## Squeezed quadrature fluctuations in a gravitational wave detector using squeezed light |

Optics Express, Vol. 21, Issue 16, pp. 19047-19060 (2013)

http://dx.doi.org/10.1364/OE.21.019047

Acrobat PDF (1117 KB)

### Abstract

Squeezed states of light are an important tool for optical measurements below the shot noise limit and for optical realizations of quantum information systems. Recently, squeezed vacuum states were deployed to enhance the shot noise limited performance of gravitational wave detectors. In most practical implementations of squeezing enhancement, relative fluctuations between the squeezed quadrature angle and the measured quadrature (sometimes called squeezing angle jitter or phase noise) are one limit to the noise reduction that can be achieved. We present calculations of several effects that lead to quadrature fluctuations, and use these estimates to account for the observed quadrature fluctuations in a LIGO gravitational wave detector. We discuss the implications of this work for quantum enhanced advanced detectors and even more sensitive third generation detectors.

© 2013 OSA

## 1. Introduction

2. C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D **23**, 1693 (1981). [CrossRef]

5. LIGO Scientific Collaboration, “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nature Photon. doi: [CrossRef] (2013).

7. H Grote, K Danzmann, K Dooley, R Schnabel, J Slutzky, and H Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. **1****10**, 181101 (2013). [CrossRef]

8. K. Wódkiewicz and M. S. Zubairy, “Effect of laser fluctuations on squeezed states in a degenerate parametric amplifier,” Phys. Rev. A **27**, 2003–2007 (1983). [CrossRef]

9. D. D. Crouch and S. L. Braunstein, “Limitations to squeezing in a parametric amplifier due to pump quantum fluctuations,” Phys. Rev. A **38**, 4696–4711 (1988). [CrossRef] [PubMed]

10. P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H. A. Bachor, and J. Gao, “Optimization and transfer of vacuum squeezing from a below threshold optical parametric oscillator,” J. Opt. B: Quantum S. O. **1**, 469–474 (1999). [CrossRef]

5. LIGO Scientific Collaboration, “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nature Photon. doi: [CrossRef] (2013).

7. H Grote, K Danzmann, K Dooley, R Schnabel, J Slutzky, and H Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. **1****10**, 181101 (2013). [CrossRef]

11. 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,” Class. Quant. Grav. **29**, 145015–145029. (2012). [CrossRef]

12. T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehment, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. **104**, **25**, 251102 (2010). [CrossRef] [PubMed]

13. T. Aoki, G. Takahashi, and A. Furasawa, “Squeezing at 946 nm with periodically poled KTiOPO_{4},” Opt. Express **14**(15), 6930–6935 (2006). [CrossRef] [PubMed]

15. A. Franzen, B. Hage, J. DiGuglielmo, J. Fiurásek, and R. Schnabel, “Experimental demonstration of continuous variable purification of squeezed states,” Phys. Rev. Lett. **97**, 150505 (2006). [CrossRef] [PubMed]

*η*is the total detection efficiency (the product of the escape efficiency of the optical parametric oscillator (OPO),the propagation, homodyne and photo detector efficiencies);

*x*is the normalized nonlinear coupling (

*g*is the parametric gain);

*θ̃*is the root mean squared (RMS) quadrature fluctuation; Ω is the measurement frequency; and

*τ*is the cavity round trip time and

*R*

_{i}is a power reflectivity for each loss mechanism). An increase in the nonlinear coupling parameter

*x*increases the amount of both squeezing and anti squeezing generated; in the presence of quadrature fluctuations there is an optimal value of

*x*at which the benefit due to increased squeezing is balanced against the increase in noise introduced by quadrature fluctuations from the anti-squeezed quadrature, as will be seen in Section 4. This means that as long as adequate second harmonic pump power is available and technical noise is negligible, the losses and total quadrature fluctuations in an experiment determine the maximum level of squeezing that can possibly be measured, illustrated in Fig. 1.

5. LIGO Scientific Collaboration, “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nature Photon. doi: [CrossRef] (2013).

