Precise measurements on a quantum phase transition in antiferromagnetic spinor Bose-Einstein condensates

TL;DR

This paper reports the first sub-Hz precision measurement of a quantum phase transition in antiferromagnetic spinor Bose-Einstein condensates, demonstrating the use of dynamical methods for high-precision quantum gas studies.

Contribution

It introduces a highly precise measurement technique for quantum phase transitions using dynamical behavior in spinor Bose-Einstein condensates, surpassing previous equilibrium-based methods.

Findings

Achieved 250 mHz uncertainty in the transition point measurement.

Validated the agreement of instability rates with Bogoliubov de-Gennes predictions.

Demonstrated the importance of removing magnetic field inhomogeneities.

Abstract

We have experimentally investigated the quench dynamics of antiferromagnetic spinor Bose-Einstein condensates in the vicinity of a zero temperature quantum phase transition at zero quadratic Zeeman shift $q$. The rate of instability shows good agreement with predictions based upon solutions to the Bogoliubov de-Gennes equations. A key feature of this work was removal of magnetic field inhomogeneities, resulting in a steep change in behavior near the transition point. The quadratic Zeeman shift at the transition point was resolved to 250 milliHertz uncertainty, equivalent to an energy resolution of $k_B \times 12$ picoKelvin. To our knowledge, this is the first demonstration of sub-Hz precision measurement of a phase transition in quantum gases. Our results point to the use of dynamics, rather than equilibrium studies for high precision measurements of phase transitions in quantum gases.