## Generation of squeezed light with a monolithic optical parametric oscillator: Simultaneous achievement of phase matching and cavity resonance by temperature control |

Optics Express, Vol. 18, Issue 19, pp. 20143-20150 (2010)

http://dx.doi.org/10.1364/OE.18.020143

Acrobat PDF (770 KB)

### Abstract

We generate squeezed state of light at 860 nm with a monolithic optical parametric oscillator. The optical parametric oscillator consists of a periodically poled KTiOPO_{4} crystal, both ends of which are spherically polished and mirror-coated. We achieve both phase matching and cavity resonance by controlling only the temperature of the crystal. We observe up to −8.0±0.2 dB of squeezing with the bandwidth of 142 MHz. Our technique makes it possible to drive many monolithic cavities simultaneously by a single laser. Hence our monolithic optical parametric oscillator is quite suitable to continuous-variable quantum information experiments where we need a large number of highly squeezed light beams.

© 2010 Optical Society of America

## 1. Introduction

1. C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D **23**, 1693–1708 (1981). [CrossRef]

2. K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. Mckenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, “A quantum-enhanced prototype gravitational-wave detector,” Nature Phys. **4**, 472–476 (2008). [CrossRef]

4. N. J. Cerf, G. Leuchs, and E. S. Polzik, *Quantum Information with Continuous Variables of Atoms and Light* (Imperial College Press, 2007). [CrossRef]

6. T. Aoki, G. Takahashi, T. Kajiya, J. Yoshikawa, S. L. Braunstein, P. van Loock, and A. Furusawa, “Quantum error correction beyond qubits,” Nature Phys. **5**, 541–546 (2009). [CrossRef]

7. R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of Squeezed States Generated by Four-Wave Mixing in an Optical Cavity,” Phys. Rev. Lett. **55**, 2409–2412 (1985). [CrossRef] [PubMed]

8. L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of Squeezed States by Parametric Down Conversion,” Phys. Rev. Lett. **57**, 2520–2523 (1986). [CrossRef] [PubMed]

9. R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-Band Parametric Deamplification of Quantum Noise in an Optical Fiber,” Phys. Rev. Lett. **57**, 691–694 (1986). [CrossRef] [PubMed]

10. S. Suzuki, H. Yonezawa, F. Kannari, M. Sasaki, and A. Furusawa, “7 dB quadrature squeezing at 860 nm with periodically poled KTiOPO_{4},” Appl. Phys. Lett. **89**, 061116 (2006). [CrossRef]

11. 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**, 4321–4327 (2007). [CrossRef] [PubMed]

12. K. Goda, E. E. Mikhailov, O. Miyakawa, S. Saraf, S. Vass, A. Weinstein, and N. Mavalvala, “Generation of a stable low-frequency squeezed vacuum field with periodically poled KTiOPO_{4} at 1064 nm,” Opt. Lett. **33**, 92–94 (2008). [CrossRef] [PubMed]

13. H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. **100**, 033602 (2008). [CrossRef] [PubMed]

14. G. Masada, T. Suzudo, Y. Satoh, H. Ishizuki, T. Taira, and A. Furusawa, “Efficient generation of highly squeezed light with periodically poled MgO:LiNbO_{3},” Opt. Express **18**, 13114–13121(2010). [CrossRef] [PubMed]

15. M. Mehmet, H. Vahlbruch, N. Lastzka, K. Danzmann, and R. Schnabel, “Observation of squeezed states with strong photon-number oscillations,” Phys Rev A **81**, 013814 (2010). [CrossRef]

16. H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, “The GEO600 squeezed light source,” Class. Quantum Grav. **27**, 084027 (2010). [CrossRef]

*et al.*[15

15. M. Mehmet, H. Vahlbruch, N. Lastzka, K. Danzmann, and R. Schnabel, “Observation of squeezed states with strong photon-number oscillations,” Phys Rev A **81**, 013814 (2010). [CrossRef]

_{3}are spherically polished and mirror-coated. Thanks to the extremely low intra-cavity loss, which is an advantage of monolithic OPO, they observed such a highly squeezing at 1064 nm. Besides, they also demonstrated a broad spectrum of the squeezing over 170 MHz. Note that squeezing bandwidth of a conventional bow-tie OPO is limited to around 10 MHz [11

11. 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**, 4321–4327 (2007). [CrossRef] [PubMed]

*et al.*did not lock the OPO cavity length [15

15. M. Mehmet, H. Vahlbruch, N. Lastzka, K. Danzmann, and R. Schnabel, “Observation of squeezed states with strong photon-number oscillations,” Phys Rev A **81**, 013814 (2010). [CrossRef]

