## Observation of a comb of optical squeezing over many gigahertz of bandwidth

Optics Express, Vol. 15, Issue 9, pp. 5310-5317 (2007)

http://dx.doi.org/10.1364/OE.15.005310

Acrobat PDF (668 KB)

### Abstract

We experimentally demonstrate the generation of optical squeezing at multiple longitudinal modes and transverse Hermite-Gauss modes of an optical parametric amplifier. We present measurements of approximately 3 dB squeezing at baseband, 1.7 GHz, 3.4 GHz and 5.1 GHz which correspond to the first, second and third resonances of the amplifier. We show that both the magnitude and the bandwidth of the squeezing at the higher longitudinal modes is greater than can be observed at baseband. The squeezing observed is the highest frequency squeezing reported to date.

© 2007 Optical Society of America

## 1. Introduction

1. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. **74**, 145–195 (2002); F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature **421**, 238–241 (2003). [CrossRef]

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

3. B.J. Meers and K.A. Strain “Modulation, signal, and quantum noise in interferometers,” Phys. Rev. A **44**, 4693–4703 (1991). [CrossRef] [PubMed]

6. P.G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. **75**, 4337–4341 (1995). [CrossRef] [PubMed]

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

8. Y. J. Lu and Z. Y. Ou, “Optical parametric oscillator far below threshold: Experiment versus theory,” Phys. Rev. A **62**033804 (2000). [CrossRef]

*et. al*. [7

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

10. A.E. Dunlop, E.H. Huntington, C.C. Harb, and T.C. Ralph, “Generation of a frequency comb of squeezing in an optical parametric oscillator,” Phys. Rev. A **73**, 013817 (2006). [CrossRef]

11. G.N. Milford, C. C. Harb, and E. H. Huntington, “Shot noise limited, microwave bandwidth photodetector design,” Rev. Sci. Instrum. **77**, 114701 (2006). [CrossRef]

## 2. Experimental Setup

^{3}and is made from bulk LiNbO

_{3}which is 7% doped with MgO and phase-matched at 60

*°*C. The OPA cavity is linear and is formed by the rear surface of the crystal (radius of curvature = 8 mm, high reflector at 532 nm, R=99.9% at 1064 nm) and an external mirror (radius of curvature = 75 mm, R=13% at 532 nm and R=96% at 1064 nm). The front surface of the crystal has a radius of curvature of 8 mm and is anti-reflection coated at both 1064 nm and 532 nm. The optical path length (OPL) of the OPA cavity is approximately 90 mm giving an FSR of 1.7 GHz.

_{00}or TEM

_{10}mode at 1064 nm, with oscillation threshold at 200 mW and 350 mW pump power respectively. The system is operated as a de-amplifier with gains of 0.3 and 0.45 for the TEM

_{00}and TEM

_{10}modes respectively. Due to the fact that the system is operating in de-amplification mode lower gain values produce greater de-amplification. When operated as a squeezer, the OPA is seeded with 5 mW incident on the greater than 99.9% reflecting surface.

_{00}spatial mode of the incoming beam to higher order modes resonant in the cavity by misaligning the input beam. The output of the MTC is used to seed the OPA from the rear surface and as the local oscillator in subsequent measurements.

_{00}, and 4.2 mW for TEM

_{10}. The quantum noise level calibration was achieved by direct measurement of the local oscillator at the appropriate photocurrent.

14. “43 GBit/s DPSK Balanced Photoreceiver,” http://www.u2t.de/pdf/Preliminary_Datasheet_BPRV2123_V10.pdf.

15. M.B. Gray, D.A. Shaddock, C.C. Harb, and H.-A. Bachor, “Photodetector designs for low-noise, broadband, and high-power applications,” Rev. Sci. Instrum. **69**, 3755–3762 (1998). [CrossRef]

*μ*m diameter InGaAs photodiode with quantum efficiency of more than 95% using an AD829 amplifier in transimpedance mode. This detector had greater than 10 dB clearance between electronic noise and quantum noise from DC and 30 MHz. Note that the locking detectors for both the MTC and the OPA were of a lumped element design using 1 mm InGaAs photodiodes and LMH6624 amplifiers in transimpedance mode.

