Characterization of a DFG comb showing quadratic scaling of the phase noise with frequency

End-to-end topology for fiber comb based optical frequency transfer at the 10-21 level

We introduce a simple and robust scheme for optical frequency transfer of an ultra-stable source light field via an optical frequency comb to a field at a target optical frequency, where highest stability is required, e.g., for the interrogation of an optical clock. The scheme relies on a topology for end-to-end suppression of the influence of optical path-length fluctuations, which is attained by actively phase-stabilized delivery, combined with common-path propagation. This approach provides a robust stability improvement without the need for additional isolation against environmental disturbances such as temperature, pressure or humidity changes. We measure residual frequency transfer instabilities by comparing the frequency transfers carried out with two independent combs simultaneously. Residual fractional frequency instabilities between two systems of 8 × 10^-18 at 1 s and 3 × 10^-21 at 10⁵ s averaging time are observed. We discuss the individual noise contributions to the residual instability. The presented scheme is technically simple, robust against environmental parameter fluctuations and enables an ultra-stable frequency transfer, e.g., to optical clock lasers or to lasers in gravitational wave detectors.

Deterministic Nonlinear Transformations of Phase Noise in Quantum-Limited Frequency Combs

Optical phase noise of femtosecond lasers is analyzed over various steps of broadband nonlinear frequency conversion. The intrinsic phase jitter of our system originates from quantum statistics in the mode-locked oscillator. Supercontinuum generation by four-wave-mixing processes preserves a noise minimum at the optical carrier frequency. From there, a quadratic increase of the comb linewidth results with mutually anticorrelated phase fluctuations of both spectral wings. Passive phase locking by difference frequency generation strongly enhances the optical phase noise to a level equaling the carrier-envelope phase jitter of the fundamental comb. The same value results from quadratic extrapolation of the optical phase noise to radio frequencies. Our findings are consistent with a fully deterministic transformation of phase noise according to the elastic tape model.

Phase transfer between three visible lasers for coherent population trapping

Stringent conditions on the phase relation of multiple photons are a prerequisite for novel protocols of high-resolution coherent spectroscopy. In a recent experiment, we have implemented an interrogation process of a Ca⁺-ion cloud based on three-photon coherent population trapping, with the potential to serve as a frequency reference in the THz range. This high-resolution interrogation has been made possible by phase-locking both laser sources for cooling and repumping of the trapped ions to a clock laser at 729 nm by means of an optical frequency comb. The clock laser, a titanium-sapphire laser built in our lab locked onto two high-finesse cavities reaches a linewidth of a few Hertz and a frequency stability below 10^-14 at 1 s, performances which can be copied onto the two other sources. In this paper, we discuss the performances of the phase transfer between the three involved lasers via the optical frequency comb.

Ultrabroadband out-of-loop characterization of the carrier-envelope phase noise of an offset-free Er:fiber frequency comb

Recent demonstrations of passively phase-locked fiber-based combs motivate broadband characterization of the noise associated with the stabilized carrier-envelope offset frequency. In our study, we analyze the phase noise of a 100 MHz Er:fiber system in a wide range spanning from microhertz to the Nyquist frequency. An interferometric detection method enables analysis of the high-frequency output of an f-to-2f interferometer. The dominant contribution of a broadband white noise floor at high frequencies attests quantum-limited performance. An out-of-loop measurement of the carrier-envelope phase reveals its jitter to be as low as 250 mrad when integrated over 12 orders of magnitude of the radio-frequency spectrum.

Optical Stabilization of a Microwave Oscillator for Fountain Clock Interrogation

We describe an optical frequency stabilization scheme of a microwave oscillator that is used for the interrogation of primary cesium fountain clocks. Because of its superior phase noise properties, this scheme, which is based on an ultrastable laser and a femtosecond laser frequency comb, overcomes the frequency instability limitations of fountain clocks given by the previously utilized quartz-oscillator-based frequency synthesis. The presented scheme combines the transfer of the short-term frequency instability of an optical cavity and the long-term frequency instability of a hydrogen maser to the microwave oscillator and is designed to provide continuous long-term operation for extended measurement periods of several weeks. The utilization of the twofold stabilization scheme on the one hand ensures the referencing of the fountain frequency to the hydrogen maser frequency and on the other hand results in a phase noise level of the fountain interrogation signal, which enables fountain frequency instabilities at the 2.5 ×10^-14 (τ/s)^-1/2 level that are quantum projection noise limited.

Enhancement of the performance of a fiber-based frequency comb by referencing to an acetylene-stabilized fiber laser

We demonstrate a significant improvement in the performance of a fiber-based frequency comb when a GPS-disciplined Rb clock is replaced with an acetylene-stabilized laser as the frequency reference. We have developed a compact, maintenance-free acetylene-stabilized fiber laser with a sub-kHz short-term linewidth and an Allan deviation below 3×10^-13 for integration times above 1 s. Switching the comb reference from the Rb clock to the acetylene-stabilized laser improves both comb tooth linewidth and Allan deviation by about two orders of magnitude. Furthermore, long-term measurements of the acetylene-stabilized laser frequency with reference to the GPS-disciplined clock indicate a potential relative frequency uncertainty of 2 × 10^-12.