## Toward real-time quantum imaging with a single pixel camera |

Optics Express, Vol. 21, Issue 6, pp. 7549-7559 (2013)

http://dx.doi.org/10.1364/OE.21.007549

Acrobat PDF (1752 KB)

### Abstract

We present a workbench for the study of real-time quantum imaging by measuring the frame-by-frame quantum noise reduction of multi-spatial-mode twin beams generated by four wave mixing in Rb vapor. Exploiting the multiple spatial modes of this squeezed light source, we utilize spatial light modulators to selectively pass macropixels of quantum correlated modes from each of the twin beams to a high quantum efficiency balanced detector. In low-light-level imaging applications, the ability to measure the quantum correlations between individual spatial modes and macropixels of spatial modes with a single pixel camera will facilitate compressive quantum imaging with sensitivity below the photon shot noise limit.

© 2013 OSA

## 1. Introduction

11. O. Aytür and P. Kumar, “Squeezed-light generation with a mode-locked q-switched laser and detection by using a matched local oscillator,” Opt. Lett. **17**, 529–531 (1992) [CrossRef] [PubMed] .

12. D. Smithey, M. Beck, M. Belsley, and M. Raymer, “Sub-shot-noise correlation of total photon number using macroscopic twin pulses of light,” Phys. Rev. Lett. **69**, 2650–2653 (1992) [CrossRef] [PubMed] .

10. G. Brida, M. Genovese, and I. Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nature Photon. **4**, 227–230 (2010) [CrossRef] .

^{85}Rb vapor. This ‘quantum movie projector’ exhibits real-time quantum noise reduction as a continuous series of images are flashed across the SLM, thereby allowing for the analysis of the quantum noise reduction present in arbitrary spatial modes in real-time. There is a limited literature that applies compressive sampling algorithms to pseudothermal [13

13. L. Jiying, Z. Jubo, L. Chuan, and H. Shisheng, “High-quality quantum-imaging algorithm and experiment based on compressive sensing,” Opt. Lett. **35**, 1206–1208 (2010) [CrossRef] [PubMed] .

14. O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” App. Phys. Lett. **95**, 131110 (2009) [CrossRef] .

15. P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, “Entangled-photon compressive ghost imaging,” Phys. Rev. A **84**, 061804 (2011) [CrossRef] .

## 2. Experimental techniques

^{85}Rb vapor based on a double-Λ system between the hyperfine ground states and the D1 excited states. The hot

^{85}Rb vapor in a 12.5 mm thick antireflection coated glass cell absorbs two photons from the pump beam (weakly focused to a waist of 1 mm and denoted by ‘P’ in Fig. 1(b)) thereby generating a coherence between the two ground states. The probe beam (focused to a waist of 450

*μ*m and denoted by ‘Pr’ in Fig. 1(b)) is red-shifted from the pump frequency by roughly 3 GHz via a double-pass acousto-optic-modulator in order to stimulate the re-emission of photons into the probe frequency with the simultaneous emission of photons into the conjugate beam (‘C’ in Fig. 1(b)) that is blue-shifted from the pump by 3 GHz. Because of the strong amplitude correlations between these twin beams, the amplitude difference noise measured with a balanced photodiode and shown in Fig. 1(c) is below the photon shot noise limit (SNL) for most sideband frequencies between 50 kHz and 5 MHz. All squeezing values reported in this manuscript were measured at a sideband frequency of 500 kHz with 20 kHz resolution bandwidth and 3 kHz video bandwidth. In each case, the average of the 401 datapoints in each spectrum was used as the reported noise level. The combined systematic and statistical uncertainty in each data point is 0.1 dB. Because of the presence of a buffer gas in the Rb vapor cell used for this experiment, increased Doppler broadening limited the maximum squeezing to 4.5 dB below the SNL. Vapor cells with no buffer gas demonstrate 15–20% less absorption of the probe field within the cell, yielding quantum noise reduction of greater than 9 dB inferred with no losses.

*μ*m provided intensity SLM functionality, thereby yielding real-time control over what spatial modes undergo four-wave mixing in the vapor cell. Because the quantum noise reduction observed in individual coherence areas within an image is highly dependent on the pump-probe overlap, the observed squeezing is expected to be smaller for images with higher order spatial frequencies that would yield poor overlap at the Fourier plane in the vapor cell. This is a similar result to that seen when masks were used to imprint various images on the probe beam prior to four-wave mixing [1

1. V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science **321**, 544–547 (2008) [CrossRef] [PubMed] .

## 3. Real-time quantum imaging

## 4. Single pixel quantum imaging

11. O. Aytür and P. Kumar, “Squeezed-light generation with a mode-locked q-switched laser and detection by using a matched local oscillator,” Opt. Lett. **17**, 529–531 (1992) [CrossRef] [PubMed] .

