Polarization speed meter for gravitational-wave detection

Andrew R. Wade, Kirk McKenzie, Yanbei Chen, Daniel A. Shaddock, Jong H. Chow, and David E. McClelland

Phys. Rev. D 86, 062001 – Published 5 September 2012

Abstract

We propose a modified configuration of an advanced gravitational-wave detector that is a speed-meter-type interferometer with improved sensitivity with respect to quantum noise. With the addition of polarization-controlling components to the output of an arm cavity Michelson interferometer, an orthogonal polarization state of the interferometer can be used to store signal, returning it later with opposite phase to cancel position information below the storage bandwidth of the opposite mode. This modification provides an alternative to an external kilometer-scale Fabry-Pérot cavity, as presented in earlier work of Purdue and Chen [Phys. Rev. D 66, 122004 (2002)]. The new configuration requires significantly less physical infrastructure to achieve speed meter operation. The quantity of length and alignment degrees of freedom is also reduced. We present theoretical calculations to show that such a speed meter detector is capable of beating the strain sensitivity imposed by the standard quantum limit over a broad range of frequencies for Advanced Laser Interferometer Gravitational-wave Observatory-like parameters. The benefits and possible difficulties of implementing such a scheme are outlined. We also present results for tuning of the speed meter by adjusting the degree of polarization coupling, a novel possibility that does not exist in previously proposed designs, showing that there is a smooth transition from speed meter operation to that of a signal-recycling Michelson behavior.

Received 21 May 2012

DOI:https://doi.org/10.1103/PhysRevD.86.062001

Authors & Affiliations

Andrew R. Wade¹, Kirk McKenzie², Yanbei Chen³, Daniel A. Shaddock¹, Jong H. Chow¹, and David E. McClelland¹

¹Centre for Gravitational Physics, Department of Quantum Science, The Australian National University, Canberra, ACT, 0200, Australia
²Jet Propulsion Laboratory (JPL), California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California 91109, USA
³Theoretical Astrophysics 350-17, California Institute of Technology, Pasadena, California 91125, USA

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Vol. 86, Iss. 6 — 15 September 2012

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Figure 1
Schematic of the polarization speed meter configuration. Horizontal linear polarization fields a, b, e and f and vertical fields c, d, g and h are indicated in red and blue respectively. Arm cavities are formed between the test mass mirrors and the arm cavity mirrors $T_{i}$ , photons undergo a number of round trips, increasing their response to changes in the optical path due to GW. Carrier laser light is injected into the left port of the configuration in the horizontal polarization where the Michelson is held to its dark fringe on transmission. Differential test mass motion generates phase modulation sidebands in the horizontal polarization at the quadrature field point $f_{i}^{'}$ . The quarter-wave plate ( $λ / 4$ ) and output coupler mirror ( $T_{o}$ ) couple these signals into an orthogonal polarization so that stored signals may couple back $π$ out of phase to cancel position signals below the bandwidth of the polarization storage. The polarizing beam splitter isolates the two polarizations from each other so that the vertical polarization port can be closed with a mirror to prevent vacuum noise coupling in, and signals may be read out on the horizontal port only. The horizontal polarization is detected with a homodyne detector.Reuse & Permissions
Figure 2
Plot of the amplitude of the radiation pressure coupling function, $κ$ , as a function of frequency. This shows a constant degree of coupling from the amplitude to the phase quadrature for frequencies up to 100 Hz. Below this bandwidth a homodyne readout angle may be chosen that projects out noise contribution from the amplitude quadrature. This plot is produced from the parameters presented in Table with two choices of arm cavity finesse set by a $T_{i}$ of 0.10 and 0.05. Circulating power was fixed at 850 kW with the power at the beam splitter adjusted for each of the $T_{i}$ . Labels on curves indicate the beam splitter power and arm cavity mirror transmissivity.Reuse & Permissions
Figure 3
Strain-equivalent quantum noise contribution as a function of frequency for the polarization-folded speed meter. Here three curves are displayed: two for the different choices of arm cavity mirror transmissivity $T_{i} = 0.10$ and $T_{i} = 0.05$ and a third that is the Advanced LIGO quantum noise contribution calculated using the software package GWINC [14]. Labels on curves indicate the choice of $T_{i}$ and the beam splitter power to ensure circulating power at 850 kW. Also, for the polarization speed meter calculations, the homodyne readout phase has been adjusted to cancel amplitude quadrature contributions to the noise. It is shown here that the configuration can match the SQL using the parameters presented in Table over a broad range of frequencies. Over a narrower range operation ( $T_{i} = 0.05$ ) the configuration can be less than the SQL by factors of four. The sensitivity no longer matches the slope of the SQL when the function $κ$ is no longer constant in frequency.Reuse & Permissions
Figure 4
Plot of radiation pressure coupling function, $κ$ , as function of frequency for different choices of quarter-wave plate rotation $θ$ . As the degree of wave plate rotation approaches zero degrees the bandwidth of speed meter operation narrows. The configuration approaches the behavior of signal recycling as the coupling function is no longer constant as a function of frequency. The arm cavity circulating power for these plots was adjusted to 850 kW. All other parameters are as presented in Table .Reuse & Permissions
Figure 5
Plot of gravitational strain-referenced noise sensitivity as a function of frequency for different choices of quarter-wave plate rotation $θ$ . Corresponding to the evolution of the radiation pressure coupling function, $κ$ (see Fig. 4), for different choices of $θ$ sensitivities beats the standard quantum limit below the roll off of the $κ$ function. Homodyne readout angles are chosen for each choice of $θ$ that cancel contributions of amplitude noise obscuring the GW signal. The bandwidth of speed meter operation narrows as the degree of coupling between the polarizations is turned down (i.e., the quarter-wave plate is oriented toward zero). The arm cavity circulating power for these plots was set to 850 kW, and all other parameters are as presented in Table .Reuse & Permissions

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