High-performance, compact optical standard.

We describe a high-performance, compact optical frequency standard based on a microfabricated Rb vapor cell and a low-noise, external cavity diode laser operating on the Rb two-photon transition at 778 nm. The optical standard achieves an instability of 1.8×10-13τ-1/2 for times less than 100 s and a flicker noise floor of 1×10-14 out to 6000 s. At long integration times, the instability is limited by variations in optical probe power and the ac Stark shift. The retrace was measured to 5.7×10-13 after 30 h of dormancy. Such a simple, yet high-performance optical standard could be suitable as an accurate realization of the meter or, if coupled with an optical frequency comb, as a compact atomic clock comparable to a hydrogen maser.

Coherent optical clock down-conversion for microwave frequencies with 10-18 instability.

Optical atomic clocks are poised to redefine the Système International (SI) second, thanks to stability and accuracy more than 100 times better than the current microwave atomic clock standard. However, the best optical clocks have not seen their performance transferred to the electronic domain, where radar, navigation, communications, and fundamental research rely on less stable microwave sources. By comparing two independent optical-to-electronic signal generators, we demonstrate a 10-gigahertz microwave signal with phase that exactly tracks that of the optical clock phase from which it is derived, yielding an absolute fractional frequency instability of 1 × 10-18 in the electronic domain. Such faithful reproduction of the optical clock phase expands the opportunities for optical clocks both technologically and scientifically for time dissemination, navigation, and long-baseline interferometric imaging.

Demonstration of a Timescale Based on a Stable Optical Carrier.

We report on the first timescale based entirely on optical technology. Existing timescales, including those incorporating optical frequency standards, rely exclusively on microwave local oscillators owing to the lack of an optical oscillator with the required frequency predictability and stability for reliable steering. We combine a cryogenic silicon cavity exhibiting improved long-term stability and an accurate ^{87}Sr lattice clock to form a timescale that outperforms them all. Our timescale accumulates an estimated time error of only 48±94 ps over 34 days of operation. Our analysis indicates that this timescale is capable of reaching a stability below 1×10^{-17} after a few months of averaging, making timekeeping at the 10^{-18} level a realistic prospect.

Ramsey-Bordé Matter-Wave Interferometry for Laser Frequency Stabilization at 10

We demonstrate Ramsey-Bordé (RB) atom interferometry for high performance laser stabilization with fractional frequency instability <2×10^{-16} for timescales between 10 and 1000s. The RB spectroscopy laser interrogates two counterpropagating ^{40}Ca beams on the ^{1}S_{0}-^{3}P_{1} transition at 657 nm, yielding 1.6 kHz linewidth interference fringes. Fluorescence detection of the excited state population is performed on the (4s4p) ^{3}P_{1}-(4p^{2}) ^{3}P_{0} transition at 431 nm. Minimal thermal shielding and no vibration isolation are used. These stability results surpass performance from other thermal atomic or molecular systems by 1 to 2 orders of magnitude, and further improvements look feasible.

Optical-Clock-Based Time Scale.

A time scale is a procedure for accurately and continuously marking the passage of time. It is exemplified by Coordinated Universal Time (UTC) and provides the backbone for critical navigation tools such as the Global Positioning System. Present time scales employ microwave atomic clocks, whose attributes can be combined and averaged in a manner such that the composite is more stable, accurate, and reliable than the output of any individual clock. Over the past decade, clocks operating at optical frequencies have been introduced that are orders of magnitude more stable than any microwave clock. However, in spite of their great potential, these optical clocks cannot be operated continuously, which makes their use in a time scale problematic. We report the development of a hybrid microwave-optical time scale, which only requires the optical clock to run intermittently while relying upon the ensemble of microwave clocks to serve as the flywheel oscillator. The benefit of using a clock ensemble as the flywheel oscillator instead of a single clock can be understood by the Dick-effect limit. This time scale demonstrates for the first time subnanosecond accuracy over a few months, attaining a fractional frequency stability of 1.45 × 10-16 at 30 days and reaching the 10-17 decade at 50 days, with respect to UTC. This time scale significantly improves the accuracy in timekeeping and could change the existing time-scale architectures.

Microresonator Brillouin laser stabilization using a microfabricated rubidium cell.

