Using squeezed states it is possible to surpass the standard quantum limit of measurement uncertainty by reducing the measurement uncertainty of one property at the expense of another complementary property [1]. Squeezed states were first demonstrated in optical fields [2] and later with ensembles of pseudo spin-1/2 atoms using non-linear atom-light interactions [3]. Recently, collisional interactions in ultracold atomic gases have been used to generate a large degree of quadrature spin squeezing in two-component Bose condensates [4,5]. For pseudo spin-1/2 systems, the complementary properties are the different components of the total spin vector S , which fully characterize the state on an SU(2) Bloch sphere. Here, we measure squeezing in a spin-1 Bose condensate, an SU(3) system, which requires measurement of the rank-2 nematic or quadrupole tensor Q ij as well to fully characterize the state. Following a quench through a nematic to ferromagnetic quantum phase transition, squeezing is observed in the variance of the quadratures up to −8.3 +0.6 −0.7 dB (−10.3 +0.7 −0.9 dB corrected for detection noise) below the standard quantum limit. This spin-nematic squeezing is observed for negligible occupation of the squeezed modes and is analogous to optical two-mode vacuum squeezing. This work has potential applications to continuous variable quantum information and quantum-enhanced magnetometry.The study of many-body quantum entangled states including atomic spin squeezed states is an active research frontier. In addition to being intrinsically fascinating, such states have applications in precision measurements [6], quantum information and fundamental tests of quantum mechanics [7]. Atomic squeezed states were first considered for ensembles of two-level (pseudo spin-1/2) atoms. For spin-1/2 particles, coherent states of the system are uniquely specified by the components of the total spin vector S , typically illustrated on a SU(2) Bloch sphere. For particles with higher spin, additional degrees of freedom beyond the spin vector are required to fully specify the state. For spin-1 particles, a natural basis to describe the wavefunction is the SU(3) Cartesian dipole-quadrupole basis, consisting of the three components of the spin vector,Ŝ i , and the moments of the rank-2 quadrupole or nematic tensor,Q ij ({i, j} ∈ {x, y, z}). In matrix form, the nematic moments can be written. Spin-1 atomic Bose-Einstein condensates [9-13] provide an exceptionally clean experimental platform to investigate the quantum dynamics of many-body spin sys-tems. They feature controllable quantum phase transitions, well-understood underlying microscopic models, and flexible defect-free geometries. Importantly, it is possible to initialize non-equilibrium or excited states of the system and to directly measure both the spin vector and the nematic tensor using standard atomic state manipulation tools. Law, et al., demonstrated that the spinor interaction can be written as total spin angular momentum, λŜ 2 whereŜ 2 =Ŝ 2x +Ŝ 2 y +Ŝ 2 z [14]. It is ...
Leveraging the unrivalled performance of optical clocks as key tools for geo-science, for astronomy and for fundamental physics beyond the standard model requires comparing the frequency of distant optical clocks faithfully. Here, we report on the comparison and agreement of two strontium optical clocks at an uncertainty of 5 × 10−17 via a newly established phase-coherent frequency link connecting Paris and Braunschweig using 1,415 km of telecom fibre. The remote comparison is limited only by the instability and uncertainty of the strontium lattice clocks themselves, with negligible contributions from the optical frequency transfer. A fractional precision of 3 × 10−17 is reached after only 1,000 s averaging time, which is already 10 times better and more than four orders of magnitude faster than any previous long-distance clock comparison. The capability of performing high resolution international clock comparisons paves the way for a redefinition of the unit of time and an all-optical dissemination of the SI-second.
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