arXiv subjects

Jacques Millo

Publications and source records attributed to Jacques Millo.

At least 19 recordsLinked to original sources

arXiv2026

Vocabulary, Physical Quantities and Units for the Measurement of Amplitude Noise and Phase Noise

The widespread use of non-SI quantities and units, together with improper and misleading terminology, generates confusion in the domain of phase and amplitude noise. We discuss such physical quantities, units and terms with the purpose of stimulating a discussion between labs, and to agree for the full adoption of the International System of Units (SI) and clear, unambiguous terminology.

physics.ins-det↗

arXiv2025

Sub-kelvin measurement of silicon thermal expansion with a Fabry-P\'erot cavity stabilized laser

In this letter, we report the measurement of the coefficient of thermal expansion (CTE) of single-crystal silicon from 655 mK to 16 K using an ultra-stable laser based on a single-crystal silicon Fabry-Perot cavity. Below 1 K temperatures, the CTE is in the $10^{-13}$ K$^{-1}$ range with a lowest point at $\boldsymbol{\alpha(}655$ mK$ \boldsymbol{)=} 3.5 \pm 0.4 \times 10^{-13}$ K$^{-1}$. We produce a theoretical model based on Debye and Einstein models to effectively approximate the CTE measured in this temperature range. This is the lowest-temperature CTE measurement of silicon to date, as well as the lowest operating temperature for an ultra-stable Fabry-Perot cavity for laser frequency stabilization.

physics.optics↗

arXiv2025

Phase noise measurement of semiconductor optical amplifiers

We introduce a novel measurement method for the phase noise measurement of optical amplifiers, topologically similar to the Heterodyne Mach-Zehnder Interferometer but governed by different principles, and we report on the measurement of a fibered amplifier at 1.55 $\mu\mathrm{m}$ wavelength. The amplifier under test (DUT) is inserted in one arm of a symmetrical Mach-Zehnder interferometer, with an AOM in the other arm. We measure the phase noise of the RF beat detected at the Mach-Zehnder output. The phase noise floor of the amplifier decreases proportionally to the reciprocal of the laser power at the amplifier input, down to $-125$ $\mathrm{dBrad^2/Hz}$ at $f=100$ $\mathrm{kHz}$. The DUT flicker noise cannot be measured because it is lower than the background of the setup. This sets an upper bound of the amplifier noise at $-32$ $\mathrm{dBrad^2/Hz}$ at $f=1$ $\mathrm{Hz}$, which corresponds to a frequency stability of $5.2{\times}10^{-17}/\tau$ (Allan deviation), where $\tau$ is the integration time. Such noise level is lower than that of most Fabry-Perot cavity-stabilized lasers. These results are of interest in a wide range of applications including metrology, instrumentation, optical communications, or fiber links.

physics.optics↗

arXiv2025

Development of a laser stabilized on an ultra-stable silicon cryogenic Fabry-Perot cavity for dark matter detection

Astrophysical observations suggest the existence of an unknown kind of matter in the Universe, in the frame of the $\Lambda$CDM model. The research field of dark matter covers an energy scale going from massive objects to ultra-light scalar fields, which are the focus of the present work. It is supposed that ultra-light scalar fields affect the length of objects, whereas the speed of light stays unchanged. It follows that Fabry-Perot cavities are ideal tools for ultra-light dark matter detection since the fluctuations in the length of a cavity can be detected on the frequency of the laser stabilized to it. At FEMTO-ST, we have set up an ultra-stable silicon cavity suitable for a test of detection of ultra-light dark matter in an energy range close to 10$^{-10}$ eV. Our 14 cm cavity is composed of two mirrors optically bonded to an ultra-rigid spacer, with each element made in single-crystal of silicon, and cooled at 17 K in order to cancel the first order thermal expansion coefficient of the silicon spacer. The projected fractional frequency stability of the laser is $3 \times 10^{-17}$, mainly limited by the thermal noise of the amorphous dielectric reflective coatings. To reach this remarkable stability, several effects have to be reduced below the thermal noise limit. While the contribution of the residual amplitude modulation is now acceptable, we are currently implementing a laser power lock with residual fluctuations lower than 3~nW and a piezoelectric-based servo loop to actively reduce the vibration noise that has to be inferior to $-110 \textrm{~dB(m s}^{-2})^2/\textrm{Hz}$ at 1 Hz. Here, we present both the status of the development of our ultra-stable laser and the mechanical response of the cavity in the presence of ultra-light dark matter.

