Test of Special Relativity Using a Fiber Network of Optical Clocks.

Phase compensated optical fiber links enable high accuracy atomic clocks separated by thousands of kilometers to be compared with unprecedented statistical resolution. By searching for a daily variation of the frequency difference between four strontium optical lattice clocks in different locations throughout Europe connected by such links, we improve upon previous tests of time dilation predicted by special relativity. We obtain a constraint on the Robertson-Mansouri-Sexl parameter |α|≲1.1×10^{-8}, quantifying a violation of time dilation, thus improving by a factor of around 2 the best known constraint obtained with Ives-Stilwell type experiments, and by 2 orders of magnitude the best constraint obtained by comparing atomic clocks. This work is the first of a new generation of tests of fundamental physics using optical clocks and fiber links. As clocks improve, and as fiber links are routinely operated, we expect that the tests initiated in this Letter will improve by orders of magnitude in the near future.

Generation and detection of a sub-Poissonian atom number distribution in a one-dimensional optical lattice.

We demonstrate preparation and detection of an atom number distribution in a one-dimensional atomic lattice with the variance -14 dB below the Poissonian noise level. A mesoscopic ensemble containing a few thousand atoms is trapped in the evanescent field of a nanofiber. The atom number is measured through dual-color homodyne interferometry with a pW-power shot noise limited probe. Strong coupling of the evanescent probe guided by the nanofiber allows for a real-time measurement with a precision of ±8 atoms on an ensemble of some 10(3) atoms in a one-dimensional trap. The method is very well suited for generating collective atomic entangled or spin-squeezed states via a quantum nondemolition measurement as well as for tomography of exotic atomic states in a one-dimensional lattice.

Antiferromagnetic spatial ordering in a quenched one-dimensional spinor gas.

We have experimentally observed the emergence of spontaneous antiferromagnetic spatial order in a sodium spinor Bose-Einstein condensate that was quenched through a magnetic phase transition. For negative values of the quadratic Zeeman shift, a gas initially prepared in the F=1, m(F)=0 state collapsed into a dynamically evolving superposition of all three spin projections, m(F)=0, ±1. The quench gave rise to rich, nonequilibrium behavior where both nematic and magnetic spin waves were generated. We characterized the spatiotemporal evolution through two particle correlations between atoms in each pair of spin states. These revealed dramatic differences between the dynamics of the spin correlations and those of the spin populations.

Quantum phase transition in an antiferromagnetic spinor Bose-Einstein condensate.

We have experimentally observed the dynamics of an antiferromagnetic sodium Bose-Einstein condensate quenched through a quantum phase transition. Using an off-resonant microwave field coupling the F = 1 and F = 2 atomic hyperfine levels, we rapidly switched the quadratic energy shift q from positive to negative values. At q = 0, the system undergoes a transition from a polar to antiferromagnetic phase. We measured the dynamical evolution of the population in the F = 1, mF = 0 state in the vicinity of this transition point and observed a mixed state of all 3 hyperfine components for q < 0. We also observed the coarsening dynamics of the instability for q < 0, as it nucleated small domains that grew to the axial size of the cloud.

A clock network for geodesy and fundamental science.

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.