## Photon-number squeezing with a noisy femtosecond fiber laser amplifier source using a collinear balanced detection technique |

Optics Express, Vol. 21, Issue 21, pp. 25099-25106 (2013)

http://dx.doi.org/10.1364/OE.21.025099

Acrobat PDF (1342 KB)

### Abstract

We experimentally demonstrate photon-number squeezing at 1.55 μm using a noisy erbium-doped fiber amplifier (EDFA). We employ a collinear balanced detection (CBD) technique, where the intensity noise at a specific radio frequency is canceled between two pulse trains. In spite of substantially large excess noise (>10dB) in an EDFA due to amplified spontaneous emission, we successfully cancel the intensity noise and achieve a shot noise limit at a specific radio frequency with the CBD technique. We exploit two sets of fiber polarization interferometers to generate squeezed light and observe a maximal photon-number squeezing of −2.6dB.

© 2013 OSA

## 1. Introduction

1. S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. **77**(2), 513–577 (2005). [CrossRef]

2. L. Vaidman, “Teleportation of quantum states,” Phys. Rev. A **49**(2), 1473–1476 (1994). [CrossRef] [PubMed]

3. S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. **80**(4), 869–872 (1998). [CrossRef]

4. C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. **69**(20), 2881–2884 (1992). [CrossRef] [PubMed]

5. S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A **61**(4), 042302 (2000). [CrossRef]

6. A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. **67**(6), 661–663 (1991). [CrossRef] [PubMed]

7. 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**(6), 691–694 (1986). [CrossRef] [PubMed]

8. S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, “Observation of optical soliton photon-number squeezing,” Phys. Rev. Lett. **77**(18), 3775–3778 (1996). [CrossRef] [PubMed]

9. M. Rosenbluh and R. M. Shelby, “Squeezed optical solitons,” Phys. Rev. Lett. **66**(2), 153–156 (1991). [CrossRef] [PubMed]

10. S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-number squeezed solitons from an asymmetric fiber-optic Sagnac interferometer,” Phys. Rev. Lett. **81**(12), 2446–2449 (1998). [CrossRef]

11. M. Margalit, C. X. Yu, E. P. Ippen, and H. A. Haus, “Cross phase modulation squeezing in optical fibers,” Opt. Express **2**(3), 72–76 (1998). [CrossRef] [PubMed]

12. N. Nishizawa, K. Sone, J. Higuchi, M. Mori, K. Yamane, and T. Goto, “Squeezed vacuum generation using symmetric nonlinear polarization interferometer,” Jpn. J. Appl. Phys. **41**(Part 2, No. 2A), L130–L132 (2002). [CrossRef]

13. J. Heersink, V. Josse, G. Leuchs, and U. L. Andersen, “Efficient polarization squeezing in optical fibers,” Opt. Lett. **30**(10), 1192–1194 (2005). [CrossRef] [PubMed]

12. N. Nishizawa, K. Sone, J. Higuchi, M. Mori, K. Yamane, and T. Goto, “Squeezed vacuum generation using symmetric nonlinear polarization interferometer,” Jpn. J. Appl. Phys. **41**(Part 2, No. 2A), L130–L132 (2002). [CrossRef]

14. J. Higuchi, N. Nishizawa, M. Mori, K. Yamane, and T. Goto, “Nonlinear polarization interferometer for photon number squeezed light generation,” Jpn. J. Appl. Phys. **40**(Part 2, No. 11B), L1220–L1222 (2001). [CrossRef]

15. K. Nose, Y. Ozeki, T. Kishi, K. Sumimura, N. Nishizawa, K. Fukui, Y. Kanematsu, and K. Itoh, “Sensitivity enhancement of fiber-laser-based stimulated Raman scattering microscopy by collinear balanced detection technique,” Opt. Express **20**(13), 13958–13965 (2012). [CrossRef] [PubMed]

## 2. Experiment and Results

### 2.1 Noise reduction with the CBD technique

*τ*. The photocurrent contributed by the pulse trains is given bywhere

*I*

_{1}(

*t*) and

*I*

_{2}(

*t*) are the photocurrent contributed by the first and second pulses, respectively. Equation (1) does not contain an interference term because no pulses temporally overlap each other. In the Fourier domain, we can obtainwhere

*I*(

*ω*),

*I*

_{1}(

*ω*), and

*I*

_{2}(

*ω*) are the Fourier transforms of

*I*(

*t*),

*I*

_{1}(

*t*), and

*I*

_{2}(

*t*), respectively. Equation (2) indicates that the photocurrents were added up destructively at

*ω*=

*π*/

*τ*. When selecting

*τ*equal to the interval of the pulse train of light, one can reduce the side-band spectral power density at a radio frequency corresponding to the half of the pulse repetition rate. Since in general the quantum noise of light is evaluated in the radio frequency sideband, it is very useful if the intensity noise power at a certain radio frequency is canceled.

