## Imaging using quantum noise properties of light |

Optics Express, Vol. 20, Issue 15, pp. 17050-17058 (2012)

http://dx.doi.org/10.1364/OE.20.017050

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### Abstract

We show that it is possible to estimate the shape of an object by measuring only the fluctuations of a probing field, allowing us to expose the object to a minimal light intensity. This scheme, based on noise measurements through homodyne detection, is useful in the regime where the number of photons is low enough that direct detection with a photodiode is difficult but high enough such that photon counting is not an option. We generate a few-photon state of multi-spatial-mode vacuum-squeezed twin beams using four-wave mixing and direct one of these twin fields through a binary intensity mask whose shape is to be imaged. Exploiting either the classical fluctuations in a single beam or quantum correlations between the twin beams, we demonstrate that under some conditions quantum correlations can provide an enhancement in sensitivity when estimating the shape of the object.

© 2012 OSA

## 1. Introduction

## 2. Four-wave mixing and squeezed light detection

17. Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A **82**, 033819 (2010). [CrossRef]

^{85}Rb vapor (Fig. 1(a)–(b)). The 4WM process converts two photons from a single pump beam into a pair of photons emitted into twin fields referred to as the probe and conjugate. These twin beams exhibit strong amplitude correlations such that the amplitude difference noise is below the SNL [18

18. C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A **78**, 043816 (2008). [CrossRef]

*θ*. We subtract the noise of the probe and conjugate generalized quadratures to obtain the noise of the joint quadrature

*θ*and

_{p}*θ*,

_{c}*θ*+

_{p}*θ*=

_{c}*π*. We therefore only need to control the phase of one of the LOs (using a PZT-mounted mirror) to detect the level of squeezing between the probe and conjugate.

^{85}Rb cell heated to 110°C. The probe and conjugate frequencies are unseeded, so the resulting probe and conjugate fields are generated from spontaneous emission. The frequency of the pump beam is detuned 800 MHz to the blue of the |5

^{2}

*S*

_{1/2},

*F*= 2〉 → |5

^{2}

*P*

_{1/2},

*F*= 3〉 transition at 795 nm. After separating the pump beam from the probe and conjugate beams with a polarizing beam splitter, each beam is sent to a balanced homodyne detector using a pair of matched photodiodes with quantum efficiencies of approximately 95%. The total optical path losses from the 4WM process to the homodyne detection are approximately 4%.

## 3. Experimental procedure

19. 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 **7**, S421–S428 (2005). [CrossRef]

## 4. Results

*O*: Δ

_{est}*N*represents the measured standard deviation of a given noise power

*N*and

*N*quantifies the “noise on the noise,” which incorporates both sources of statistical uncertainty and technical noise.

*O*for the classical and quantum schemes. As Fig. 3(b) suggests, the quantum noise imaging technique provides a higher sensitivity to changes in the overlap than the classical technique. Although the comparable magnitudes of

_{est}*O*, the difference between the curves in Fig. 3(b) can be explained by the variation of Δ

_{est}*N*with overlap. Specifically, the value of Δ

*N*is expected to scale with the noise power

*N*. For a given overlap the magnitudes of

*N*for the quantum technique will yield a smaller value of Δ

*O*.

_{est}*O*for overlaps above 0.9 in Fig. 3(b) for the quantum and classical techniques. The angular enhancement factor of 3.8 was obtained by separately calibrating the measured LO-mask overlap as a function of the angle between the LO bow tie and the mask. The indicated uncertainties here and in the figures represent one standard deviation, combined statistical and systematic uncertainties.

_{est}## 5. “Alphabet gun” test

*D*denotes the deviation in the noise power for LO letter

^{i}*i*,

## 6. Conclusion

11. E. Brambilla, L. Caspani, O. Jedrkiewicz, L. A. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A **77**, 053807 (2008). [CrossRef]

## References and links

1. | V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nature Photon |

2. | M. I. Kolobov, “The spatial behavior of non-classical light,” Rev. Mod. Phys. |

3. | M. I. Kolobov, |

4. | N. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Multi-spatial-mode single-beam quadrature squeezed states of light from four-wave mixing in hot rubidium vapor,” Opt. Express |

5. | V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. |

6. | M. I. Kolobov and C. Fabre, “Quantum limits on optical resolution,” Phys. Rev. Lett. |

7. | N. Treps, N. Gross, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science |

8. | V. Giovannetti, S. Lloyd, and L. Maccone, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A |

9. | N. Treps, U. Andersen, B. Buchler, P. K. Lam, A. Maitre, H.-A. Bachor, and C. Fabre, “Surpassing the standard quantum limit for optical imaging using nonclassical multimode light,” Phys. Rev. Lett |

10. | J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” JOSA B |

11. | E. Brambilla, L. Caspani, O. Jedrkiewicz, L. A. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A |

12. | L. A. Lugiato and A. Gatti, “Spatial structure of a squeezed vacuum,” Phys. Rev. Lett. |

