Noise characterization of an ultra-stable laser for optical clocks.

We report on the development and performance evaluation of an ultra-stable laser for an 27Al+ optical clock. After a series of noise suppressions, especially the vibrational and temperature fluctuation noise, the 30 cm long cavity stabilized laser obtains a frequency instability of 1.3 × 10-16 @1 s. This result is predicted by noise summation and confirmed by the three-cornered hat method. The 27Al+ optical clock transition is also used to characterize the laser frequency noise, and consistent results are yielded. This is the first reported instance of using single ion optical clocks to measure the frequency noise of ultra-stable lasers, as far as we know. With the implementation of the ultra-stable clock laser, an ultra-narrow linewidth clock transition of 2.8 Hz is obtained.

Ultra-stable cryogenic sapphire cavity laser with an instability reaching 2 × 10-16 based on a low vibration level cryostat.

Cryogenic ultra-stable lasers have extremely low thermal noise limits and frequency drifts, but they are more seriously affected by vibration noise from cryostats. Main material candidates for cryogenic ultra-stable cavities include silicon and sapphire. Although sapphire has many excellent properties at low temperature, the development of sapphire-based cavities is less advanced than that of silicon-based. Using a homemade cryogenic sapphire cavity, we develop an ultra-stable laser source with a frequency instability of 2(1) × 10-16. This is the best frequency instability level among similar systems using cryogenic sapphire cavities reported so far. Low vibration performance of the cryostat is demonstrated with a two-stage vibration isolation, and the vibration suppression is optimized by tuning the mixing ratio of the gas-liquid-helium. With this technique, the linear power spectral densities of vibrations at certain frequencies higher than tens of hertz are suppressed by two orders of magnitude in all directions.

Three-wave differential locking scheme in a 12-m-perimeter large-scale passive laser gyroscope.

Large-scale laser gyroscopes with sufficiently high sensitivity for measurement of the rotation rate of the Earth Ω E are inertial sensors with the capability to provide Earth orientation parameters, i.e., rotation rate and polar motion in near real time. Larger-scale passive resonant gyroscopes (PRGs) theoretically have a lower shot-noise limit. However, the cavity perimeter fluctuations and laser frequency noise become challenges in a passive gyro. In this paper, we introduce a three-wave differential locking scheme for large-scale PRGs, resulting in an in situ measurement of the cavity perimeter with nanometer resolution. Furthermore, the laser frequency noise is effectively suppressed with an additional gain of 30 dB by a double-stage locking system, based on the three-wave differential locking scheme. Finally, the rotation rate resolution of our 3m×3m gyroscope improves to 1.1×10-9 r a d/s over 200 s. The simplicity, robustness, and effectiveness of the locking scheme are important to the long-term operation of large-scale PRGs aiming for applications in the geosciences.

Time delay interferometry with a transfer oscillator.

In this work, we experimentally perform time delay interferometry by using a transfer oscillator, which is capable of reducing the laser frequency noise and the clock noise simultaneously in the post processing. The iodine frequency reference is coherently downconverted to the microwave frequency using a laser frequency comb. The residual noise of the downconversion network is 5 × 10-6Hz/Hz1/2 at 0.7 mHz, and 4 × 10-6Hz/Hz1/2 at 0.1 Hz, indicating high homology between the optical frequency and the microwave frequency. We carry out time delay interferometry with the aid of the electrical delay module, which can introduce large time delays. The results show that the laser frequency noise and the clock noise can be reduced simultaneously by ten and three orders of magnitude, respectively, in the frequency band from 0.1 mHz to 0.1 Hz. The performance of the noise reduction can reach 6 × 10-8Hz/Hz1/2 at 0.1 mHz, and 7 × 10-7Hz/Hz1/2 at 1 mHz, meeting the requirements of the space-borne gravitational wave detection. Our work will be able to offer an alternative method for the frequency comb-based time delay interferometry in the future space-borne gravitational wave detectors.

Single step zero-thermal-expansion temperature measurement of optical reference cavities.