13. H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. **100**, 033602 (2008). [CrossRef] [PubMed]

17. 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 an optical parametric oscillator,” J. Opt. B: Quantum Semiclass. Opt. **1**, 469–474 (1999). [CrossRef]

_{4}(PPKTP) monolithic OPOs. By controlling only the temperature of the crystal, we achieve both phase matching and cavity resonance of the monolithic OPO. We generate −8.0±0.2 dB of squeezing with a squeezing spectrum over 142 MHz. Our technique enables us to drive many monolithic OPOs simultaneously. Moreover our setup is quite simple and stable compared to the previous experiments. Hence our PPKTP monolithic OPO is easily applied to future quantum information experiments in which several broadband and high-level squeezed lights are required.

## 2. PPKTP monolithic OPO

11. 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**, 4321–4327 (2007). [CrossRef] [PubMed]

*µ*m. One end of the crystal has a high reflection coating, and the other has a partial transmittance coating for 860 nm. We investigate three monolithic OPOs which have different partial transmittance coating, 11.8 % (labeled as No.1), 8.2 % (No.2) and 4.4 % (No.3). For a second harmonic beam (430 nm), both ends have an anti-reflection coating. In other words, our OPOs are resonant only on the fundamental laser frequency. We do not use a doubly resonant OPO as in Ref. [15

**81**, 013814 (2010). [CrossRef]

*a*-cut for both fundamental and second harmonic beams polarized along the

*c*-axis. The poling period is 4.3

*µm*, and noncritical phase matching is achieved around 40 °C. In order to fulfill both resonance and phase matching conditions simultaneously, we control only the temperature of the crystal. Phase matching is characterized by conversion efficiency

*η*from fundamental to second harmonic beam as [18],

*l*is the crystal length, and

*λ*is the wavelength of the fundamental beam. Δ

*n*

^{(2ω)}

*and Δ*

_{Z}*n*

^{(ω)}

*are deviations of refractive indices from phase matching condition. These refractive indices are along*

_{Z}*Z*(

*c*)-axis for the second harmonic beam (2

*ω*) and the fundamental beam (

*ω*), respectively. Roughly speaking, the phase matching is achieved (that is,

*η*≥ 0.5) under the condition of ∣Δ

*kl*∣ ≤

*π*. Then the temperature range of phase matching Δ

*T*

_{PM}can be calculated as,

*dn*

^{(2ω)}

*/*

_{Z}*dT*and

*dn*

^{(ω)}

_{Z}/

*dT*are given from Ref. [19] as 5.10×10

^{−5}K

^{−1}and 3.57×10

^{−5}K

^{−1}, respectively. Note that if we choose a doubly resonant OPO, effective crystal length would be double and Δ

*T*

_{PM}would be a half. The resonance condition is given by 2

*ln*

^{(ω)}

_{Z}=

*mλ*where m is an integer. We can calculate a free spectrum range in terms of temperature Δ

*T*

_{FSR}as,

*T*

_{PM}>Δ

*T*

_{FSR}, we can achieve both resonance and phase matching condition simultaneously by changing only the temperature.

*T*

_{PM}and Δ

*T*

_{FSR}are calculated as 2.5 °C and 1.2 °C, respectively. We have at least two resonance peaks in the range of phase matching temperature. Although phase matching condition

*η*may not be perfectly optimized under the resonance condition, we can obtain

*at least*86 % of

*η*compared to that in the perfect phase matching condition. Therefore we can achieve near-optimal condition by just controlling the temperature of the crystal.

## 3. Experimental setup

_{3}crystal [14

14. G. Masada, T. Suzudo, Y. Satoh, H. Ishizuki, T. Taira, and A. Furusawa, “Efficient generation of highly squeezed light with periodically poled MgO:LiNbO_{3},” Opt. Express **18**, 13114–13121(2010). [CrossRef] [PubMed]

*µ*W in the squeezed beam. Note that we need only one auxiliary beam for locking system while several auxiliary beams, which are often frequency-shifted, are usually used [10

10. S. Suzuki, H. Yonezawa, F. Kannari, M. Sasaki, and A. Furusawa, “7 dB quadrature squeezing at 860 nm with periodically poled KTiOPO_{4},” Appl. Phys. Lett. **89**, 061116 (2006). [CrossRef]

