## Generation and delayed retrieval of spatially multimode Raman scattering in warm rubidium vapors |

Optics Express, Vol. 20, Issue 28, pp. 29540-29552 (2012)

http://dx.doi.org/10.1364/OE.20.029540

Acrobat PDF (1179 KB)

### Abstract

We apply collective Raman scattering to create, store and retrieve spatially multimode light in warm rubidium-87 vapors. The light is created in a spontaneous Stokes scattering process. This is accompanied by the creation of counterpart collective excitations in the atomic ensemble – the spin waves. After a certain storage time we coherently convert the spin waves into the light in deterministic anti-Stokes scattering. The whole process can be regarded as a delayed four-wave mixing which produces pairs of correlated, delayed random images. Storage of higher order spatial modes up to microseconds is possible owing to usage of a buffer gas. We study the performance of the Raman scattering, storage and retrieval of collective excitations focusing on spatial effects and the influence of decoherence caused by diffusion of rubidium atoms in different buffer gases. We quantify the number of modes created and retrieved by analyzing statistical correlations of intensity fluctuations between portions of the light scattered in the far field.

© 2012 OSA

## 1. Introduction

1. L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature **414**, 413–418 (2001). [CrossRef] [PubMed]

2. J. Appel, E. Figueroa, D. Korystov, M. Lobino, and A. Lvovsky, “Quantum memory for squeezed light,” Phys. Rev. Lett. **100**, 093602 (2008). [CrossRef] [PubMed]

3. K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Storage and retrieval of a squeezed vacuum,” Phys. Rev. Lett. **100**, 093601 (2008). [CrossRef] [PubMed]

4. K. Hammerer, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. **82**, 1041–1093 (2010). [CrossRef]

5. K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik, “Quantum memory for entangled continuous-variable states,” Nature Phys. **7**, 13–16 (2010). [CrossRef]

6. J. Nunn, K. Reim, K. C. Lee, V. O. Lorenz, B. J. Sussman, I. A. Walmsley, and D. Jaksch, “Multimode memories in atomic ensembles,” Phys. Rev. Lett. **101**, 260502 (2008). [CrossRef] [PubMed]

7. D. V. Vasilyev, I. V. Sokolov, and E. S. Polzik, “Quantum volume hologram,” Phys. Rev. A **81**, 020302 (2010). [CrossRef]

8. 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 **20**, 12350–12358 (2012). [CrossRef] [PubMed]

9. D. Higginbottom, B. Sparkes, M. Rancic, O. Pinel, M. Hosseini, P. Lam, and B. Buchler, “Spatial-mode storage in a gradient-echo memory,” Phys. Rev. A **86**, 023801 (2012). [CrossRef]

10. 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]

11. V. Boyer, A. Marino, and P. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. **100**, 143601 (2008). [CrossRef] [PubMed]

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

13. M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A **24**, 1980–1993 (1981). [CrossRef]

14. J. Kołodyński, J. Chwedeńczuk, and W. Wasilewski, “Eigenmode description of Raman scattering in atomic vapors in the presence of decoherence,” Phys. Rev. A **86**, 013818 (2012). [CrossRef]

15. P. H. S. Ribeiro, C. H. Monken, and G. A. Barbosa, “Measurement of coherence area in parametric downconversion luminescence,” Appl. Opt. **33**, 352–355 (1994). [CrossRef] [PubMed]

16. A. Marino, V. Boyer, R. Pooser, P. Lett, K. Lemons, and K. Jones, “Delocalized correlations in twin light beams with orbital angular momentum,” Phys. Rev. Lett. **101**, 093602 (2008). [CrossRef] [PubMed]

11. V. Boyer, A. Marino, and P. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. **100**, 143601 (2008). [CrossRef] [PubMed]

17. F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. **94**, 183602 (2005). [CrossRef] [PubMed]

14. J. Kołodyński, J. Chwedeńczuk, and W. Wasilewski, “Eigenmode description of Raman scattering in atomic vapors in the presence of decoherence,” Phys. Rev. A **86**, 013818 (2012). [CrossRef]

## 2. Generator

**k**

*−*

_{w}**k**

*is mapped onto the spatial phase of an atomic excitation. The excitation takes on a form of a coherent spin wave and acquires a wave vector*

_{s}**K**=

**k**

*−*

_{p}**k**

*. At the readout stage the stored phase given by the wave vector*

_{s}**K**adds to the read beam field wave vector

**k**

*leading to scattering of anti-Stokes photons*

_{r}**k**

*in the direction opposite to the Stokes ones, as illustrated in Fig. 1(c). With*

_{a}*z*-axis along the write beam and

**k**

*-vector and the scattering in the*

_{w}*x*–

*z*plane the spin wave wave vector

**K**equals: where

*θ*is the scattering angle and the numbers correspond to 6.8 GHz Stokes shift (F=1→ F=2 scattering) at D1 line.

