## Balanced homodyne readout for quantum limited gravitational wave detectors |

Optics Express, Vol. 22, Issue 4, pp. 4224-4234 (2014)

http://dx.doi.org/10.1364/OE.22.004224

Acrobat PDF (958 KB)

### 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.

© 2014 Optical Society of America

## 1. Introduction

1. LIGO Laboratory, LIGO web site: http://www.ligo.caltech.edu/

4. KAGRA, KAGRA web site: http://gwcenter.icrr.u-tokyo.ac.jp/en

5. G. M. Harry, and The LIGO Scientific Collaboration, “Advanced LIGO: the next generation of gravitational wave detectors,” Classical Quantum Gravity **27**(8), 084006 (2010). [CrossRef]

6. Gravitational Wave International Committee (GWIC) Roadmap, 2010, https://gwic.ligo.org/roadmap/

7. LIGO Scientific Collaboration, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Rep. Prog. Phys. **72**(7), 076901 (2009). [CrossRef]

8. T. T. Fricke, N. D. Smith-Lefebvre, R. Abbott, R. Adhikari, K. L. Dooley, M. Evans, P. Fritschel, V. V. Frolov, K. Kawabe, J. S. Kissel, B. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Classical Quantum Gravity , **29**(6), 065005 (2012). [CrossRef]

9. A. Buonanno, Y. Chen, and N. Mavalvala, “Quantum noise in laser-interferometer gravitational-wave detectors with a heterodyne readout scheme,” Phys. Rev. D **67**(12), 122005 (2003). [CrossRef]

12. LIGO Scientific Collaboration, “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photonics **7**, 613–619 (2013). [CrossRef]

13. W. Chaibi and F. Bondu, “Optomechanical issues in the gravitational wave detector Advanced VIRGO,” C. R. Phys. **12**(9–10), 888–897 (2011). [CrossRef]

14. R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. **1**(8), 121 (2010). [CrossRef] [PubMed]

15. The fact that gravitational wave detectors would benefit from this scheme is apparently clear to quantum optics researchers, as it appears to have been mistakenly assumed by: H. Müller-Ebhardt, H. Rehbein, C. Li, Y. Mino, K. Somiya, R. Schnabel, K. Danzmann, and Y Chen, “Quantum-state preparation and macroscopic entanglement in gravitational-wave detectors,” Phys. Rev. A **80**(4), 043802 (2009). [CrossRef]

16. B. J. Meers and K. A. Strain, “Modulation, signal, and quantum noise in interferometers,” Phys. Rev. A **44**(7), 4693 (1991). [CrossRef] [PubMed]

*assumed*to be a free parameter, though no provision is made for producing the needed field [17

17. H. Kimble, Y. Levin, A. Matsko, K. Thorne, and S. Vyatchanin, “Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics,” Phys. Rev. D **65**(2), 022002 (2001). [CrossRef]

21. F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, and C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D **83**, 062003 (2011). [CrossRef]

17. H. Kimble, Y. Levin, A. Matsko, K. Thorne, and S. Vyatchanin, “Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics,” Phys. Rev. D **65**(2), 022002 (2001). [CrossRef]

19. P. Purdue and Y. Chen, “Practical speed meter designs for quantum nondemolition gravitational-wave interferometers,” Phys. Rev. D **66**(12), 122004 (2002). [CrossRef]

## 2. DC readout

*ϕ*caused by a passing gravitational wave thus produces an AS port field component, If this is the only field at the AS port, however, the power measured there will be only second order in

_{GW}*A*(i.e.,

_{GW}*ϕ*= −

_{X}*ϕ*=

_{Y}*ϕ*+

_{DC}*ϕ*, sends a static field

_{GW}*A*to the AS port, where The presence of

_{DC}*A*causes the power at the AS port to show a linear response to

_{DC}*A*proportional to the leaked field amplitude where

_{GW}*P*is the power measured at the AS port, and we neglect the term second order in

_{AS}*A*.