12. D. Smithey, M. Beck, M. Belsley, and M. Raymer, “Sub-shot-noise correlation of total photon number using macroscopic twin pulses of light,” Phys. Rev. Lett. **69**, 2650–2653 (1992) [CrossRef] [PubMed] .

*single spatial mode*phase-insensitive amplifier [12

12. D. Smithey, M. Beck, M. Belsley, and M. Raymer, “Sub-shot-noise correlation of total photon number using macroscopic twin pulses of light,” Phys. Rev. Lett. **69**, 2650–2653 (1992) [CrossRef] [PubMed] .

*S*= 10 log

_{10}(1 −

*η*−

*η*/

*G*), where

*G*is the total gain of the 4WM process (approximately 4 in this experiment), and

*η*corresponds to the transmission of the vapor cell-DMD-detector system. While the DMD generally exhibits 60% diffraction efficiency into the zero order mode, additional attenuation occurs with each image placed on its surface, since some incident light falls onto pixels which are turned “off” (set to reflect light away from the detector).

*μ*W per coherence area. The actual number is slightly less, because the nonzero intensity size of the beams on the DMD extended to approximately three to four times the beam width, meaning the total power was distributed among slightly more coherence areas. Nonetheless, this power per coherence area is in stark contrast to quantum imaging experiments with spontaneous parametric downconversion which rely on photon counting, and easily satisfies the condition of a large number of photons per coherence area needed for quantum imaging.

*α*is the coefficient vector comprising no more than K significant nonzero values. CI theory provides the framework to acquire such an image via the linear projection: where y is an M-dimensional measurement vector, A is an M-by-N sensing matrix, x is the N dimensional signal of interest, and Γ is the acquisition noise. CI is attractive for single pixel imaging applications because it allows for image reconstruction with only

*M*≈

*KlogN*measurements, and the use of sparse arrays instead of individual pixels significantly increase the signal to noise ratio in applications where the dominant noise source is the shot noise. In addition, real-time compressive imaging is now a viable technology [16

16. T. Do, L. Gan, N. Nguyen, and T. Tran, “Fast and efficient compressive sensing using structurally random matrices,” IEEE Trans. Signal Process. **60**, 139–154 (2012) [CrossRef] .

*x*from

*y*. After comparing various permutations of random orthonormal matrices and Hadamard matrices it was determined that individual rows randomly sampled from block Hadamard matrices [16

16. T. Do, L. Gan, N. Nguyen, and T. Tran, “Fast and efficient compressive sensing using structurally random matrices,” IEEE Trans. Signal Process. **60**, 139–154 (2012) [CrossRef] .

19. E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory **52**, 489–509 (2006) [CrossRef] .

20. M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Sig. Process **1**, 586 –597 (2007) [CrossRef] .

## 5. Conclusions

## Acknowledgments

## References and links

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

2. | Q. Glorieux, J. B. Clark, A. M. Marino, Z. Zhou, and P. D. Lett, “Temporally multiplexed storage of images in a gradient echo memory,” Opt. Express |

3. | D.-S. Ding, Z.-Y. Zhou, B.-S. Shi, X.-B. Zou, and G.-C. Guo, “Image transfer through two sequential four-wave-mixing processes in hot atomic vapor,” Phys. Rev. A |

4. | J. B. Clark, Z. Zhou, Q. Glorieux, A. M. Marino, and P. D. Lett, “Imaging using quantum noise properties of light,” Opt. Express |

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

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

7. | N. V. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Noiseless optical amplifier operating on hundreds of spatial modes,” Phys. Rev. Lett. |

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

9. | M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H.-A. Bachor, P. K. Lam, N. Treps, P. Buchhave, C. Fabre, and C. C. Harb, “Tools for multimode quantum information: Modulation, detection, and spatial quantum correlations,” Phys. Rev. Lett. |

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

11. | O. Aytür and P. Kumar, “Squeezed-light generation with a mode-locked q-switched laser and detection by using a matched local oscillator,” Opt. Lett. |

12. | D. Smithey, M. Beck, M. Belsley, and M. Raymer, “Sub-shot-noise correlation of total photon number using macroscopic twin pulses of light,” Phys. Rev. Lett. |

13. | L. Jiying, Z. Jubo, L. Chuan, and H. Shisheng, “High-quality quantum-imaging algorithm and experiment based on compressive sensing,” Opt. Lett. |

14. | O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” App. Phys. Lett. |

15. | P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, “Entangled-photon compressive ghost imaging,” Phys. Rev. A |

16. | T. Do, L. Gan, N. Nguyen, and T. Tran, “Fast and efficient compressive sensing using structurally random matrices,” IEEE Trans. Signal Process. |

