## Frequency up-conversion of quantum images |

Optics Express, Vol. 20, Issue 6, pp. 6644-6656 (2012)

http://dx.doi.org/10.1364/OE.20.006644

Acrobat PDF (974 KB)

### Abstract

We develop the theory of frequency up-conversion of an arbitrary spatially-broadband quantum state (quantum image), deriving the analytical solutions for the cases of plane-wave pump and short crystal with arbitrary pump. By using an example of the quantum image imposed by the orbital angular momentum of the pump beam in spontaneous parametric down-conversion, we show that 99%-fidelity up-conversion of quantum images from an infrared wavelength to the visible wavelength can be obtained in periodically-poled lithium-niobate crystals at reasonable pump intensities well below the crystal damage threshold.

© 2012 OSA

## 1. Introduction

1. C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D Part. Fields **26**(8), 1817–1839 (1982). [CrossRef]

*temporal*bandwidth of the parametric processes, has already been used to make noiseless amplifiers for fiber-optic communications [2

2. D. Levandovsky, M. Vasilyev, and P. Kumar, “Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier,” Opt. Lett. **24**(14), 984–986 (1999). [CrossRef] [PubMed]

6. Z. Tong, C. Lundstrom, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Gruner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics **5**(7), 430–436 (2011). [CrossRef]

*spatial*bandwidth of these processes also enables their use for noiseless amplification of

*classical*images [7

7. M. Kolobov, “The spatial behavior of nonclassical light,” Rev. Mod. Phys. **71**(5), 1539–1589 (1999). [CrossRef]

11. E. Lantz and F. Devaux, “Parametric amplification of images: from time gating to noiseless amplification,” J. Sel. Top. Quantum Electron. **14**(3), 635–647 (2008). [CrossRef]

*quantum*images, in which multimode squeezed vacuum is used to suppress the loss of information at the periphery of a soft aperture of a spatially-broadband optical receiver [12

12. P. Kumar, V. Grigoryan, and M. Vasilyev, “Noise-free amplification: towards quantum laser radar,” *the 14th Coherent Laser Radar Conference*, Snowmass, CO, July 2007. http://space.hsv.usra.edu/CLRC/presentations/Kumar.ppt

13. J. E. Midwinter, “Image conversion from 1.6 μm to the visible in lithium niobate,” Appl. Phys. Lett. **12**(3), 68–70 (1968). [CrossRef]

14. J. M. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett. **68**(14), 2153–2156 (1992). [CrossRef] [PubMed]

15. H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett. **105**(9), 093604 (2010). [CrossRef] [PubMed]

16. M. T. Rakher, L. Ma, O. T. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics **4**(11), 786–791 (2010). [CrossRef]

17. A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecom-wavelength conversion,” Nat. Phys. **6**(11), 894–899 (2010). [CrossRef]

19. L. V. Magdenko, I. V. Sokolov, and M. I. Kolobov, “Quantum teleportation of optical images with frequency conversion,” Opt. Spectrosc. **103**(1), 62–66 (2007). [CrossRef]

20. A. S. Chirkin and E. V. Makeev, “Simultaneous phase-sensitive parametric amplification and up-conversion of an optical image,” J. Opt. B Quantum Semiclassical Opt. **7**(12), S500–S506 (2005). [CrossRef]

21. E. V. Makeev and A. S. Chirkin, “Quantum fluctuations of parametrically amplified and up-converted optical images in consecutive wave interactions,” J. Russ. Laser Res. **27**(5), 466–474 (2006). [CrossRef]

^{(2)}crystal pumped by a beam carrying orbital angular momentum [22

22. G. A. Barbosa and H. H. Arnaut, “Twin photons with angular-momentum entanglement: phase matching,” Phys. Rev. A **65**(5), 053801 (2002). [CrossRef]

23. A. R. Altman, K. G. Köprülü, E. Corndorf, P. Kumar, and G. A. Barbosa, “Quantum imaging of nonlocal spatial correlations induced by orbital angular momentum,” Phys. Rev. Lett. **94**(12), 123601 (2005). [CrossRef] [PubMed]