16. S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”

17. 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. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Class. and Quant. Grav. **29**, 065005 (2012). [CrossRef]

11. 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,” Class. Quant. Grav. **29**, 145015–145029. (2012). [CrossRef]

18. S. Chua, M. Stefszky, C. Mow-Lowry, B. Buchler, S. Dwyer, D. Shaddock, P. K. Lam, and D. McClelland, “Backscatter tolerant squeezed light source for advanced gravitational-wave detectors,” Opt. Lett. **36**(23) 4680–4682 (2011). [CrossRef] [PubMed]

19. S. Chelkowski, H. Vahlbruch, K. Danzmann, and R. Schnabel, “Coherent control of broadband vacuum squeezing,” Phys. Rev. A **75**, 043814 (2007). [CrossRef]

## 2. Fluctuations of squeezed quadrature produced by an OPO

*θ*), as illustrated by the red trace in Fig. 3. Any shift in the phase of the second harmonic pump (

_{B}*δθ*) causes a shift of the quadrature angle away from the minimum noise point by

_{B}*δθ*/2, a mechanism that has long been considered a limitation to the level of squeezing [8

_{B}8. K. Wódkiewicz and M. S. Zubairy, “Effect of laser fluctuations on squeezed states in a degenerate parametric amplifier,” Phys. Rev. A **27**, 2003–2007 (1983). [CrossRef]

9. D. D. Crouch and S. L. Braunstein, “Limitations to squeezing in a parametric amplifier due to pump quantum fluctuations,” Phys. Rev. A **38**, 4696–4711 (1988). [CrossRef] [PubMed]

23. J. Gea-Banacloche and M. S. Zubairy, “Influence of pump-phase fluctuations on the squeezing in a degenerate parametric oscillator,” Phys. Rev. A **42**, 1742–1751 (1990). [CrossRef] [PubMed]

24. M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A **30**, 1386–1391 (1984). [CrossRef]

25. C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A **31**, 3761–3774 (1985). [CrossRef] [PubMed]

*δL*in the cavity length away from resonance will detune the fundamental field by Δ

*=*

_{a}*ωδL/L̄*where

*L̄*is the cavity length on resonance and

*ω*is the laser frequency. The second harmonic field will also have a detuning, Δ

*= 2Δ*

_{b}*. Fig. 3 shows that the effect of OPO cavity length offsets on the output field variance is well approximated as shift of the pump phase, meaning that it is well described as a shift of the squeezed quadrature. Because the cavity length fluctuations will be at frequencies small compared to the cavity linewidths, we can use this static dependence to approximate the level of quadrature fluctuations caused by cavity length fluctuations. By taking derivatives around a point where the variance (*

_{a}*V*) has a linear dependence on the pump phase (

*θ*=

_{B}*π*/2 is chosen for convenience), we can find the first order squeezing angle shift (

*dθ*) caused by a cavity length change, For our OPO, operated with a nonlinear gain of 10, this gives a coupling of 90 ± 4 mrad squeezed quadrature rotation per nanometer cavity length change. Cavity length fluctuations that occur above the 10 kHz bandwidth of the quadrature control loop directly couple to quadrature fluctuations in this way.

_{sqz}26. K. McKenzie, M. B. Gray, P. K. Lam, and D. E. McClelland, “Nonlinear phase matching locking via optical readout,” Opt. Express **14**, 11256–11264 (2006). [CrossRef] [PubMed]

27. A. Khalaidovski, H. Vahlbruch, N. Lastzka, C. Gräf, K. Danzmann, H. Grote, and R. Schnabel, “Long-term stable squeezed vacuum state of light for gravitational wave detectors,” Class. and Quant. Grav. **29**, 075001 (2012). [CrossRef]

28. K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A **72**, 043819 (2005). [CrossRef]

*ε*

_{0}is the nonlinear coupling parameter at the phase matching temperature,

*T*

_{0}is the phase matching temperature, and

*κ*is a constant that depends on the phase matching type and crystal used (0.579/K for quasi phase matching in PPKTP as used in this experiment). A change in temperature will also cause a shift in the cavity resonance condition, the more important effect in our case. To produce audio frequency squeezing the field used to lock the length of an OPO must be either the second harmonic [11

11. 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,” Class. Quant. Grav. **29**, 145015–145029. (2012). [CrossRef]

18. S. Chua, M. Stefszky, C. Mow-Lowry, B. Buchler, S. Dwyer, D. Shaddock, P. K. Lam, and D. McClelland, “Backscatter tolerant squeezed light source for advanced gravitational-wave detectors,” Opt. Lett. **36**(23) 4680–4682 (2011). [CrossRef] [PubMed]