17. | D. Smith, J. Gore, T. Yankeelov, and E. Welch, “Real-time compressive sensing MRI reconstruction using GPU computing and split bregman methods,” Int. J. of Biomed. Imag. |

18. | R. Pooser, B. Lawrie, and W. Grice, “Compressive sampling low light beam profiler using structural random matrices with a semilocal randomizer,” In Preparation. |

19. | E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory |

20. | M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Sig. Process |

21. | C. Li, W. Yin, H. Jiang, and Y. Zhang, “An efficient augmented lagrangian method with applications to total variation minimization,” Tech. Rep. TR12-13, Computational and Applied Mathematics, Rice University, Houston, TX, (2012). |

**OCIS Codes**

(270.0270) Quantum optics : Quantum optics

(270.6570) Quantum optics : Squeezed states

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: January 14, 2013

Revised Manuscript: March 8, 2013

Manuscript Accepted: March 8, 2013

Published: March 19, 2013

**Citation**

B. J. Lawrie and R. C. Pooser, "Toward real-time quantum imaging with a single pixel camera," Opt. Express **21**, 7549-7559 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-6-7549

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### References

- V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science321, 544–547 (2008). [CrossRef] [PubMed]
- Q. Glorieux, J. B. Clark, A. M. Marino, Z. Zhou, and P. D. Lett, “Temporally multiplexed storage of images in a gradient echo memory,” Opt. Express20, 12350–12358 (2012). [CrossRef] [PubMed]
- D.-S. Ding, Z.-Y. Zhou, B.-S. Shi, X.-B. Zou, and G.-C. Guo, “Image transfer through two sequential four-wave-mixing processes in hot atomic vapor,” Phys. Rev. A85, 053815 (2012). [CrossRef]
- J. B. Clark, Z. Zhou, Q. Glorieux, A. M. Marino, and P. D. Lett, “Imaging using quantum noise properties of light,” Opt. Express20, 17050–17058 (2012). [CrossRef]
- E. Brambilla, L. Caspani, O. Jedrkiewicz, L. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A77, 053807 (2008). [CrossRef]
- 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]
- N. V. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Noiseless optical amplifier operating on hundreds of spatial modes,” Phys. Rev. Lett.109, 043602 (2012). [CrossRef] [PubMed]
- M. I. Kolobov and C. Fabre, “Quantum limits on optical resolution,” Phys. Rev. Lett.85, 3789–3792 (2000). [CrossRef] [PubMed]
- M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H.-A. Bachor, P. K. Lam, N. Treps, P. Buchhave, C. Fabre, and C. C. Harb, “Tools for multimode quantum information: Modulation, detection, and spatial quantum correlations,” Phys. Rev. Lett.98, 083602 (2007). [CrossRef] [PubMed]
- G. Brida, M. Genovese, and I. Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nature Photon.4, 227–230 (2010). [CrossRef]
- O. Aytür and P. Kumar, “Squeezed-light generation with a mode-locked q-switched laser and detection by using a matched local oscillator,” Opt. Lett.17, 529–531 (1992). [CrossRef] [PubMed]
- D. Smithey, M. Beck, M. Belsley, and M. Raymer, “Sub-shot-noise correlation of total photon number using macroscopic twin pulses of light,” Phys. Rev. Lett.69, 2650–2653 (1992). [CrossRef] [PubMed]
- L. Jiying, Z. Jubo, L. Chuan, and H. Shisheng, “High-quality quantum-imaging algorithm and experiment based on compressive sensing,” Opt. Lett.35, 1206–1208 (2010). [CrossRef] [PubMed]
- O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” App. Phys. Lett.95, 131110 (2009). [CrossRef]
- P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, “Entangled-photon compressive ghost imaging,” Phys. Rev. A84, 061804 (2011). [CrossRef]
- T. Do, L. Gan, N. Nguyen, and T. Tran, “Fast and efficient compressive sensing using structurally random matrices,” IEEE Trans. Signal Process.60, 139–154 (2012). [CrossRef]
- D. Smith, J. Gore, T. Yankeelov, and E. Welch, “Real-time compressive sensing MRI reconstruction using GPU computing and split bregman methods,” Int. J. of Biomed. Imag.2012, 864827 (2012).
- R. Pooser, B. Lawrie, and W. Grice, “Compressive sampling low light beam profiler using structural random matrices with a semilocal randomizer,” In Preparation.
- E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory52, 489–509 (2006). [CrossRef]
- M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Sig. Process1, 586 –597 (2007). [CrossRef]
- C. Li, W. Yin, H. Jiang, and Y. Zhang, “An efficient augmented lagrangian method with applications to total variation minimization,” Tech. Rep. TR12-13, Computational and Applied Mathematics, Rice University, Houston, TX, (2012).

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