*e.g*[16].). Therefore, the vacuum noise remains even at perfect cancellation by CBD. When the vacuum states added to the signal pulses are phase modulated during nonlinear pulse propagation in an optical fiber, we can extract only the phase modulated vacuum state at perfect cancellation by CBD.

*τ*= 1/

*f*rep, where

*f*rep is the repetition rate, to one of the two pulse trains and added another delay (∆

*τ*) to prevent optical interference at the recombination. The two pulse trains with identical optical power were combined at a non-polarized beam splitter (BS).

17. C. Silberhorn, “Detecting quantum light,” Contemp. Phys. **48**(3), 143–156 (2007). [CrossRef]

17. C. Silberhorn, “Detecting quantum light,” Contemp. Phys. **48**(3), 143–156 (2007). [CrossRef]

*τ*was varied from 6.7 ps to 2.5 ns. There was no influence of ∆

*τ*on the noise reduction performance with CBD. Therefore, in the following experiment, the delay ∆

*τ*was kept constant at 6.7 ps unless it is specified. The intensity noise can be canceled at a radio frequency of 23.8 MHz. Figure 2 shows the relative noise levels of the initial pulse train and two pulse trains recorded at 23 MHz. We clearly confirmed that the intensity noise of the two pulse trains was coincident to the SNLs at 23.8 MHz. In Fig. 2, plots for the two pulse trains indicate slightly lower relative noise than the SNL, especially at higher laser powers. These are a measurement error caused by underestimation of the launched laser powers. The deviation in the relative intensity noise measurement itself using a radio frequency spectrum analyzer is ~0.05dB.

*τ*= 1.67 ns. The intensity noise of the femtosecond pulse train was canceled at 22 MHz, which exactly corresponds to ∆

*τ*= 1.67 ns.

*τ*was adjusted at 6.7 psec. The noise levels of the two pulse trains after propagation through two separate fibers were coincident with the SNLs. We successfully canceled the intensity noise even after propagation through separate fibers. In contrast, the noise levels of the two pulse trains after propagation through a common fiber greatly exceeded the SNLs. The change in ∆

*τ*did not improve the noise reduction performance. Small delay ∆

*τ*of 6.7 ps is sufficiently shorter than the characteristic frequency of the guided acoustic-wave Brillouin scattering (GAWBS), which may be a major noise source through fiber propagation [18

18. R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B Condens. Matter **31**(8), 5244–5252 (1985). [CrossRef] [PubMed]

### 2.2 Photon- number squeezing

14. J. Higuchi, N. Nishizawa, M. Mori, K. Yamane, and T. Goto, “Nonlinear polarization interferometer for photon number squeezed light generation,” Jpn. J. Appl. Phys. **40**(Part 2, No. 11B), L1220–L1222 (2001). [CrossRef]

## 3. Conclusion

## References and links

1. | S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. |

2. | L. Vaidman, “Teleportation of quantum states,” Phys. Rev. A |

3. | S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. |

4. | C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. |

5. | S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A |

6. | A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. |

7. | 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. |

8. | S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, “Observation of optical soliton photon-number squeezing,” Phys. Rev. Lett. |

9. | M. Rosenbluh and R. M. Shelby, “Squeezed optical solitons,” Phys. Rev. Lett. |

10. | S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-number squeezed solitons from an asymmetric fiber-optic Sagnac interferometer,” Phys. Rev. Lett. |

11. | M. Margalit, C. X. Yu, E. P. Ippen, and H. A. Haus, “Cross phase modulation squeezing in optical fibers,” Opt. Express |

12. | N. Nishizawa, K. Sone, J. Higuchi, M. Mori, K. Yamane, and T. Goto, “Squeezed vacuum generation using symmetric nonlinear polarization interferometer,” Jpn. J. Appl. Phys. |