16. G. Gonzalez, *Microwave Transistor Amplifiers: Analysis and Design, 2 ^{nd}* Ed, (Prentice Hall, 1996). [PubMed]

11. G.N. Milford, C. C. Harb, and E. H. Huntington, “Shot noise limited, microwave bandwidth photodetector design,” Rev. Sci. Instrum. **77**, 114701 (2006). [CrossRef]

*pin*InGaAs photodiode, a microwave bandwidth amplifier and an inter-connecting matching network. This matching network achieves a broad-band power match between the AC shot noise power developed by the photodiode and the amplifier’s 50 Ω input impedance. The photodetector is constructed as a microstrip circuit allowing close integration of the photodiode and associated bias circuitry, mi-crostrip matching network and amplifier components (Mini-Circuits ERA MMIC [17

17. Mini-Circuits, www.mini-circuits.com

11. G.N. Milford, C. C. Harb, and E. H. Huntington, “Shot noise limited, microwave bandwidth photodetector design,” Rev. Sci. Instrum. **77**, 114701 (2006). [CrossRef]

## 3. Theory

10. A.E. Dunlop, E.H. Huntington, C.C. Harb, and T.C. Ralph, “Generation of a frequency comb of squeezing in an optical parametric oscillator,” Phys. Rev. A **73**, 013817 (2006). [CrossRef]

*V*(ω), and the variance in the phase quadrature is denoted

^{+}_{out}*V*(

^{-}_{out}*ω*) where

*ω*is the Fourier frequency, i.e. the difference frequency between the optical carrier and the sidebands. The output variances are:

*T*/τ and it is assumed to be set only by the transmission

*T*of the output coupling mirror and the cavity round trip time τ. The nonlinear frequency conversion rate is χ and the down conversion bandwidth of the crystal is taken to be large compared to the Fourier frequencies of interest. The nonlinear frequency conversion rate is χ = 2β

_{inχ}

^{(2)}where χ

^{(2)}is the second order coefficient of nonlinearity for the nonlinear material and β

_{in}is the amplitude of the pump field (assumed to be real without loss of generality). Equation 1 describes the frequency and phase dependent amplification (amplitude quadrature variance) or de-amplification (phase quadrature variance) of the noise of the seed. Minima in the squeezing spectrum are separated in frequency by the cavity free-spectral range (FSR) and occur at Fourier frequencies of ω =

*m*ω

_{FSR}= 2

*πm*/τ for

*m*= 0,1,2,⋯ within the downconversion bandwidth. Note that the resonance at

*m*= 0 is the baseband squeezing spectrum. The downconversion bandwidth in a bulk nonlinear material of length L is estimated to be 10

*c*/

*nL*(c is the speed of light in vacuum, n is the refractive index of the material) [18

18. M. G. Raymer, Jaewoo Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A **72**023825 (2005). [CrossRef]

*m*≈ 60 for the crystals described herein.

- intracavity loss of the OPA plus escape efficiency of output coupling, (23±3)%;
- optical losses between the OPA and the detection beamsplitter, (6±1)%;
- the quantum efficiency of the photodetector, worst case (8±2)%;
- non-ideal overlap of the local oscillator with the squeezed beam, (7±2)%; and
- loss of squeezing at the 90/10 detection beamsplitter, (10±0.1)%.

## 4. Experimental Results

_{00}and TEM

_{10}. On average the observed TEM

_{00}squeezing at baseband is approximately 2.5 dB and 3 dB at the higher resonances. Similarly, the observed TEM

_{10}squeezing at baseband is approximately 2 dB and 2.5 dB at the higher resonances. Note that the shape of the squeezing is dictated by the linewidth of the cavity and thus the profile of squeezing at higher FSRs is symmetric and the bandwidth is twice that of the baseband spectrum.

