About

Erich Mueller is a Professor in the Department of Physics at Cornell University, with a focus on theoretical condensed-matter physics, atomic, molecular, and optical physics, and quantum information. His research centers on the theory of atoms cooled to nanokelvin temperatures, where atoms are described as wave-packets rather than classical billiard balls. He investigates how simple inter-atomic interactions lead to complex collective behavior, aiming to refine the understanding of fundamental physics through atomic systems. Mueller's work often involves designing cold atom experiments to elucidate phenomena from other fields such as solid state physics, nuclear physics, and high energy physics, and he collaborates closely with experimentalists at Cornell and elsewhere. His approach combines analytic and numerical techniques to explore topics like ultracold atomic gases, quantum optics, and exotic quantum phenomena.

Research topics

• Quantum mechanics
• Physics
• Computer Science
• Mathematics
• Condensed matter physics
• Statistical physics
• Optoelectronics

Selected publications

• Checkerboard Bose Hubbard Ladders using Transmon Arrays

  arXiv (Cornell University) · 2026-05-08

  preprintOpen accessSenior author

  Adding a sublattice bias to the two dimensional Bose Hubbard model greatly enriches the available physics, and introduces knobs which can be used to control and interrogate the quantum state. We describe the physics of this checkerboard Bose Hubbard model and how it can be explored using transmon arrays. We show that the sublattice bias brings the commensurate superfluid phase into an experimentally accessible regime, and gives new probes. We characterize the superfluid and insulating phases, with careful attention to finite size effects.

  PublisherDOI

• Checkerboard Bose Hubbard Ladders using Transmon Arrays

  ArXiv.org · 2026-05-08

  articleOpen accessSenior author

  Adding a sublattice bias to the two dimensional Bose Hubbard model greatly enriches the available physics, and introduces knobs which can be used to control and interrogate the quantum state. We describe the physics of this checkerboard Bose Hubbard model and how it can be explored using transmon arrays. We show that the sublattice bias brings the commensurate superfluid phase into an experimentally accessible regime, and gives new probes. We characterize the superfluid and insulating phases, with careful attention to finite size effects.

  PublisherOA PDF

• Spin-spiral instability of the Nagaoka ferromagnet in the crossover between square and triangular lattices

  Physical review. B./Physical review. B · 2026-04-01

  articleOpen accessSenior author

  We study the hard-core Fermi-Hubbard model in the crossover between square and triangular lattices near half-filling. As was recognized by Nagaoka in the 1960s, on the square lattice the presence of a single hole leads to ferromagnetic spin ordering. On the triangular lattice, geometric frustration instead leads to a spin-singlet ground state, which can be associated with a 120-degree spiral order. On lattices which interpolate between square and triangular, there is a phase transition at which the ferromagnetic order becomes unstable to a spin spiral. We model this transition, finding the exact location of the spin-spiral instability.

  PublisherOA PDFDOI

• Multipartite entanglement structures in quantum stabilizer states

  Physical review. A/Physical review, A · 2025-06-16

  preprintOpen accessSenior author

  We develop a method for visualizing the internal structure of multipartite entanglement in pure stabilizer states. Our algorithm graphically organizes the many-body correlations in a hierarchical structure. This provides a rich taxonomy from which one can simultaneously extract many quantitative features of a state including some traditional quantities such as entanglement depth, k-uniformity and entanglement entropy. Our method also presents an alternative computational tool for extracting the exact entanglement depth and all separable partitions of a stabilizer state. Our construction is gauge invariant and goes beyond traditional entanglement measures by visually revealing how quantum information and entanglement is distributed. We use this tool to analyze the internal structures of prototypical stabilizer states (GHZ state, cluster state, stabilizer error correction codes) and are able to contrast the complexity of highly entangled volume law states generated by random unitary operators and random projective measurements.

  PublisherOA PDFDOI

• Kinetic magnetism in the crossover between the square and triangular lattice Fermi-Hubbard models

  ArXiv.org · 2025-06-18

  preprintOpen accessSenior author

  We calculate the spin correlations that result from the motion of a single dopant in the hard-core Fermi-Hubbard model, as the geometry evolves from a square to a triangular lattice. In particular, we consider the square lattice with an additional hopping along one diagonal, whose strength is continuously varied. We use a high-temperature expansion which expresses the partition function as a sum over closed paths taken by the dopant. We sample thousands of diagrams in the space of closed paths using the quantum Monte Carlo approach of Raghavan and Elser [1,2], which is free of finite-size effects and allows us to simulate temperatures as low as $T \sim 0.3|t|$, even in cases where there is a sign problem. For the case of a hole dopant, we find a crossover from kinetic ferromagnetism to kinetic antiferromagnetism as the geometry is tuned from square to triangular, which can be observed in current quantum gas microscopes.

