Long-Term Stability Analysis Toward <10-14 Level for a Highly Compact POP Rb Cell Atomic Clock.

Long-term frequency instabilities in vapor-cell clocks mainly arise from fluctuations of the experimental and environmental parameters that are converted to clock frequency fluctuations via various physical processes. Here, we discuss the frequency sensitivities and the resulting stability limitations at one-day timescale for a rubidium vapor-cell clock based on a compact magnetron-type cavity operated in air (no vacuum environment). Under ambient laboratory conditions, the external atmospheric pressure fluctuations may dominantly limit the clock stability via the barometric effect. We establish a complete long-term instability budget for our clock operated under stable pressure conditions. Where possible, the fluctuations of experimental parameters are measured via the atomic response. The measured clock instability of at one day is limited by the intensity light-shift effect, which could further be reduced by active stabilization of the laser intensity or stronger optical pumping. The analyses reported here show the way toward simple, compact, and low-power vapor-cell atomic clocks with excellent long-term stabilities ≤ 10-14 at one day when operated in ambient laboratory conditions.

Barometric Effect in Vapor-Cell Atomic Clocks.

Vapor-cell atomic clocks are compact and high-performance frequency references employed in various applications ranging from telecommunication to global positioning systems. Environmental sensitivities are often the main sources of long-term instabilities of the clock frequency. Among these sensitivities, the environmental pressure shift describes the clock frequency change with respect to the environmental pressure variations. We report here on our theoretical and experimental analysis of the environmental pressure shift on rubidium atomic frequency standards (RAFSs) operated under open atmosphere. By using an unsealed high-performance laser-pumped rubidium standard, we demonstrate that the deformation of the vapor-cell volume induced by the environmental pressure changes (i.e., barometric effect) is the dominant environmental pressure shift in a standard laboratory environment. An experimental barometric coefficient of /hPa is derived, in good agreement with theory and with previously reported measurements of frequency shifts of RAFS operated when transiting to vacuum.

Characterization of Frequency-Doubled 1.5- m Lasers for High-Performance Rb Clocks.

We report on the characterization of two fiber-coupled 1.5- diode lasers, frequency-doubled and stabilized to Rubidium (Rb) atomic resonances at 780 nm. Such laser systems are of interest in view of their implementation in Rb vapor-cell atomic clocks, as an alternative to lasers emitting directly at 780 nm. The spectral properties and the instabilities of the frequency-doubled lasers are evaluated against a state-of-the-art compact Rb-stabilized laser system based on a distributed-feedback laser diode emitting at 780 nm. All three lasers are frequency stabilized using essentially identical Doppler-free spectroscopy schemes. The long-term optical power fluctuations at 780 nm are measured, simultaneously with the frequency instability measurements done by three beat notes established between the three lasers. One of the frequency-doubled laser systems shows at 780 nm excellent spectral properties. Its relative intensity noise <10-12 Hz-1 is one order of magnitude lower than the reference 780-nm laser, and the frequency noise <106 Hz2/Hz is limited by the laser current source. Its optical frequency instability is at s, limited by the reference laser, and better than at all timescales up to one day. We also evaluate the impact of the laser spectral properties and instabilities on the Rb atomic clock performance, in particular taking into account the light-shift effect. Optical power instabilities on long-term timescales, largely originating from the frequency-doubling stage, are identified as a limitation in view of high-performance Rb atomic clocks.

Rb vapor-cell clock demonstration with a frequency-doubled telecom laser.

We employ a recently developed laser system, based on a low-noise telecom laser emitting around 1.56 µm, to evaluate its impact on the performance of an Rb vapor-cell clock in a continuous-wave double-resonance scheme. The achieved short-term clock instability below 2.5·10-13·τ-1/2 demonstrates, for the first time, the suitability of a frequency-doubled telecom laser for this specific application. We measure and study quantitatively the impact of laser amplitude and frequency noises and of the ac Stark shift, which limit the clock frequency stability on short timescales. We also report on the detailed noise budgets and demonstrate experimentally that, under certain conditions, the short-term stability of the clock operated with the low-noise telecom laser is improved by a factor of three compared to clock operation using the direct 780-nm laser.

Self-induced transparency and coherent population trapping of 87Rb vapor in a mode-locked laser.

Simultaneous self-induced transparency and a dark line resonance are observed inside a mode-locked laser. The circulating pulse, tuned to the 795-nm optical resonance of rubidium, has sufficient intensity to create at each passage a population inversion-return to ground state, typical of self-induced transparency. A drop in fluorescence (dark line resonance), is observed as the repetition rate is tuned to a submultiple of the hyperfine ground-state splitting.