**k**

*while the spin wave modes around the origin of the*

_{w}**K**-vector space. The modes resemble Laguerre-Gaussian functions [14

14. J. Kołodyński, J. Chwedeńczuk, and W. Wasilewski, “Eigenmode description of Raman scattering in atomic vapors in the presence of decoherence,” Phys. Rev. A **86**, 013818 (2012). [CrossRef]

*L*. The Raman growth parameters of higher order modes slowly diminish along with mode number. Typically the number of significantly excited modes is close to the Fresnel number of the write beam

*F*= |

*k*|

_{w}*w*

^{2}/(2

*πL*) if the decoherence is neglected [13

13. M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A **24**, 1980–1993 (1981). [CrossRef]

**K**which correspond to abrupt spatial variations. They are easily washed off by diffusion of the atoms in a buffer gas during the storage. Therefore in the experiment we expect the number of retrieved modes

*N*to be lower than the Fresnel number of the write beam

*F*.

*n*(

_{s}*θ*,

_{x}*θ*) and

_{y}*n*(

_{a}*θ*,

_{x}*θ*) respectively. In the ideal case of a plane-wave write and read beam we would expect that every point in

_{y}*n*

_{s,a}(

*θ*,

_{x}*θ*) should carry information about the spin wave with

_{y}**K**

_{⊥}= |

*k*|(

_{s}*θ*,

_{x}*θ*). In case of a finite write and read beam widths

_{y}*w*we expect the ideal images to be blurred due to beams wave vector spread. The true images should be close to the convolution of atomic excitations distribution in the sample with the read beam distribution in

**k**

_{⊥}-space.

## 3. Experimental setup

^{87}Rb atoms to

*F*= 1 ground level. Both the write and the read lasers were external cavity diode lasers from Toptica. They were detuned from the F = 1 → F′ = 1 transition by 1 GHz to the red and by 1 GHz from the F = 2 → F′ = 2 transition to the blue respectively. Both were additionally cleaned up spectrally as well as spatially by Fabry-Perrot cavities with FSR=13.6 GHz.

*μ*s and its 4.2 mm full width at 1/

*e*

^{2}waist diameter ensured bleaching of the medium in the volume were the Raman scattering took place. The write pulse started immediately after the pump pulse. The 1/

*e*

^{2}beam diameter was 2.16 mm. Pulse duration varied from 200 ns to 10

*μ*s and the power up to 17 mW. After the write pulse we inserted a variable storage delay. Finally a read pulse was directed onto the cell and converted the spin waves into anti-Stokes photons. The 1/

*e*

^{2}beam diameter was 1.76 mm.

^{87}Rb. The cell was mounted inside a two-layer magnetic shielding and was heated with bifilar wound copper coils. For comparison we used three cells containing different buffer gases, 1 torr or 0.5 torr Krypton or 5 torr Neon.

^{85}Rb cell. We decided to use this method due to its simplicity but one may alternatively use Fabry-Perrot interferometers [26

26. S. Manz, T. Fernholz, J. Schmiedmayer, and J.-W. Pan, “Collisional decoherence during writing and reading quantum states,” Phys. Rev. A **75**, 040101 (2007). [CrossRef]

*μ*rad angle inside the cell. We also calibrated sensitivity with a power meter. Since the overlapping write and read beams were tilted with respect to each another, the corresponding Stokes and the anti-Stokes scattering light fell on distinct regions of the sensor. The camera was incapable of resolving the light temporally and we always captured both the Stokes and the anti-Stokes scattering integrated over the duration of write and read pulse. For each setting of the pulse lengths, powers and the storage time we captured 500 or 10000 separate images of the scattered light with a cycle rate of about 90 Hz. Despite the usage of an interference filter before the camera we had some background coming from spontaneous emission in the pumping process. Thus the reference set of 100 frames with pump and write beams was saved for background subtraction.

*n*(

_{s}*θ*,

_{x}*θ*)〉 and 〈

_{y}*n*(

_{a}*θ*,

_{x}*θ*)〉 respectively. The average intensities presented below were calculated subtracting the background. The main origin of the background was the stray fluorescence of the atoms emitted during pumping. It was sufficiently stable to calculate it with high precision from 100 frames. We find that the average intensity of the scattered light was symmetric around the driving beam. Therefore we averaged it with respect to the polar angle to obtain 〈

_{y}*n*(

_{s}*θ*)〉 and 〈

*n*(

_{a}*θ*)〉 with better signal to noise ratio. For calculating second order moments, including intensity correlations, we collected data sets containing 10000 frames.

