The 1D anyon Hubbard model and beyond: towards experimental realization of a non-abelian holonomy in an optical lattice experiment
ORAL
Abstract
In this quantum gas microscopy experiment, we use quasi-periodic driving to engineer the effective exchange statistics of bosonic Rb-87 atoms in a 1-dimensional (1D) optical lattice, realizing the 1D Anyon-Hubbard Model (AHM) with a tunable statistical phase. In our previous work, we engineered the ground state of this Hamiltonian at multiple values of the statistical phase θ, measuring key characteristics of the ground state through both in situ density and expansion dynamics.
With this successful demonstration of adiabatic control in the AHM, we are now equipped to use this model as the foundation for engineering non-abelian holonomy [1]. The AHM hosts a chirally protected degenerate zero energy subspace that persists at all values of θ. Our goal is to ramp a system of two bosons on three sites into the associated 2-fold degenerate subspace, then adiabatically ramp the statistical phase in a complete loop from 0 to 2π. This ramp realizes a non-abelian holonomy: a unitary transformation of the state within the degenerate subspace that depends only on the path in parameter space. This unitary transformation, known as the Wilczek-Zee phase, is the non-abelian equivalent of the geometric Berry phase, while the degeneracy of the zero energy subspace ensures that there is no dynamical phase contribution and the process is holonomic. Our current progress has revealed several important challenges to overcome in realizing this state, most notably the role of potential disorder in lifting the degeneracy of the subspace.
[1] F. Theel, M. Bonkhoff, P. Schmelcher, T. Posske, and N. L. Harshman, "Chirally Protected State Manipulation by Tuning One-Dimensional Statistics." Phys. Rev. Lett. 135, 063401 (2025). https://doi.org/10.1103/kzf6-yx24
With this successful demonstration of adiabatic control in the AHM, we are now equipped to use this model as the foundation for engineering non-abelian holonomy [1]. The AHM hosts a chirally protected degenerate zero energy subspace that persists at all values of θ. Our goal is to ramp a system of two bosons on three sites into the associated 2-fold degenerate subspace, then adiabatically ramp the statistical phase in a complete loop from 0 to 2π. This ramp realizes a non-abelian holonomy: a unitary transformation of the state within the degenerate subspace that depends only on the path in parameter space. This unitary transformation, known as the Wilczek-Zee phase, is the non-abelian equivalent of the geometric Berry phase, while the degeneracy of the zero energy subspace ensures that there is no dynamical phase contribution and the process is holonomic. Our current progress has revealed several important challenges to overcome in realizing this state, most notably the role of potential disorder in lifting the degeneracy of the subspace.
[1] F. Theel, M. Bonkhoff, P. Schmelcher, T. Posske, and N. L. Harshman, "Chirally Protected State Manipulation by Tuning One-Dimensional Statistics." Phys. Rev. Lett. 135, 063401 (2025). https://doi.org/10.1103/kzf6-yx24
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Presenters
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Perrin C Segura
- Harvard University