Compact high-performance continuous-wave double-resonance rubidium standard with 1.4 × 10(-13) τ(-1/2) stability.

We present our studies on a compact high-performance continuous wave (CW) double-resonance (DR) rubidium frequency standard in view of future portable applications. Our clock exhibits a short-term stability of 1.4 × 10(-13) τ(-1/2), consistent with the short-term noise budget for an optimized DR signal. The metrological studies on the medium- to longterm stability of our Rb standard with measured stabilities are presented. The dependence of microwave power shift on light intensity, and the possibility to suppress the microwave power shift is demonstrated. The instabilities arising from the vapor cell geometric effect are evaluated, and are found to act on two different time scales (fast and slow stem effects). The resulting medium- to long-term stability limit is around 5.5 × 10(-14). Further required improvements, particularly focusing on medium- to long-term clock performance, are discussed.

Compact microwave cavity for high performance rubidium frequency standards.

The design, realization, and characterization of a compact magnetron-type microwave cavity operating with a TE(011)-like mode are presented. The resonator works at the rubidium hyperfine ground-state frequency (i.e., 6.835 GHz) by accommodating a glass cell of 25 mm diameter containing rubidium vapor. Its design analysis demonstrates the limitation of the loop-gap resonator lumped model when targeting such a large cell, thus numerical optimization was done to obtain the required performances. Microwave characterization of the realized prototype confirmed the expected working behavior. Double-resonance and Zeeman spectroscopy performed with this cavity indicated an excellent microwave magnetic field homogeneity: the performance validation of the cavity was done by achieving an excellent short-term clock stability as low as 2.4 × 10(-13) τ(-1/2). The achieved experimental results and the compact design make this resonator suitable for applications in portable atomic high-performance frequency standards for both terrestrial and space applications.

Microfabricated chip-scale rubidium plasma light source for miniature atomic clocks.

We present the microfabrication and characterization of a low-power, chip-scale Rb plasma light source, designed for optical pumping in miniature atomic clocks. A dielectric barrier discharge (DBD) configuration is used to ignite a Rb plasma in a micro-fabricated Rb vapor cell on which external indium electrodes were deposited. The device is electrically driven at frequencies between 1 and 36 MHz, and emits 140 µW of stable optical power while coupling less than 6 mW of electrical power to the discharge cell. Optical powers of up to 15 and 9 µW are emitted on the Rb D2 and D1 lines, respectively. Continuous operation of the light source for several weeks has been demonstrated, showing its capacity to maintain stable optical excitation of Rb atoms in chip-scale double-resonance atomic clocks.

Pulsed optically pumped rubidium clock with high frequency-stability performance.

In this paper, we present the performance of a vapor-cell rubidium frequency standard working in the pulsed regime, in which the clock signal is represented by a Ramsey pattern observed on an optically detected laser absorption signal. The main experimental results agree with previously reported theoretical predictions. In particular, we measured a relative frequency stability of σy(τ) - 1.6 × 10(-13)τ-1/2 for integration times, τ, up to 200 s, which represents a record in short-term stability for a vapor-cell clock. We also discuss the most important physical phenomena that contribute to this result.

Methods and evaluation of frequency aging in distributed-feedback laser diodes for rubidium atomic clocks.

Distributed-feedback laser diodes emitting at 780 nm have been evaluated, with respect to the aging of the injection current required for reaching the rubidium D2 resonance line. Results obtained for lasers operating in air and in vacuum for 9 months are reported. When operated at constant temperature, the laser current required for emission at the wavelength of the desired atomic resonance is found to decrease by 50 to 80 µA per month. The impact of this result on the lifetime and long-term performances of laser-pumped rubidium atomic clocks is discussed.

Laser offset-frequency locking up to 20 GHz using a low-frequency electrical filter technique.

A simple, easy-to-implement, and robust technique is reported to offset lock two semiconductor lasers with a frequency difference easily adjustable up to a couple of tens of gigahertz (10 and 19 GHz experimentally demonstrated). The proposed scheme essentially makes use of low-frequency control electronics and may be implemented with any type of single mode semiconductor laser, without any requirement for the laser linewidth. The technique is shown to be very similar to the wavelength modulation spectroscopy method commonly used for laser stabilization onto molecular absorption lines, as demonstrated by experimental results obtained using 935 nm laser diodes.