A vibration-insensitive optical cavity and absolute determination of its ultrahigh stability

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.

Gravimetry through non-linear optomechanics

Precision gravimetry is key to a number of scientific and industrial applications, including climate change research, space exploration, geological surveys and fundamental investigations into the nature of gravity.  A variety of quantum systems, such as atom interferometry and on-chip-Bose–Einstein condensates have thus far been investigated to this aim. Here, we propose a new method which involves using a quantum optomechanical system for measurements of gravitational acceleration. As a proof-of-concept, we investigate the fundamental sensitivity for gravitational accelerometry of a cavity optomechanical system with a trilinear radiation pressure light-matter interaction. The phase of the optical output encodes the gravitational acceleration g and is the only component which needs to be measured. We prove analytically that homodyne detection is the optimal readout method and we predict an ideal fundamental sensitivity of Δg = 10⁻¹⁵ ms⁻² for state-of-the-art parameters of optomechanical systems, showing that they could, in principle, surpass the best atomic interferometers even for low optical intensities. Further, we show that the scheme is strikingly robust to the initial thermal state of the oscillator.

Precise gravimetric measurements are an important but challenging task. Here, Qvarfort et al. theoretically show that, in an optomechanical cavity, only the phase of the optical output needs to be measured to obtain a precise value for the gravitational acceleration with high sensitivity.

Simultaneous Measurements of CO and CO2 Employing Wavelength Modulation Spectroscopy Using a Signal Averaging Technique at 1.578 μm

A resolved line pair was selected for simultaneous measurement of carbon monoxide (CO) and carbon dioxide (CO₂) in the near-infrared (NIR) region. The spectral lines of CO and CO₂ at 1.578 µm were measured by wavelength modulation spectroscopy (WMS)-2 f and the absorption was enhanced with a multipass absorption cell. The white noise was further reduced by averaging technology. The detection sensitivity (1σ) for the system is estimated at 2.63 × 10^-7cm^-1 for direct absorption spectroscopy. The ultimate detection limits of CO₂ and CO mixed with pure N₂ at 75 Torr are 29 parts per million (ppm) and 47 ppm, respectively. It is demonstrated that the signal is highly linear with the concentration in the range of 100-800 ppm. Based on an Allan variation analysis, the minimum detectable limit of CO₂ and CO is 7.5 and 14 ppm, respectively. The response time of the system is about 30 s and a relationship of temperature dependence was obtained. As an example, an in situ measurement of exhaust of alkane combustion emission is presented.

Thermal-noise-limited higher-order mode locking of a reference cavity

Higher-order mode locking has been proposed to reduce the thermal noise limit of reference cavities. By locking a laser to the HG₀₂ mode of a 10-cm long all ultra-low expansion (ULE) cavity and measuring its performance with the three-cornered-hat method among three independently stabilized lasers, we demonstrate a thermal-noise-limited performance of a fractional frequency instability of 4.9×10^-16. The results match the theoretical models with higher-order optical modes. The achieved laser instability improves the all ULE short cavity results to a new low level.

Characterization of electrical noise limits in ultra-stable laser systems

We demonstrate thermal noise limited and shot noise limited performance of ultra-stable diode laser systems. The measured heterodyne beat linewidth between such two independent diode lasers reaches 0.74 Hz. The frequency instability of one single laser approaches 1.0 × 10^-15 for averaging time between 0.3 s and 10 s, which is close to the thermal noise limit of the reference cavity. Taking advantage of these two ultra-stable laser systems, we systematically investigate the ultimate electrical noise contributions, and derive expressions for the closed-loop spectral density of laser frequency noise. The measured power spectral density of the beat frequency is compared with the theoretically calculated closed-loop spectral density of the laser frequency noise, and they agree very well. It illustrates the power and generality of the derived closed-loop spectral density formula of the laser frequency noise. Our result demonstrates that a 10^-17 level locking in a wide frequency range is feasible with careful design.