State-of-the-art laser frequency stability has been pushed to the 10-17 level. The laser reference cavity is typically nested in a multi-layer thermal enclosure to increase vacuum thermal time constant and thermally controlled at the zero-thermal-expansion temperature to reduce the external temperature fluctuation effect. It is rather time consuming to accurately determine the zero-thermal-expansion temperature for a large thermal time constant system. Here we develop a fast method for measuring the zero-thermal-expansion temperature of the cavity by relying on just one single temperature scan. We first develop a theoretical model to predict the performance of the laser locked to the reference cavity, and then construct an evaluation system for verification of the model. The zero-thermal-expansion temperature of a 30-cm cavity is measured to be 4.3±0.5 °C. The fast and high precision method for determining the zero-thermal-expansion temperature will be valuable in improving long-term frequency stabilities of cavity stabilized lasers.

Vibration Property of a Cryogenic Optical Resonator within a Pulse-Tube Cryostat.

Cryogenic ultrastable laser cavities push laser stability to new levels due to their lower thermal noise limitation. Vibrational noise is one of the major obstacles to achieve a thermal-noise-limited cryogenic ultrastable laser system. Here, we carefully analyze the vibrational noise contribution to the laser frequency. We measure the vibrational noise from the top of the pulse-tube cryocooler down to the experiment space. Major differences emerge between room and cryogenic temperature operation. We cooled a homemade 6 cm sapphire optical resonator down to 3.4 K. Locking a 1064 nm laser to the resonator, we measure a frequency stability of 1.3×10-15. The vibration sensitivities change at different excitation frequencies. The vibrational noise analysis of the laser system paves the way for in situ accurate evaluation of vibrational noise for cryogenic systems. This may help in cryostat design and cryogenic precision measurements.

Development of a deep-ultraviolet pulse laser source operating at 234†nm for direct cooling of Al+ ion clocks.

We report on the development of a 250-MHz 234 nm deep-ultraviolet pulse source based on a flexible wavelength-conversion scheme. The scheme is based on a frequency-doubled optical parametric oscillator (FD-OPO) together with a cascaded frequency conversion process. We use a χ(2) nonlinear envelope equation to guide the design of an intra-cavity OPO crystal, demonstrating a flexible broadband tunable feature and providing as high as watt-level of a frequency-doubled signal output centered at 850 nm, which is served as an input wave for the cascaded frequency conversion process. As much as 3.0 mW of an average power at 234 nm is obtained, with an rms power stability of better than 1% over 20 minutes. This deep-ultraviolet pulse laser source can be used for many applications in quantum optics and for direct laser cooling of Al+ ion clocks.

Proposal for phase-sensitive heterodyne detection in large-scale passive resonant gyroscopes.

Large-scale passive resonant gyroscopes (PRGs) have been utilized in the measurement of Earth rotation. We report on a scheme of phase-sensitive heterodyne detection in large-scale PRGs. By injecting three separated beams into different longitudinal modes of the ring cavity and self-demodulating the detected signals, the backscattering disturbance and the cavity length fluctuation effect both can be isolated. With the implementation of this new scheme, we can obtain the Earth rotation signal with a Sagnac frequency that is twice of that of the traditional scheme, which enhance the equivalent scale factor of the laser gyroscopes. On the other hand, the quantum noise limit of the instrument can also be further suppressed due to the improvement of the signal-to-noise ratio. With this new scheme, the theoretical rotational sensitivity of a 3 m × 3 m large scale PRG can be as low as 10-12 rad/s/Hz. With this rotational sensitivity, the measurement of the length of day or the test of the general relativity can be realized.

Noise Analysis of a Passive Resonant Laser Gyroscope.

Large-scale laser gyroscopes have found important applications in Earth sciences due to their self-sufficient property of measurement of the Earth's rotation without any external references. In order to extend the relative rotation measurement accuracy to a better level so that it can be used for the determination of the Earth orientation parameters (EOP), we investigate the limitations in a passive resonant laser gyroscope (PRG) developed at Huazhong University of Science and Technology (HUST) to pave the way for future development. We identify the noise sources from the derived noise transfer function of the PRG. In the frequency range below 10-2Hz, the contribution of free-spectral-range (FSR) variation is the dominant limitation, which comes from the drift of the ring cavity length. In the 10-2 to 103Hz frequency range, the limitation is due to the noises of the frequency discrimination system, which mainly comes from the residual amplitude modulation (RAM) in the frequency range below 2 Hz. In addition, the noise contributed by the Mach-Zehnder-type beam combiner is also noticeable in the 0.01 to 2 Hz frequency range. Finally, possible schemes for future improvement are also discussed.

