signatures of Hall viscosity in lowest Landau level superfluids

Seth Musser, Hart Goldman, T. Senthil

Published Jul 24, 2024• 8 citations
arXivHTMLPDF

Abstract

Hall viscosity is a nondissipative viscosity occurring in systems with broken time-reversal symmetry, such as quantum Hall phases and $p+ip$ superfluids. Despite Hall viscosity's expected ubiquity and past observations in: classical soft matter, optical, and graphene systems, it has yet to be measured experimentally in any macroscopic quantum state of matter. Toward this end, we describe the observable effects of Hall viscosity in a simple family of rotating Bose-Einstein condensates of electrically neutral bosons, in which all of the bosons condense into a single lowest Landau level (LLL) orbital. Such phases are accessible to current cold atom experiments, and we dub them LLL superfluids. We demonstrate that LLL superfluids possess a nonuniversal Hall viscosity, leading to a range of observable consequences such as rotation of vortex-antivortex dipoles and wave-vector-dependent corrections to the speed of sound. Furthermore, using a coherent state path integral approach, we present a microscopic derivation of the Landau-Ginzburg equations of a LLL superfluid, showing explicitly how Hall viscosity enters.

DOI
10.1103/physrevb.110.024515

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Hall viscosity is a nondissipative viscosity occurring in systems with broken time-reversal symmetry, such as quantum Hall phases and p+ipp+ipp+ip superfluids. Despite Hall viscosity's expected ubiquity and past observations in: classical soft matter, optical, and graphene systems, it has yet to be measured experimentally in any macroscopic quantum state of matter. Toward this end, we describe the observable effects of Hall viscosity in a simple family of rotating Bose-Einstein condensates of electrically neutral bosons, in which all of the bosons condense into a single lowest Landau level (LLL) orbital. Such phases are accessible to current cold atom experiments, and we dub them LLL superfluids. We demonstrate that LLL superfluids possess a nonuniversal Hall viscosity, leading to a range of observable consequences such as rotation of vortex-antivortex dipoles and wave-vector-dependent corrections to the speed of sound. Furthermore, using a coherent state path integral approach, we present a microscopic derivation of the Landau-Ginzburg equations of a LLL superfluid, showing explicitly how Hall viscosity enters.
We develop a low-energy effective field theory of a two-dimensional bosonic superfluid on the lowest Landau level at zero temperature and identify a Berry term that governs the dynamics of coarse-grained superfluid degrees of freedom. For an infinite vortex crystal we compute how the Berry term affects the low-energy spectrum of soft collective Tkachenko oscillations and nondissipative Hall responses of the particle number current and stress tensor. This term gives rise to a quadratic in momentum term in the Hall conductivity, but does not generate a nondissipative Hall viscosity.
Abstract Topological superfluidity is an important concept in electronic materials as well as ultracold atomic gases1. However, although progress has been made by hybridizing superconductors with topological substrates, the search for a material—natural or artificial—that intrinsically exhibits topological superfluidity has been ongoing since the discovery of the superfluid 3He-A phase2. Here we report evidence for a globally chiral atomic superfluid, induced by interaction-driven time-reversal symmetry breaking in the second Bloch band of an optical lattice with hexagonal boron nitride geometry. This realizes a long-lived Bose–Einstein condensate of 87Rb atoms beyond present limits to orbitally featureless scenarios in the lowest Bloch band. Time-of-flight and band mapping measurements reveal that the local phases and orbital rotations of atoms are spontaneously ordered into a vortex array, showing evidence of the emergence of global angular momentum across the entire lattice. A phenomenological effective model is used to capture the dynamics of Bogoliubov quasi-particle excitations above the ground state, which are shown to exhibit a topological band structure. The observed bosonic phase is expected to exhibit phenomena that are conceptually distinct from, but related to, the quantum anomalous Hall effect3–7 in electronic condensed matter.
Realizing fractional quantum Hall (FQH) states in ultracold atomic systems remains a major goal despite numerous experimental advances in the last few decades. Recent progress in trap anisotropy control under rapid rotation has renewed interest in ultracold atomic FQH physics, enabling experiments that impart much larger angular momentum per particle and offer in situ imaging with resolution finer than the cyclotron orbit size. In this paper, we present a theoretical investigation of a rapidly rotating anisotropic Bose gas. By projecting the full Hamiltonian, including both kinetic and interaction terms, onto the lowest Landau level, we derive a compact two-parameter model that captures the effects of interaction strength, rotation rate, and anisotropy. Using exact diagonalization and density matrix renormalization group, we obtain a phase diagram that features broken-symmetry phases and topologically ordered quantum Hall states, while also highlighting the distinctive physics arising from the system's edges. Our results demonstrate the potential for future theoretical and experimental exploration of anisotropic quantum fluids, offering a unified framework for weakly interacting Bose condensates, vortex matter, and strongly correlated topological phases.
Measurement techniques based upon the Hall effect are invaluable tools in condensed-matter physics. When an electric current flows perpendicular to a magnetic field, a Hall voltage develops in the direction transverse to both the current and the field. In semiconductors, this behavior is routinely used to measure the density and charge of the current carriers (electrons in conduction bands or holes in valence bands)--internal properties of the system that are not accessible from measurements of the conventional resistance. For strongly interacting electron systems, whose behavior can be very different from the free electron gas, the Hall effect's sensitivity to internal properties makes it a powerful tool; indeed, the quantum Hall effects are named after the tool by which they are most distinctly measured instead of the physics from which the phenomena originate. Here we report the first observation of a Hall effect in an ultracold gas of neutral atoms, revealed by measuring a Bose-Einstein condensate's transport properties perpendicular to a synthetic magnetic field. Our observations in this vortex-free superfluid are in good agreement with hydrodynamic predictions, demonstrating that the system's global irrotationality influences this superfluid Hall signal.
We derive a low-energy effective field theory for chiral superfluids, which accounts for both spontaneous symmetry breaking and fermionic ground-state topology. Using the theory, we show that the odd (or Hall) viscosity tensor, at small wave vector, contains a dependence on the chiral central charge ccc of the boundary degrees of freedom, as well as additional nonuniversal contributions. We identify related bulk observables which allow for a bulk measurement of ccc. In Galilean invariant superfluids, only the particle current and density responses to strain and electromagnetic fields are required. To complement our results, the effective theory is benchmarked against a perturbative computation within a canonical microscopic model.
Abstract The dominance of interactions over kinetic energy lies at the heart of strongly correlated quantum matter, from fractional quantum Hall liquids, to atoms in optical lattices and twisted bilayer graphene. Crystalline phases often compete with correlated quantum liquids, and transitions between them occur when the energy cost of forming a density wave approaches zero. A prime example occurs for electrons in high magnetic fields, where the instability of quantum Hall liquids towards a Wigner crystal is heralded by a roton-like softening of density modulations at the magnetic length. Remarkably, interacting bosons in a gauge field are also expected to form analogous liquid and crystalline states. However, combining interactions with strong synthetic magnetic fields has been a challenge for experiments on bosonic quantum gases. Here, we study the purely interaction-driven dynamics of a Landau gauge Bose-Einstein condensate in and near the lowest Landau level. We observe a spontaneous crystallization driven by condensation of magneto-rotons, excitations visible as density modulations at the magnetic length. Increasing the cloud density smoothly connects this behaviour to a quantum version of the Kelvin-Helmholtz hydrodynamic instability, driven by the sheared internal flow profile of the rapidly rotating condensate. At long times the condensate self-organizes into a persistent array of droplets, separated by vortex streets, which are stabilized by a balance of interactions and effective magnetic forces.