Balanced homodyne readout for quantum limited gravitational wave detectors

Peter Fritschel; Matthew Evans; Valery Frolov

doi:10.1364/OE.22.004224

Optics Express
Vol. 22,
Issue 4,
pp. 4224-4234
(2014)
•https://doi.org/10.1364/OE.22.004224

Balanced homodyne readout for quantum limited gravitational wave detectors

Peter Fritschel, Matthew Evans, and Valery Frolov

Open Access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Peter Fritschel, Matthew Evans, and Valery Frolov, "Balanced homodyne readout for quantum limited gravitational wave detectors," Opt. Express 22, 4224-4234 (2014)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

Balanced homodyne detection is typically used to measure quantum-noise-limited optical beams, including squeezed states of light, at audio-band frequencies. Current designs of advanced gravitational wave interferometers use some type of homodyne readout for signal detection, in part because of its compatibility with the use of squeezed light. The readout scheme used in Advanced LIGO, called DC readout, is however not a balanced detection scheme. Instead, the local oscillator field, generated from a dark fringe offset, co-propagates with the signal field at the anti-symmetric output of the beam splitter. This article examines the alternative of a true balanced homodyne detection for the readout of gravitational wave detectors such as Advanced LIGO. Several practical advantages of the balanced detection scheme are described.

Full Article | PDF Article

More Like This

Squeezed light for advanced gravitational wave detectors and beyond

E. Oelker, L. Barsotti, S. Dwyer, D. Sigg, and N. Mavalvala
Opt. Express 22(17) 21106-21121 (2014)

Squeezed quadrature fluctuations in a gravitational wave detector using squeezed light

S. Dwyer, L. Barsotti, S. S. Y. Chua, M. Evans, M. Factourovich, D. Gustafson, T. Isogai, K. Kawabe, A. Khalaidovski, P. K. Lam, M. Landry, N. Mavalvala, D. E. McClelland, G. D. Meadors, C. M. Mow-Lowry, R. Schnabel, R. M. S. Schofield, N. Smith-Lefebvre, M. Stefszky, C. Vorvick, and D. Sigg
Opt. Express 21(16) 19047-19060 (2013)

Parallel phase modulation scheme for interferometric gravitational-wave detectors

M. T. Hartman, V. Quetschke, D. B. Tanner, D. H. Reitze, and G. Mueller
Opt. Express 22(23) 28327-28337 (2014)

Previous Article Next Article

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.

Fig. 1 A simplified interferometer with DC readout.

Download Full Size | PDF

Fig. 2 A simplified interferometer with balanced homodyne readout.

Download Full Size | PDF

Fig. 3 An interferometer with signal mirror (SRM) for recycling or signal extraction, combined with balanced homodyne readout. The BHR scheme includes an output mode cleaner (OMC) and a similar LO mode cleaner (LMC) which pass the gravitational wave signal and LO fields respectively, while rejecting unwanted light in other spatial modes. The OMC and LMC are shown associated with the readout beam splitter (BS2) and photodiodes (PD A and B, in the blue shaded area) to indicated that these parts may be rigidly mounted together to ensure optimal overlap between the LO and signal field. The SRM in this figure can be replaced with a variety of QND readout schemes, such as variational readout [17] and speed meters [19], which depend on being able to choose the homodyne readout angle independent of the DC response of the interferometer.

Download Full Size | PDF

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

A_{A S} = r_{B S} e^{i ϕ_{X}} A_{E X} - t_{B S} e^{i ϕ_{Y}} A_{E Y} = \frac{A_{I N}}{2} (e^{i ϕ_{X}} - e^{i ϕ_{Y}})

A_{G W} = \frac{A_{I N}}{2} (e^{i ϕ_{G W}} - e^{- i ϕ_{G W}}) ≃ i ϕ_{G W} A_{I N}

A_{A S} ≃ i (ϕ_{D C} + ϕ_{G W}) A_{I N} = A_{D C} + A_{G W} .

P_{A S} = {| A_{D C} |}^{2} + A_{D C}^{*} A_{G W} + A_{D C} A_{G W}^{*} = {| A_{D C} |}^{2} + 2 ℛ e (A_{D C} A_{G W}^{*})

P_{A S} = {\bar{P}}_{A S} + 2 ℛ e ({\bar{A}}_{D C} {(A_{G W} + ε {\bar{A}}_{D C})}^{*})

A_{P O} = (1 + ε) {\bar{A}}_{P O} and {\bar{P}}_{P O} = {\bar{A}}_{P O}^{2}

P_{A} = {\bar{P}}_{P O} / 2 + ℛ e (e^{i ϕ} {\bar{A}}_{P O} {(A_{G W} + ε e^{i ϕ} {\bar{A}}_{P O})}^{*})

P_{B} = {\bar{P}}_{P O} / 2 + ℛ e (e^{i ϕ} {\bar{A}}_{P O} {(- A_{G W} + ε e^{i ϕ} {\bar{A}}_{P O})}^{*})

P_{A} + P_{B} = {\bar{P}}_{P O} (1 + 2 ε)

P_{A} - P_{B} = 2 ℛ e (e^{i ϕ} {\bar{A}}_{P O} A_{G W}^{*})

ν_{n} = 2 \sqrt{k_{B} T R} \leq ε R \sqrt{2 h ν P_{A S}} / (α F_{S Q Z})

V_{D C} = ε R P_{A S} = \frac{2 k_{B} T}{ε h ν} F_{S Q Z}^{2} ≃ 5 V F_{S Q Z}^{2} .

Abstract

Cited By

Figures (3)

Equations (12)

Optics Express