Four-level Active Optical Clock Research Articles

Antiresonant Fabry-Pérot cavity with ultralow finesse

The exact expressions of finesse and full width at half maximum (FWHM) of the Airy distribution of a Fabry-P\'erot (FP) resonator are derived, which solves the breakdown problem at ultralow reflectivity in traditional formulas. We demonstrate that, when the cavity-mirror reflectivity $R\ensuremath{\rightarrow}0$, the FWHM approaches half of the free spectral range rather than infinity; moreover, the cavity finesse $\mathcal{F}$ approaches 2 rather than zero. These expressions are useful for the development of bad-cavity lasers, such as the four-level active optical clock based on the strong atomic transition of cesium. Also, the exact expressions of the FWHM and finesse of the reflection distribution composed of reflected mode profiles are derived, which separately intersect with that of the Airy one at $R=0$. In addition, the characteristics of an antiresonant cavity, the frequency of which is exactly at the center of two adjacent resonant cavity modes, are analyzed. It is demonstrated that at the resonant and antiresonant frequencies the enhancement and inhibition of intracavity light intensity caused by the FP cavity are symmetrical in the logarithmic view. Furthermore, we provide a universal expression of the cavity-enhancement factor rather than the classical representation of ``$\text{2}\mathcal{F}/\phantom{\text{2}\mathcal{F}\ensuremath{\pi}}\phantom{\rule{0.0pt}{0ex}}\ensuremath{\pi}$,'' which is inadequate for the high-loss cavity because the cavity-enhancement factor should naturally reach 1 when $R\ensuremath{\rightarrow}0$. Finally, we extend the application of the antiresonant cavity to an inhibited laser, the frequency of which has a stronger suppression effect on the cavity-length thermal noise than the traditional resonant laser.

Cs 728 nm Laser Spectroscopy and Faraday Atomic Filter

We mainly present the 728 nm laser spectroscopy and Faraday atomic filter of Cs atoms with 650 MHz linewidth and 2.6% transmission based on an electrodeless discharge vapor lamp, compared with Rb 728 nm laser spectroscopy. Accidentally, this remarkably strong Cs 728 nm transition from the 6F7/2 state to the 5D5/2 state is only about 2.5 GHz away from the Rb 728 nm transition of the future potential four-level active optical clock, once laser cooled and trapped from the 7S1/2 state to the 5P1/2 state, as we proposed previously. A Faraday atomic filter stabilized 728 nm laser using a Cs electrodeless discharge vapor lamp with a power of 10mW will provide a frequency reference to evaluate the performance of the potential Rb four-level active optical clock at 728 nm with power less than 1 nW by 2.5 GHz heterodyne measurements.

Laser 728 nm Spectroscopy of Electrodeless Discharge Rb Lamp

We mainly report the 728.0 nm transition between 7S1/2 and 5P1/2 laser spectroscopy of an electrodeless discharge Rb vapor lamp, which is the clock transition of a potential four-level active optical clock, once laser cooled and trapped Rb atoms are pumped by 359.2 nm laser. To realize this proposition, we study the linewidth and absorption characteristics of the 728.0 nm laser absorption spectrum of a rubidium electrodeless discharge vapor lamp with varying lamp temperature and rf driving power respectively, measured by an external cavity diode laser in a Littrow configuration. The measured 728.0 nm spectrum of a glass cell filled with Rb and Ar buffer gases in the electrodeless discharge Rb lamp based Faraday filter stabilized laser can be a heterodyne comparison reference for the weak power output of a possible cold Rb four-level active optical clock at 728.0 nm clock transition with laser cooled and trapped atoms. To the best of our knowledge, there has not been any research reported on Rb 728.0 nm laser spectroscopy in detail.

Realization of population inversion between 7S1/2 and 6P3/2 levels of cesium for four-level active optical clock

We demonstrate experimentally the population inversion between 7S1/2 and 6P3/2 levels of cesium in thermal cesium cell with a 455.5 nm pumping laser. We calculate the relative population probabilities at each level theoretically with the density matrix method. In a steady state, 5.8% atoms are at 7S1/2 level and 2.9% at 6P3/2 level, which builds up the population inversion between the two levels. We obtain the fluorescence spectra produced in thermal cesium cell in our experiment. The measured relative intensity of each available fluorescence spectral line in the experiment agrees very well with the theoretical result. The demonstrated population inversion between 7S1/2 and 6P3/2 levels can be used to construct an active optical clock of four-level system with a wavelength of 1469.9 nm.

Magic Wavelengths for a Lattice Trapped Rubidium Four-Level Active Optical Clock

After being pumped from the 5s1/2 ground state to the 6p1/2 state, the population inversion between 6s1/2 and 5p1/2,3/2 can be established for a rubidium four-level active optical clock. We calculate the ac Stark shift due to lattice trapping laser which dominates the frequency shift of clock transition in a lattice trapped rubidium four-level active optical clock. Several magic wavelengths are found, which can form desired optical lattice trapping potential. By choosing a proper intensity and linewidth of the trapping laser, the fractional frequency uncertainty of clock transition due to the ac Stark shift of the trapping laser, is estimated to be below 10−18.