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

arXiv:1501.01349 · Physical Review A

Quantum noise of a white-light cavity using a double-pumped gain medium

Yiqiu Ma, Haixing Miao, Chunnong Zhao, Yanbei Chen

Published Aug 5, 2015• 18 citations
arXivHTMLPDF

Abstract

Laser interferometric gravitational-wave detectors implement Fabry-P\'erot cavities to increase their peak sensitivity. However, this is at the cost of reducing their detection bandwidth, which originates from the propagation phase delay of the light. The ``white-light-cavity'' idea, first proposed by Wicht et al. [Opt. Commun. 34, 431 (1997)], is to circumvent this limitation by introducing anomalous dispersion, using a double-pumped gain medium, to compensate for such a phase delay. In this article, starting from the Hamiltonian of the atom-light interaction, we apply an input-output formalism to evaluate the quantum noise of the system. We find that apart from the additional noise associated with the parametric amplification process noted by others, the stability condition for the entire system poses an additional constraint. By surveying the parameter regimes where the gain medium remains stable (not lasing) and stationary, we find that there is no net enhancement of the shot-noise-limited sensitivity. Therefore, other gain media or different parameter regimes should be explored for realizing the white-light cavity.

DOI
10.1103/physreva.92.023807

Related papers

Squeezed light for the interferometric detection of high-frequency gravitational waves

Roman Schnabel, J. Harms, K. A. Strain +1 more

The quantum noise of the light field is a fundamental noise source in interferometric gravitational wave detectors. Injected squeezed light is capable of reducing the quantum noise contribution to the detector noise floor to values that surpass the so-called Standard-Quantum-Limit (SQL). In particular, squeezed light is useful for the detection of gravitational waves at high frequencies where interferometers are typically shot-noise limited, although the SQL might not be beaten in this case. We theoretically analyze the quantum noise of the signal-recycled laser interferometric gravitational-wave detector GEO600 with additional input and output optics, namely frequency-dependent squeezing of the vacuum state of light entering the dark port and frequency-dependent homodyne detection. We focus on the frequency range between 1 kHz and 10 kHz, where, although signal recycled, the detector is still shot-noise limited. It is found that the GEO600 detector with present design parameters will benefit from frequency dependent squeezed light. Assuming a squeezing strength of -6 dB in quantum noise variance, the interferometer will become thermal noise limited up to 4 kHz without further reduction of bandwidth. At higher frequencies the linear noise spectral density of GEO600 will still be dominated by shot-noise and improved by a factor of 10^{6dB/20dB}~2 according to the squeezing strength assumed. The interferometer might reach a strain sensitivity of 6x10^{-23} above 1 kHz (tunable) with a bandwidth of around 350 Hz. We propose a scheme to implement the desired frequency dependent squeezing by introducing an additional optical component to GEO600s signal-recycling cavity.

arXiv:gr-qc/0401119•Classical and Quantum Gravity•Feb 12, 2004•26 citations

Beating the Standard Sensitivity-Bandwidth Limit of Cavity-Enhanced Interferometers with Internal Squeezed-Light Generation

M. Korobko, L. Kleybolte, S. Ast +3 more

The shot-noise limited peak sensitivity of cavity-enhanced interferometric measurement devices, such as gravitational-wave detectors, can be improved by increasing the cavity finesse, even when comparing fixed intracavity light powers. For a fixed light power inside the detector, this comes at the price of a proportional reduction in the detection bandwidth. High sensitivity over a large span of signal frequencies, however, is essential for astronomical observations. It is possible to overcome this standard sensitivity-bandwidth limit using nonclassical correlations in the light field. Here, we investigate the internal squeezing approach, where the parametric amplification process creates a nonclassical correlation directly inside the interferometer cavity. We theoretically analyze the limits of the approach and measure 36% increase in the sensitivity-bandwidth product compared to the classical case. To our knowledge, this is the first experimental demonstration of an improvement in the sensitivity-bandwidth product using internal squeezing, opening the way for a new class of optomechanical force sensing devices.

