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

Optics Letters

Frequency-doubling of continuous laser light in the Laguerre–Gaussian modes LG0,0 and LG3,3

J. Heinze, H. Vahlbruch, B. Willke

Published Aug 12, 2020• 8 citations
Publisher

Abstract

For future generations of gravitational wave detectors, it is proposed to use the helical Laguerre–Gaussian L G 3 , 3 mode to reduce thermal noise, which limits the detector sensitivity. At the same time, this requires the efficient generation of squeezed vacuum states in the L G 3 , 3 mode for quantum noise reduction. Since this technique includes the process of second harmonic generation (SHG), we experimentally compare the conversion efficiency and harmonic output field of the L G 0 , 0 and L G 3 , 3 modes in a cavity-enhanced SHG using the same 7% doped M g O : L i N b O 3 crystal. Conversion efficiencies of 96% and 45% are achieved, respectively. The influence of mode mismatches and astigmatism is analyzed to estimate the ratio of the pump mode-dependent effective nonlinearities to be d 0 , 0 / d 3 , 3 ∼ 5 . Furthermore, we show that absorption loss in the crystal is more relevant for the L G 3 , 3 mode.

DOI
10.1364/ol.402371

Related papers

Observation of Squeezed States of Light in Higher-Order Hermite-Gaussian Modes with a Quantum Noise Reduction of up to 10 dB

J. Heinze, B. Willke, H. Vahlbruch

Mirror thermal noise will be a main limitation for the sensitivities of the next-generation ground-based gravitational-wave detectors (Einstein Telescope and Cosmic Explorer) at signal frequencies around 100 Hz. Using a higher-order spatial laser mode instead of the fundamental mode is one proposed method to further mitigate mirror thermal noise. In the current detectors, quantum noise is successfully reduced by the injection of squeezed vacuum states. The operation in a higher-order mode would then require the efficient generation of squeezed vacuum states in this mode to maintain a high quantum noise reduction. In our setup, we generate continuous-wave squeezed states at a wavelength of 1064 nm in the fundamental and three higher-order Hermite-Gaussian modes up to a mode order of 6 using a type-I optical parametric amplifier. We present a significant milestone with a quantum noise reduction of up to 10 dB at a measurement frequency of 4 MHz in the higher-order modes and pave the way for their usage in future gravitational-wave detectors as well as in other quantum noise limited experiments.

Physical Review Letters•Feb 25, 2022•27 citations

Generation of squeezed states of light by intracavity frequency doubling

Silvania F. Pereira, Min Xiao, J. D. Miller +2 more

We have generated squeezed states of light by the process of second harmonic conversion within an optical cavity resonant at both fundamental and harmonic frequencies. The experiment consists of a standing-wave cavity containing a crystal of lithium niobate doped with magnesium oxide and driven by the field from a frequency-stabilized Nd:YAG laser (incident power, ~10 mW). The total field reflected from the cavity illuminates a pair of high quantum efficiency photodiodes, whose individual photocurrents are summed. Observations of squeezing are made by analyzing the spectral density of fluctuations for this sum photo-current while the cavity detuning is scanned through resonance. An intensity regulator holds the reflected light intensity constant during the scan by control of the incident light level. Reductions in photocurrent fluctuations of 12% relative to the vacuum-state or shot-noise level are achieved for frequency offsets near 4 MHz. Since significantly higher degrees of squeezing are predicted by our theoretical analysis, we discuss those processes that currently limit the observed noise reduction, including phase noise produced by the intracavity crystal in the absence of nonlinear conversion.

