Active optical clock based on four-level quantum system

Abstract

Active optical clock, a new conception of atomic clock, has been proposed recently. In this work, we propose a scheme of active optical clock based on four-level quantum system. The final accuracy and stability of two-level quantum system are limited by second-order Doppler shift of thermal atomic beam. To three-level quantum system, they are mainly limited by light shift of pumping laser field. These limitations can be avoided effectively by applying the scheme proposed here. Rubidium atom four-level quantum system, as a typical example, is discussed. The population inversion between 6S 1/2 and 5P 3/2 states can be built up at a time scale of 10 −6 s. With the mechanism of active optical clock, in which the cavity mode linewidth is much wider than that of the laser gain profile, it can output a laser with quantum-limited linewidth narrower than 1 Hz in theory. An experimental configuration is designed to realize this active optical clock. Optical clocks have demonstrated great improvements in stability and accuracy over the microwave frequency standards. Since the proposal of active optical clock [1-3], a number of neutral atoms with two-level, three-level and four-level at thermal beam, laser cooling and trapping configurations have been investigated recently [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. The potential quantumlimited linewidth of active optical clock is narrower than mHz, and it is possible to reach this unprecedented linewidth since the thermal noise of cavity mode can be reduced dramatically with the mechanism of active optical clock. It has been recognized that active optical clock has the potential to improve the stability of the best atomic clocks by about 2 orders of magnitude [9,10,15].Until now, the major experimental schemes of active optical clock are based on trapped quantum system and atomic beam quantum system. To the latter, the residual Doppler shift will be the main limitation, thus the final accuracy and stability of two-level quantum system are limited by second-order Doppler shift of thermal atomic beam. Laser *Corresponding author (email: ztg@pku.edu.cn) cooled and trapped quantum system provides a solution to this limitation. As for three-level quantum system, the system stability and accuracy are mainly affected by the light shift of pumping laser. Four-level quantum system can overcome these limitations and thus will be a better choice for active optical clock with improved performance [6].Rubidium, as one of alkali metals, has been investigated as the critical research atom of Bose-Einstein condensate, photonic Josephson effect, fractionalized vortices in lattice due to the mature technique of laser cooling and trapping [16][17][18].We have investigated several alkali metals including potassium, rubidium and cesium and found that the four-level quantum systems of these elements are appropriate choices based on the mechanism of active optical clock. Here we take rubidium atom as an example. The population inversion can be realized as shown in Figure 1.A 421.7 nm las...

Realization of phase locking in good-bad-cavity active optical clock

“…Therefore, the laser frequency of the AOC will not follow the fluctuations of the cavity length exactly, but in a form of the suppressed cavity-pulling effect, and the extent of the suppression equals the bad-cavity coefficient a, where a = Γ cavity Γ gain . Since it was proposed, various types of active atomic systems have been investigated [20][21][22][23][24][25][26][27]. Recently, a superradiant pulse from the strontium clock transition with a fractional Allan deviation of 6.7(1) × 10 −16 at 1 s has been realized [27].…”

Atomic optical stimulated amplifier with optical filtering of ultra-narrow bandwidth

“…Analogous to ref. 44 , for Cs atoms we have with Γ 23 , Γ 24 , Γ 35 , Γ 36 , Γ 51 corresponding to the relaxation rates of transitions 7 P 1/2 − 7 S 1/2 , 7 P 1/2 − 5 D 3/2 , 7 S 1/2 − 6 P 3/2 , 7 S 1/2 − 6 P 1/2 , and 6 P 1/2 − 6 S 1/2 , respectively. Some of the energy levels are not displayed in Fig.…”

Stabilizing diode laser to 1 Hz-level Allan deviation with atomic spectroscopy for Rb four-level active optical frequency standard

“…The ultra-stable 420 nm laser is used as a pump source, which pumps Rb atoms from 5S 1∕2 state to 6P 3∕2 state. The atoms will decay to the 6S 1∕2 state from 6P 3∕2 state, and the population inversion between 6S 1∕2 state and 5P 3∕2 state will occur owing to the longer lifetime of the 6S 1∕2 state [37][38][39]57]. Under the effect of the bad cavity [50], the 1367 nm active optical signal output will be realized.…”