Smoother Ticking Through Topology

Imagine walking a tightrope in a windstorm. Every gust threatens to knock you off balance. Now imagine that the rope itself is designed in such a way that it naturally resists the wind, keeping you steady even when conditions are less than ideal. That’s the kind of protection topological physics offers to quantum systems.

In the world of atomic clocks, the “tightrope” is the delicate quantum state of atoms trapped in a lattice of laser light. These states are exquisitely sensitive to time and frequency, which is what makes optical lattice clocks so precise. But they’re also vulnerable to noise—tiny fluctuations in laser intensity, temperature, or magnetic fields can nudge the atoms off their ideal path, degrading the clock’s performance.

The new study, led by JILA postdoctoral researchers Tianrui Xu and Anjun Chu of Ana Maria Rey’s group, together with postdoc Kyungtae Kim of Jun Ye’s group, and in collaboration with James Thompson and JILA visiting Fellow Tillman Esslinger, proposes a way to stabilize these quantum states using the principles of topological phases of matter, a branch of physics that deals with properties that remain unchanged under continuous deformations. In these systems, the quantum states are 'knotted' in its quasimomentum space. Such 'knotting', quantified by the 'topological invariants' of the wavefunctions, remains constant even when the system is perturbed in ways that it does not change the global symmetry of the system.

Rey explains, “while discovering topological phases has been a big deal in condensed matter and atomic physics, what could be even more exciting is figuring out how these systems can help us build better sensors. For example, the quantum Hall effect, a topological state, has already been super useful—it has helped us measure the Hall resistance with incredible precision, which in turn lets us pin down constants like the fine-structure constant and even the elementary electron charge with great accuracy. Right now, atomic clocks are limited by laser noise. Even when we do clever tricks like comparing two clocks at once, we are still not hitting the theoretical limit of how precise they should be. So, the question is, can we use topology to improve state-of-the art clocks? This was the main question we tried to answer, and we found out that indeed it is possible.”

From Quantum Simulation to Quantum Sensing

Over the past decade, JILA has been at the forefront of both quantum simulation and quantum sensing. In one line of research, scientists use ultracold atoms to simulate exotic phases of matter, such as those found in high-temperature superconductors or topological insulators. In another, they build some of the world’s most accurate clocks and sensors, capable of detecting tiny changes in gravity or time dilation across millimeters.

Until now, these two fields have largely developed in parallel. But the new study brings them together, showing that the same topological phases explored in quantum simulators can also enhance the performance of quantum sensors.

At the heart of the proposal is the Su-Schrieffer-Heeger (SSH) model, a simple yet powerful model that provides the essential intuitions of topological phases and phase transitions. Originally developed to describe electrons in polyacetylene, a type of polymer, the SSH model describes a chain of sites with alternating strong and weak connections, leading to topological edge states and the corresponding topological bulk properties, both protected by symmetry.

JILA researchers propose implementing this model in a one-dimensional optical lattice clock (OLC) tilted by gravity or by an applied force. In this setup, known as Wannier-Stark OLC, atomic tunneling between lattice sites can be controlled by laser drives, as demonstrated by the collaboration of the Rey group and Jun Ye’s lab in recent years. In this study, the Rey group proposes to use two laser tones to create a hybrid synthetic lattice combining atomic internal states and the position of the atoms, leading to a natural realization of the SSH model. 

One of the key innovations in the study is a new spectroscopic protocol that leverages the topological properties of the SSH model. In conventional Rabi spectroscopy, atoms are driven between two states using a single laser tone, and the resulting oscillations are used to measure the transition frequency between the two states. However, this method is sensitive to noise in the laser amplitude, which can distort the signal.

In the SSH-based protocol, the resulting dynamics of the atomic wavefunctions under two laser tones depends on the 1D topological invariant of the SSH model known as the winding number—a quantity that is robust against many types of noise.

JILA researchers have shown that the winding number can be measured by tracking the displacement of the atomic wavefunction over time. This protocol can thus in-turn be used as a spectroscopic probe for atomic transition frequencies. Numerical simulations show that this “SSH spectroscopy” is less sensitive to both global and local amplitude noise than the traditional Rabi spectroscopy. In particular, the statistical noise scales more favorably with the number of atoms, suggesting that the protocol could be especially useful in future clocks that interrogate millions of atoms simultaneously.

Measuring Gravity with Quantum Pumps

The study also explores how topological physics can enhance matter-wave interferometry, a technique used to measure forces like gravity by splitting and recombining atomic wave packets. In a typical matter-wave interferometer, atoms are pushed apart using a sequence of laser pulses, allowed to evolve in different gravitational potentials, and then brought back together to measure the accumulated phase difference.

However, imperfections in the laser pulses can introduce errors, limiting the sensitivity of the device. To address this, the Rey group proposes using a technique known as Thouless pumping—an adiabatic process in which particles are transported across a lattice by slowly varying the system’s parameters.

In their proposed “topological pumping protocol,” atoms are adiabatically moved apart and then recombined using a sequence of laser-driven transitions that trace out a topologically-nontrivial path in parameter space. Here, a topological non-trivial path means   a trajectory that is robust to changes in system parameters. This method is inherently robust to many types of experimentally-relevant noise and can achieve larger separations with lower uncertainty than conventional pulse sequences.

Simulations show that the topological protocol outperforms traditional methods in terms of both signal strength and noise resilience, especially when the number of atoms is large. This could pave the way for new types of interferometers capable of measuring gravitational gradients or testing fundamental physics with reduced sensitivity to experimental noise.

Topologically Enhanced Clocks

The proposed protocols are designed to be compatible with existing optical lattice clock platforms, such as those developed in Jun Ye’s lab at JILA. These clocks already operate with extraordinary precision—recent experiments have achieved fractional uncertainties below 10⁻¹⁸—but further improvements are needed to reach the standard quantum limit (SQL), the ultimate sensitivity allowed by quantum mechanics for uncorrelated atoms.

By reducing classical noise, the topological approach offers a practical path toward SQL-limited performance. It also opens the door to new applications, such as measuring gravitational redshifts over even shorter distances or detecting tiny variations in fundamental constants.

Moreover, the study suggests that the same principles could be extended to more complex systems, including higher-dimensional lattices or atoms with multiple internal states. This could enable the exploration of richer topological phases and their potential benefits for quantum sensing and metrology.

In the quantum world, precision often comes at the cost of fragility. But topology offers a way to have both precision and protection. By embedding topological structures into the architecture of optical lattice clocks, the Rey group has outlined a strategy for making these devices more resilient to noise, more sensitive to signals, and more versatile in their applications.

As JILA researchers continue to refine these protocols and bring them into the lab, we may soon see a new generation of quantum sensors that are not only more accurate, but also more robust, thanks to the hidden geometry of quantum states.
 

This research is supported by the U.S. Air Force Office of Scientific Research, the U.S. Department of Energy Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator, NIST, NSF, Swiss National Science Foundation, Heising-Simons Foundation, Simons Foundation, and Sloan Foundation.

_{Written by Steven Burrows, JILA Science Communications Manager}