24. M. L. Marable, S.-K. Choi, and P. Kumar, “Measurement of quantum-noise correlations in parametric image amplification,” Opt. Express **2**(3), 84–92 (1998). [CrossRef] [PubMed]

26. J. L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of sub-shot-noise correlations of spatial fluctuations in the photon-counting regime,” Phys. Rev. Lett. **101**(23), 233604 (2008). [CrossRef] [PubMed]

27. V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science **321**(5888), 544–547 (2008). [CrossRef] [PubMed]

## 2. Theory of quantum image conversion

*E*

_{2}= 0), Eq. (1) is reduced to the paraxial Helmholtz equation, whose solution for the normalized fields in the Fourier domain is given bywhere

31. S.-K. Choi, R.-D. Li, C. Kim, and P. Kumar, “Traveling-wave optical parametric amplifier: investigation of its phase-sensitive and phase-insensitive gain response,” J. Opt. Soc. Am. B **14**(7), 1564 (1997). [CrossRef]

32. C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, “Transverse effects and mode couplings in OPOs,” Appl. Phys. B **66**(6), 685–699 (1998). [CrossRef]

### Analytical solution 1: plane-wave pump

*same*spatial-frequency components of the input and the up-converted images. The correlations in the

*R*, whereas those outside the up-conversion spatial bandwidth experience very low conversion efficiency. For input images whose quantum features are contained within the spatial bandwidth of the up-conversion process, the output quantum image will reproduce all the information from the input with high fidelity. And vice versa, for images with broader spatial frequency content, the non-unity conversion efficiency

*R*is equivalent to loss and results in reduction of the fidelity of the up-converted state. We also note that the up-conversion takes place equally for both quadratures of the image, and no underlying symmetry of the image is required (this is in contrast to the phase-sensitive amplification process, which requires symmetry between the signal’s positive- and negative-spatial-frequency components, leading to a flat phase front of the image [7

7. M. Kolobov, “The spatial behavior of nonclassical light,” Rev. Mod. Phys. **71**(5), 1539–1589 (1999). [CrossRef]

30. M. Vasilyev, N. Stelmakh, and P. Kumar, “Estimation of the spatial bandwidth of an optical parametric amplifier with plane-wave-pump,” J. Mod. Opt. **56**(18-19), 2029–2033 (2009). [CrossRef]

35. M. Vasilyev, M. Annamalai, N. Stelmakh, and P. Kumar, “Quantum properties of a spatially-broadband traveling-wave phase-sensitive optical parametric amplifier,” J. Mod. Opt. **57**(19), 1908–1915 (2010). [CrossRef]

### Analytical solution 2: short crystal with inhomogeneous pump

*z*-dependence of the pump is neglected. One can then introduce parameters

*t*and

*r*aswhereso that the solution takes the form of point-by-point (pixel-by-pixel) up-conversion with efficiency

*R*= |

*r*|

^{2}:which is equivalent to the beam-splitter transformation.

## 3. Example of quantum image conversion

22. G. A. Barbosa and H. H. Arnaut, “Twin photons with angular-momentum entanglement: phase matching,” Phys. Rev. A **65**(5), 053801 (2002). [CrossRef]

23. A. R. Altman, K. G. Köprülü, E. Corndorf, P. Kumar, and G. A. Barbosa, “Quantum imaging of nonlocal spatial correlations induced by orbital angular momentum,” Phys. Rev. Lett. **94**(12), 123601 (2005). [CrossRef] [PubMed]

37. K. G. Köprülü, Y.-P. Huang, G. A. Barbosa, and P. Kumar, “Lossless single-photon shaping via heralding,” Opt. Lett. **36**(9), 1674–1676 (2011). [CrossRef] [PubMed]

*z*-propagating pump

*E*(

_{p}*x*,

*y*) of frequency ω

*= 2ω*

_{p}_{1}(here we use subscript “

*p*” to distinguish the SPDC pump from the up-conversion pump denoted by subscript “2”). Assuming that the SPDC crystal length

*l*

_{SPDC}is much smaller than the Rayleigh distance of the pump, the SPDC state can be approximated for low pump intensities (i.e., neglecting multiple-pair generation) by an unnormalized wavefunctionwhere

*F*is the joint two-photon wavefunction in the momentum space given by

*z*-integral gives the phase-mismatch factor, and the (

*x*,

*y*)-integral gives the spatial Fourier transform

*k*≈

_{i}*k*.