arXiv:1702.01044•Physical Review Letters•Apr 7, 2017•53 citations

Gravitational wave detection using laser interferometry beyond the standard quantum limit

M. Heurs

Interferometric gravitational wave detectors (such as advanced LIGO) employ high-power solid-state lasers to maximize their detection sensitivity and hence their reach into the universe. These sophisticated light sources are ultra-stabilized with regard to output power, emission frequency and beam geometry; this is crucial to obtain low detector noise. However, even when all laser noise is reduced as far as technically possible, unavoidable quantum noise of the laser still remains. This is a consequence of the Heisenberg Uncertainty Principle, the basis of quantum mechanics: in this case, it is fundamentally impossible to simultaneously reduce both the phase noise and the amplitude noise of a laser to arbitrarily low levels. This fact manifests in the detector noise budget as two distinct noise sources—photon shot noise and quantum radiation pressure noise—which together form a lower boundary for current-day gravitational wave detector sensitivities, the standard quantum limit of interferometry. To overcome this limit, various techniques are being proposed, among them different uses of non-classical light and alternative interferometer topologies. This article explains how quantum noise enters and manifests in an interferometric gravitational wave detector, and gives an overview of some of the schemes proposed to overcome this seemingly fundamental limitation, all aimed at the goal of higher gravitational wave event detection rates. This article is part of a discussion meeting issue ‘The promises of gravitational-wave astronomy’.

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Apr 16, 2018•10 citations

Realization of a negative dispersion medium at 1064nm in an optomechanical resonator for enhancing the sensitivity-bandwidth product in a gravitational-wave detector

Minchuan Zhou, Seunghwi Kim, Gaurav Bahl +1 more

Recently, we had proposed an optically-pumped five-level Gain EIT (GEIT) system, which has a transparency dip superimposed on a gain profile and exhibits a negative dispersion suitable for the white light cavity (WLC) enhanced interferometric gravitational wave detector [Phys. Rev. D. 92, 082002 (2015)]. Using this system as the negative dispersion medium (NDM) in the WLC-SR (signal recycling) scheme, we get an enhancement in the quantum noise (QN) limited sensitivity-bandwidth product by a factor of ~18. We have also shown how to realize such a system in practice using Zeeman sublevels in $^{87}$Rb at 795nm [Opt. Commun. 402, 382-388 (2017)]. However, aLIGO operates at 1064nm and suitable transitions in Rb or other alkali atoms are not available at this wavelength. Therefore, it is necessary to consider a system that is consistent with the operating wavelength of aLIGO. Here, we present the realization of such an NDM at 1064nm with a microresonator, which supports optomechanical interaction. A strong control field is applied at a higher frequency, and, under certain conditions, a probe field at a lower frequency experiences a peak at the center of an absorption profile, and a negative dispersion in the transmission. Unlike in the GEIT case, we use the compound-cavity signal-recycling (CC-SR) scheme, where an auxiliary mirror is inserted in the dark port of the detector, and show that the enhancement factor can be as high as ~15. However, using the parameters required for the sensitivity enhancement, the optomechanical system enters an instability region where the control field is depleted. We present an observer based feedback control process used to stabilize the CC-SR system.

arXiv:1610.07255•Oct 24, 2016•0 citations

Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors

Alessandra Buonanno, Yanbei Chen

It has long been thought that the sensitivity of laser interferometric gravitational-wave detectors is limited by the free-mass standard quantum limit, unless radical redesigns of the interferometers or modifications of their input or output optics are introduced. Within a fully quantum-mechanical approach we show that in a second-generation interferometer composed of arm cavities and a signal recycling cavity, e.g., the LIGO-II configuration, (i) quantum shot noise and quantum radiation-pressure-fluctuation noise are dynamically correlated, (ii) the noise curve exhibits two resonant dips, (iii) the standard quantum limit can be beaten by a factor of 2, over a frequency range $\ensuremath{\Delta}f/f\ensuremath{\sim}1,$ but at the price of increasing noise at lower frequencies.

arXiv:gr-qc/0102012•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Jul 30, 2001•304 citations