We frequency stabilize the output of a miniature stimulated Brillouin scattering (SBS) laser to rubidium atoms in a microfabricated cell to realize a laser system with frequency stability at the 10-11 level over seven decades in averaging time. In addition, our system has the advantages of robustness, low cost and the potential for integration that would lead to still further miniaturization. The SBS laser operating at 1560 nm exhibits a spectral linewidth of 820 Hz, but its frequency drifts over a few MHz on the 1 hour timescale. By locking the second harmonic of the SBS laser to the Rb reference, we reduce this drift by a factor of 103 to the level of a few kHz over the course of an hour. For our combined SBS and Rb laser system, we measure a frequency noise of 4 × 104 Hz2/Hz at 10 Hz offset frequency which rapidly rolls off to a level of 0.2 Hz2/Hz at 100 kHz offset. The corresponding Allan deviation is ≤2 × 10-11 for averaging times spanning 10-4 to 103 s. By optically dividing the signal of the laser down to microwave frequencies, we generate an RF signal at 2 GHz with phase noise at the level of -76 dBc/Hz and -140 dBc/Hz at offset frequencies of 10 Hz and 10 kHz, respectively.

Broadband noise limit in the photodetection of ultralow jitter optical pulses.

Applications with optical atomic clocks and precision timing often require the transfer of optical frequency references to the electrical domain with extremely high fidelity. Here we examine the impact of photocarrier scattering and distributed absorption on the photocurrent noise of high-speed photodiodes when detecting ultralow jitter optical pulses. Despite its small contribution to the total photocurrent, this excess noise can determine the phase noise and timing jitter of microwave signals generated by detecting ultrashort optical pulses. A Monte Carlo simulation of the photodetection process is used to quantitatively estimate the excess noise. Simulated phase noise on the 10 GHz harmonic of a photodetected pulse train shows good agreement with previous experimental data, leading to the conclusion that the lowest phase noise photonically generated microwave signals are limited by photocarrier scattering well above the quantum limit of the optical pulse train.

Optical amplification and pulse interleaving for low-noise photonic microwave generation.

We investigate the impact of pulse interleaving and optical amplification on the spectral purity of microwave signals generated by photodetecting the pulsed output of an Er:fiber-based optical frequency comb. It is shown that the microwave phase noise floor can be extremely sensitive to delay length errors in the interleaver, and the contribution of the quantum noise from optical amplification to the phase noise can be reduced ∼10 dB for short pulse detection. We exploit optical amplification, in conjunction with high power handling modified unitraveling carrier photodetectors, to generate a phase noise floor on a 10 GHz carrier of -175 dBc/Hz, the lowest ever demonstrated in the photodetection of a mode-locked fiber laser. At all offset frequencies, the photodetected 10 GHz phase noise performance is comparable to or better than the lowest phase noise results yet demonstrated with stabilized Ti:sapphire frequency combs.

Photonic microwave generation with high-power photodiodes.

We utilized and characterized high-power, high-linearity modified unitraveling carrier (MUTC) photodiodes for low-phase-noise photonic microwave generation based on optical frequency division (OFD). When illuminated with picosecond pulses from a repetition-rate-multiplied gigahertz Ti:sapphire modelocked laser, the photodiodes can achieve a 10 GHz signal power of +14 dBm. Using these diodes, we generated a 10 GHz microwave tone with less than 500 attoseconds absolute integrated timing jitter (1 Hz-10 MHz) and a phase noise floor of -177 dBc/Hz.We also characterized the electrical response, amplitude-to-phase conversion, saturation, and residual noise of the MUTC photodiodes.

State-of-the-art RF signal generation from optical frequency division.

We present the design of a novel, ultralow-phase-noise frequency synthesizer implemented with extremely-low-noise regenerative frequency dividers. This synthesizer generates eight outputs, viz. 1.6 GHz, 320 MHz, 160 MHz, 80 MHz, 40 MHz, 20 MHz, 10 MHz and 5 MHz for an 8 GHz input frequency. The residual single-sideband (SSB) phase noises of the synthesizer at 5 and 10 MHz outputs at 1 Hz offset from the carrier are -150 and -145 dBc/Hz, respectively, which are unprecedented phase noise levels. We also report the lowest values of phase noise to date for 5 and 10 MHz RF signals achieved with our synthesizer by dividing an 8 GHz signal generated from an ultra-stable optical-comb-based frequency division. The absolute SSB phase noises achieved for 5 and 10 MHz signals at 1 Hz offset are -150 and -143 dBc/Hz, respectively; at 100 kHz offset, they are -177 and -174 dBc/Hz, respectively. The phase noise of the 5 MHz signal corresponds to a frequency stability of approximately 7.6 × 10(-15) at 1 s averaging time for a measurement bandwidth (BW) of 500 Hz, and the integrated timing jitter over 100 kHz BW is 20 fs.