_{GW}*A*= (1 +

_{DC}*ε*)

*Ā*, such that where terms second order in

_{DC}*ε*have been dropped, and the average power at the AS port is

*A*), relative to the field produced by the gravitational wave signal (

_{DC}*A*), is fixed. This relative phase is zero in our simple interferometer example, but will in general not be zero for more realistic interferometers. In principle, some control over the LO phase is possible if the field amplitudes from the two arms are not identical; i.e. if

_{GW}*A*≠

_{EX}*A*. Such an imbalance will produce a static AS port field in quadrature to the

_{EY}*A*given in Eq. (3), and the LO will be the sum of these two static fields. By varying the amplitude of the differential offset, the phase as well as the amplitude of the LO field can therefore be adjusted. In practice, however, the static AS field due to amplitude imbalance is typically small compared to the desired LO amplitude. The LO will thus be dominated by the differential offset field, and the achievable phase variation of the LO will be small.

_{DC}## 3. Balanced homodyne readout for Gravitational Wave detectors

*P*+

_{A}*P*, while the gravitational wave signal appears in

_{B}*P*−

_{A}*P*. That is, where the complex phase

_{B}*e*is included explicitly to highlight the fact that the LO phase is no longer tied to the gravitational wave signal phase as it is in DC readout.

^{iϕ}20. J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, and R. Schnabel, “Squeezed-input, optical-spring, signal-recycled gravitational-wave detectors,” Phys. Rev. D **68**(4), 042001 (2003). [CrossRef]

22. Suitable RF sidebands are already present in all modern interferometric gravitational wave detectors: P. Fritschel, R. Bork, G. Gonzalez, N. Mavalvala, D. Ouimette, H. Rong, D. Sigg, and M. Zucker, “Readout and control of a power-recycled interferometric gravitational-wave antenna,” Appl. Opt. **40**(28), 4988–4998 (2001). [CrossRef]

*PD*and

_{A}*PD*in Fig. 2) [23

_{B}23. H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. **110**, 181101 (2013). [CrossRef] [PubMed]

*ϕ*in Fig. 2).

24. K. McKenzie, M. B. Gray, P. K. Lam, and D. E. McClelland, “Technical limitations to homodyne detection at audio frequencies,” Appl. Opt. **46**, 3389–3395 (2007). [CrossRef] [PubMed]

25. M. S. Stefszky, C. M. Mow-Lowry, S. S. Y Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidovski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical Quantum Gravity **29**(14), 145015 (2012). [CrossRef]

25. M. S. Stefszky, C. M. Mow-Lowry, S. S. Y Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidovski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical Quantum Gravity **29**(14), 145015 (2012). [CrossRef]

## 4. Mode cleaning cavities

*contrast defect*: the AS port contains some power in higher-order optical modes, even at the dark fringe, due to imperfect optics. To prevent the contrast defect from increasing shot noise on the gravitational wave readout detectors, an “output mode cleaner” cavity (OMC) is placed between the AS port and the readout detectors [8

8. T. T. Fricke, N. D. Smith-Lefebvre, R. Abbott, R. Adhikari, K. L. Dooley, M. Evans, P. Fritschel, V. V. Frolov, K. Kawabe, J. S. Kissel, B. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Classical Quantum Gravity , **29**(6), 065005 (2012). [CrossRef]

26. N. Smith-Lefebvre, S. Ballmer, M. Evans, S. J. Waldman, K. Kawabe, V. Frolov, and N. Mavalvala, “Optimal alignment sensing of a readout mode cleaner cavity,” Opt. Lett. **36**(22), 4365–4367 (2011). [CrossRef] [PubMed]

25. M. S. Stefszky, C. M. Mow-Lowry, S. S. Y Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidovski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical Quantum Gravity **29**(14), 145015 (2012). [CrossRef]

## 5. BHR in Advanced LIGO

*PO*in Fig. 2). This surface is anti-reflection coated with a typical reflectivity of 50–100 ppm. Over the anticipated interferometer input power range of 25 – 125 W, the LO power would be in the range 25 – 250 mW. In Advanced LIGO, this PO beam already propagates through some of the same telescoping optics as the AS beam, before it is captured by an in-vacuum beam dump. To use the beam as an LO for BHR, the beam dump would be replaced by a few beam directing optics to bring the beam into the output vacuum chamber, where the new LMC would be located along with the existing OMC.

