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Atomic clocks provide the most accurate definition for time. The precision of atomic clock has been improved by many orders of magnitude since the first atomic clock was built. However, the interatomic interaction usually suppress the precision of atomic clock. As a result, it is especially meaningful to study the interaction effect in atomic clock, which is considered to be helpful in improving the precision and accuracy of atomic clock. In order to characterize the collision effect induced clock shift, we theoretically study the collision clock shift in the Rabi spectrum, caused by the short-range interaction between two Fermi atoms in harmonic potential. Given that the short-range interatomic interaction is generally weak, and that the parameters of external lattice laser field are in the Lamb-Dicke regime, we make an approximation that the spatial wave-function of the Fermi atoms does not change, and then derive the motion equation for the internal wave-function under the external Rabi driving field. We solve the equation of motion by the perturbative method, and obtain the solution to first order, and thus derive the expression of the collision clock shift of the Rabi spectrum in terms of the interatomic interaction and the external Rabi driving laser field parameters for specific spatial wave-functions of atoms. Finally, we use the exact expression of the Green’s function in harmonic potential to obtain the averaged clock shift of collision at finite temperatures. Our results relate the atomic interaction with atomic clock shift, and provide a unified description of all partial waves of atomic interaction induced clock shift. Therefore, it becomes much more convenient to study the contributions of different partial waves to atomic clock shift. On the other hand, our results indicate that through precisely measuring the clock shift, the information about the interatomic interactions can also be obtained. In addition, our results for two interacting atoms can inspire the future study of real many-body interacting system which will be the next research topic.

We demonstrate a high-repetition-rate Er-doped all fiber laser with nonlinear-polarization-rotation mode-locking. The highest repetition rate of the laser is 217 MHz. The fiber laser has a very simple and compact structure and can output a stable mode-locking pulse only by using one polarization-dependent isolator and a polarization controller. The pulse width, spectral width and signal-to-noise ratio are measured to be 69 fs, 56 nm and 76 dB respectively.

A saturable absorber of 3.9% modulation depth was prepared on the surface of a fiber clad with single-walled carbon nanotubes (SWCNT) using chemical corrosion method. An all-fiber Er-doped fiber laser was setup with a ring cavity, and was mode-locked successfully by evanescent field mode-locking using prepared saturable absorber of single-walled carbon nanotubes. A 147 fs mode-locking pulse is obtained near 1556 nm with a 3 dB bandwidth of 24 nm. The output power is 21 mW at a pump power of 520 mW, corresponding to a pulse energy of 0.14 nJ with a repetition rate of 150 MHz.

Support vector regression (SVR) is an effective method for the predication of chaotic time-series, which is a fundamental topic of nonlinear dynamics. Through analyzing the possible variation of support vector sets after new samples are inserted to the training set, a novel SVR algorithm is proposed; thus an online learning algorithm is set up. In connection with the specific characteristics of chaotic signals, a wavelet kernel satisfying wavelet frames is also presented. The wavelet kernel can approximate arbitrary functions, and is especially suitable for local processing; hence the generalization ability of SVR is improved. To illustrate the good performance of the online wavelet SVR, a benchmark problem, i.e. the online prediction of chaotic Mackey-Glass time-series, is considered. The simulation results indicate that the online wavelet SVR algorithm outperforms the existing algorithms in higher efficiency of learning as well as better accuracy of prediction.