Absolute and relative stability of an optical frequency reference based on spectral hole burning in Eu3+:Y2SiO5.

We present and analyze four frequency measurements designed to characterize the performance of an optical frequency reference based on spectral hole burning in Eu3+:Y2SiO5. The first frequency comparison, between a single unperturbed spectral hole and a hydrogen maser, demonstrates a fractional frequency drift rate of 5×10(-18) s(-1). Optical frequency comparisons between a pattern of spectral holes, a Fabry-Pérot cavity, and an Al(+) optical atomic clock show a short-term fractional frequency stability of 1×10(-15)τ(-1/2) that averages down to 2.5(-0.5)(+1.1)×10(-16) at τ=540 s (with linear frequency drift removed). Finally, spectral-hole patterns in two different Eu(3+):Y2SiO(5) crystals located in the same cryogenic vessel are compared, yielding a short-term stability of 7×10(-16)τ(-1/2) that averages down to 5.5(-0.9)(+1.8)×10(-17) at τ=204 s (with quadratic frequency drift removed).

Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider.

We present an optical frequency divider based on a 200 MHz repetition rate Er:fiber mode-locked laser that, when locked to a stable optical frequency reference, generates microwave signals with absolute phase noise that is equal to or better than cryogenic microwave oscillators. At 1 Hz offset from a 10 GHz carrier, the phase noise is below -100 dBc/Hz, limited by the optical reference. For offset frequencies >10 kHz, the phase noise is shot noise limited at -145 dBc/Hz. An analysis of the contribution of the residual noise from the Er:fiber optical frequency divider is also presented.

Measurement and real-time cancellation of vibration-induced phase noise in a cavity-stabilized laser.

We demonstrate a method to measure and actively reduce the coupling of vibrations to the phase noise of a cavity-stabilized laser. This method uses the vibration noise of the laboratory environment rather than active drive to perturb the optical cavity. The laser phase noise is measured via a beat note with a second unperturbed ultra-stable laser while the vibrations are measured by accelerometers positioned around the cavity. A Wiener filter algorithm extracts the frequency and direction dependence of the cavity response function. Once the cavity response function is known, real-time noise cancellation can be implemented by use of the accelerometer measurements to predict and then cancel the laser phase fluctuations. We present real-time noise cancellation that results in a 25 dB reduction of the laser phase noise power spectral density.

Control of the frequency comb from a modelocked Erbium-doped fiber laser.

We show that a stretched-pulse mode-locked fiber laser produces a welldefined frequency comb, providing a compact source of frequency combs and allowing comb-based optical frequency metrology to be extended into the 1.55 microm region. This is achieved by comparing the frequency doubled output of the fiber laser to that of a mode-locked Ti:Sapphire laser, after the two lasers are synchronized. The offset frequency of the fiber laser frequency comb is found to be highly sensitive to the pump power, which enables the implementation of a feedback loop to control the offset frequency. The resulting RMS frequency jitter of the heterodyne beat signal is 355 kHz (0.5 Hz - 102 kHz BW) for this initial demonstration.

Nonlinear phase noise generated in air-silica microstructure fiber and its effect on carrier-envelope phase.

We present measurements of the nonlinear phase noise that is due to amplitude-to-phase conversion in air-silica microstructure fiber that is utilized to broaden the frequency comb from a mode-locked femtosecond laser to an optical octave. When the octave of the continuum is employed to phase stabilize the laser-pulse train, this phase noise causes a change in the carrier-envelope phase of 3784-rad/nJ change in pulse energy. As a result, the jitter on the carrier-envelope phase that is due to fiber noise, from 0.03 Hz-55 kHz, is ~0.5rad .

Long-term carrier-envelope phase coherence.

The carrier-envelope phase of the pulse train emitted by a 10-fs mode-locked laser has been stabilized such that carrier-envelope phase coherence is maintained for at least 150 s (measurement limited). The phase coherence time was measured independently of the feedback loop.