Annual Meeting Optical Society of America•Jan 1, 1988•0 citations

Multi-spatial-mode effects in squeezed-light-enhanced interferometric gravitational wave detectors

Daniel Töyrä, Daniel Brown, McKenna Davis +5 more

Proposed near-future upgrades of the current advanced interferometric gravitational wave detectors include the usage of frequency dependent squeezed light to reduce the current sensitivity-limiting quantum noise. We quantify and describe the degradation effects that spatial mode-mismatches between optical resonators have on the squeezed field. These mode-mismatches can to first order be described by scattering of light into second-order Gaussian modes. As a demonstration of principle, we also show that squeezing the second-order Hermite-Gaussian modes ${\mathrm{HG}}_{02}$ and ${\mathrm{HG}}_{20}$, in addition to the fundamental mode, has the potential to increase the robustness to spatial mode-mismatches. This scheme, however, requires independently optimised squeeze angles for each squeezed spatial mode, which would be challenging to realise in practise.

arXiv:1704.08237•Physical review. D/Physical review. D.•Jul 13, 2017•17 citations

High-efficiency squeezed light generation for gravitational wave detectors

Moritz Mehmet, H. Vahlbruch

The engineering of strongly squeezed vacuum states of light is a key technology for the reduction of quantum noise in gravitational wave detectors. We report on the observation of up to 12.0 dB squeezed vacuum states of light at the wavelength of 1064 nm in the frequency band from 10 Hz to 100 kHz. This is the strongest squeezing reported to date within this detection band. The squeezed states were generated in a half-monolithic, standing-wave cavity optical parametric amplifier, which was resonant for the fundamental and harmonic light fields. We chose appropriate reflectivities to obtain a significant reduction of the required pump power, which was 8.6 mW only. Our analysis revealed that the residual measurement phase noise was smaller than 3.5 mrad rms and that the squeezed light source provided up to 14 dB of squeezing for a downstream application. The experiment was electronically stabilized in all relevant degrees of freedom, demonstrating the applicability of the linear, doubly resonant cavity topology for current and future gravitational wave detectors.

Classical and Quantum Gravity•Nov 27, 2018•45 citations

Quantum noise reduction for gravitational-wave interferometers with non-classical states

M. J. Yap

The detection of the binary neutron star inspiral GW170817 by the Advanced Laser Interferometer Gravitational Wave Observatory (LIGO) and Advanced Virgo, followed by counterpart observations across a broad electromagnetic spectrum, marks the dawn of multi-messenger astronomy. The discovery rate and potential of gravitational-wave astronomy is limited by the detector's sensitivity. A key challenge in improving the sensitivity of gravitational-wave detectors is to reduce quantum noise which arises due to the quantum nature of light. A well established technique to reduce the quantum noise in the detector is by replacing the coherent vacuum fluctuations entering the readout port with a squeezed vacuum state. This technique has been successfully demonstrated at the GEO-600 and LIGO Hanford detector, and is now in routine operation in current gravitational wave detectors. This thesis presents research from three experiments to develop quantum noise reduction techniques for next-generation gravitational wave detector using non-classical quantum states such as squeezed states. Current proposals for future generation gravitational wave detectors, such as LIGO Voyager, plan to utilise cryogenic silicon instead of fused silica as the test mass material. This is to improve the power handling of the detector and reduce thermal noise. The switch to silicon test masses requires a change of laser wavelength to the 2 micron region. In the first experiment, we built and operated the first squeezed vacuum source at a wavelength of 1984 nm. With a stable squeezing ellipse phase control employed, 3.9 dB of squeezing was measured, predominately limited by losses due to the low quantum efficiency of the photodiode. The squeezed vacuum system presented is compatible with future detectors and is a key pathfinder experiment to inform the design of cryogenic silicon interferometers. The quantum nature of light results in quantum radiation pressure noise that limits the low frequency sensitivity of gravitational wave detectors. In collaboration with Louisiana State University, the second experiment demonstrates the reduction of quantum radiation pressure noise by injecting bright squeezed light into a centimetre-scale optomechanical cavity at room temperature. The experiment involves the development and integration of a low-frequency bright squeezed source to reduce the quantum radiation pressure noise by 1.2 dB at 20 kHz. The result also represents the lowest frequency bright squeezed state measured from a crystal-based squeezer. Quadrature rotation of the injected squeezed state is required to achieve broadband quantum noise reduction in gravitational wave detectors due to the quantum back-action effect. This requires the squeezed state to interact with a low loss optical filter with a low frequency bandwidth prior to injection and represents a significant technical challenge. The final experiment presented in this thesis demonstrates an alternate method where frequency-dependent squeezing with Einstein-Podolsky-Rosen (EPR) entangled states is generated. When integrated into a gravitational wave detector, the alternate method allows the detector to simultaneously serve as the optical filter, eliminating the need for the additional apparatus.