19. S. Chelkowski, H. Vahlbruch, K. Danzmann, and R. Schnabel, “Coherent control of broadband vacuum squeezing,” Phys. Rev. A **75**, 043814 (2007). [CrossRef]

20. H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Coherent control of vacuum squeezing in the gravitational-wave detection band,” Phys. Rev. Lett. **97**, 011101 (2006). [CrossRef] [PubMed]

*τ*is the cavity round trip time. Taking both of these effects into account, the variance as a function of the input pump phase can be found using Eqs. (11), (13), and (14), and is plotted as the blue curve in Fig. 3. Again taking derivatives around

*θ*=

_{B}*π*/2 we can find the linear shift in the squeezed quadrature angle caused by a temperature change:

*mrad*, too small to be significant in our experiment. Over 60 hours, our pump power fluctuated by 5%, enough to cause degradation of the measured squeezing as seen in [27

27. A. Khalaidovski, H. Vahlbruch, N. Lastzka, C. Gräf, K. Danzmann, H. Grote, and R. Schnabel, “Long-term stable squeezed vacuum state of light for gravitational wave detectors,” Class. and Quant. Grav. **29**, 075001 (2012). [CrossRef]

## 3. Relative quadrature fluctuations introduced by measurement and control schemes

*T*

_{SB}is the power transmission of the sidebands through the OMC,

*P̄*

_{SB}is the average power in each sideband,

*dP*

_{SB}is the difference between the sidebands powers,

*P*

_{CD}is the power of the contrast defect field, and

*P*

_{sig}is the power in the signal field. The squeezing angle jitter added by this modulation is small in our case due to the excellent filtering provided by the OMC, and only contributes 3.1 ± 0.4 mrad.

## 4. Measurements of relative quadrature fluctuations

*g*=100 on a balanced homodyne detector showed that the total quadrature fluctuations intrinsic to the squeezed state source were 18.6 ± 5.7 mrad before injection into the interferometer, consistent with the level of squeezed quadrature fluctuations we predict based on OPO length noise. Assuming that length fluctuations are the dominant source of quadrature angle errors, we can infer from our high nonlinear gain measurements that the RMS quadrature fluctuations will be 21 ± 6 mrad when the nonlinear gain is 10, the normal operating point.

_{00}mode because of the Gouy phase shift. This means that relative alignment shifts change the lock point of the coherent locking loop, and alignment jitter couples to quadrature fluctuations. A change in alignment will shift the relative quadrature angle by an amount: where

*ij*spatial modes to th amplitude of the 00 mode for the interferometer field and the coherent quadrature control field respectively, and

*ϕ*is the difference between the relative phases of the

_{ij}*ij*modes and the relative phases of TEM

_{00}modes of the two beams. This coupling becomes second-order when the two beams are well aligned, as shown by the reduced quadrature fluctuations measured by the green point in Fig. 5 using a finely tuned alignment.

## 5. Implications for future gravitational wave detectors with squeezing

29. G. M. Harry, (for the LIGO Scientific Collaboration), “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quant. Grav. **27**, 084006 (2010). [CrossRef]

**29**, 145015–145029. (2012). [CrossRef]

31. Einstein gravitational wave telescope conceptual design study. https://tds.ego-gw.it/ql/?c=7954

32. K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B: Quantum S. O. **7**, S421 (2005). [CrossRef]

7. H Grote, K Danzmann, K Dooley, R Schnabel, J Slutzky, and H Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. **1****10**, 181101 (2013). [CrossRef]

**1****10**, 181101 (2013). [CrossRef]

27. A. Khalaidovski, H. Vahlbruch, N. Lastzka, C. Gräf, K. Danzmann, H. Grote, and R. Schnabel, “Long-term stable squeezed vacuum state of light for gravitational wave detectors,” Class. and Quant. Grav. **29**, 075001 (2012). [CrossRef]

26. K. McKenzie, M. B. Gray, P. K. Lam, and D. E. McClelland, “Nonlinear phase matching locking via optical readout,” Opt. Express **14**, 11256–11264 (2006). [CrossRef] [PubMed]