8. T. T. Fricke, N. D. Smith-Lefebvre, R. Abbott, R. Adhikari, K. L. Dooley, M. Evans, P. Fritschel, V. V. Frolov, K. Kawabe, J. S. Kissel, B. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Classical Quantum Gravity , **29**(6), 065005 (2012). [CrossRef]

^{−4}) is at least as large as that provided by a Faraday isolator; thus no additional isolator should be required in the LO path. Furthermore, since the AS port does not contain a large LO field, a Faraday isolator may not be required in this path either.

*R*to produce a measurable voltage, and that the thermal voltage noise of that resistor is the dominant source of readout electronics noise. The resistor voltage noise must be smaller, by a safety factor

*α*, than the quantum noise to be measured: where

*k*= 4.1 × 10

_{B}T^{−21}J at room temperature,

*hν*= 1.8 × 10

^{−19}J for 1064 nm photons, and a high quality photo-diode converts these photons to electrons with

*ε*≃ 0.85A/W. The introduction of squeezing would reduce the shot-noise component by a factor in the range 2 <

*F*< 3. The constant voltage at the output of a trans-impedance amplifier, designed with

_{SQZ}*α*= 10 such that thermal noise is well below quantum noise, turns out to be independent of the detected power: This is a reasonable value in the absence of squeezing, but becomes technically challenging with

27. P. C. D. Hobbs, “Ultrasensitive laser measurements without tears,” Appl. Opt. **36**, 903–920 (1997). [CrossRef] [PubMed]

## 6. Conclusion

*optimal*readout quadrature. These features make balanced homodyne readout essentially imperative in future gravitational wave detector design.

## References and links

1. | LIGO Laboratory, LIGO web site: http://www.ligo.caltech.edu/ |

2. | Virgo Collaboration, Virgo web site: http://wwwcascina.virgo.infn.it/ |

3. | GEO600, GEO web site: http://geo600.aei.mpg.de/ |

4. | KAGRA, KAGRA web site: http://gwcenter.icrr.u-tokyo.ac.jp/en |

5. | G. M. Harry, and The LIGO Scientific Collaboration, “Advanced LIGO: the next generation of gravitational wave detectors,” Classical Quantum Gravity |

6. | Gravitational Wave International Committee (GWIC) Roadmap, 2010, https://gwic.ligo.org/roadmap/ |

7. | LIGO Scientific Collaboration, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Rep. Prog. Phys. |

8. | T. T. Fricke, N. D. Smith-Lefebvre, R. Abbott, R. Adhikari, K. L. Dooley, M. Evans, P. Fritschel, V. V. Frolov, K. Kawabe, J. S. Kissel, B. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Classical Quantum Gravity , |

9. | A. Buonanno, Y. Chen, and N. Mavalvala, “Quantum noise in laser-interferometer gravitational-wave detectors with a heterodyne readout scheme,” Phys. Rev. D |

10. | D. E. McClelland, N. Mavalvala, Y. Chen, and R. Schnabel, “Advanced interferometry, quantum optics and optomechanics in gravitational wave detectors,” Laser Photonics Rev. |

11. | LIGO Scientific Collaboration, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nat. Phys. |

12. | LIGO Scientific Collaboration, “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photonics |

13. | W. Chaibi and F. Bondu, “Optomechanical issues in the gravitational wave detector Advanced VIRGO,” C. R. Phys. |