•Jan 1, 2020•0 citations

A novel technique for laser mode-matching in gravitational wave detectors

M Carlassara

Current interferometric gravitational wave detectors were designed to be limited, in much of their sensitive band, by quantum noise in the form of shot noise (at high frequency) or quantum radiation pressure noise (at low frequency). In the current observation run (O3), a squeezed light source has been used to manipulate quantum noise and surpass the limits imposed by the circulating laser power by injecting nonclassical states of the electromagnetic field, called squeezed vacuum states, in the interferometer's dark port. Recent O3 results show that this technique was able to reduce the shot noise contribution to the noise spectral density by about one half. To surpass the so called standard quantum limit across the entire sensitivity band, an even more complex variation of this technique will be implemented, which requires the use of a so called “filter cavity” to reflect the squeezed quantum field and rotate the squeezing angle as a function of frequency. The performance of this techniques is however severely limited by light losses. One big contributor to optical losses is the mismatch between the squeezed vacuum beam, the beam circulating into the interferometer and, in the near future, the filter cavity fundamental transverse spatial mode. To be able to monitor and actively correct mode mismatch, an accurate, online sensing technique is needed. A possible solution consists in the introduction of an Electro-Optic Lens (EOL) that can induce radio-frequency sidebands in the Laguerre-Gauss 10 (LG10) transverse mode of the beam. If the modulation frequency is tuned in a way that one sideband is at the cavity LG10 frequency, then the resonance breaks the symmetry of the two sidebands and converts phase modulation into amplitude modulation, making it possible to retrieve an error signal directly from the cavity reflected electric field with the same single-element photodetector used for the Pound Drever Hall (PDH) locking technique. This error signal carries information about the magnitude and nature of the mismatch, providing all is needed to inform a dedicated feedback loop with a suitable actuator to maintain the mismatch at or below the 1% level. The goal of this thesis is to demonstrate the technique on a dedicated bench-top experiment employing an EOL prototype device. The EOL alignment and working point, as well as the cavity lock parameters were optimized in an already existing setup. Simulations and theoretical calculations of the cavity reflected field were performed to evaluate the system non-idealities: both Electro-Optic Modulator (for PDH technique) and EOL modulations effects and interactions, as well as some system imperfections were considered. The simulations confirm that this technique requires a stable cavity lock condition, and for this reason an accurate study and optimization of the feedback loop parameters was done. In conclusion, a characterization of the EOL error signal response to different mismatch conditions are presented.