astro-ph.IM↗

arXiv2025

Guidelines for designs for ultrastable laser with $\mathbf{10^{-17}}$ fractional frequency instability

Lasers with long coherence time and narrow linewidth are an essential tool for quantum sensors and clocks. Ultrastable cavities and laser systems are now commercially available with fractional frequency instabilities in the mid $10^{-16}$ range. This document aims to provide technical guidance for researchers starting in the field of ultrastable lasers and to give an outlook toward the next generation of improved ultrastable lasers. These guidelines have arisen from the scope of the EMPIR project ``Next generation ultrastable lasers'' ( https://www.ptb.de/empir2021/nextlasers ) with contributions from the European project partners.

physics.optics↗

arXiv2025

Offset sideband locking to iodine for laser cooling on the $\mathrm{{}^1 S_0}\rightarrow \mathrm{{}^3 P_1}$ transition of ${}^{171}\mathrm{Yb}$

We present absolute frequency measurements of a laser stabilized using an offset sideband locking technique on the P(49)24-1 rovibrational transition of $^{127}\mathrm{I}_2$ near 556 nm. The P(49)24-1 transition is offset by 4.8 GHz from the intercombination transition of ${}^{171}\mathrm{Yb}$. A dual-tone electro-optical modulator is employed to bridge this frequency gap, enabling frequency stabilization of the 556 nm laser near the Yb transition, achieving a fractional frequency stability of $1.2 \times 10^{-11}$ at one second. We thoroughly characterize the frequency shifts associated with this locking scheme, with typical systematic effects fractional uncertainties of $9 \times 10^{-12}$.

physics.ins-det↗

arXiv2024

Short-term stability of a microcell optical reference based on Rb atom two-photon transition at 778 nm

We report on the development and short-term stability characterization of an optical frequency reference based on the spectroscopy of the rubidium two-photon transition at 778 nm in a microfabricated vapor cell. When compared against a 778 nm reference signal extracted from a frequency-doubled cavity-stabilized telecom laser, the short-term stability of the microcell frequency standard is 3.5 $\times$ 10$^{-13}$ $\tau^{-1/2}$ until 200~s, in good agreement with a phase noise level of $+$ 43 dBrad$^2$/Hz at 1~Hz offset frequency. The two main contributions to the short-term stability of the microcell reference are currently the photon shot noise and the intermodulation effect induced by the laser frequency noise. With still a relevant margin of progress, these results show the interest of this spectroscopic approach for the demonstration of high-stability miniaturized optical vapor cell clocks. Such clocks are poised to be highly beneficial for applications in navigation, communications, and metrology.

physics.atom-ph↗

arXiv2024

Towards a sub-kelvin cryogenic Fabry-Perot silicon cavity

We report on the development of a sub-kelvin, single-crystal silicon Fabry-Perot cavity. Operating such a cavity below 1~K should reduce the thermal noise limit of the cavity, and by this way address the current limitations of ultrastable lasers. To further decrease mechanical losses, mirrors with silicon substrates and crystalline coatings are optically contacted to the spacer, resulting in a room-temperature finesse of 220,000. To operate our cavity at sub-kelvin temperatures, we use a dilution refrigerator able to reach temperatures down to 10 mK. We have designed a mechanical mount to house our cavity in such a cryostat, with optimized heat transfer that will decrease the cooldown time for temperatures below 1~K. The estimated thermal noise is projected to be $\sim 7{\times}10^{-19}$ at 100~mK. However, silicon cavities with crystalline mirror coatings at cryogenic temperatures have shown birefringence correlated frequency fluctuations as well as unknown additional noise mechanisms \cite{yu2023, kedar2023}. We have measured a room-temperature TEM$_{00}$ birefringent mode splitting of about 250 kHz. Understanding and measuring these noise mechanisms will be a key to attaining fractional frequency stabilities beyond state-of-the-art.

physics.ins-det↗

arXiv2023

Phase noise of a microwave photonic channel: direct-current versus external electro-optic modulation

We characterize the phase noise of a microwave photonic channel, where a 10 GHz signal is carried by an intensity-modulated light beam over a short optical fiber, and detected. Two options are compared, (i) an electro-optic modulator (EOM), and (ii) the direct modulation of the laser current. The 1.55~$\mu$m laser and the detector are the same. The effect of experimental parameters is investigated, the main of which are the microwave power and the laser bias current. The main result is that the upper bound of the phase flicker is $-117$~dBrad$^2$ in the case of the EOM, limited by the background noise of the setup. In contrast, with direct modulation of the laser, the flicker is of $-114$ to $-100$~dBrad$^2$, depending on the laser bias current (50--90~mA), and the highest noise occurs at the lowest bias. Our results are of interest in communications, radar systems, instrumentation and metrology.