## 6. Appendix 1: Calculation of squeezed quadrature angle in an OPO including detunings and imperfect phase matching

## 7. Appendix 2: Calculation of control signals including detunings and imperfect phase matching

*a*

_{s}) and idler (

*a*

_{i}). Assuming that the signal and idler fields are small compared to the second harmonic field the parametric approximation holds and the second harmonic field is described by Eq. (9). Ignoring quantum fluctuations, the equations of motion are: and their hermitian conjugates, where Δ

_{s}= Δ

*+ Ω*

_{a}_{offs}and Δ

_{i}= Δ

*− Ω*

_{a}_{offs}are the detunings of the signal and idler fields when the frequency offset of the injected field from the fundamental frequency is Ω

_{offs}. Because the control bandwidth is small compared to the cavity linewidth, we find the response of the error signals to a static change by setting the derivatives to zero and solving the set of equations. The input output relations can be used to find the coherent control fields in reflection off the OPO,

*A*

_{s,r},

*A*

_{i,r}and transmitted towards the interferometer,

*A*

_{s,t},

*A*

_{i,t}: The error signal in reflection off of the cavity (demodulated at twice the frequency offset of the injected field from the interferometer with a demodulation phase

*ϕ*

_{dm1}is proportional to: In transmission the beat note with the local oscillator (

*A*

_{LO}) is demodulated at the offset frequency with a demodulation phase

*ϕ*

_{dm2}to give a signal proportional to: The relative phase between the main squeezing laser and the coherent sideband injected into the OPO is adjusted to zero the reflected (coherent field) error signal, so the impact of fluctuations can be found by setting the error signal to zero and solving numerically for change in the phase of

*A*. This phase is then propagated to the transmitted (quadrature control) error signal, and the shift of the pump phase required to zero this error signal gives the response of the entire coherent quadrature control scheme to a disturbance. The response of this scheme is the same as the response of the quadrature angle itself to fluctuations of the second harmonic pump phase, local oscillator phase, or path length from the OPO to the detector; this is a good control scheme to use to correct for fluctuations from those sources. Temperature and length fluctuations give rise to lock point errors in this control scheme.

_{s,in}## Acknowledgments

## References and links

1. | The LIGO Scientific Collaboration, , “LIGO: The laser interferometer gravitational-wave observatory,” Rep. Prog. Phys. |

2. | C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D |

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

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

5. | LIGO Scientific Collaboration, “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nature Photon. doi: [CrossRef] (2013). |

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

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

8. | K. Wódkiewicz and M. S. Zubairy, “Effect of laser fluctuations on squeezed states in a degenerate parametric amplifier,” Phys. Rev. A |

9. | D. D. Crouch and S. L. Braunstein, “Limitations to squeezing in a parametric amplifier due to pump quantum fluctuations,” Phys. Rev. A |

10. | P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H. A. Bachor, and J. Gao, “Optimization and transfer of vacuum squeezing from a below threshold optical parametric oscillator,” J. Opt. B: Quantum S. O. |

11. | 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,” Class. Quant. Grav. |

12. | T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehment, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. |

13. | T. Aoki, G. Takahashi, and A. Furasawa, “Squeezing at 946 nm with periodically poled KTiOPO |

14. | Y. Takeno, M. Yukawa, H. Yonezawa, and A. Furusawa, “Observation of −9 dB quadrature squeezing with improvement of phase stability in homodyne measurement,” Opt. Express |

15. | A. Franzen, B. Hage, J. DiGuglielmo, J. Fiurásek, and R. Schnabel, “Experimental demonstration of continuous variable purification of squeezed states,” Phys. Rev. Lett. |

16. | S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,” |

17. | 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. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Class. and Quant. Grav. |

18. | S. Chua, M. Stefszky, C. Mow-Lowry, B. Buchler, S. Dwyer, D. Shaddock, P. K. Lam, and D. McClelland, “Backscatter tolerant squeezed light source for advanced gravitational-wave detectors,” Opt. Lett. |

19. | S. Chelkowski, H. Vahlbruch, K. Danzmann, and R. Schnabel, “Coherent control of broadband vacuum squeezing,” Phys. Rev. A |

20. | H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Coherent control of vacuum squeezing in the gravitational-wave detection band,” Phys. Rev. Lett. |

21. | K. McKenzie, N. Grosse, W. P. Bowen, S. E. Whitcomb, M. B. Gray, D. E. McClelland, and P. K. Lam, “Squeezing in the audio gravitational-wave detection band,” Phys. Rev. Lett. |