**15**, 4321–4327 (2007). [CrossRef] [PubMed]

12. K. Goda, E. E. Mikhailov, O. Miyakawa, S. Saraf, S. Vass, A. Weinstein, and N. Mavalvala, “Generation of a stable low-frequency squeezed vacuum field with periodically poled KTiOPO_{4} at 1064 nm,” Opt. Lett. **33**, 92–94 (2008). [CrossRef] [PubMed]

14. G. Masada, T. Suzudo, Y. Satoh, H. Ishizuki, T. Taira, and A. Furusawa, “Efficient generation of highly squeezed light with periodically poled MgO:LiNbO_{3},” Opt. Express **18**, 13114–13121(2010). [CrossRef] [PubMed]

16. H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, “The GEO600 squeezed light source,” Class. Quantum Grav. **27**, 084027 (2010). [CrossRef]

**15**, 4321–4327 (2007). [CrossRef] [PubMed]

## 4. Results and discussions

*x*. Here we define

*P*and

*P*are pump power and the oscillation threshold power of the OPO, respectively.

_{th}*P*is estimated as 283 mW from parametric amplification [11

_{th}**15**, 4321–4327 (2007). [CrossRef] [PubMed]

*R*′

_{±}which is given as [11

**15**, 4321–4327 (2007). [CrossRef] [PubMed]

*κ*is overall propagation efficiency outside the OPO,

*T*is the output coupler transmittance,

*L*is the intra-cavity loss of the OPO,

*f*is the measurement frequency,

*f*

_{0}is a frequency of half width at half maximum of the OPO, and

*is fluctuation of phase locking. Theoretical curves in Fig. 3(b) are fitted to the experimental data with the parameter*θ ˜

*.*θ ˜

*is given as 2.0 degree which is consistent with 1.5 degree in Ref. [11*θ ˜

**15**, 4321–4327 (2007). [CrossRef] [PubMed]

*T*/(

*T*+

*L*). The escape efficiency is considered as an effective transmittance. The intra-cavity loss is measured 0.8 % and then the escape efficiency is 0.937 which corresponds to 6.3 % effective loss. The propagation coefficient

*κ*is given as 0.968 by taking into account homodyne visibility (0.986), propagation efficiency (0.998) and quantum efficiency of photo diode (0.998). Then the total loss outside the OPO is counted as 3.2 %. The intra-cavity loss may be caused by crystal defects or imperfect polishing. In a future work, it should be improved.

*R*

_{−}increases up to

*R*

^{min}_{−}[15

**81**, 013814 (2010). [CrossRef]

*x*)

*f*

_{0}. Estimated bandwidth of our squeezing is 142 MHz, which is more than ten times wider than that of a conventional bow-tie OPO [11

**15**, 4321–4327 (2007). [CrossRef] [PubMed]

**81**, 013814 (2010). [CrossRef]

_{3},” Opt. Express **18**, 13114–13121(2010). [CrossRef] [PubMed]

## 5. Conclusion

## Acknowledgments

## References and links

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

2. | K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. Mckenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, “A quantum-enhanced prototype gravitational-wave detector,” Nature Phys. |

3. | S. L. Braunstein and A. K. Pati, |

4. | N. J. Cerf, G. Leuchs, and E. S. Polzik, |

5. | R. Ukai, N. Iwata, Y. Shimokawa, S. C. Armstrong, A. Politi, J. Yoshikawa, P. van Loock, and A. Furusawa, “Demonstration of unconditional one-way quantum computations for continuous variables,” arXiv: 1001.4860 [quant-ph] (2010). |

6. | T. Aoki, G. Takahashi, T. Kajiya, J. Yoshikawa, S. L. Braunstein, P. van Loock, and A. Furusawa, “Quantum error correction beyond qubits,” Nature Phys. |

7. | R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of Squeezed States Generated by Four-Wave Mixing in an Optical Cavity,” Phys. Rev. Lett. |

8. | L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of Squeezed States by Parametric Down Conversion,” Phys. Rev. Lett. |

9. | R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-Band Parametric Deamplification of Quantum Noise in an Optical Fiber,” Phys. Rev. Lett. |

10. | S. Suzuki, H. Yonezawa, F. Kannari, M. Sasaki, and A. Furusawa, “7 dB quadrature squeezing at 860 nm with periodically poled KTiOPO |

11. | 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 |

12. | K. Goda, E. E. Mikhailov, O. Miyakawa, S. Saraf, S. Vass, A. Weinstein, and N. Mavalvala, “Generation of a stable low-frequency squeezed vacuum field with periodically poled KTiOPO |

13. | H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. |

14. | G. Masada, T. Suzudo, Y. Satoh, H. Ishizuki, T. Taira, and A. Furusawa, “Efficient generation of highly squeezed light with periodically poled MgO:LiNbO |

