Compact and ultrastable photonic microwave oscillator.

Frequency comb synthesized microwaves have been so far realized with tabletop systems, operated in well-controlled environments. Here, we demonstrate state-of-the-art ultrastable microwave synthesis with a compact rack-mountable apparatus. We present absolute phase noise characterization of a 12 GHz signal using an ultrastable laser at $\sim{194}\;{\rm THz}$∼194THz and an Er:fiber comb divider, obtaining $ - {83}\;{\rm dBc/Hz}$-83dBc/Hz at 1 Hz and $ \lt - {166}\;{\rm dBc/Hz}$<-166dBc/Hz for offsets greater than 5 kHz. Employing semiconductor coating mirrors for the same type of transportable optical frequency reference, we show that $ - {105}\;{\rm dBc/Hz}$-105dBc/Hz at 1 Hz is supported by demonstrating a residual noise limit of division and detection process of $ - {115}\;{\rm dBc/Hz}$-115dBc/Hz at 1 Hz. This level of fidelity paves the way for the deployment of ultrastable photonic microwave oscillators and for operating transportable optical clocks.

Accurate control of optoelectronic amplitude to phase noise conversion in photodetection of ultra-fast optical pulses.

When illuminating a photodiode with modulated laser light, optical intensity fluctuations of the incident beam are converted into phase fluctuations of the output electrical signal. This amplitude to phase noise conversion (APC) thus imposes a stringent constraint on the relative intensity noise (RIN) of the laser carrier when dealing with ultra-low phase noise microwave generation. Although the APC vanishes under certain conditions, it exhibits random fluctuations preventing efficient long-term passive stabilization schemes. In this paper, we present a digital coherent modulation-demodulation system for automatic measurement and control of the APC of a photodetector. The system is demonstrated in the detection of ultra-short optical pulses with an InGaAs photodetector and enables stable generation of ultra-low phase noise microwave signals with RIN rejection beyond 50 dB. This simple system can be used in various optoelectronic schemes, making photodetection virtually insensitive to the RIN of the lasers. We utilize this system to investigate the impact of the radiofrequency (RF) transmission line at the output of the photodetector on the APC coefficient that can affect the accuracy of the measurement in certain cases.

Phase noise characterization of sub-hertz linewidth lasers via digital cross correlation.

Phase noise or frequency noise is a key metric to evaluate the short-term stability of a laser. This property is of great interest for the applications but delicate to characterize, especially for narrow linewidth lasers. In this Letter, we demonstrate a digital cross-correlation scheme to characterize the absolute phase noise of sub-hertz linewidth lasers. Three 1542 nm ultra-stable lasers are used in this approach. For each measurement, two lasers act as references to characterize a third one. Phase noise power spectral density from 0.5 Hz to 0.8 MHz Fourier frequencies can be derived for each laser by a mere change in the configuration of the lasers. To the best of our knowledge, this is the first time showing the phase noise of sub-hertz linewidth lasers with no reference limitation. We also present an analysis of the laser phase noise performance.

Dual photo-detector system for low phase noise microwave generation with femtosecond lasers.

Low phase noise microwave signals can be generated by photo-detecting the pulse train of an optical frequency comb locked to a high spectral purity continuous-wave optical reference. Amplitude-to-phase noise conversion is, however, a well-known limitation to this technique. Great care is usually required to overcome this constraint due to its strong dependence on the impinging optical power. Here we demonstrate the combined use of "magic point" operating conditions of photodetectors, pulse repetition rate multipliers, and coherent addition of microwave signals to realize a microwave extraction device largely immune to amplitude-to-phase conversion effects over a large range of impinging optical powers.

Characterizing a fiber-based frequency comb with electro-optic modulator.

We report on the characterization of a commercial- core fiber-based frequency comb equipped with an intracavity free-space electro-optic modulator (EOM). We investigate the relationship between the noise of the pump diode and the laser relative intensity noise (RIN) and demonstrate the use of a low-noise current supply to substantially reduce the laser RIN. By measuring several critical transfer functions, we evaluate the potential of the EOM for comb repetition rate stabilization. We also evaluate the coupling to other relevant parameters of the comb. From these measurements, we infer the capabilities of the femtosecond laser comb to generate very-low-phase-noise microwave signals when phase-locked to a high-spectral-purity ultra-stable laser.

Advanced noise reduction techniques for ultra-low phase noise optical-to-microwave division with femtosecond fiber combs.

We report what we believe to be the lowest phase noise optical-to-microwave frequency division using fiber-based femtosecond optical frequency combs: a residual phase noise of -120 dBc/Hz at 1 Hz offset from an 11.55 GHz carrier frequency. Furthermore, we report a detailed investigation into the fundamental noise sources which affect the division process itself. Two frequency combs with quasi-identical configurations are referenced to a common ultrastable cavity laser source. To identify each of the limiting effects, we implement an ultra-low noise carrier-suppression measurement system, which avoids the detection and amplification noise of more conventional techniques. This technique suppresses these unwanted sources of noise to very low levels. In the Fourier frequency range of ∼200 Hz to 100 kHz, a feed-forward technique based on a voltage-controlled phase shifter delivers a further noise reduction of 10 dB. For lower Fourier frequencies, optical power stabilization is implemented to reduce the relative intensity noise which causes unwanted phase noise through power-to-phase conversion in the detector. We implement and compare two possible control schemes based on an acousto-optical modulator and comb pump current. We also present wideband measurements of the relative intensity noise of the fiber comb.

Accuracy evaluation of an optical lattice clock with bosonic atoms.

We report what we believe to be the first accuracy evaluation of an optical lattice clock based on the S01-->P03 transition of an alkaline earth boson, namely, Sr88 atoms. This transition has been enabled by using a static coupling magnetic field. The clock frequency is determined to be 429228066418009(32)Hz. The isotopic shift between Sr87 and Sr88 is 62188135Hz with fractional uncertainty 5x10(-7). We discuss the necessary conditions to reach a clock accuracy of 10(-17) or less by using this scheme.