22. | K. McKenzie, “Squeezing in the audio gravitational wave detection band,” Ph.D. thesis, Australian National University (2008). |

23. | J. Gea-Banacloche and M. S. Zubairy, “Influence of pump-phase fluctuations on the squeezing in a degenerate parametric oscillator,” Phys. Rev. A |

24. | M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A |

25. | C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A |

26. | K. McKenzie, M. B. Gray, P. K. Lam, and D. E. McClelland, “Nonlinear phase matching locking via optical readout,” Opt. Express |

27. | A. Khalaidovski, H. Vahlbruch, N. Lastzka, C. Gräf, K. Danzmann, H. Grote, and R. Schnabel, “Long-term stable squeezed vacuum state of light for gravitational wave detectors,” Class. and Quant. Grav. |

28. | K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A |

29. | G. M. Harry, (for the LIGO Scientific Collaboration), “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quant. Grav. |

30. | A Khalaidovski, “Beyond the quantum limit: A squeezed light laser in GEO600,” Ph.D. thesis, Gottfried Wilhelm Leibniz Universität Hannover (2011). |

31. | Einstein gravitational wave telescope conceptual design study. https://tds.ego-gw.it/ql/?c=7954 |

32. | K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B: Quantum S. O. |

33. | C. M. Caves and B. L. Schumaker, “New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states,” Phys. Rev. A |

34. | B. Buchler, “Electro-optic control of quantum measurements,” Ph.D. thesis, Australian National University (2001). |

**OCIS Codes**

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(190.4970) Nonlinear optics : Parametric oscillators and amplifiers

(270.2500) Quantum optics : Fluctuations, relaxations, and noise

(270.6570) Quantum optics : Squeezed states

(350.1270) Other areas of optics : Astronomy and astrophysics

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: June 11, 2013

Revised Manuscript: July 25, 2013

Manuscript Accepted: July 26, 2013

Published: August 2, 2013

**Citation**

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, "Squeezed quadrature fluctuations in a gravitational wave detector using squeezed light," Opt. Express **21**, 19047-19060 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-16-19047