13. | J. Heersink, V. Josse, G. Leuchs, and U. L. Andersen, “Efficient polarization squeezing in optical fibers,” Opt. Lett. |

14. | J. Higuchi, N. Nishizawa, M. Mori, K. Yamane, and T. Goto, “Nonlinear polarization interferometer for photon number squeezed light generation,” Jpn. J. Appl. Phys. |

15. | K. Nose, Y. Ozeki, T. Kishi, K. Sumimura, N. Nishizawa, K. Fukui, Y. Kanematsu, and K. Itoh, “Sensitivity enhancement of fiber-laser-based stimulated Raman scattering microscopy by collinear balanced detection technique,” Opt. Express |

16. | S. Barnett and P. Radmore, |

17. | C. Silberhorn, “Detecting quantum light,” Contemp. Phys. |

18. | R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B Condens. Matter |

**OCIS Codes**

(060.7140) Fiber optics and optical communications : Ultrafast processes in fibers

(190.7110) Nonlinear optics : Ultrafast nonlinear optics

(270.6570) Quantum optics : Squeezed states

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: July 8, 2013

Revised Manuscript: September 7, 2013

Manuscript Accepted: September 9, 2013

Published: October 14, 2013

**Citation**

Shota Sawai, Hikaru Kawauchi, Kenichi Hirosawa, and Fumihiko Kannari, "Photon-number squeezing with a noisy femtosecond fiber laser amplifier source using a collinear balanced detection technique," Opt. Express **21**, 25099-25106 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-21-25099

Sort: Year | Journal | Reset

### References

- S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys.77(2), 513–577 (2005). [CrossRef]
- L. Vaidman, “Teleportation of quantum states,” Phys. Rev. A49(2), 1473–1476 (1994). [CrossRef] [PubMed]
- S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett.80(4), 869–872 (1998). [CrossRef]
- C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett.69(20), 2881–2884 (1992). [CrossRef] [PubMed]
- S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A61(4), 042302 (2000). [CrossRef]
- A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett.67(6), 661–663 (1991). [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(6), 691–694 (1986). [CrossRef] [PubMed]
- S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, “Observation of optical soliton photon-number squeezing,” Phys. Rev. Lett.77(18), 3775–3778 (1996). [CrossRef] [PubMed]
- M. Rosenbluh and R. M. Shelby, “Squeezed optical solitons,” Phys. Rev. Lett.66(2), 153–156 (1991). [CrossRef] [PubMed]
- S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-number squeezed solitons from an asymmetric fiber-optic Sagnac interferometer,” Phys. Rev. Lett.81(12), 2446–2449 (1998). [CrossRef]
- M. Margalit, C. X. Yu, E. P. Ippen, and H. A. Haus, “Cross phase modulation squeezing in optical fibers,” Opt. Express2(3), 72–76 (1998). [CrossRef] [PubMed]
- N. Nishizawa, K. Sone, J. Higuchi, M. Mori, K. Yamane, and T. Goto, “Squeezed vacuum generation using symmetric nonlinear polarization interferometer,” Jpn. J. Appl. Phys.41(Part 2, No. 2A), L130–L132 (2002). [CrossRef]
- J. Heersink, V. Josse, G. Leuchs, and U. L. Andersen, “Efficient polarization squeezing in optical fibers,” Opt. Lett.30(10), 1192–1194 (2005). [CrossRef] [PubMed]
- J. Higuchi, N. Nishizawa, M. Mori, K. Yamane, and T. Goto, “Nonlinear polarization interferometer for photon number squeezed light generation,” Jpn. J. Appl. Phys.40(Part 2, No. 11B), L1220–L1222 (2001). [CrossRef]
- K. Nose, Y. Ozeki, T. Kishi, K. Sumimura, N. Nishizawa, K. Fukui, Y. Kanematsu, and K. Itoh, “Sensitivity enhancement of fiber-laser-based stimulated Raman scattering microscopy by collinear balanced detection technique,” Opt. Express20(13), 13958–13965 (2012). [CrossRef] [PubMed]
- S. Barnett and P. Radmore, Methods in Theoretical Quantum Optics (Oxford University Press, 2003).
- C. Silberhorn, “Detecting quantum light,” Contemp. Phys.48(3), 143–156 (2007). [CrossRef]
- R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B Condens. Matter31(8), 5244–5252 (1985). [CrossRef] [PubMed]

## 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.