_{s}_{02}with orbital momentum

*l*= 2 is shown in purple as an example. For non-collinear phase matching (i.e., for

*k*≠ 2

_{p}*k*), the SPDC photons are emitted in the pattern of a phase-matched cone [red ring of radius

_{s}*q*

_{0}in Fig. 1(a)]. The image obtained by direct detecting the SPDC simply reflects this ring shape [see insert 1 in Fig. 1(a)]. The coincidence count measurement, on the other hand, reveals the underlying quantum structure of this image. In particular, if an idler photon at spatial frequency

_{02}]. The resulting product is sketched by the two green dots in Fig. 1(a), while its actual calculated shape is shown by the insert 3 in the same Figure. If the pump is a simple fundamental Gaussian beam LG

_{00}, this product takes the form shown by the insert 2. Thus, the spatial mode of the heralded single-photon state of the signal depends on the pump profile. This property is only observable in coincidence counting and represents a quantum image.

*l*

_{FC}by a 1:1 telescope and that the up-conversion pump is a plane wave (i.e., the conversion obeys the formulas for Analytical Solution 1 in Section 2), propagating in the same direction as the SPDC pump, as depicted in Fig. 1(b). The mode at frequency ω

_{3}is in the vacuum state at the input of the up-converter. For a single-photon input at frequency ω

_{1}and spatial frequency

*z*=

*l*

_{FC}, and

_{1}(or ω

_{3}, respectively), with all other modes in a vacuum state. Thus, the SPDC state (16) after up-conversion becomes:

*q*

^{2}

*z*/(2

*k*

_{3}), which is equivalent to observing the far-field pattern in the Fourier plane of a lens.

*r*= 1 and

*t*= 0 and denoted simply “Heralded” below; it is also the same as the ideal up-conversion of the state heralded prior to frequency conversion):

*F*and the up-conversion coefficient

*r** in the transverse momentum space. Thus, to maximize the fidelity of the up-converted quantum image, one needs to ensure that

*r** is close to unity over the range of spatial frequencies where

*F*has non-zero values. We note that the fidelity is the same regardless of whether the idler photon is detected before or after up-conversion (however, the probability of detection of the idler photon will be lower after imperfect up-conversion).

*q*

_{i}_{0}=

*q*

_{0}(which corresponds to Δ

*k*= 0 in the plane-wave pump case), so we will assume

_{z}*k*

_{eff}= 0 takes place at

*q*=

*q*=

_{s}*q*

_{0}, i.e.,and

*k*

_{1}=

*k*. Thus, the phase-matched bands of both the up-conversion and the SPDC are centered at

_{s}*r** = 1 for γ

*l*

_{FC}= |κ|

*l*

_{FC}= π/2, i.e.

*l*

_{FC}= π/(2|κ|). The first zero of

*r** in Eq. (7) takes place at

*l*

_{FC}= π (i.e.,

*k*

_{z}from Eq. (18) with

*q*=

_{i}*q*

_{0}and

*n*/

_{s}*n*

_{1}is the ratio of the signal-wave refractive indices in the SPDC and up-conversion crystals.

