Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optical and Quantum Sensing and Precision Metrology II

Sub-nano-scale phase sensing and improvement by squeezing

Jean-Claude M. Diels, Xiaobing Zhu, M. Lenzner

Published Mar 8, 2023• 0 citations
Publisher

Abstract

Extreme sensitivity in measuring minute changes of phase is traditionally achieved by marvels of technology, such as a high finesse (10^6) Fabry-Perot interferometer, probed with lasers of only 1 Hz linewidth, and complex electronics. We will show that the same result can be obtained with standard unstabilized lasers emitting dual frequency combs. The source of combs has a coherence time in the microsecond range, yet a mutual coherence time between the combs of 100 s is achieved.

DOI
10.1117/12.2657382

Related papers

Phase Nanoscopy with Correlated Frequency Combs

Xiaobing Zhu, M. Lenzner, Jean‐Claude Diels

This study addresses any sensor based on measuring a physical quantity through the phase of a probing beam. This includes sensing of rotation, acceleration, index change, displacement, fields… While most phase measurements are made by detecting an amplitude change in interfering beams, we detect instead a phase change through a relative frequency shift of two correlated frequency combs. This paper explores the limit sensitivity that this method can achieve, when the combs are generated in an Optical Parametric Oscillator (OPO), pumped synchronously by a train of femtosecond pulses separated by half the OPO cavity round-trip time. It is shown that a phase difference as small as 0.4 nanoradians can be resolved between the two pulses circulating in the cavity. This phase difference is one order of magnitude better than the previous record. The root-mean-square deviation of the measured phase over measuring time is close to the standard quantum limit (phase-photon number uncertainty product of 0.66). Innovations that made such improved performances possible include a more stable OPO cavity design; a stabilization system with a novel purely electronic locking of the OPO cavity length relative to that of the pump laser; a shorter pump laser cavity; and a square pulse generator for driving a 0.5 mm pathlength lithium niobate phase modulator. Future data acquisition improvements are suggested that will bring the phase sensitivity exactly to the standard quantum limit, and beyond the quantum limit by squeezing.

Sensors•Dec 28, 2022•1 citation

An optical innovation for metrology at the quantum limit of precision

Frequency-comb lasers are measuring sticks of the optical world and are used in metrology and sensing applications owing to their rigid, comb-like light spectra and metronomic pulsed output. A frequency comb with time-programmable pulses breaks this rigid mould and, in a demonstration of its utility, measures distances at the quantum limit of precision. A frequency-comb laser can be programmed to change pulse timing with high precision, to improve the sensitivity of distance measurements.

Nature•Oct 17, 2022•0 citations

Intracavity coherent interaction of mode-locked pulse train with resonant medium

Koji Masuda

Resonant interactions of a mode-locked pulse train with intracavity samples, namely rubidium-87 (Rb-87) vapor and Fabry-Perot etalon, placed inside a laser cavity are studied in the light of developing ultra-sensitive laser sensors to measure a small magnetic field and a minute change of index of refraction of a sample material, respectively. A Rb-87 vapor provides an opportunity for a compact high-sensitivity atomic magnetometer due to its accessibility by the standard laser sources and to the large ensemble magnetization. By employing the ultrasensitive interferometric technique utilizing the intracavity properties of a mode-locked laser, the performance of the Rb-87 magnetometer can be further improved. The fundamental properties of coherent interaction between a mode-locked pulse train and a Rb-87 vapor are studied in numerical calculations of 3 x 3 density matrix equations and the reduced wave equation, which are then examined in experiments. In particular, a coherent dark-state is created by the pulse train and is further enhanced by means of spectral shaping or polarization modulation of the excitation pulse train. Experiments performed inside a laser cavity show that the atomic coherence is still preserved due to the coherent nature of interaction between the Rb-87 vapor and the ultrashort pulses occurred within a short time scale compared to the atomic relaxation times, which results in nonlinear propagation of the pulses as well as an observation of the dark-line resonance inside the laser cavity. A Fabry-Perot etalon is a type of optical cavity and serves as a tuning element of the frequency of cw-lasers. By inserting a Fabry-Perot etalon inside a mode-locked laser, the cavity resonance modes are modified due to a coupling between the two cavities, which leads to unique temporal and spectral characteristics of the resultant pulse train and its frequency comb. Both the temporal and spectral properties of the pulse train are studied in detail in experiments as well as in numerical calculations. In particular, it will be shown that the coupling between low frequency modes from the laser repetition rate and high frequency modes from the Fabry-Perot pulse train can be exploited for a new interferometric technique to measure a minute change in the index of refraction of the etalon.