Input spectrum for heterodyne detection in advanced gravitational wave detectors without non-stationary shot-noise

P. T. Beyersdorf

Future interferometric gravitational wave detectors will make use of the coupling between shot noise and radiation pressure noise that produces a squeezed output for the quantum noise at the dark-port of the interferometer allowing these interferometers to operate with a sensitivity that exceeds the standard quantum limit at certain frequencies. The ability of the detector to take advantage of this squeezed output state depends in part on the readout system used. With the phase modulated laser input planned for these interferometers the quantum-noise limited sensitivity is slightly better when homodyne (rather than heterodyne) detection is used. We show that by modifying the laser input spectrum for these interferometers, readout with heterodyne detection can be made to have the same quantum-noise limited sensitivity as readout with homodyne detection.

arXiv:gr-qc/0609113•Sep 25, 2006•0 citations
Laser interferometric gravitational-wave detectors implement Fabry-P'erot cavities to increase their peak sensitivity. However, this is at the cost of reducing their detection bandwidth, which originates from the propagation phase delay of the light. The ``white-light-cavity'' idea, first proposed by Wicht et al. [Opt. Commun. 34, 431 (1997)], is to circumvent this limitation by introducing anomalous dispersion, using a double-pumped gain medium, to compensate for such a phase delay. In this article, starting from the Hamiltonian of the atom-light interaction, we apply an input-output formalism to evaluate the quantum noise of the system. We find that apart from the additional noise associated with the parametric amplification process noted by others, the stability condition for the entire system poses an additional constraint. By surveying the parameter regimes where the gain medium remains stable (not lasing) and stationary, we find that there is no net enhancement of the shot-noise-limited sensitivity. Therefore, other gain media or different parameter regimes should be explored for realizing the white-light cavity.
The quantum noise of the light field is a fundamental noise source in interferometric gravitational wave detectors. Injected squeezed light is capable of reducing the quantum noise contribution to the detector noise floor to values that surpass the so-called Standard-Quantum-Limit (SQL). In particular, squeezed light is useful for the detection of gravitational waves at high frequencies where interferometers are typically shot-noise limited, although the SQL might not be beaten in this case. We theoretically analyze the quantum noise of the signal-recycled laser interferometric gravitational-wave detector GEO600 with additional input and output optics, namely frequency-dependent squeezing of the vacuum state of light entering the dark port and frequency-dependent homodyne detection. We focus on the frequency range between 1 kHz and 10 kHz, where, although signal recycled, the detector is still shot-noise limited. It is found that the GEO600 detector with present design parameters will benefit from frequency dependent squeezed light. Assuming a squeezing strength of -6 dB in quantum noise variance, the interferometer will become thermal noise limited up to 4 kHz without further reduction of bandwidth. At higher frequencies the linear noise spectral density of GEO600 will still be dominated by shot-noise and improved by a factor of 10^{6dB/20dB}~2 according to the squeezing strength assumed. The interferometer might reach a strain sensitivity of 6x10^{-23} above 1 kHz (tunable) with a bandwidth of around 350 Hz. We propose a scheme to implement the desired frequency dependent squeezing by introducing an additional optical component to GEO600s signal-recycling cavity.
The shot-noise limited peak sensitivity of cavity-enhanced interferometric measurement devices, such as gravitational-wave detectors, can be improved by increasing the cavity finesse, even when comparing fixed intracavity light powers. For a fixed light power inside the detector, this comes at the price of a proportional reduction in the detection bandwidth. High sensitivity over a large span of signal frequencies, however, is essential for astronomical observations. It is possible to overcome this standard sensitivity-bandwidth limit using nonclassical correlations in the light field. Here, we investigate the internal squeezing approach, where the parametric amplification process creates a nonclassical correlation directly inside the interferometer cavity. We theoretically analyze the limits of the approach and measure 36% increase in the sensitivity-bandwidth product compared to the classical case. To our knowledge, this is the first experimental demonstration of an improvement in the sensitivity-bandwidth product using internal squeezing, opening the way for a new class of optomechanical force sensing devices.
