Solitons are among the most distinguishing fundamental excitations in a wide range of non-linear systems such as water in narrow channels, high speed optical communication, molecular biology and astrophysics. Stabilized by a balance between spreading and focusing, solitons are wavepackets, which share some exceptional generic features like form-stability and particle-like properties. Ultracold quantum gases represent very pure and well-controlled non-linear systems, therefore offering unique possibilities to study soliton dynamics. Here we report on the first observation of long-lived dark and dark-bright solitons with lifetimes of up to several seconds as well as their dynamics in highly stable optically trapped 87 Rb Bose-Einstein condensates. In particular, our detailed studies of dark and dark-bright soliton oscillations reveal the particle-like nature of these collective excitations for the first time. In addition, we discuss the collision between these two types of solitary excitations in Bose-Einstein condensates. The dynamics of non-linear systems plays an essential role in nature, ranging from strong non-linear interactions of elementary particles to non-linear wave phenomena in oceanography and meteorology. A special class of non-linear phenomena are solitons with interesting particle and wave-like behaviour. Reaching back to the observation of "waves of translation" in a narrow water channel by Scott-Russell in 1834 [1], solitons are nowadays recognized to appear in various systems as different as astrophysics, molecular biology and non-linear optics [2]. They are characterized as localized solitary wavepackets that maintain their shape and amplitude caused by a self-stabilization against dispersion via a non-linear interaction. While an early theoretical explanation of this non-dispersive wave phenomenon was given by Korteweg and de Vries in the late 19th century it was not before 1965 that numerical simulations of Zabusky and Kruskal theoretically proved that these solitary waves preserve their identity in collisions [3,4]. This revelation led to the term "soliton" for this type of collective excitation. Nowadays solitons are a very active field of research in many areas of science. In the field of non-linear optics they attract enormous attention due to applications in fast data transfer. Bose-Einstein condensates (BEC) of weakly interacting atoms offer fascinating possibilities for the study of nonlinear phenomena, as they are very pure samples of ultracold gases building up an effective macroscopic wave function of up to mm size. Non-linear effects like collective excitations [5], four-wave mixing [6] and vortices [7,8] have been studied, to name only a few examples. The existence and some fundamental properties of solitons have been deduced from few experiments employing ultra-cold quantum gases. Bright solitons, characterized as non-spreading matter-wave packets, have been observed in BEC with attractive interaction [9,10,11] where they represent the ground state of the system. In a repulsively...
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.
Over the last years the exciting developments in the field of ultracold atoms confined in optical lattices have led to numerous theoretical proposals devoted to the quantum simulation of problems e.g. known from condensed matter physics. Many of those ideas demand for experimental environments with non-cubic lattice geometries. In this paper we report on the implementation of a versatile three-beam lattice allowing for the generation of triangular as well as hexagonal optical lattices. As an important step the superfluid-Mott insulator (SF-MI) quantum phase transition has been observed and investigated in detail in this lattice geometry for the first time. In addition to this we study the physics of spinor Bose-Einstein condensates (BEC) in the presence of the triangular optical lattice potential, especially spin changing dynamics across the SF-MI transition. Our results suggest that below the SF-MI phase transition, a well-established mean-field model describes the observed data when renormalizing the spin-dependent interaction. Interestingly this opens new perspectives for a lattice driven tuning of a spin dynamics resonance occurring through the interplay of quadratic Zeeman effect and spin-dependent interaction. We finally discuss further lattice configurations which can be realized with our setup.
We present experimental data showing the head-on collision of dark solitons generated in an elongated Bose-Einstein condensate. No discernable interaction can be recorded, in full agreement with the fundamental theoretical concepts of solitons as mutually transparent quasiparticles. Our soliton generation technique allows for the creation of solitons with different depths; hence, they can be distinguished and their trajectories be followed. Simulations of the 1D-Gross-Pitaevskii equation have been performed to compare the experiment with a mean-field description.
Optical clocks are not only powerful tools for prime fundamental research, but are also deemed for the re-definition of the SI base unit second as they now surpass the performance of caesium atomic clocks in both accuracy and stability by more than an order of magnitude. However, an important obstacle in this transition has so far been the limited reliability of the optical clocks that made a continuous realization of a timescale impractical. In this paper, we demonstrate how this situation can be resolved and that a timescale based on an optical clock can be established that is superior to one based on even the best caesium fountain clocks. The paper also gives further proof of the international consistency of strontium lattice clocks on the 10 −16 accuracy level, which is another prerequisite for a change in the definition of the second.
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