*q*is the spatial bandwidth of the SPDC pump beam [i.e., the blue circle in Fig. 2(a) should be larger than the checkered purple ring]. For the quantum images of interest,

_{p}*q*

_{0}to the SPDC spatial bandwidth

*q*

_{0}. It is also helpful to calculate the spatial bandwidth (at the first zero of the sinc function) of the signal for the “lowpass” configuration (i.e., assuming

*q*=

_{i}*q*

_{0}= 0):which allows us to express the dimensionless parameters

*M*and

*N*asand

*l*, the parameter

*M*, and the ratio of the up-conversion to the SPDC crystal lengths

*l*

_{FC}/

*l*

_{SPDC}is shown in Fig. 3 for ω

_{2}/ ω

_{3}= 2/3 and

*N*= 10. The results indicate that high fidelity can be achieved in all cases by having a sufficiently short

*l*

_{FC}. However, because shortening

*l*

_{FC}requires increasing the up-conversion pump power, the plots show that the configuration of Fig. 2 is clearly preferable as it achieves higher fidelity for a given up-conversion crystal length.

_{2}= λ

*= 780 nm, λ*

_{p}_{1}= 2λ

_{2}= 1560 nm, and the up-converted wavelength λ

_{3}= (1/λ

_{1}+ 1/λ

_{2})

^{–1}= 2λ

_{2}/3 = λ

_{1}/3 = 520 nm. Both SPDC and wavelength conversion can be implemented, for example, in PPLN crystals (

*n*=

_{s}*n*

_{1}≈

*n*

_{2}=

*n*≈

_{p}*n*

_{3}≈2.14). The (one-sided) angle at which the signal beam emerges in the free space is θ

*=*

_{s}*q*

_{0}

*n*/

_{s}*k*. Assuming the parameters θ

_{s}*= 0.04 rad,*

_{s}*M*= 4, and

*N*= 10 — which are similar to those in [23

23. A. R. Altman, K. G. Köprülü, E. Corndorf, P. Kumar, and G. A. Barbosa, “Quantum imaging of nonlocal spatial correlations induced by orbital angular momentum,” Phys. Rev. Lett. **94**(12), 123601 (2005). [CrossRef] [PubMed]

*= 0.07 rad,*

_{s}*M*= 4, and

*N*= 8.3), but at a different signal wavelength — we obtain

*l*

_{SPDC}=

*N*λ

*/ θ*

_{s}n_{s}

_{s}^{2}= 20.9 mm and

*a*

_{0}

*= (λ*

_{p}

_{p}l_{SPDC}/

*n*)

_{p}^{1/2}

*M*/(2π) = 55.5 μm. Then, in order to achieve the fidelity η = 99% with the configuration of Fig. 2, one needs to employ the up-conversion crystals with lengths

*l*

_{FC}= 16.7 mm, 6.26 mm, and 4.17 mm for the cases of SPDC pumping by the LG

_{00}, LG

_{02}, and LG

_{04}modes, respectively. This corresponds to the peak up-conversion pump intensities of 2.4, 17.2, and 38.7 MW/cm

^{2}, respectively, where all three intensity numbers are well below the ~250-MW/cm

^{2}optical damage threshold of the lithium-niobate crystal. In contrast to the case of Fig. 2, the configuration of Fig. 1 requires significantly shorter lengths

*l*

_{FC}of 2.5 mm, 1.67 mm, and 1.46 mm to achieve the same fidelity, taking the up-conversion pump requirements to the intensity levels of 108, 241, and 318 MW/cm

^{2}, respectively, where only the first number is safely below the crystal damage threshold. While the configuration of Fig. 2 requires lower pump intensities, it also makes it more difficult to spatially separate the up-converted image from the up-conversion pump. For our chosen example, where the up-conversion pump’s near-infrared wavelength lies within the spectral response of silicon detectors, a strong dichroic filtering might be needed to prevent the pump beam from affecting the signal detection.