15. | M. Mehmet, H. Vahlbruch, N. Lastzka, K. Danzmann, and R. Schnabel, “Observation of squeezed states with strong photon-number oscillations,” Phys Rev A |

16. | H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, “The GEO600 squeezed light source,” Class. Quantum Grav. |

17. | 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 an optical parametric oscillator,” J. Opt. B: Quantum Semiclass. Opt. |

18. | A. Yariv, |

19. | G. G. Gurzadian, V. G. Dmitriev, and D. N. Nikogosian, |

**OCIS Codes**

(120.2920) Instrumentation, measurement, and metrology : Homodyning

(270.6570) Quantum optics : Squeezed states

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: July 19, 2010

Revised Manuscript: September 1, 2010

Manuscript Accepted: September 1, 2010

Published: September 7, 2010

**Citation**

Hidehiro Yonezawa, Koyo Nagashima, and Akira Furusawa, "Generation of squeezed light with a monolithic optical parametric oscillator: Simultaneous achievement of phase matching and cavity resonance by temperature control," Opt. Express **18**, 20143-20150 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-19-20143

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### References

- C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D Part. Fields 23, 1693–1708 (1981). [CrossRef]
- K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. Mckenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, “A quantum-enhanced prototype gravitational-wave detector,” Nat. Phys. 4, 472–476 (2008). [CrossRef]
- S. L. Braunstein and A. K. Pati, Quantum Information with Continuous Variables (Kluwer Academic Publishers, Dordrecht, 2003).
- N. J. Cerf, G. Leuchs, and E. S. Polzik, Quantum Information with Continuous Variables of Atoms and Light (Imperial College Press, 2007). [CrossRef]
- R. Ukai, N. Iwata, Y. Shimokawa, S. C. Armstrong, A. Politi, J. Yoshikawa, P. van Loock, and A. Furusawa, “Demonstration of unconditional one-way quantum computations for continuous variables,” arXiv: 1001.4860 [quant-ph] (2010).
- T. Aoki, G. Takahashi, T. Kajiya, J. Yoshikawa, S. L. Braunstein, P. van Loock, and A. Furusawa, “Quantum error correction beyond qubits,” Nat. Phys. 5, 541–546 (2009). [CrossRef]
- R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of Squeezed States Generated by Four-Wave Mixing in an Optical Cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985). [CrossRef] [PubMed]
- L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of Squeezed States by Parametric Down Conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986). [CrossRef] [PubMed]
- R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-Band Parametric Deamplification of Quantum Noise in an Optical Fiber,” Phys. Rev. Lett. 57, 691–694 (1986). [CrossRef] [PubMed]
- S. Suzuki, H. Yonezawa, F. Kannari, M. Sasaki, and A. Furusawa, “7 dB quadrature squeezing at 860 nm with periodically poled KTiOPO4,” Appl. Phys. Lett. 89, 061116 (2006). [CrossRef]
- 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, 4321–4327 (2007). [CrossRef] [PubMed]
- K. Goda, E. E. Mikhailov, O. Miyakawa, S. Saraf, S. Vass, A. Weinstein, and N. Mavalvala, “Generation of a stable low-frequency squeezed vacuum field with periodically poled KTiOPO4 at 1064 nm,” Opt. Lett. 33, 92–94 (2008). [CrossRef] [PubMed]
- H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (2008). [CrossRef] [PubMed]
- G. Masada, T. Suzudo, Y. Satoh, H. Ishizuki, T. Taira, and A. Furusawa, “Efficient generation of highly squeezed light with periodically poled MgO:LiNbO3,” Opt. Express 18, 13114–13121 (2010). [CrossRef] [PubMed]
- M. Mehmet, H. Vahlbruch, N. Lastzka, K. Danzmann, and R. Schnabel, “Observation of squeezed states with strong photon-number oscillations,” Phys. Rev. A 81, 013814 (2010). [CrossRef]
- H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gr¨af, K. Danzmann, and R. Schnabel, “The GEO600 squeezed light source,” Class. Quantum Gravity 27, 084027 (2010). [CrossRef]
- 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 an optical parametric oscillator,” J. Opt. B Quantum Semiclassical Opt. 1, 469–474 (1999). [CrossRef]
- A. Yariv, Optical Electronics in Modern Communications 5th ed. (Oxford University Press, Oxford New York, 1997).
- G. G. Gurzadian, V. G. Dmitriev, and D. N. Nikogosian, Handbook of Nonlinear Optical Crystals (Springer, 1999).

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