physics.optics↗

arXiv2023

Fully digital platform for local ultra-stable optical frequency distribution

This article reports on the use of a Field Programmable Gate Array (FPGA) platform for local ultra-stable optical frequency distribution through a 90 m-long fiber network. This platform is used to implement a fully digital treatment of the Doppler-cancellation scheme required by fiber links to be able to distribute ultra-stable frequencies. We present a novel protocol that uses aliased images of a digital synthesizer output to directly generate signals above the Nyquist frequency. This approach significantly simplifies the setup, making it easy to duplicate within a local fiber network. We demonstrate performances enabling the distribution of an optical signal with an instability below $10^{-17}$ at 1 s at the receiver end. We also use the board to implement an original characterization method. It leads to an efficient characterization of the disturbance rejection of the system that can be realized without accessing the remote output of the fiber link.

physics.ins-det↗

arXiv2022

Residual amplitude modulation at the $10^{-7}$ level for ultra-stable lasers

The stabilization of lasers on ultra-stable optical cavities by the Pound-Drever-Hall (PDH) technique is a widely used method. The PDH method relies on the phase-modulation of the laser, which is usually performed by an electro-optic modulator (EOM). When approaching the $10^{-16}$ level, this technology requires an active control of the residual amplitude modulation (RAM) generated by the EOM in order to bring the frequency stability of the laser down to the thermal noise limit of the ultra-stable cavity. In this article, we report on the development of an active system of RAM reduction based on a free space EOM, which is used to perform PDH-stabilization of a laser on a cryogenic silicon cavity. A RAM stability of $1.4 \times 10^{-7}$ is obtained by employing a digital servo that stabilizes the EOM DC electric field, the crystal temperature and the laser power. Considering an ultra-stable cavity with a finesse of $2.5\times 10^5$, this RAM level would contribute to the fractional frequency instability at the level of about $5\times 10^{-19}$, well below the state of the art thermal noise limit of a few $ 10^{-17}$.

physics.optics↗

arXiv2021

Digital Doppler-cancellation servo for ultra-stable optical frequency dissemination over fiber

Progress made in optical references, including ultra-stable Fabry-Perot cavities, optical frequency combs and optical atomic clocks, have driven the need for ultra-stable optical fiber networks. Telecom-wavelength ultra-pure optical signal transport has been demonstrated on distances ranging from the laboratory scale to the continental scale. In this manuscript, we present a Doppler-cancellation setup based on a digital phase-locked loop for ultra-stable optical signal dissemination over fiber. The optical phase stabilization setup is based on a usual heterodyne Michelson-interferometer setup, while the Software Defined Radio (SDR) implementation of the phase-locked loop is based on a compact commercial board embedding a field programmable gate array, analog-to-digital and digital-to-analog converters. Using three different configurations including an undersampling method, we demonstrate a 20 m long fiber link with residual fractional frequency instability as low as $10^{-18}$ at 1000 s, and an optical phase noise of $-70$ dBc/Hz at 1 Hz with a telecom frequency carrier.

physics.ins-det↗

arXiv2019

Ultra-compact reference ULE cavity

We present a first experimental characterization of our ultra-compact, ultra-stable laser. The heart of the apparatus is an original Fabry-Perot cavity with a 25 mm length and a pyramidal geometry, equipped with highly-reflective crystalline coatings. The cavity, along with its vacuum chamber and optical setup, fits inside a 30 L volume. We have measured the cavity thermal and vibration sensitivities, and present a first estimation of the cavity fractional frequency instability at $\sigma_y(1\rm{s})=7.5{\times}10^{-15}$.

physics.ins-det↗

arXiv2019

Generation of very high-order high purity Gaussian modes via spatial light modulation