•Jun 1, 2020•0 citations
For future generations of gravitational wave detectors, it is proposed to use the helical Laguerre–Gaussian L G 3 , 3 mode to reduce thermal noise, which limits the detector sensitivity. At the same time, this requires the efficient generation of squeezed vacuum states in the L G 3 , 3 mode for quantum noise reduction. Since this technique includes the process of second harmonic generation (SHG), we experimentally compare the conversion efficiency and harmonic output field of the L G 0 , 0 and L G 3 , 3 modes in a cavity-enhanced SHG using the same 7% doped M g O : L i N b O 3 crystal. Conversion efficiencies of 96% and 45% are achieved, respectively. The influence of mode mismatches and astigmatism is analyzed to estimate the ratio of the pump mode-dependent effective nonlinearities to be d 0 , 0 / d 3 , 3 ∼ 5 . Furthermore, we show that absorption loss in the crystal is more relevant for the L G 3 , 3 mode.
Mirror thermal noise will be a main limitation for the sensitivities of the next-generation ground-based gravitational-wave detectors (Einstein Telescope and Cosmic Explorer) at signal frequencies around 100 Hz. Using a higher-order spatial laser mode instead of the fundamental mode is one proposed method to further mitigate mirror thermal noise. In the current detectors, quantum noise is successfully reduced by the injection of squeezed vacuum states. The operation in a higher-order mode would then require the efficient generation of squeezed vacuum states in this mode to maintain a high quantum noise reduction. In our setup, we generate continuous-wave squeezed states at a wavelength of 1064 nm in the fundamental and three higher-order Hermite-Gaussian modes up to a mode order of 6 using a type-I optical parametric amplifier. We present a significant milestone with a quantum noise reduction of up to 10 dB at a measurement frequency of 4 MHz in the higher-order modes and pave the way for their usage in future gravitational-wave detectors as well as in other quantum noise limited experiments.
We have generated squeezed states of light by the process of second harmonic conversion within an optical cavity resonant at both fundamental and harmonic frequencies. The experiment consists of a standing-wave cavity containing a crystal of lithium niobate doped with magnesium oxide and driven by the field from a frequency-stabilized Nd:YAG laser (incident power, ~10 mW). The total field reflected from the cavity illuminates a pair of high quantum efficiency photodiodes, whose individual photocurrents are summed. Observations of squeezing are made by analyzing the spectral density of fluctuations for this sum photo-current while the cavity detuning is scanned through resonance. An intensity regulator holds the reflected light intensity constant during the scan by control of the incident light level. Reductions in photocurrent fluctuations of 12% relative to the vacuum-state or shot-noise level are achieved for frequency offsets near 4 MHz. Since significantly higher degrees of squeezing are predicted by our theoretical analysis, we discuss those processes that currently limit the observed noise reduction, including phase noise produced by the intracavity crystal in the absence of nonlinear conversion.
Proposed near-future upgrades of the current advanced interferometric gravitational wave detectors include the usage of frequency dependent squeezed light to reduce the current sensitivity-limiting quantum noise. We quantify and describe the degradation effects that spatial mode-mismatches between optical resonators have on the squeezed field. These mode-mismatches can to first order be described by scattering of light into second-order Gaussian modes. As a demonstration of principle, we also show that squeezing the second-order Hermite-Gaussian modes HG02{\mathrm{HG}}_{02}HG02​ and HG20{\mathrm{HG}}_{20}HG20​, in addition to the fundamental mode, has the potential to increase the robustness to spatial mode-mismatches. This scheme, however, requires independently optimised squeeze angles for each squeezed spatial mode, which would be challenging to realise in practise.
The engineering of strongly squeezed vacuum states of light is a key technology for the reduction of quantum noise in gravitational wave detectors. We report on the observation of up to 12.0 dB squeezed vacuum states of light at the wavelength of 1064 nm in the frequency band from 10 Hz to 100 kHz. This is the strongest squeezing reported to date within this detection band. The squeezed states were generated in a half-monolithic, standing-wave cavity optical parametric amplifier, which was resonant for the fundamental and harmonic light fields. We chose appropriate reflectivities to obtain a significant reduction of the required pump power, which was 8.6 mW only. Our analysis revealed that the residual measurement phase noise was smaller than 3.5 mrad rms and that the squeezed light source provided up to 14 dB of squeezing for a downstream application. The experiment was electronically stabilized in all relevant degrees of freedom, demonstrating the applicability of the linear, doubly resonant cavity topology for current and future gravitational wave detectors.
