Phase transitions are ubiquitous in nature, ranging from protein folding and denaturisation, to the superconductor-insulator quantum phase transition, to the decoupling of forces in the early universe. Remarkably, phase transitions can be arranged into universality classes, where systems having unrelated microscopic physics exhibit identical scaling behaviour near the critical point. Here we present an experimental and theoretical study of the Bose-Einstein condensation phase transition of an atomic gas, focusing on one prominent universal element of phase transition dynamics: the spontaneous formation of topological defects during a quench through the transition [1, 2, 3]. While the microscopic dynamics of defect formation in phase transitions are generally difficult to investigate, particularly for superfluid phase transitions [4, 5, 6, 7], Bose-Einstein condensates (BECs) offer unique experimental and theoretical opportunities for probing such details. Although spontaneously formed vortices in the condensation transition have been previously predicted to occur [8, 9], our results encompass the first experimental observations and statistical characterisation of spontaneous vortex formation in the condensation transition. Using microscopic theories [10, 11, 12, 13, 14, 15, 16, 17] that incorporate atomic interactions and quantum and thermal fluctuations of a finite-temperature Bose gas, we simulate condensation and observe vortex formation in close quantitative agreement with our experimental results. Our studies provide further understanding of the development of coherence in superfluids, and may allow for direct investigation of universal phase-transition dynamics.

We report observations of vortex formation by merging and interfering multiple (87)Rb Bose-Einstein condensates (BECs) in a confining potential. In this experiment, a single harmonic potential well is partitioned into three sections by a barrier, enabling the simultaneous formation of three independent, uncorrelated BECs. The BECs may either automatically merge together during their growth, or for high-energy barriers, the BECs can be merged together by barrier removal after their formation. Either process may instigate vortex formation in the resulting BEC, depending on the initially indeterminate relative phases of the condensates and the merging rate.

Rydberg atom electric field sensors are projected to enable novel capabilities for resilient communications and sensing. This quantum sensor is small-size, highly sensitive, and broadly tunable, and it has the potential for performing precision vector electric field and angle-of-arrival measurements. While these atomic electric field sensors will not replace traditional receivers in commodity applications for RF signal reception, these sensors could be an enabling technology in niche application spaces. This review outlines the principles of operation of atomic electric field sensors and compares their performance capabilities to traditional RF receivers. It also highlights recent research and development efforts in atomic electric field sensing and identifies applications for which these sensors are projected to impact communications and remote sensing.