We experimentally demonstrate the conversion of a fundamental $\text{TEM}_{00}$ laser mode at 1064\,nm to higher order Hermite-Gaussian modes (HG) of arbitrary order via a commercially available liquid crystal Spatial Light Modulator (SLM). We particularly studied the $\text{HG}_{5,5}/\text{HG}_{10,10}/\text{HG}_{15,15}$ modes. A two-mirror plano-spherical cavity filters the higher-order modes spatially. We analyze the cleaned modes via a three-mirror diagnosis cavity and measure a mode purity of 96/93/78\% and a conversion efficiency of 6.6\%/3.7\%/1.7\% respectively. The generated high-purity Hermite-Gaussian modes can be employed for the mitigation of mirror thermal noise in optical cavities for both optical clocks and gravitational wave (GW) detectors. HG modes are then converted into high order LG modes which can be of particular interest in cold atom physics.

gr-qc↗

arXiv2018

Photonic Generation of High Power, Ultrastable Microwave Signals by Vernier Effect in a Femtosecond Laser Frequency Comb

Optical frequency division of an ultrastable laser to the microwave frequency range by an optical frequency comb has allowed the generation of microwave signals with unprecedently high spectral purity and stability. However, the generated microwave signal will suffer from a very low power level if no external optical frequency comb repetition rate multiplication device is used. This paper reports theoretical and experimental studies on the beneficial use of the Vernier effect together with the spectral selective filtering in a double directional coupler add-drop optical fibre ring resonator to increase the comb repetition rate and generate high power microwaves. The studies are focused on two selective filtering aspects: the high rejection of undesirable optical modes of the frequency comb and the transmission of the desirable modes with the lowest possible loss. Moreover, the conservation of the frequency comb stability and linewidth at the resonator output is particularly considered. Accordingly, a fibre ring resonator is designed, fabricated, and characterized, and a technique to stabilize the resonator's resonance comb is proposed. A significant power gain is achieved for the photonically generated beat note at 10 GHz. Routes to highly improve the performances of such proof-of-concept device are also discussed.

physics.ins-det↗

arXiv2017

Residual Phase Noise Measurement of Optical Second Harmonic Generation in PPLN Waveguides

We report on the characterization, including residual phase noise and fractional frequency instability, of fiber-coupled PPLN non-linear crystals. These components are devoted to frequency doubling 871 nm light from an extended-cavity diode laser to produce a 435.5 nm beam, corresponding to the ytterbium ion electric quadrupole clock transition. We measure doubling efficiencies of up to 117.5 %/W. Using a Mach-Zehnder interferometer and an original noise rejection technique, the residual phase noise of the doublers is estimated to be lower than ${\rm -35\, dBrad^2/Hz}$ at 1 Hz, making these modules compatible with up-to-date optical clocks and ultra-stable cavities. The influence of external parameters such as pump laser frequency and intensity is investigated, showing that they do not limit the stability of the frequency-doubled signal. Our results demonstrate that such compact, fiber-coupled modules are suitable for use in ultra-low phase noise metrological experiments, including transportable optical atomic clocks.

physics.ins-det↗

arXiv2016

Compact Yb$^+$ optical atomic clock project: design principle and current status

We present the design of a compact optical clock based on the $^2S_{1/2} \rightarrow ^2D_{3/2}$ 435.5 nm transition in $^{171}$Yb$^+$. The ion trap will be based on a micro-fabricated circuit, with surface electrodes generating a trapping potential to localize a single Yb ion a few hundred $\mu$m from the electrodes. We present our trap design as well as simulations of the resulting trapping pseudo-potential. We also present a compact, multi-channel wavelength meter that will permit the frequency stabilization of the cooling, repumping and clear-out lasers at 369.5 nm, 935.2 nm and 638.6 nm needed to cool the ion. We use this wavelength meter to characterize and stabilize the frequency of extended cavity diode lasers at 369.5 nm and 638.6 nm.

physics.atom-ph↗

arXiv2015

Frequency stability of a wavelength meter and applications to laser frequency stabilization

Interferometric wavelength meters have attained frequency resolutions down to the MHz range. In particular, Fizeau interferometers, which have no moving parts, are becoming a popular tool for laser characterization and stabilization. In this article, we characterize such a wavelength meter using an ultra-stable laser in terms of relative frequency instability $\sigma_y(\tau)$ and demonstrate that it can achieve a short-term instability $\sigma_y(1 s) \approx 2{\times}10^{-10}$ and a frequency drift of order $10$ MHz/day. We use this apparatus to demonstrate frequency control of a near-infrared laser, where a frequency instability below $3{\times}10^{-10}$ from 1 s to 2000 s is achieved. Such performance is for example adequate for ions trapping and atoms cooling experiments.

physics.optics↗