14. | R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. |

15. | The fact that gravitational wave detectors would benefit from this scheme is apparently clear to quantum optics researchers, as it appears to have been mistakenly assumed by: H. Müller-Ebhardt, H. Rehbein, C. Li, Y. Mino, K. Somiya, R. Schnabel, K. Danzmann, and Y Chen, “Quantum-state preparation and macroscopic entanglement in gravitational-wave detectors,” Phys. Rev. A |

16. | B. J. Meers and K. A. Strain, “Modulation, signal, and quantum noise in interferometers,” Phys. Rev. A |

17. | H. Kimble, Y. Levin, A. Matsko, K. Thorne, and S. Vyatchanin, “Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics,” Phys. Rev. D |

18. | A. Buonanno and Y. Chen, “Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors,” Phys. Rev. D |

19. | P. Purdue and Y. Chen, “Practical speed meter designs for quantum nondemolition gravitational-wave interferometers,” Phys. Rev. D |

20. | J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, and R. Schnabel, “Squeezed-input, optical-spring, signal-recycled gravitational-wave detectors,” Phys. Rev. D |

21. | F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, and C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D |

22. | Suitable RF sidebands are already present in all modern interferometric gravitational wave detectors: P. Fritschel, R. Bork, G. Gonzalez, N. Mavalvala, D. Ouimette, H. Rong, D. Sigg, and M. Zucker, “Readout and control of a power-recycled interferometric gravitational-wave antenna,” Appl. Opt. |

23. | H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. |

24. | K. McKenzie, M. B. Gray, P. K. Lam, and D. E. McClelland, “Technical limitations to homodyne detection at audio frequencies,” Appl. Opt. |

25. | M. S. Stefszky, C. M. Mow-Lowry, S. S. Y Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidovski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical Quantum Gravity |

26. | N. Smith-Lefebvre, S. Ballmer, M. Evans, S. J. Waldman, K. Kawabe, V. Frolov, and N. Mavalvala, “Optimal alignment sensing of a readout mode cleaner cavity,” Opt. Lett. |

27. | P. C. D. Hobbs, “Ultrasensitive laser measurements without tears,” Appl. Opt. |

**OCIS Codes**

(000.2780) General : Gravity

(120.2920) Instrumentation, measurement, and metrology : Homodyning

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(270.5570) Quantum optics : Quantum detectors

(270.6570) Quantum optics : Squeezed states

**ToC Category:**

Detectors

**History**

Original Manuscript: November 6, 2013

Revised Manuscript: January 22, 2014

Manuscript Accepted: January 22, 2014

Published: February 18, 2014

**Citation**

Peter Fritschel, Matthew Evans, and Valery Frolov, "Balanced homodyne readout for quantum limited gravitational wave detectors," Opt. Express **22**, 4224-4234 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-4-4224