Design verification of large time constant thermal shields for optical reference cavities

In order to achieve high frequency stability in ultra-stable lasers, the Fabry-Pérot reference cavities shall be put inside vacuum chambers with large thermal time constants to reduce the sensitivity to external temperature fluctuations. Currently, the determination of thermal time constants of vacuum chambers is based either on theoretical calculation or time-consuming experiments. The first method can only apply to simple system, while the second method will take a lot of time to try out different designs. To overcome these limitations, we present thermal time constant simulation using finite element analysis (FEA) based on complete vacuum chamber models and verify the results with measured time constants. We measure the thermal time constants using ultrastable laser systems and a frequency comb. The thermal expansion coefficients of optical reference cavities are precisely measured to reduce the measurement error of time constants. The simulation results and the experimental results agree very well. With this knowledge, we simulate several simplified design models using FEA to obtain larger vacuum thermal time constants at room temperature, taking into account vacuum pressure, shielding layers, and support structure. We adopt the Taguchi method for shielding layer optimization and demonstrate that layer material and layer number dominate the contributions to the thermal time constant, compared with layer thickness and layer spacing.

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.

Ultra-stable radio frequency dissemination in free space

We demonstrate an ultra-stable radio frequency (RF) dissemination scheme over 80 m free space. The frequency dissemination stability is 3.2 × 10(-13)/s and 4.4 × 10(-17)/day, which can be applied to transfer frequency signal without compromising its stability in a global navigation satellite system (GNSS) or radio astronomy.

Optical spectrum analyzer with quantum-limited noise floor

Interactions between atoms and lasers provide the potential for unprecedented control of quantum states. Fulfilling this potential requires detailed knowledge of frequency noise in optical oscillators with state-of-the-art stability. We demonstrate a technique that precisely measures the noise spectrum of an ultrastable laser using optical lattice-trapped 87Sr atoms as a quantum projection noise-limited reference. We determine the laser noise spectrum from near dc to 100 Hz via the measured fluctuations in atomic excitation, guided by a simple and robust theory model. The noise spectrum yields a 26(4) mHz linewidth at a central frequency of 429 THz, corresponding to an optical quality factor of 1.6×10(16). This approach improves upon optical heterodyne beats between two similar laser systems by providing information unique to a single laser and complements the traditionally used Allan deviation which evaluates laser performance at relatively long time scales. We use this technique to verify the reduction of resonant noise in our ultrastable laser via feedback from an optical heterodyne beat. Finally, we show that knowledge of our laser's spectrum allows us to accurately predict the laser-limited stability for optical atomic clocks.

Spherical reference cavities for frequency stabilization of lasers in non-laboratory environments

We present an optical cavity design that is insensitive to both vibrations and orientation. The design is based on a spherical cavity spacer that is held rigidly at two points on a diameter of the sphere. Coupling of the support forces to the cavity length is reduced by holding the sphere at a "squeeze insensitive angle" with respect to the optical axis. Finite element analysis is used to calculate the acceleration sensitivity of the spherical cavity for the ideal geometry as well as for several varieties of fabrication errors. The measured acceleration sensitivity for an initial, sub-ideal version of the mounted cavity is 4.0(5)×10(-11)/g, 1.6(3)×10(-10)/g, and 3.1(1)×10(-10)/g (where g = 9.81 m/s2) for accelerations along the vertical and two horizontal directions, and the fractional frequency stability of a laser locked to the cavity is 1.2×10(-15) between 0.4 and 13 s. This low acceleration sensitivity combined with the orientation insensitivity that comes with a rigid mount indicates that this cavity design could allow frequency stable lasers to operate in non-laboratory environments.

CaF2 whispering-gallery-mode-resonator stabilized-narrow-linewidth laser

A fiber laser is stabilized by introducing a calcium fluoride (CaF(2)) whispering-gallery-mode resonator as a filtering element in a ring cavity. It is set up using a semiconductor optical amplifier as a gain medium. The resonator is critically coupled through prisms, and used as a filtering element to suppress the laser linewidth. A three-cornered-hat method is used and shows a stability of 10(-11) after 10 micros. Using the self-heterodyne beat technique, the linewidth is determined to be 13 kHz. This implies an enhancement factor of 10(3) with respect to the passive cavity linewidth.

Practical tests for distinguishing slow light from saturable absorption

A series of practical tests of slow light (light with reduced group velocity) in saturable absorbers is proposed. These include experimental tests for saturable absorption, which can mimic slow light effects in saturable media, the dependence of slow light on the mutual coherence of pump and probe, since both slow and fast light effects can be simulated with incoherent sources, and the influence of polarization. The principal requirements for practical observation of spectral hole burning are reviewed and shown to be achievable for a wide range of saturable media with the narrow line sources now available.