## 4. Summary

## Acknowledgments

## References and links

1. | C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D Part. Fields |

2. | D. Levandovsky, M. Vasilyev, and P. Kumar, “Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier,” Opt. Lett. |

3. | D. Levandovsky, M. Vasilyev, and P. Kumar, ““Near-noiseless amplification of light by a phase-sensitive fibre amplifier,” PRAMANA–,” J. Phys. |

4. | W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3 dB noise figure in high-gain phase-sensitive fibre amplifier,” Electron. Lett. |

5. | R. Slavík, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics |

6. | Z. Tong, C. Lundstrom, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Gruner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics |

7. | M. Kolobov, “The spatial behavior of nonclassical light,” Rev. Mod. Phys. |

8. | S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless optical amplification of images,” Phys. Rev. Lett. |

9. | K. Wang, G. Yang, A. Gatti, and L. Lugiato, “Controlling the signal-to-noise ratio in optical parametric image amplification,” J. Opt. B Quantum Semiclassical Opt. |

10. | A. Mosset, F. Devaux, and E. Lantz, “Spatially noiseless optical amplification of images,” Phys. Rev. Lett. |

11. | E. Lantz and F. Devaux, “Parametric amplification of images: from time gating to noiseless amplification,” J. Sel. Top. Quantum Electron. |

12. | P. Kumar, V. Grigoryan, and M. Vasilyev, “Noise-free amplification: towards quantum laser radar,” |

13. | J. E. Midwinter, “Image conversion from 1.6 μm to the visible in lithium niobate,” Appl. Phys. Lett. |

14. | J. M. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett. |

15. | H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett. |

16. | M. T. Rakher, L. Ma, O. T. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics |

17. | A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecom-wavelength conversion,” Nat. Phys. |

18. | P. Scotto, P. Colet, A. Jacobo, and M. S. Miguel, “Optical image processing in second-harmonic generation,” chapter 8 in |

19. | L. V. Magdenko, I. V. Sokolov, and M. I. Kolobov, “Quantum teleportation of optical images with frequency conversion,” Opt. Spectrosc. |

20. | A. S. Chirkin and E. V. Makeev, “Simultaneous phase-sensitive parametric amplification and up-conversion of an optical image,” J. Opt. B Quantum Semiclassical Opt. |

21. | E. V. Makeev and A. S. Chirkin, “Quantum fluctuations of parametrically amplified and up-converted optical images in consecutive wave interactions,” J. Russ. Laser Res. |

22. | G. A. Barbosa and H. H. Arnaut, “Twin photons with angular-momentum entanglement: phase matching,” Phys. Rev. A |

23. | A. R. Altman, K. G. Köprülü, E. Corndorf, P. Kumar, and G. A. Barbosa, “Quantum imaging of nonlocal spatial correlations induced by orbital angular momentum,” Phys. Rev. Lett. |

24. | M. L. Marable, S.-K. Choi, and P. Kumar, “Measurement of quantum-noise correlations in parametric image amplification,” Opt. Express |

25. | O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. |

26. | J. L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of sub-shot-noise correlations of spatial fluctuations in the photon-counting regime,” Phys. Rev. Lett. |

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

28. | A. Gavrielides, P. Peterson, and D. Cardimona, “Diffractive imaging in three-wave interactions,” J. Appl. Phys. |

29. | M. Vasilyev, N. Stelmakh, and P. Kumar, “Phase-sensitive image amplification with elliptical Gaussian pump,” Opt. Express |

30. | M. Vasilyev, N. Stelmakh, and P. Kumar, “Estimation of the spatial bandwidth of an optical parametric amplifier with plane-wave-pump,” J. Mod. Opt. |

31. | S.-K. Choi, R.-D. Li, C. Kim, and P. Kumar, “Traveling-wave optical parametric amplifier: investigation of its phase-sensitive and phase-insensitive gain response,” J. Opt. Soc. Am. B |

32. | C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, “Transverse effects and mode couplings in OPOs,” Appl. Phys. B |

33. | K. G. Köprülü and O. Aytür, “Analysis of Gaussian-beam degenerate optical parametric amplifiers for the generation of quadrature-squeezed states,” Phys. Rev. A |

34. | K. G. Köprülü and O. Aytür, “Analysis of the generation of amplitude-squeezed light with Gaussian-beam degenerate optical parametric amplifiers,” J. Opt. Soc. Am. B |