•Jan 1, 2014•3 citations

Comb-assisted ultrastable laser system for quantum technologies

Michele Giunta, Martin Wolferstetter, Nikolai Lilienfein +5 more

Quantum technologies are nowadays emerging as enabling tools for practical applications, such as quantum sensing, quantum computing and quantum metrology. Lasers play a central role in many of these technological platforms, e.g. for atomic clocks, ion-based or neutral atom-based quantum computers or atom interferometers. Here we present a complete laser system to cool, trap and control strontium atoms in an optical lattice or in tweezer arrays. A sub-Hz linewidth master laser, locked to a high-finesse optical cavity provides the frequency reference for an ultra-low noise comb. The rack-mounted laser system consists of all cooling, repumping, and clock lasers stabilized to the optical frequency comb. Each of the involved laser frequencies can therefore be tuned and mapped in the frequency domain with a high degree of stability. The system is controlled via a software interface, allowing to operate the cold-atom-based physics package autonomously. The system is tailored for the operation of 88Sr or 87Sr optical lattice clocks, or for quantum computing applications, but other sub-Hz lasers could be obtained by phase locking additional clock laser frequencies to the ultra-stable comb, enabling convenient and accurate optical frequency ratio measurements. The laser system architecture and the relevant characterization measurements will be presented, proposing some user-cases such as quantum computing and atom interferometry on strontium atoms. This represents a technological leap for quantum optics, allowing to explore further applications of quantum sensors outside a traditional lab.

Optical and Quantum Sensing and Precision Metrology•Mar 4, 2021•1 citation

Sub-dekahertz Ultraviolet Spectroscopy of 199Hg+

Robert J. Rafac, Brent C. Young, James A. Beall +3 more

Using a laser that is frequency locked to a Fabry-P\'erot \'etalon of high finesse and stability, we probe the ${5d}^{10}6s^{2}S_{1/2}(F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0)\ensuremath{\leftrightarrow}{5d}^{9}{6s}^{2}^{2}D_{5/2}(F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2)$ $\ensuremath{\Delta}{m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ electric-quadrupole transition of a single laser-cooled ${}^{199}{\mathrm{Hg}}^{+}$ ion stored in a cryogenic radio-frequency ion trap. We observe Fourier-transform limited linewidths as narrow as 6.7 Hz at 282 nm ( $1.06\ifmmode\times\else\texttimes\fi{}{10}^{15}\phantom{\rule{0ex}{0ex}}\mathrm{Hz}$), yielding a line $Q\ensuremath{\approx}1.6\ifmmode\times\else\texttimes\fi{}{10}^{14}$. We perform a preliminary measurement of the ${5d}^{9}{6s}^{2}^{2}D_{5/2}$ electric-quadrupole shift due to interaction with the static fields of the trap, and discuss the implications for future trapped-ion optical frequency standards.

arXiv:physics/0007002•Physical Review Letters•Sep 18, 2000•265 citations

Frequency Comb Measures Quantum Interference

Philip Ball

A multiwavelength laser source known as a frequency comb provides a new technique for atom interferometry, potentially leading to new tests of fundamental physics.