Sort: Year | Journal | Reset

### References

- The LIGO Scientific Collaboration, , “LIGO: The laser interferometer gravitational-wave observatory,” Rep. Prog. Phys.72, 076901 (2009).
- C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D23, 1693 (1981). [CrossRef]
- R. Schnabel, N. Mavalvala, D.E. McClelland, and P.K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun.1, 121. (2010). [CrossRef] [PubMed]
- D.E. McClelland, N. Mavalvala, Y. Chen, and R. Schnabel, “Advanced interferometry, quantum optics and optomechanics in gravitational wave detectors,” Laser and Photonics Rev.5, 677–696 (2011).
- LIGO Scientific Collaboration, “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nature Photon. doi:(2013). [CrossRef]
- LIGO Scientific Collaboration, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nature Phys.7(12) 962–965 (2011).
- H Grote, K Danzmann, K Dooley, R Schnabel, J Slutzky, and H Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett.110, 181101 (2013). [CrossRef]
- K. Wódkiewicz and M. S. Zubairy, “Effect of laser fluctuations on squeezed states in a degenerate parametric amplifier,” Phys. Rev. A27, 2003–2007 (1983). [CrossRef]
- D. D. Crouch and S. L. Braunstein, “Limitations to squeezing in a parametric amplifier due to pump quantum fluctuations,” Phys. Rev. A38, 4696–4711 (1988). [CrossRef] [PubMed]
- P. K. Lam, T. C. Ralph, B. C. Buchler, D. E. McClelland, H. A. Bachor, and J. Gao, “Optimization and transfer of vacuum squeezing from a below threshold optical parametric oscillator,” J. Opt. B: Quantum S. O.1, 469–474 (1999). [CrossRef]
- 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,” Class. Quant. Grav.29, 145015–145029. (2012). [CrossRef]
- T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehment, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett.104, 25, 251102 (2010). [CrossRef] [PubMed]
- T. Aoki, G. Takahashi, and A. Furasawa, “Squeezing at 946 nm with periodically poled KTiOPO4,” Opt. Express14(15), 6930–6935 (2006). [CrossRef] [PubMed]
- Y. Takeno, M. Yukawa, H. Yonezawa, and A. Furusawa, “Observation of −9 dB quadrature squeezing with improvement of phase stability in homodyne measurement,” Opt. Express15, 4321–4327 (2007). [CrossRef] [PubMed]
- A. Franzen, B. Hage, J. DiGuglielmo, J. Fiurásek, and R. Schnabel, “Experimental demonstration of continuous variable purification of squeezed states,” Phys. Rev. Lett.97, 150505 (2006). [CrossRef] [PubMed]
- S. S. Y. Chua, S. Dwyer, L. Barsotti, D. Sigg, R. M. S. Schofield, V. V. Frolov, K. Kawabe, M. Evans, G. D. Meadors, M. Factourovich, R. Gustafson, C. Vorvick, M. Landry, A. Khalaidovski, M. S. Stefszky, C. M. Mow-Lowry, B. C. Buchler, D. A. Shaddock, P. K. Lam, R. Schnabel, N. Mavalvala, and D. E. McClelland, are preparing a manuscript to be called “Impact of backscattered-light in a squeezing-enhanced interferometric gravitational-wave detector,”
- 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. J. Slagmolen, and S. J. Waldman, “DC readout experiment in Enhanced LIGO,” Class. and Quant. Grav.29, 065005 (2012). [CrossRef]
- S. Chua, M. Stefszky, C. Mow-Lowry, B. Buchler, S. Dwyer, D. Shaddock, P. K. Lam, and D. McClelland, “Backscatter tolerant squeezed light source for advanced gravitational-wave detectors,” Opt. Lett.36(23) 4680–4682 (2011). [CrossRef] [PubMed]
- S. Chelkowski, H. Vahlbruch, K. Danzmann, and R. Schnabel, “Coherent control of broadband vacuum squeezing,” Phys. Rev. A75, 043814 (2007). [CrossRef]
- H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Coherent control of vacuum squeezing in the gravitational-wave detection band,” Phys. Rev. Lett.97, 011101 (2006). [CrossRef] [PubMed]
- K. McKenzie, N. Grosse, W. P. Bowen, S. E. Whitcomb, M. B. Gray, D. E. McClelland, and P. K. Lam, “Squeezing in the audio gravitational-wave detection band,” Phys. Rev. Lett.93, 161105 (2004). [CrossRef] [PubMed]
- K. McKenzie, “Squeezing in the audio gravitational wave detection band,” Ph.D. thesis, Australian National University (2008).
- J. Gea-Banacloche and M. S. Zubairy, “Influence of pump-phase fluctuations on the squeezing in a degenerate parametric oscillator,” Phys. Rev. A42, 1742–1751 (1990). [CrossRef] [PubMed]
- M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A30, 1386–1391 (1984). [CrossRef]
- C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A31, 3761–3774 (1985). [CrossRef] [PubMed]
- K. McKenzie, M. B. Gray, P. K. Lam, and D. E. McClelland, “Nonlinear phase matching locking via optical readout,” Opt. Express14, 11256–11264 (2006). [CrossRef] [PubMed]
- A. Khalaidovski, H. Vahlbruch, N. Lastzka, C. Gräf, K. Danzmann, H. Grote, and R. Schnabel, “Long-term stable squeezed vacuum state of light for gravitational wave detectors,” Class. and Quant. Grav.29, 075001 (2012). [CrossRef]
- K. Goda, K. McKenzie, E. E. Mikhailov, P. K. Lam, D. E. McClelland, and N. Mavalvala, “Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A72, 043819 (2005). [CrossRef]
- G. M. Harry, (for the LIGO Scientific Collaboration), “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quant. Grav.27, 084006 (2010). [CrossRef]
- A Khalaidovski, “Beyond the quantum limit: A squeezed light laser in GEO600,” Ph.D. thesis, Gottfried Wilhelm Leibniz Universität Hannover (2011).
- Einstein gravitational wave telescope conceptual design study. https://tds.ego-gw.it/ql/?c=7954
- K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B: Quantum S. O.7, S421 (2005). [CrossRef]
- C. M. Caves and B. L. Schumaker, “New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states,” Phys. Rev. A31, 3068–3092 (1985). [CrossRef] [PubMed]
- B. Buchler, “Electro-optic control of quantum measurements,” Ph.D. thesis, Australian National University (2001).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.