_{10}mode than observed for the TEM

_{00}. This is because the OPA is pumped with the second harmonic of the seed beam at 532 nm in the TEM

_{00}spatial mode. This pumping scheme is optimal when generating a TEM

_{00}squeezed beam but results in reduced squeezing in comparison to TEM

_{10}. This effect is described in detail in Lassen

*et. al*. [20

20. M. Lassen, V. Delaubert, C.C. Harb, P.K. Lam, N. Treps, and H-A. Bachor, “Generation of squeezing in higher order Hermite-Gaussian modes with an optical parametric amplifier,” J. of the Euro Opt. Soc.-RP. **1**, 06003 (2006). [CrossRef]

_{00}(1706.3 MHz, 3428.2 MHz and 5162.5 MHz) and TEM

_{10}(1710.5 MHz, 3431.3 MHz and 5164.0 MHz) modes do not occur at the same frequencies, nor are successive minima separated by the same frequency spacing. The frequency of the first minimum of the TEM

_{00}mode implies that the OPL of the OPA cavity is 87.7 mm compared to 87.9 mm inferred from the first minimum of the TEM

_{10}mode. Each of the subsequent minima in the squeezing for the TEM

_{00}mode imply that the OPL of the cavity successively shortens by 300

*μ*m. Differences in the inferred OPL are not insignificant compared to the total OPL of the cavity. This effect requires further investigation.

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. **93**, 161105 (2004). [CrossRef] [PubMed]

22. H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a Squeezed-Light-Enhanced Power- and Signal-Recycled Michelson Interferometer,” Phys. Rev. Lett. **95**, 211102 (2005). [CrossRef] [PubMed]

*Acknowledgments*- This work was supported by the Australian Research Council Centres of Excellence scheme.

## 5. Conclusion

## References and links

1. | N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. |

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

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

4. | M. Nielsen and I. Chuang, |

5. | R.W. Boyd, |

6. | P.G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. |

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

8. | Y. J. Lu and Z. Y. Ou, “Optical parametric oscillator far below threshold: Experiment versus theory,” Phys. Rev. A |

9. | C. Fabre and S. Reynaud, |

10. | A.E. Dunlop, E.H. Huntington, C.C. Harb, and T.C. Ralph, “Generation of a frequency comb of squeezing in an optical parametric oscillator,” Phys. Rev. A |

11. | G.N. Milford, C. C. Harb, and E. H. Huntington, “Shot noise limited, microwave bandwidth photodetector design,” Rev. Sci. Instrum. |

12. | B. Yurke, P.G. Kaminsky, and R.E. Miller, “Observation of 4.2-K equilibrium-noise squeezing via a Josephson-parametric amplifier,” Phys. Rev. Lett. |

13. | R.W.P. Drever, J.L. Hall, F.V. Kowalski, J. Hough, G.M. Ford, A.J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B |

14. | “43 GBit/s DPSK Balanced Photoreceiver,” http://www.u2t.de/pdf/Preliminary_Datasheet_BPRV2123_V10.pdf. |

15. | M.B. Gray, D.A. Shaddock, C.C. Harb, and H.-A. Bachor, “Photodetector designs for low-noise, broadband, and high-power applications,” Rev. Sci. Instrum. |

16. | G. Gonzalez, |

17. | Mini-Circuits, www.mini-circuits.com |

18. | M. G. Raymer, Jaewoo Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A |

19. | D. F. Walls and G. J. Milburn, |

20. | M. Lassen, V. Delaubert, C.C. Harb, P.K. Lam, N. Treps, and H-A. Bachor, “Generation of squeezing in higher order Hermite-Gaussian modes with an optical parametric amplifier,” J. of the Euro Opt. Soc.-RP. |

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. | H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a Squeezed-Light-Enhanced Power- and Signal-Recycled Michelson Interferometer,” Phys. Rev. Lett. |