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### References

- LIGO Laboratory, LIGO web site: http://www.ligo.caltech.edu/
- Virgo Collaboration, Virgo web site: http://wwwcascina.virgo.infn.it/
- GEO600, GEO web site: http://geo600.aei.mpg.de/
- KAGRA, KAGRA web site: http://gwcenter.icrr.u-tokyo.ac.jp/en
- G. M. Harry, and The LIGO Scientific Collaboration, “Advanced LIGO: the next generation of gravitational wave detectors,” Classical Quantum Gravity 27(8), 084006 (2010). [CrossRef]
- Gravitational Wave International Committee (GWIC) Roadmap, 2010, https://gwic.ligo.org/roadmap/
- LIGO Scientific Collaboration, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Rep. Prog. Phys. 72(7), 076901 (2009). [CrossRef]
- T. T. Fricke, N. D. Smith-Lefebvre, R. Abbott, R. Adhikari, K. L. Dooley, M. Evans, P. Fritschel, V. V. Frolov, K. Kawabe, J. S. Kissel, B. J. Slagmolen, S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Classical Quantum Gravity, 29(6), 065005 (2012). [CrossRef]
- A. Buonanno, Y. Chen, N. Mavalvala, “Quantum noise in laser-interferometer gravitational-wave detectors with a heterodyne readout scheme,” Phys. Rev. D 67(12), 122005 (2003). [CrossRef]
- D. E. McClelland, N. Mavalvala, Y. Chen, R. Schnabel, “Advanced interferometry, quantum optics and optomechanics in gravitational wave detectors,” Laser Photonics Rev. 5, 677–696 (2011).
- LIGO Scientific Collaboration, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nat. Phys. 7(12), 962–965 (2011). [CrossRef]
- LIGO Scientific Collaboration, “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photonics 7, 613–619 (2013). [CrossRef]
- W. Chaibi, F. Bondu, “Optomechanical issues in the gravitational wave detector Advanced VIRGO,” C. R. Phys. 12(9–10), 888–897 (2011). [CrossRef]
- R. Schnabel, N. Mavalvala, D. E. McClelland, P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1(8), 121 (2010). [CrossRef] [PubMed]
- The fact that gravitational wave detectors would benefit from this scheme is apparently clear to quantum optics researchers, as it appears to have been mistakenly assumed by: H. Müller-Ebhardt, H. Rehbein, C. Li, Y. Mino, K. Somiya, R. Schnabel, K. Danzmann, Y Chen, “Quantum-state preparation and macroscopic entanglement in gravitational-wave detectors,” Phys. Rev. A 80(4), 043802 (2009). [CrossRef]
- B. J. Meers, K. A. Strain, “Modulation, signal, and quantum noise in interferometers,” Phys. Rev. A 44(7), 4693 (1991). [CrossRef] [PubMed]
- H. Kimble, Y. Levin, A. Matsko, K. Thorne, S. Vyatchanin, “Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics,” Phys. Rev. D 65(2), 022002 (2001). [CrossRef]
- A. Buonanno, Y. Chen, “Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors,” Phys. Rev. D 64(4), 042006 (2001). [CrossRef]
- P. Purdue, Y. Chen, “Practical speed meter designs for quantum nondemolition gravitational-wave interferometers,” Phys. Rev. D 66(12), 122004 (2002). [CrossRef]
- J. Harms, Y. Chen, S. Chelkowski, A. Franzen, H. Vahlbruch, K. Danzmann, R. Schnabel, “Squeezed-input, optical-spring, signal-recycled gravitational-wave detectors,” Phys. Rev. D 68(4), 042001 (2003). [CrossRef]
- F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D 83, 062003 (2011). [CrossRef]
- Suitable RF sidebands are already present in all modern interferometric gravitational wave detectors: P. Fritschel, R. Bork, G. Gonzalez, N. Mavalvala, D. Ouimette, H. Rong, D. Sigg, M. Zucker, “Readout and control of a power-recycled interferometric gravitational-wave antenna,” Appl. Opt. 40(28), 4988–4998 (2001). [CrossRef]
- H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. 110, 181101 (2013). [CrossRef] [PubMed]
- K. McKenzie, M. B. Gray, P. K. Lam, D. E. McClelland, “Technical limitations to homodyne detection at audio frequencies,” Appl. Opt. 46, 3389–3395 (2007). [CrossRef] [PubMed]
- M. S. Stefszky, C. M. Mow-Lowry, S. S. Y Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidovski, R. Schnabel, P. K. Lam, D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical Quantum Gravity 29(14), 145015 (2012). [CrossRef]
- N. Smith-Lefebvre, S. Ballmer, M. Evans, S. J. Waldman, K. Kawabe, V. Frolov, N. Mavalvala, “Optimal alignment sensing of a readout mode cleaner cavity,” Opt. Lett. 36(22), 4365–4367 (2011). [CrossRef] [PubMed]
- P. C. D. Hobbs, “Ultrasensitive laser measurements without tears,” Appl. Opt. 36, 903–920 (1997). [CrossRef] [PubMed]

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