  PublisherOA PDFDOI

• Entanglement depth dataset

  ArXiv.org · 2025-11-11

  preprintOpen accessSenior author

  The zipped files contain the dataset used in making Figs. 2,3,5 and 6 with description of the dataset in a word file called 'Data details' included separately for each zipped file. The file calculationcode.jl includes the Julia code used to generate this dataset.

  PublisherOA PDFDOI

• Resonating Kagome Dimer coverings in Rydberg atom arrays

  ArXiv.org · 2025-06-26

  preprintOpen accessSenior author

  Motivated by experiments on Rydberg atom arrays, we explore the properties of uniform quantum superpositions of kagome dimer configurations and construct an efficient algorithm for experimentally producing them. We begin by considering the thin cylinder limit, where these states have simple descriptions. We then develop a matrix product representation of the states on arbitrary cylinders, which leads to a natural protocol to efficiently grow them. We explain how our approach can be adapted to other quantum computing hardware.

  PublisherOA PDFDOI

• Vacancy-assisted superfluid drag

  Physical review. A/Physical review, A · 2025-05-05 · 2 citations

  articleSenior author

  The authors theoretically study superfluid drag in the two-component hard-core Bose-Hubbard model, analyzing how the hard-core constraints correlate particle motion. They derive analytical results in the jamming limit of vanishing hole density and use complementary numerical techniques to study finite hole densities in two-dimensional lattices.

  PublisherDOI

• Imaging propagating terahertz collective modes in two-dimensional semiconductor double layers

  ArXiv.org · 2025-11-28

  preprintOpen access

  Two-dimensional transition metal dichalcogenide (TMD) semiconductors exhibit a wide range of novel phenomena at millielectronvolt (terahertz-frequency) energy scales, including superconducting and correlation-induced insulating gaps that are frequently accompanied by symmetry breaking. However, due to the subwavelength dimensions and the often low conductivities of these systems, their intrinsic THz plasmons and meV-scale excitation gaps are difficult to access experimentally. Here we report an optical readout method that can image propagating THz-frequency collective modes in real time. The method relies on a strong coupling between the optical polarons of monolayer TMD semiconductors and the local THz fields in a waveguide, which enables us to image THz plasmons with micron scale spatial resolution and determine their propagation group velocities. Moreover, at finite magnetic fields, we observe coherent cyclotron oscillations resulting from Landau level repopulation induced by the THz field. Our findings provide a new near-field platform for probing collective excitations in strongly correlated two-dimensional semiconductors and enable "all-photonic" TMD-based architectures for time-domain THz plasmonics and optoelectronics.

  PublisherOA PDFDOI

• Kinetic magnetism in the crossover between the square and triangular lattice Fermi-Hubbard models

  Physical review. B./Physical review. B · 2025-10-22 · 3 citations

  articleSenior author

  The ground state of the hard-core Fermi-Hubbard model with a single hole (and otherwise half-filled) is a ferromagnet on the square lattice, but an antiferromagnet on the triangular lattice, as those spin patterns minimize the kinetic energy of the hole. What is the magnetic behavior as one interpolates between these two geometries? Using a sophisticated quantum Monte Carlo algorithm, the authors determine here the magnetic correlations as the lattice is varied. Their calculations are performed in the thermodynamic limit and at temperatures comparable to current cold-atom experiments. They find a magnetic crossover between the two geometries, and calculate signatures of it that are observable in these experiments.

  PublisherDOI

Recent grants

• Gauge Fields In Cold Atoms

  NSF · $270k · 2011–2014

• Frontiers of Cold Atom Theory

  NSF · $360k · 2024–2027

• Many Body Physics of Cold Atomic Gases

  NSF · $270k · 2008–2011

• Theoretical AMO Studies for Enhanced Understanding and Control of Emergent Quantum Physics

  NSF · $354k · 2018–2022

• Theoretical Studies of Rotating Trapped Atomic Gases

  NSF · $240k · 2005–2008

Frequent coauthors

• Kaden R. A. Hazzard

  21 shared

• Stefan S. Natu

  Amazon (United States)

  19 shared

• Stefan K. Baur

  14 shared

• Theja N. De Silva

  Cornell University

  12 shared

• Shovan Dutta

  A. Alikhanyan National Laboratory

  11 shared

• Ran Wei

  Guizhou Forestry Science Research Institute

  11 shared

• Tin-Lun Ho

  The Ohio State University

  11 shared

• Thomas G. Kiely

  Cornell University

  10 shared

Awards & honors

• Robert A and Donna B Paul Award for excellence in advising (…
• Fellow, American Physical Society (2015)
• Alfred P. Sloan Fellow (2005-2007)