Local-oscillator noise coupling in balanced homodyne readout for advanced gravitational wave detectors

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Local-oscillator noise coupling in balanced homodyne readout for advanced gravitational wave detectors

Sebastian Steinlechner, Bryan W. Barr, Angus S. Bell, Stefan L. Danilishin, Andreas Gläfke, Christian Gräf, Jan-Simon Hennig, E. Alasdair Houston, Sabina H. Huttner, Sean S. Leavey, Daniela Pascucci, Borja Sorazu, Andrew Spencer, Kenneth A. Strain, Jennifer Wright, and Stefan Hild

Phys. Rev. D 92, 072009 – Published 20 October 2015

Abstract

The second generation of interferometric gravitational wave detectors are quickly approaching their design sensitivity. For the first time these detectors will become limited by quantum backaction noise. Several backaction evasion techniques have been proposed to further increase the detector sensitivity. Since most proposals rely on a flexible readout of the full amplitude- and phase-quadrature space of the output light field, balanced homodyne detection is generally expected to replace the currently used DC readout. Up to now, little investigation has been undertaken into how balanced homodyne detection can be successfully transferred from its ubiquitous application in tabletop quantum optics experiments to large-scale interferometers with suspended optics. Here we derive implementation requirements with respect to local-oscillator noise couplings and highlight potential issues with the example of the Glasgow Sagnac Speed Meter experiment, as well as for a future upgrade to the Advanced LIGO detectors.

Received 25 June 2015

DOI:https://doi.org/10.1103/PhysRevD.92.072009

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

Sebastian Steinlechner, Bryan W. Barr, Angus S. Bell, Stefan L. Danilishin, Andreas Gläfke, Christian Gräf, Jan-Simon Hennig, E. Alasdair Houston, Sabina H. Huttner, Sean S. Leavey, Daniela Pascucci, Borja Sorazu, Andrew Spencer, Kenneth A. Strain, Jennifer Wright, and Stefan Hild

SUPA, School of Physics and Astronomy, The University of Glasgow, Glasgow G12 8QQ, United Kingdom

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Vol. 92, Iss. 7 — 1 October 2015

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Images

Figure 1
Schematic of balanced homodyne detection. The signal field is overlapped on a 50:50 beam splitter with a strong LO. Both beam-splitter outputs are detected with a high-efficiency photodiode and subtracted from each other. Here, a direct photocurrent subtraction circuit is shown. The readout quadrature can be selected by adjusting the relative phase $ϕ$ between signal and LO field. RTI, transimpedance-gain setting resistor.
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Figure 2
Requirement on local-oscillator path-length stability depending on the residual DC power level in the signal field. The blue curve is calculated from (17) for a wavelength of 1064 nm, while the orange dashed curve is a simulated curve using the interferometry simulation tool Finesse [23]. We have indicated the requirements for the Glasgow Sagnac Speed Meter; see Sec. 5 below. In addition, we have added an indicative value for the high-frequency upgrade to GEO 600, based on based on the residual fundamental mode content in its output port [24].
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Figure 3
Experimental demonstration of the effect of phase noise on the local-oscillator beam, and its dependence on signal beam power. The traces were measured with a FFT analyzer as $V_{rms}$ , averaged 10 times and then normalized to the shot-noise level.
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Figure 4
Illustration of fields in the output port of a Michelson interferometer after recombination of the fields in the $x$ arm and $y$ arm. The externally supplied local oscillator (red) is chosen to be aligned to the gravitational wave signal’s quadrature (blue). A slight detuning of one of the arms leads to a dark-fringe offset (green), corresponding to additional light in the signal quadrature which will amplify the LO’s amplitude fluctuations. In contrast, an imbalance of the arms will result in additional light in the orthogonal quadrature (orange), and thus amplifies phase fluctuations of the local oscillator.
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Figure 5
Fields in the output port of a Sagnac interferometer, where the clockwise (cw) and counterclockwise (ccw) beams interfere destructively. The signal quadrature (blue) is readout with the help of an externally supplied local oscillator (red). An imbalance in the splitting ratio of the main beam splitter leads to light power in the orthogonal quadrature (orange). Contrary to the Michelson interferometer, there cannot be a static detuning of only one one of the two beams and so there is no DC field in the signal quadrature.
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Figure 6
Simulated requirements on the local-oscillator amplitude stability for the Glasgow Sagnac Speed Meter experiment, depending on main beam-splitter imbalance. The traces were simulated with Finesse [23] and do not include noise sources other than quantum noise for the sensitivity modelling.
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