**OCIS Codes**

(040.5160) Detectors : Photodetectors

(190.4970) Nonlinear optics : Parametric oscillators and amplifiers

(270.6570) Quantum optics : Squeezed states

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: February 26, 2007

Revised Manuscript: April 2, 2007

Manuscript Accepted: April 6, 2007

Published: April 16, 2007

**Citation**

R. J. Senior, G. N. Milford, J. Janousek, A. E. Dunlop, K. Wagner, H.-A. Bachor, T. C. Ralph, E. H. Huntington, and C. C. Harb, "Observation of a comb of optical squeezing over many gigahertz of
bandwidth," Opt. Express **15**, 5310-5317 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-9-5310

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### References

- 1. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002); F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, P. Grangier, "Quantum key distribution using gaussian-modulated coherent states," Nature 421, 238-241 (2003). [CrossRef]
- C.M. Caves, "Quantum-mechanical noise in an interferometer," Phys. Rev. D 23, 1693-1708 (1981). [CrossRef]
- B.J. Meers and K.A. Strain "Modulation, signal, and quantum noise in interferometers," Phys. Rev. A 44, 4693-4703 (1991). [CrossRef] [PubMed]
- M. Nielsen and I. Chuang, Quantum computation and quantum information, (Cambridge University Press, Cambridge, UK, 2000).
- R.W. Boyd, Nonlinear Optics, (Academic Press, 1992).
- P.G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, "New High-Intensity Source of Polarization-Entangled Photon Pairs," Phys. Rev. Lett. 75, 4337-4341 (1995). [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]
- Y. J. Lu and Z. Y. Ou, "Optical parametric oscillator far below threshold: Experiment versus theory," Phys. Rev. A 62033804 (2000). [CrossRef]
- C. Fabre and S. Reynaud, Quantum noise in optical systems: A semiclassical approach, J. Dalibard, J.M. Raimond and J. Zinn-Justin, eds. (Les Houches, Session LIII, 1990).
- A.E. Dunlop, E.H. Huntington, C.C. Harb, and T.C. Ralph, "Generation of a frequency comb of squeezing in an optical parametric oscillator," Phys. Rev. A 73, 013817 (2006). [CrossRef]
- G.N. Milford, C. C. Harb, and E. H. Huntington, "Shot noise limited, microwave bandwidth photodetector design," Rev. Sci. Instrum. 77, 114701 (2006). [CrossRef]
- B. Yurke, P.G. Kaminsky, and R.E. Miller, "Observation of 4.2-K equilibrium-noise squeezing via a Josephsonparametric amplifier," Phys. Rev. Lett. 60, 764-767 (1988). [CrossRef] [PubMed]
- R.W.P. Drever, J.L. Hall, F.V. Kowalski, J. Hough, G.M. Ford, A.J. Munley and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B B31, 97-105 (1983). [CrossRef]
- "43 GBit/s DPSK Balanced Photoreceiver," http://www.u2t.de/pdf/Preliminary Datasheet BPRV2123 V10.pdf.
- M.B. Gray, D.A. Shaddock, C.C. Harb, and H.-A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998). [CrossRef]
- G. Gonzalez, Microwave Transistor Amplifiers: Analysis and Design, 2nd Ed, (Prentice Hall, 1996). [PubMed]
- Mini-Circuits, http://www.mini-circuits.com
- M. G. Raymer, J. Noh, K. Banaszek and I. A. Walmsley, "Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity," Phys. Rev. A 72023825 (2005). [CrossRef]
- D. F. Walls and G. J. Milburn, Quantum Optics, (Springer-Verlag, New York, 1994).
- M. Lassen, V. Delaubert, C.C. Harb, P.K. Lam, N. Treps, H-A. Bachor, "Generation of squeezing in higher order Hermite-Gaussian modes with an optical parametric amplifier," J. of the Euro Opt. Soc.-RP. 1, 06003 (2006). [CrossRef]
- 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]
- H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, "Demonstration of a Squeezed-Light-Enhanced Power- and Signal-Recycled Michelson Interferometer," Phys. Rev. Lett. 95, 211102 (2005). [CrossRef] [PubMed]

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