Zhiyi Bi

Frequency Uncertainty for Optically Referenced Femtosecond Laser Frequency Combs

We present measurements and analysis of the currently known relative frequency uncertainty of femtosecond laser frequency combs (FLFCs) based on Kerr-lens mode-locked Ti:sapphire lasers. Broadband frequency combs generated directly from the laser oscillator, as well as octave-spanning combs generated with nonlinear optical fiber are compared. The relative frequency uncertainty introduced by an optically referenced FLFC is measured for both its optical and microwave outputs. We find that the relative frequency uncertainty of the optical and microwave outputs of the FLFC can be as low as 8times10-20 and 1.7times10-18, with a confidence level of 95%, respectively. Photo-detection of the optical pulse train introduces a small amount of excess noise, which degrades the stability and subsequent relative frequency uncertainty limit of the microwave output to 2.6times10-17

First international comparison of femtosecond laser combs at the International Bureau of Weights and Measures

The first international comparison of femtosecond laser combs has been carried out at the International Bureau of Weights and Measures (BIPM). Three comb systems were involved: BIPM-C1 and BIPM-C2 from the BIPM and ECNU-C1 from the East China Normal University (ECNU). The agreement among the three combs was found to be on the subhertz level in the vicinity of 563 THz. A frequency difference measurement scheme was demonstrated that is suitable for general comb comparisons.

Frequency measurements and hyperfine structure of the R(85)33–0 transition of molecular iodine with a femtosecond optical comb

Absolute frequency measurements of the R(85)33‐0 transition of molecular iodine at the blue end of the tuning range of a frequency-doubled Nd:YAG laser are implemented with a femtosecond optical comb based on a mode-locked Ti:sapphire laser. The hyperfine structure of the R(85)33‐0 transition is observed by use of high-resolution laser spectroscopy and is measured by the femtosecond optical comb. The observed hyperfine transitions are good frequency references for both frequency-doubled Nd:YAG and Nd:YVO4 lasers in the 532-nm region. High-accuracy hyperfine constants are obtained by our fitting the measured hyperfine splittings to a four-term Hamiltonian, which includes the electric quadrupole, spin‐rotation, tensor spin‐spin, and scalar spin‐spin interactions.

International comparisons of femtosecond laser frequency combs

Two types of international comparisons of femtosecond laser frequency combs have been performed in France and the USA. Five combs were involved in the comparisons. Three combs, of which two are transportable, employ nonlinear photonic crystal fiber (PCF) to obtain a wide spectrum covering a full optical octave. The other two are based on broadband femtosecond lasers and require no PCF. The comparisons were performed by counting the optical heterodyne beats between pairs of combs. The frequency agreement among three combs was at the subhertz level in the 563 THz part of the comb spectrum when the combs were referenced to a hydrogen maser. When the combs were referenced to an optical standard, the frequency agreement among four combs was much improved and found to be at the /spl sim/10/sup -19/ level in the spectral range of 333-473 THz. The fact that this result is obtained by five independent measurement systems (combs) strengthens the conclusion that no systematic effects are present at this level.

Frequency stabilization of a 1319-nm Nd:YAG laser by saturation spectroscopy of molecular iodine

Hyperfine transitions of molecular iodine were observed by use of the frequency-doubled output of a 1319-nm Nd:YAG laser with saturation spectroscopy. The laser frequency was stabilized to the observed hyperfine transition and reached a stability of 6 x 10(-12) for a 1.5-s averaging time, improving toward the 1 x 10(-12) level after 100 s. The iodine-stabilized 1319-nm Nd:YAG laser is an excellent candidate for an optical frequency standard for telecommunication applications.

A collinear self-referencing set-up for control of the carrier-envelope offset frequency in Ti : sapphire femtosecond laser frequency combs

We demonstrate a simplified set-up for control of the carrier-envelope offset frequency (fceo) in a Ti : sapphire femtosecond laser frequency comb. A periodically poled KTiOPO4 crystal is used for second harmonic generation with zero walk-off angle, which enables collinear propagation of beating beams in the self-referencing set-up. A beat signal with a signal-to-noise ratio of more than 40 dB can be obtained within a 300 kHz bandwidth. Using this signal, fceo could be tracked to a frequency synthesizer within a few millihertz for an averaging time of 1 s, which contributed a relative stability of 8 × 10−18 in the visible region around 532 nm.

Optical frequency comb with an absolute linewidth of 0.6 Hz–1.2 Hz over an octave spectrum

We demonstrate a narrow-linewidth optical frequency comb based on a femtosecond Ti:sapphire laser by precisely phase-locking it to a subhertz-linewidth Nd:YAG laser at 1064 nm. Each comb tooth inherits the phase coherence and frequency stability of the subhertz-linewidth laser. By comparing against other independent narrow-linewidth lasers, we measured the absolute linewidth of the comb teeth to be 0.6 Hz–1.2 Hz over an octave spectrum.

0.26-Hz-linewidth ultrastable lasers at 1557 nm

Narrow-linewidth ultrastable lasers at 1.5 μm are essential in many applications such as coherent transfer of light through fiber and precision spectroscopy. Those applications all rely on the ultimate performance of the lasers. Here we demonstrate two ultrastable lasers at 1557 nm with a most probable linewidth of 0.26 Hz by independently frequency-stabilizing to the resonance of 10-cm-long ultrastable Fabry-Pérot cavities at room temperature. The fractional frequency instability of each laser system is nearly 8 × 10−16 at 1–30 s averaging time, approaching the thermal noise limit of the reference cavities. A remarkable frequency instability of 1 × 10−15 is achieved on the long time scale of 100–4000 s.

Thermal analysis of optical reference cavities for low sensitivity to environmental temperature fluctuations

The temperature stability of optical reference cavities is significant in state-of-the-art ultra-stable narrow-linewidth laser systems. In this paper, the thermal time constant and thermal sensitivity of reference cavities are analyzed when reference cavities respond to environmental perturbations via heat transfer of thermal conduction and thermal radiation separately. The analysis as well as simulation results indicate that a reference cavity enclosed in multiple layers of thermal shields with larger mass, higher thermal capacity and lower emissivity is found to have a larger thermal time constant and thus a smaller sensitivity to environmental temperature perturbations. The design of thermal shields for reference cavities may vary according to experimentally achievable temperature stability and the coefficient of thermal expansion of reference cavities. A temperature fluctuation-induced length instability of reference cavities as low as 6 × 10(-16) on a day timescale can be achieved if a two-layer thermal shield is inserted between a cavity with the coefficient of thermal expansion of 1 × 10(-10) /K and an outer vacuum chamber with temperature fluctuation amplitude of 1 mK and period of 24 hours.

Study on the clock-transition spectrum of cold 171Yb ytterbium atoms

We present a detailed study of the clock-transition spectrum of cold 171Yb ytterbium atoms in a 1D optical lattice. A typical clock-transition spectrum with a carrier-sideband structure is observed. After minimizing the power broadening effect and compensating the stray magnetic field, the carrier linewidth is narrowed to about 16 Hz for a 60 ms interrogation time. By increasing the interrogation time to 150 ms, the linewidth is further reduced to 6.8 Hz. By applying the bias magnetic field parallel to the clock-laser polarization, a two-peak spectrum corresponding to two π transitions is obtained. Finally, spin polarization of atoms to a single desired Zeeman sublevel of the ground state is also demonstrated. The presented results will be very useful for developing better optical lattice clocks.