Long-term digital frequency-stabilized laser source for large-scale passive laser gyroscopes.

We report on the development of a digitally controlled long-term frequency stabilized ultrastable laser source, which serves as an injection laser to stabilize the perimeter of a 3 m × 3 m heterolithic passive resonant gyroscope. We operate the gyroscope at two different cavity modes to reduce back-scattering coupling disturbance for gyroscope locking. This scheme increases the requirement for the injection laser frequency stability since we are using the wavelength of the laser as the length standard for the heterolithic gyroscope structure. The laser source is digitally locked to an ultrastable high-finesse Fabry-Perot cavity and a femtosecond optical frequency comb referenced to an active hydrogen maser simultaneously. The fractional frequency stability of the locked laser is better than 1.2 × 10-14 for averaging times from 0.1 s to 10 000 s. The short-term frequency stability is limited by the stability of the Fabry-Perot cavity, and the long-term frequency stability is limited by the stability of the frequency comb. The digital locking system enables the laser to run autonomously for weeks and can quickly relock itself within seconds to ensure continuous running of the gyroscope. The digital frequency stabilization technique can also fulfill the requirements of space gravitational waves detection and the next generation space gravity recovery mission.

Spontaneous generation of orbital angular momentum crystals using a monolithic Nd:YAG nonplanar ring laser.

We report the emission of localized orbital angular momentum (OAM) crystals in a millimeter-size monolithic Nd:YAG nonplanar ring laser. Narrow-linewidth single-frequency lasing in the kilohertz level featuring crystal-like vortices is obtained via phase locking of Laguerre-Gaussian modes in the cavity. It is found that the spatially degenerate OAM of high-order LG modes can be easily broken by superimposing a low-order mode, leading to crystal-like vortices. Our theoretical analysis is found to be in agreement with the experimental results for both intensity and interference patterns.

Direct generation of a narrow-linewidth Laguerre-Gaussian vortex laser in a monolithic nonplanar oscillator.

Vortex laser beams carrying orbital angular momentum have been attracting a lot of interest in recent years. Here we demonstrate the direct generation of a vortex laser in a monolithic nonplanar ring cavity. The unidirectional and single-frequency operation of Laguerre-Gaussian modes is observed and characterized. Fork interferograms have been obtained using a simple interferometer based on a plano-concave lens, and the topological charge of vortex beam is determined. A spectral linewidth as narrow as 2.3 kHz is measured by beating with a reference laser. We believe that such a high coherent vortex laser can be beneficial for numerous applications, including precision measurements and optical communications.

Note: A high-frequency signal generator based on direct digital synthesizer and field-programmable gate array.

A high-frequency signal generator based on direct digital synthesizer (DDS) and field-programmable gate array (FPGA) is presented. The FPGA provides the controlling time sequence for the DDS, which has a highest output frequency of 1.4 GHz and a frequency resolution of 190 pHz. At an output frequency of 1.2 GHz, the measured phase noise, including the contribution of the reference clock, is -65 dBc/Hz@1 Hz, while the intrinsic phase noise is -82 dBc/Hz@1 Hz. Time delay of the DDS is measured to be less than 150 ns. The signal generator is used to drive an acousto-optic modulator, and the rise time due to the whole link is 24 ns. The developed signal generator can be used in many precision measurement experiments in the fields of atomic, molecular, and optical physics.

Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link.

We have explored the performance of 2 "dark fibers" of a commercial telecommunication fiber link for a remote comparison of optical clocks. These fibers establish a network in Germany that will eventually link optical frequency standards at PTB with those at the Institute of Quantum Optics (IQ) at the Leibniz University of Hanover, and the Max Planck Institutes in Erlangen (MPL) and Garching (MPQ). We demonstrate for the first time that within several minutes a phase coherent comparison of clock lasers at the few 10(-15) level can also be accomplished when the lasers are more than 100 km apart. Based on the performance of the fiber link to the IQ, we estimate the expected stability for the link from PTB to MPQ via MPL that bridges a distance of approximately 900 km.