Physics•Oct 21, 2022•0 citations
Extreme sensitivity in measuring minute changes of phase is traditionally achieved by marvels of technology, such as a high finesse (10^6) Fabry-Perot interferometer, probed with lasers of only 1 Hz linewidth, and complex electronics. We will show that the same result can be obtained with standard unstabilized lasers emitting dual frequency combs. The source of combs has a coherence time in the microsecond range, yet a mutual coherence time between the combs of 100 s is achieved.
This study addresses any sensor based on measuring a physical quantity through the phase of a probing beam. This includes sensing of rotation, acceleration, index change, displacement, fields… While most phase measurements are made by detecting an amplitude change in interfering beams, we detect instead a phase change through a relative frequency shift of two correlated frequency combs. This paper explores the limit sensitivity that this method can achieve, when the combs are generated in an Optical Parametric Oscillator (OPO), pumped synchronously by a train of femtosecond pulses separated by half the OPO cavity round-trip time. It is shown that a phase difference as small as 0.4 nanoradians can be resolved between the two pulses circulating in the cavity. This phase difference is one order of magnitude better than the previous record. The root-mean-square deviation of the measured phase over measuring time is close to the standard quantum limit (phase-photon number uncertainty product of 0.66). Innovations that made such improved performances possible include a more stable OPO cavity design; a stabilization system with a novel purely electronic locking of the OPO cavity length relative to that of the pump laser; a shorter pump laser cavity; and a square pulse generator for driving a 0.5 mm pathlength lithium niobate phase modulator. Future data acquisition improvements are suggested that will bring the phase sensitivity exactly to the standard quantum limit, and beyond the quantum limit by squeezing.
Resonant interactions of a mode-locked pulse train with intracavity samples, namely rubidium-87 (Rb-87) vapor and Fabry-Perot etalon, placed inside a laser cavity are studied in the light of developing ultra-sensitive laser sensors to measure a small magnetic field and a minute change of index of refraction of a sample material, respectively. A Rb-87 vapor provides an opportunity for a compact high-sensitivity atomic magnetometer due to its accessibility by the standard laser sources and to the large ensemble magnetization. By employing the ultrasensitive interferometric technique utilizing the intracavity properties of a mode-locked laser, the performance of the Rb-87 magnetometer can be further improved. The fundamental properties of coherent interaction between a mode-locked pulse train and a Rb-87 vapor are studied in numerical calculations of 3 x 3 density matrix equations and the reduced wave equation, which are then examined in experiments. In particular, a coherent dark-state is created by the pulse train and is further enhanced by means of spectral shaping or polarization modulation of the excitation pulse train. Experiments performed inside a laser cavity show that the atomic coherence is still preserved due to the coherent nature of interaction between the Rb-87 vapor and the ultrashort pulses occurred within a short time scale compared to the atomic relaxation times, which results in nonlinear propagation of the pulses as well as an observation of the dark-line resonance inside the laser cavity. A Fabry-Perot etalon is a type of optical cavity and serves as a tuning element of the frequency of cw-lasers. By inserting a Fabry-Perot etalon inside a mode-locked laser, the cavity resonance modes are modified due to a coupling between the two cavities, which leads to unique temporal and spectral characteristics of the resultant pulse train and its frequency comb. Both the temporal and spectral properties of the pulse train are studied in detail in experiments as well as in numerical calculations. In particular, it will be shown that the coupling between low frequency modes from the laser repetition rate and high frequency modes from the Fabry-Perot pulse train can be exploited for a new interferometric technique to measure a minute change in the index of refraction of the etalon.
Quantum technologies are nowadays emerging as enabling tools for practical applications, such as quantum sensing, quantum computing and quantum metrology. Lasers play a central role in many of these technological platforms, e.g. for atomic clocks, ion-based or neutral atom-based quantum computers or atom interferometers. Here we present a complete laser system to cool, trap and control strontium atoms in an optical lattice or in tweezer arrays. A sub-Hz linewidth master laser, locked to a high-finesse optical cavity provides the frequency reference for an ultra-low noise comb. The rack-mounted laser system consists of all cooling, repumping, and clock lasers stabilized to the optical frequency comb. Each of the involved laser frequencies can therefore be tuned and mapped in the frequency domain with a high degree of stability. The system is controlled via a software interface, allowing to operate the cold-atom-based physics package autonomously. The system is tailored for the operation of 88Sr or 87Sr optical lattice clocks, or for quantum computing applications, but other sub-Hz lasers could be obtained by phase locking additional clock laser frequencies to the ultra-stable comb, enabling convenient and accurate optical frequency ratio measurements. The laser system architecture and the relevant characterization measurements will be presented, proposing some user-cases such as quantum computing and atom interferometry on strontium atoms. This represents a technological leap for quantum optics, allowing to explore further applications of quantum sensors outside a traditional lab.
Using a laser that is frequency locked to a Fabry-P\'erot \'etalon of high finesse and stability, we probe the ${5d}^{10}6s^{2}S_{1/2}(F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0)\ensuremath{\leftrightarrow}{5d}^{9}{6s}^{2}^{2}D_{5/2}(F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2)$ $\ensuremath{\Delta}{m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ electric-quadrupole transition of a single laser-cooled 199Hg+{}^{199}{\mathrm{Hg}}^{+}199Hg+ ion stored in a cryogenic radio-frequency ion trap. We observe Fourier-transform limited linewidths as narrow as 6.7 Hz at 282 nm ( $1.06\ifmmode\times\else\texttimes\fi{}{10}^{15}\phantom{\rule{0ex}{0ex}}\mathrm{Hz}$), yielding a line $Q\ensuremath{\approx}1.6\ifmmode\times\else\texttimes\fi{}{10}^{14}$. We perform a preliminary measurement of the ${5d}^{9}{6s}^{2}^{2}D_{5/2}$ electric-quadrupole shift due to interaction with the static fields of the trap, and discuss the implications for future trapped-ion optical frequency standards.