13. | A. Gatti and L. Lugiato, “Quantum images and critical fluctuations in the optical parametric oscillator below threshold,” Phys. Rev. A |

14. | A. M. Marino, J. B. Clark, Q. Glorieux, and P. D. Lett, E-print arXiv:1203.0577v1. |

15. | G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nature Photon |

16. | A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett. |

17. | Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A |

18. | C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A |

19. | 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 |

20. | V. Boyer, A. Marino, R. C. Pooser, and P. D. Lett, “Entangled images four four-wave mixing,” Science |

21. | M. Martinelli, N. Treps, S. Ducci, S. Gigan, A. Maitre, and C. Fabre, “Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator,” Phys. Rev. A |

22. | A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A |

23. | C. Kim and P. Kumar, “Quadrature-squeezed light detection using a self-generated matched local oscillator,” Phys. Rev. Lett. |

24. | M. B. Nasr, D. P. Goode, N. Nguyen, G. Rong, L. Yang, B. M. Reinhard, B. E. A. Saleh, and M. C. Teich, “Quantum optical coherence tomography of a biological sample,” Opt. Commun. |

**OCIS Codes**

(270.0270) Quantum optics : Quantum optics

(270.6570) Quantum optics : Squeezed states

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: May 25, 2012

Revised Manuscript: June 29, 2012

Manuscript Accepted: June 29, 2012

Published: July 11, 2012

**Citation**

Jeremy B. Clark, Zhifan Zhou, Quentin Glorieux, Alberto M. Marino, and Paul D. Lett, "Imaging using quantum noise properties of light," Opt. Express **20**, 17050-17058 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-15-17050

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### References

- V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nature Photon5, 222–229 (2011). [CrossRef]
- M. I. Kolobov, “The spatial behavior of non-classical light,” Rev. Mod. Phys.71, 1539–1589 (1999). [CrossRef]
- M. I. Kolobov, Quantum Imaging, 1st ed. (Springer, 2006).
- N. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Multi-spatial-mode single-beam quadrature squeezed states of light from four-wave mixing in hot rubidium vapor,” Opt. Express19, 21358–21369 (2011). [CrossRef] [PubMed]
- V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett.100, 143601 (2008). [CrossRef] [PubMed]
- M. I. Kolobov and C. Fabre, “Quantum limits on optical resolution,” Phys. Rev. Lett.85, 3789–3792 (2000). [CrossRef] [PubMed]
- N. Treps, N. Gross, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science301, 940–943 (2003). [CrossRef] [PubMed]
- V. Giovannetti, S. Lloyd, and L. Maccone, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A79, 013827 (2009). [CrossRef]
- N. Treps, U. Andersen, B. Buchler, P. K. Lam, A. Maitre, H.-A. Bachor, and C. Fabre, “Surpassing the standard quantum limit for optical imaging using nonclassical multimode light,” Phys. Rev. Lett88, 203601 (2002). [CrossRef] [PubMed]
- J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” JOSA B10, 2233–2238 (1993). [CrossRef]
- E. Brambilla, L. Caspani, O. Jedrkiewicz, L. A. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A77, 053807 (2008). [CrossRef]
- L. A. Lugiato and A. Gatti, “Spatial structure of a squeezed vacuum,” Phys. Rev. Lett.70, 3868–3871 (1993). [CrossRef] [PubMed]
- A. Gatti and L. Lugiato, “Quantum images and critical fluctuations in the optical parametric oscillator below threshold,” Phys. Rev. A52, 1675–1690 (1995). [CrossRef] [PubMed]
- A. M. Marino, J. B. Clark, Q. Glorieux, and P. D. Lett, E-print arXiv:1203.0577v1.
- G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nature Photon4, 227–230 (2010). [CrossRef]
- A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett.87, 123602 (2001). [CrossRef] [PubMed]
- Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A82, 033819 (2010). [CrossRef]
- C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A78, 043816 (2008). [CrossRef]
- 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. B7, S421–S428 (2005). [CrossRef]
- V. Boyer, A. Marino, R. C. Pooser, and P. D. Lett, “Entangled images four four-wave mixing,” Science321, 544 –547 (2008). [CrossRef] [PubMed]
- M. Martinelli, N. Treps, S. Ducci, S. Gigan, A. Maitre, and C. Fabre, “Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator,” Phys. Rev. A67, 023808 (2003). [CrossRef]
- A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A70, 013802 (2004). [CrossRef]
- C. Kim and P. Kumar, “Quadrature-squeezed light detection using a self-generated matched local oscillator,” Phys. Rev. Lett.73, 1605–1608 (1994). [CrossRef] [PubMed]
- M. B. Nasr, D. P. Goode, N. Nguyen, G. Rong, L. Yang, B. M. Reinhard, B. E. A. Saleh, and M. C. Teich, “Quantum optical coherence tomography of a biological sample,” Opt. Commun.282, 1154–1159 (2009). [CrossRef]

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