Realization of a Synthetic Hall Torus with a Topological Charge Pump in a Spinor Bose-Einstein Condensate

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The gist

The gist: This work reports the first experimental realization of a synthetic Hall torus using an atomic F = 1 spinor Bose-Einstein condensate confined in a ring-shaped trap, which allows for the

In short

Researchers created a synthetic Hall torus using an F=1 spinor Bose-Einstein condensate trapped in a ring and coupled via Raman and microwave fields. This setup generates azimuthal density modulations whose periodicity is dictated by the quantized toroidal flux. They demonstrated topological charge pumping by adiabatically changing axial flux, showing quantized transport, thus realizing a platform for exploring quantum Hall physics in synthetic curved spaces.

Key concepts

Synthetic Hall Torus
This is a fabricated geometry created using atomic physics instead of physical space. It involves trapping atoms in a ring and using laser fields to create an effective magnetic field that penetrates the surface, mimicking the properties of a real torus with magnetic flux.
Spinor Bose-Einstein Condensate (BEC)
This is a state where many atoms are cooled to near absolute zero and occupy the same quantum state. Using an F=1 spinor BEC allows researchers to control spin states and their interactions, which is essential for engineering the required synthetic magnetic fields.
Topological Charge Pump
This is a process where an atom's quantum state is transported around a closed loop (the torus) in a way that results in a net change in its topological charge. In this experiment, it mimics the behavior of charge pumping seen in the fractional quantum Hall effect.
Azimuthal Density Modulation
This refers to variations in how densely packed the atoms are around the ring (the azimuthal direction). The specific pattern and periodicity of these modulations are directly determined by the quantized magnetic flux threading the synthetic torus, serving as a key signature of the Hall torus geometry.

Terminology used across episodes

This episode discusses

The paper

Realization of a Synthetic Hall Torus with a Topological Charge Pump in a Spinor Bose-Einstein Condensate · Read on arXiv

T. -H. Chien, S. -C. Wu, Y. -H. Su, L. -R. Liu, N. -C Chiu, M Sarkar, * Q Zhou*, * Y.-J Lin

Institute of Atomic and Molecular Sciences, Academia Sinica · Department of Physics, University of Mumbai Department of Physics and Astronomy, Purdue University Department of Physics, National Tsing Hua University

We report the first experimental realization of a synthetic Hall torus using a spinor Bose-Einstein condensate confined in a ring-shaped trap with in situ imaging. By cyclically coupling three hyperfine spin states via Raman and microwave fields, we impose a periodic boundary condition in the synthetic dimension, which, together with a real-space ring trap, realizes a toroidal geometry with synthetic magnetic flux penetrating the surface. This flux induces azimuthal density modulations whose periodicity is uniquely determined by the quantized toroidal flux, a hallmark of the Hall torus. We then implement a topological charge pump by adiabatically varying an axial flux through the torus, inducing quantized azimuthal transport of the atoms. We further investigate the onset of these modulations as the system transitions from cylindrical to toroidal topology. Our results establish a versatile platform for exploring quantum Hall physics and topological phenomena in synthetic curved spaces.

DOI: 10.1103/xzzd-glq5

Transcript

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: We're looking at the paper: "Realization of a Synthetic Hall Torus with a Topological Charge Pump in a Spinor Bose-Einstein Condensate".

Mira: Here's the gist of the paper. This work reports the first experimental realization of a synthetic Hall torus using an atomic F = 1 spinor Bose-Einstein condensate confined in a ring-shaped trap, which allows for the emulation of topological charge pumping and probing quantum Hall physics in synthetic curved spaces.

Kai: Experimental Realization of the Torus The researchers report the "first experimental realization of a synthetic Hall torus using an atomic F = 1 spinor Bose-Einstein condensate confined in a ringshaped potential" (Page 1).

Mira: This geometry is constructed by combining a real-space ring trap with cyclic coupling between three hyperfine spin states via Raman and microwave fields, which imposes a periodic boundary condition in the synthetic dimension (Page 1).

Kai: The synthesis of the torus involves creating a "synthetic magnetic field penetrating the toroidal surface using a Raman coupling that simultaneously change the spin state mF and the center-of-mass orbital angular momentum (OAM) of the atoms" (Page 1).

Paper summary: Kai: The paper "Realization of a Synthetic Hall Torus with a Topological Charge Pump in a Spinor Bose-Einstein Condensate" describes how they built this synthetic Hall torus using an atomic F=one spinor Bose-Einstein condensate confined in a ring-shaped trap.

Mira: They achieve this geometry by cyclically coupling three hyperfine spin states using Raman and microwave fields, which imposes a periodic boundary condition in the synthetic dimension, which together with the ring trap realizes a toroidal geometry with a synthetic magnetic flux.

Lev: The core idea here is creating that synthetic magnetic field penetrating the toroidal surface through a Raman coupling that simultaneously changes the spin state mF and the center-of-mass orbital angular momentum, and this imparts a net OAM transfer of alpha = 2hbar within the same spin state, which leads to coherent interference of wavefunctions of different OAM states.

Kai: That sounds like they are actively engineering a synthetic magnetic field using laser beams with phase winding number one to couple bare spin states mF> to mF ± one>, transferring ±hbar of OAM.

Mira: And the key result they show is seeing those azimuthal density modulations where the periodicity is uniquely determined by the quantized toroidal magnetic flux, which they call a hallmark of the Hall torus geometry.

Lev: They then implement a topological charge pump by adiabatically varying an axial flux through that torus, which induces quantized azimuthal transport of the atoms.

Kai: And they show how this behavior mimics the topological charge pump on a Hall cylinder by tuning parameters like the relative phase between their microwave and Raman fields.

Conclusion: Kai: The paper "Realization of a Synthetic Hall Torus with a Topological Charge Pump in a Spinor Bose-Einstein Condensate" by Y-J. Lin, Q. Zhou, and M. Sarkar on arXiv:two thousand six hundred two point 14549v1 at February two thousand twenty-six is about making this synthetic Hall torus using the spinor Bose-Einstein condensate in a ring trap to look at quantum Hall physics in some kind of curved space.

Mira: That title is pretty descriptive of what they achieved; it points directly to the core physics being explored in this experimental setup with the spinor Bose-Einstein condensate.

Lev: What they actually built was a system where you cyclically couple three hyperfine spin states using Raman and microwave fields to impose that periodic boundary condition in the synthetic dimension.

Kai: Exactly, and they used a real-space ring trap combined with that coupling to create a toroidal geometry with synthetic magnetic flux penetrating the surface.

Mira: The key result is seeing those azimuthal density modulations where the periodicity is uniquely determined by the quantized toroidal magnetic flux, which is that hallmark of a Hall torus.

Lev: They then implement a topological charge pump by adiabatically varying an axial flux through that torus, inducing quantized azimuthal transport of the atoms.

Mira: It’s interesting because they also investigate what happens when you suddenly switch from a cylindrical to a toroidal topology by changing those coupling phases.

Lev: They probe the post-quench dynamics after turning on the microwave coupling with zero phase, seeing oscillations in the azimuthal widths of those torus peaks at frequencies around forty-one point four Hz and thirty-nine point three Hz.

Kai: So it confirms that these density nodes always exist, which points to how robust these modulations are due to their topological origin in this toroidal geometry.

Mira: This platform is pretty versatile for extending the study toward fractional quantum Hall states and topological order on even more complicated manifolds.

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