The detection of the binary neutron star inspiral GW170817 by the Advanced Laser Interferometer Gravitational Wave Observatory (LIGO) and Advanced Virgo, followed by counterpart observations across a broad electromagnetic spectrum, marks the dawn of multi-messenger astronomy. The discovery rate and potential of gravitational-wave astronomy is limited by the detector's sensitivity. A key challenge in improving the sensitivity of gravitational-wave detectors is to reduce quantum noise which arises due to the quantum nature of light. A well established technique to reduce the quantum noise in the detector is by replacing the coherent vacuum fluctuations entering the readout port with a squeezed vacuum state. This technique has been successfully demonstrated at the GEO-600 and LIGO Hanford detector, and is now in routine operation in current gravitational wave detectors. This thesis presents research from three experiments to develop quantum noise reduction techniques for next-generation gravitational wave detector using non-classical quantum states such as squeezed states. Current proposals for future generation gravitational wave detectors, such as LIGO Voyager, plan to utilise cryogenic silicon instead of fused silica as the test mass material. This is to improve the power handling of the detector and reduce thermal noise. The switch to silicon test masses requires a change of laser wavelength to the 2 micron region. In the first experiment, we built and operated the first squeezed vacuum source at a wavelength of 1984 nm. With a stable squeezing ellipse phase control employed, 3.9 dB of squeezing was measured, predominately limited by losses due to the low quantum efficiency of the photodiode. The squeezed vacuum system presented is compatible with future detectors and is a key pathfinder experiment to inform the design of cryogenic silicon interferometers. The quantum nature of light results in quantum radiation pressure noise that limits the low frequency sensitivity of gravitational wave detectors. In collaboration with Louisiana State University, the second experiment demonstrates the reduction of quantum radiation pressure noise by injecting bright squeezed light into a centimetre-scale optomechanical cavity at room temperature. The experiment involves the development and integration of a low-frequency bright squeezed source to reduce the quantum radiation pressure noise by 1.2 dB at 20 kHz. The result also represents the lowest frequency bright squeezed state measured from a crystal-based squeezer. Quadrature rotation of the injected squeezed state is required to achieve broadband quantum noise reduction in gravitational wave detectors due to the quantum back-action effect. This requires the squeezed state to interact with a low loss optical filter with a low frequency bandwidth prior to injection and represents a significant technical challenge. The final experiment presented in this thesis demonstrates an alternate method where frequency-dependent squeezing with Einstein-Podolsky-Rosen (EPR) entangled states is generated. When integrated into a gravitational wave detector, the alternate method allows the detector to simultaneously serve as the optical filter, eliminating the need for the additional apparatus.
Current interferometric gravitational wave detectors were designed to be limited, in much of their sensitive band, by quantum noise in the form of shot noise (at high frequency) or quantum radiation pressure noise (at low frequency). In the current observation run (O3), a squeezed light source has been used to manipulate quantum noise and surpass the limits imposed by the circulating laser power by injecting nonclassical states of the electromagnetic field, called squeezed vacuum states, in the interferometer's dark port. Recent O3 results show that this technique was able to reduce the shot noise contribution to the noise spectral density by about one half. To surpass the so called standard quantum limit across the entire sensitivity band, an even more complex variation of this technique will be implemented, which requires the use of a so called “filter cavity” to reflect the squeezed quantum field and rotate the squeezing angle as a function of frequency. The performance of this techniques is however severely limited by light losses. One big contributor to optical losses is the mismatch between the squeezed vacuum beam, the beam circulating into the interferometer and, in the near future, the filter cavity fundamental transverse spatial mode. To be able to monitor and actively correct mode mismatch, an accurate, online sensing technique is needed. A possible solution consists in the introduction of an Electro-Optic Lens (EOL) that can induce radio-frequency sidebands in the Laguerre-Gauss 10 (LG10) transverse mode of the beam. If the modulation frequency is tuned in a way that one sideband is at the cavity LG10 frequency, then the resonance breaks the symmetry of the two sidebands and converts phase modulation into amplitude modulation, making it possible to retrieve an error signal directly from the cavity reflected electric field with the same single-element photodetector used for the Pound Drever Hall (PDH) locking technique. This error signal carries information about the magnitude and nature of the mismatch, providing all is needed to inform a dedicated feedback loop with a suitable actuator to maintain the mismatch at or below the 1% level. The goal of this thesis is to demonstrate the technique on a dedicated bench-top experiment employing an EOL prototype device. The EOL alignment and working point, as well as the cavity lock parameters were optimized in an already existing setup. Simulations and theoretical calculations of the cavity reflected field were performed to evaluate the system non-idealities: both Electro-Optic Modulator (for PDH technique) and EOL modulations effects and interactions, as well as some system imperfections were considered. The simulations confirm that this technique requires a stable cavity lock condition, and for this reason an accurate study and optimization of the feedback loop parameters was done. In conclusion, a characterization of the EOL error signal response to different mismatch conditions are presented.