Self-bound quantum droplets are a newly discovered phase in the context of ultracold atoms. In this Letter, we report their experimental realization following the original proposal by Petrov [Phys. Rev. Lett. 115, 155302 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.155302], using an attractive bosonic mixture. In this system, spherical droplets form due to the balance of competing attractive and repulsive forces, provided by the mean-field energy close to the collapse threshold and the first-order correction due to quantum fluctuations. Thanks to an optical levitating potential with negligible residual confinement, we observe self-bound droplets in free space, and we characterize the conditions for their formation as well as their size and composition. This work sets the stage for future studies on quantum droplets, from the measurement of their peculiar excitation spectrum to the exploration of their superfluid nature.

We present interferometeric measurements of the f = 1 to f = 2 inter-hyperfine scattering lengths in a single-domain spinor Bose-Einstein condensate of 87 Rb. The inter-hyperfine interaction leads to a strong and state-dependent modification of the spin-mixing dynamics with respect to a non-interacting description. We employ hyperfine-specific Faraday-rotation probing to reveal the evolution of the transverse magnetization in each hyperfine manifold for different state preparations, and a comagnetometer strategy to cancel laboratory magnetic noise. The method allows precise determination of inter-hyperfine scattering length differences, calibrated to intra-hyperfine scattering length differences. We report (a (12) 3 −a (12) 2 )/(a (1) 2 −a (1) 0 ) = −1.27(15) and (a (12) 1 −a (12) 2 )/(a (1) 2 −a (1) 0 ) = −1.31(13), limited by atom number uncertainty. With achievable control of atom number, we estimate precisions of ≈0.3 % should be possible with this technique.

We describe a comagnetometer employing the f = 1 and f = 2 ground state hyperfine manifolds of a 87 Rb spinor Bose-Einstein condensate as co-located magnetometers. The hyperfine manifolds feature nearly opposite gyromagnetic ratios and thus the sum of their precession angles is only weakly coupled to external magnetic fields, while being highly sensitive to any effect that rotates both manifolds in the same way. The f = 1 and f = 2 transverse magnetizations and azimuth angles are independently measured by non-destructive Faraday rotation probing, and we demonstrate a 44.0(8) dB common-mode rejection in good agreement with theory. We show how spin-dependent interactions can be used to inhibit 2 → 1 hyperfine relaxing collisions, extending to ∼ 1 s the transverse spin lifetime of the f = 1, 2 mixtures. The technique could be used in high sensitivity searches for new physics on sub-millimeter length scales, precision studies of ultra-cold collision physics, and angle-resolved studies of quantum spin dynamics.

We present a magnetic sensor with energy resolution per bandwidth ER<ℏ. We show how a 87Rb single-domain spinor Bose–Einstein condensate, detected by nondestructive Faraday rotation probing, achieves single-shot low-frequency magnetic sensitivity of 72(8) fT measuring a volume V=1,091(30)  μm3 for 3.5 s, and thus, ER=0.075(16)ℏ. We measure experimentally the condensate volume, spin coherence time, and readout noise and use phase space methods, backed by three-dimensional mean-field simulations, to compute the spin noise. Contributions to the spin noise include one-body and three-body losses and shearing of the projection noise distribution, due to competition of ferromagnetic contact interactions and quadratic Zeeman shifts. Nonetheless, the fully coherent nature of the single-domain, ultracold two-body interactions allows the system to escape the coherence vs. density trade-off that imposes an energy resolution limit on traditional spin precession sensors. We predict that other Bose-condensed alkalis, especially the antiferromagnetic 23Na, can further improve the energy resolution of this method.

We propose and demonstrate cavity-enhanced polarization-rotation measurement as a means to detect magnetic effects in transparent media with greater sensitivity at equal optical disturbance to the medium. Using the Jones calculus, we compute the effective polarization rotation effect in a Fabry-Perot cavity containing a magnetic medium, including losses due to enclosure windows or other sources. The results show that when measuring polarization rotation, collecting the transmitted light has advantages in simplicity and linearity relative to collecting the reflected light. We demonstrate the technique by measuring Faraday rotation in a 87Rb atomic ensemble in the single-pass and cavity-enhanced geometries, and observe enhancement in good agreement with the theoretical predictions. We also demonstrate shot-noise-limited operation of the enhanced rotation scheme in the small-angle regime.