35. | M. Vasilyev, M. Annamalai, N. Stelmakh, and P. Kumar, “Quantum properties of a spatially-broadband traveling-wave phase-sensitive optical parametric amplifier,” J. Mod. Opt. |

36. | M. Annamalai, M. Vasilyev, N. Stelmakh, and P. Kumar, “Compact representation of spatial modes of phase-sensitive image amplifier,” the |

37. | K. G. Köprülü, Y.-P. Huang, G. A. Barbosa, and P. Kumar, “Lossless single-photon shaping via heralding,” Opt. Lett. |

**OCIS Codes**

(190.7220) Nonlinear optics : Upconversion

(190.4975) Nonlinear optics : Parametric processes

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: October 26, 2011

Revised Manuscript: January 19, 2012

Manuscript Accepted: February 14, 2012

Published: March 7, 2012

**Citation**

Michael Vasilyev and Prem Kumar, "Frequency up-conversion of quantum images," Opt. Express **20**, 6644-6656 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-6-6644

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### References

- C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D Part. Fields26(8), 1817–1839 (1982). [CrossRef]
- D. Levandovsky, M. Vasilyev, and P. Kumar, “Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier,” Opt. Lett.24(14), 984–986 (1999). [CrossRef] [PubMed]
- D. Levandovsky, M. Vasilyev, and P. Kumar, ““Near-noiseless amplification of light by a phase-sensitive fibre amplifier,” PRAMANA–,” J. Phys.56, 281 (2001).
- W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3 dB noise figure in high-gain phase-sensitive fibre amplifier,” Electron. Lett.35(22), 1954 (1999). [CrossRef]
- R. Slavík, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics4(10), 690–695 (2010). [CrossRef]
- Z. Tong, C. Lundstrom, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Gruner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics5(7), 430–436 (2011). [CrossRef]
- M. Kolobov, “The spatial behavior of nonclassical light,” Rev. Mod. Phys.71(5), 1539–1589 (1999). [CrossRef]
- S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless optical amplification of images,” Phys. Rev. Lett.83(10), 1938–1941 (1999). [CrossRef]
- K. Wang, G. Yang, A. Gatti, and L. Lugiato, “Controlling the signal-to-noise ratio in optical parametric image amplification,” J. Opt. B Quantum Semiclassical Opt.5(4), S535–S544 (2003). [CrossRef]
- A. Mosset, F. Devaux, and E. Lantz, “Spatially noiseless optical amplification of images,” Phys. Rev. Lett.94(22), 223603 (2005). [CrossRef] [PubMed]
- E. Lantz and F. Devaux, “Parametric amplification of images: from time gating to noiseless amplification,” J. Sel. Top. Quantum Electron.14(3), 635–647 (2008). [CrossRef]
- P. Kumar, V. Grigoryan, and M. Vasilyev, “Noise-free amplification: towards quantum laser radar,” the 14th Coherent Laser Radar Conference, Snowmass, CO, July 2007. http://space.hsv.usra.edu/CLRC/presentations/Kumar.ppt
- J. E. Midwinter, “Image conversion from 1.6 μm to the visible in lithium niobate,” Appl. Phys. Lett.12(3), 68–70 (1968). [CrossRef]
- J. M. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett.68(14), 2153–2156 (1992). [CrossRef] [PubMed]
- H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett.105(9), 093604 (2010). [CrossRef] [PubMed]
- M. T. Rakher, L. Ma, O. T. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics4(11), 786–791 (2010). [CrossRef]
- A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecom-wavelength conversion,” Nat. Phys.6(11), 894–899 (2010). [CrossRef]
- P. Scotto, P. Colet, A. Jacobo, and M. S. Miguel, “Optical image processing in second-harmonic generation,” chapter 8 in Quantum Imaging, ed. by M. Kolobov, Springer Verlag, New York, 2007.
- L. V. Magdenko, I. V. Sokolov, and M. I. Kolobov, “Quantum teleportation of optical images with frequency conversion,” Opt. Spectrosc.103(1), 62–66 (2007). [CrossRef]
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