The energy resolution per bandwidth E R is a figure of merit that combines the field resolution, bandwidth or duration of the measurement, and size of the sensed region. Several very different dc magnetometer technologies approach E R = , while to date none has surpassed this level. This suggests a technology-spanning quantum limit, a suggestion that is strengthened by model-based calculations for nitrogen-vacancy centres in diamond, for dc SQUID sensors, and for optically-pumped alkali-vapor magnetometers, all of which predict a quantum limit close to E R = .Here we review what is known about energy resolution limits, with the aim to understand when and how E R is limited by quantum effects. We include a survey of reported sensitivity versus size of the sensed region for a dozen magnetometer technologies, review the known model-based quantum limits, and critically assess possible sources for a technology-spanning limit, including zero-point fluctuations, magnetic self-interaction, and quantum speed limits. Finally, we describe sensing approaches that appear to be unconstrained by any of the known limits, and thus are candidates to surpass E R = .arXiv:1905.00618v1 [quant-ph]

We describe a compact, robust and versatile system for studying the macroscopic spin dynamics in a spinor Bose-Einstein condensate. Condensates of Rb 87 are produced by all-optical evaporation in a 1560 nm optical dipole trap, using a non-standard loading sequence that employs an ancillary 1529 nm beam for partial compensation of the strong differential light-shift induced by the dipole trap itself. We use near-resonant Faraday rotation probing to non-destructively track the condensate magnetization, and demonstrate few-Larmor-cycle tracking with no detectable degradation of the spin polarization. In the ferromagnetic F=1 ground state, we observe the spin orientation between atoms in the condensate is preserved, such that they precess all together like one large spin in the presence of a magnetic field. We characterize this dynamics in terms of the single-shot magnetic coherence times 1  and 2 *  , and observe them to be of several seconds, limited only by the residence time of the atoms in the trap. At the densities used, this residence is restricted only by one-body losses set by the vacuum conditions.

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.

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Entangled photons are generally collected by detection systems that select their certain spatial modes, for example using single-mode optical fibers. We derive simple and easy-to-use expressions that allow us to maximize the coupling efficiency of entangled photons with specific orbital angular momentum (OAM) correlations generated by means of spontaneous parametric downconversion. Two different configurations are considered: one in which the beams with OAM are generated by conversion from beams without OAM, and the second when beams with OAM are generated directly from the nonlinear medium. Also, an example of how to generate a maximally entangled qutrit is presented.