Interferometric gravitational wave detectors (such as advanced LIGO) employ high-power solid-state lasers to maximize their detection sensitivity and hence their reach into the universe. These sophisticated light sources are ultra-stabilized with regard to output power, emission frequency and beam geometry; this is crucial to obtain low detector noise. However, even when all laser noise is reduced as far as technically possible, unavoidable quantum noise of the laser still remains. This is a consequence of the Heisenberg Uncertainty Principle, the basis of quantum mechanics: in this case, it is fundamentally impossible to simultaneously reduce both the phase noise and the amplitude noise of a laser to arbitrarily low levels. This fact manifests in the detector noise budget as two distinct noise sources—photon shot noise and quantum radiation pressure noise—which together form a lower boundary for current-day gravitational wave detector sensitivities, the standard quantum limit of interferometry. To overcome this limit, various techniques are being proposed, among them different uses of non-classical light and alternative interferometer topologies. This article explains how quantum noise enters and manifests in an interferometric gravitational wave detector, and gives an overview of some of the schemes proposed to overcome this seemingly fundamental limitation, all aimed at the goal of higher gravitational wave event detection rates. This article is part of a discussion meeting issue ‘The promises of gravitational-wave astronomy’.
Recently, we had proposed an optically-pumped five-level Gain EIT (GEIT) system, which has a transparency dip superimposed on a gain profile and exhibits a negative dispersion suitable for the white light cavity (WLC) enhanced interferometric gravitational wave detector [Phys. Rev. D. 92, 082002 (2015)]. Using this system as the negative dispersion medium (NDM) in the WLC-SR (signal recycling) scheme, we get an enhancement in the quantum noise (QN) limited sensitivity-bandwidth product by a factor of ~18. We have also shown how to realize such a system in practice using Zeeman sublevels in 87^{87}87Rb at 795nm [Opt. Commun. 402, 382-388 (2017)]. However, aLIGO operates at 1064nm and suitable transitions in Rb or other alkali atoms are not available at this wavelength. Therefore, it is necessary to consider a system that is consistent with the operating wavelength of aLIGO. Here, we present the realization of such an NDM at 1064nm with a microresonator, which supports optomechanical interaction. A strong control field is applied at a higher frequency, and, under certain conditions, a probe field at a lower frequency experiences a peak at the center of an absorption profile, and a negative dispersion in the transmission. Unlike in the GEIT case, we use the compound-cavity signal-recycling (CC-SR) scheme, where an auxiliary mirror is inserted in the dark port of the detector, and show that the enhancement factor can be as high as ~15. However, using the parameters required for the sensitivity enhancement, the optomechanical system enters an instability region where the control field is depleted. We present an observer based feedback control process used to stabilize the CC-SR system.
It has long been thought that the sensitivity of laser interferometric gravitational-wave detectors is limited by the free-mass standard quantum limit, unless radical redesigns of the interferometers or modifications of their input or output optics are introduced. Within a fully quantum-mechanical approach we show that in a second-generation interferometer composed of arm cavities and a signal recycling cavity, e.g., the LIGO-II configuration, (i) quantum shot noise and quantum radiation-pressure-fluctuation noise are dynamically correlated, (ii) the noise curve exhibits two resonant dips, (iii) the standard quantum limit can be beaten by a factor of 2, over a frequency range $\ensuremath{\Delta}f/f\ensuremath{\sim}1,$ but at the price of increasing noise at lower frequencies.
Future interferometric gravitational wave detectors will make use of the coupling between shot noise and radiation pressure noise that produces a squeezed output for the quantum noise at the dark-port of the interferometer allowing these interferometers to operate with a sensitivity that exceeds the standard quantum limit at certain frequencies. The ability of the detector to take advantage of this squeezed output state depends in part on the readout system used. With the phase modulated laser input planned for these interferometers the quantum-noise limited sensitivity is slightly better when homodyne (rather than heterodyne) detection is used. We show that by modifying the laser input spectrum for these interferometers, readout with heterodyne detection can be made to have the same quantum-noise limited sensitivity as readout with homodyne detection.