^{87}Rb cell was estimated by measuring the absorption spectrum for the write laser attenuated to a fraction of saturation intensity right before the cell. The result was fitted with a theoretical model to estimate the gas temperature and absorption at resonance. Cell heater temperature, measured by the resistance of the windings, was adjusted so as to obtain a Doppler-broadened optical depth of 130. The stability of the setup was verified by repeating this measurement prior to and right after the proper experimental sequence. Note that the Doppler broadened optical thickness is not sensitive to the pressure broadening of the order of few natural linewidths. It is deemed that using the above method we obtain almost the same rubidium vapor pressure in all of the cells.

## 4. Results

### Decay of the spin waves

**K**|. It can be extracted from measurements of the average intensity of anti-Stokes 〈

*n*(

_{a}*θ*,

_{x}*θ*)〉 as a function of the storage time for constant write pulse parameters.

_{y}*t*= 330 ns for 0.5 torr Krypton,

_{w}*t*= 500 ns for 1 torr Krypton and

_{w}*t*= 1.8

_{w}*μ*s for 5 torr Neon. After a variable storage time

*t*a 2

_{s}*μ*s read pulse is sent down the cell to convert remaining atomic excitation to anti-Stokes light. The average intensity of anti-Stokes 〈

*n*(

_{a}*θ*,

_{x}*θ*)〉 is a Gaussian function of angles

_{y}*θ*,

_{x}*θ*. With increasing the storage time

_{y}*t*the height and width of this Gaussian decreases.

_{s}*θ*,

_{x}*θ*) with respect to the read beam corresponds to a certain transverse anti-Stokes photon wave vector

_{y}**k**

_{a,⊥}= 2

*π*(

*θ*,

_{x}*θ*)/(0.8 mm mrad). It is approximately equal to the coupled spin wave wave vector

_{y}**K**to within the uncertainty given by the read beam wave vector spread corresponding to the angular spread of 0.26 mrad. Therefore the evolution of the anti-Stokes intensity

*n*(

_{a}*θ*,

_{x}*θ*) as a function of storage time

_{y}*t*provides indication of the spin wave decay for the best coupled spin wave wave vector. In Fig. 3(a) we present typical decays along with fitted exponentials. In Fig. 3(b) we gathered decay rates as a function of angle between the read beam and scattered photons. All the errorbars plotted on the graphs correspond to the 1

_{s}*σ*uncertainty calculated from the variance of the experimental data.

8. 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 **20**, 12350–12358 (2012). [CrossRef] [PubMed]

*K*decays with rate proportional to square of its wave vector

*γ*=

_{K}*DK*

^{2}, with

*D*being the diffusion coefficient. The parabolic fits of Fig. 3(b) give the diffusion rates equal 397(27) cm

^{2}/s, 257(4) cm

^{2}/s, 146(5) cm

^{2}/s for 5 torr Neon, 0.5 torr Krypton and 1 torr Krypton respectively. The values measured for Krypton are consistent with collisions cross sections [27

27. K. Gibble and A. Gallagher, “Measurements of velocity-changing collision kernels,” Phys. Rev. A **43**, 1366–1380 (1991). [CrossRef] [PubMed]

8. 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 **20**, 12350–12358 (2012). [CrossRef] [PubMed]

28. O. Firstenberg, P. London, M. Shuker, A. Ron, and N. Davidson, “Elimination, reversal and directional bias of optical diffraction,” Nature Phys. **5**, 665–668 (2009). [CrossRef]

29. M. Shuker, O. Firstenberg, R. Pugatch, A. Ben-Kish, A. Ron, and N. Davidson, “Angular dependence of Dicke-narrowed electromagnetically induced transparency resonances,” Phys. Rev. A **76**, 023813 (2007). [CrossRef]

### Spontaneous scattering and growth of the spin wave

*n*(

_{s}*θ*,

_{x}*θ*) as a function of write pulse length

_{y}*t*can be approximated as a simple exponential, as shown for typical situations in Fig. 4(a). The duration of the write pulse is limited so that all saturation effects can be neglected.

_{w}*κ*to be a sum of three components

*κ*=

*ζ*

^{2}−

*γ*−

_{D}*γ*

_{sp}.

*ζ*

^{2}denotes the coherent scattering rate which is directly proportional to the intensity of the pumping light

*I*and atomic density. It drops for large scattering angles due to a reduced beam overlap between light fields involved.

_{w}*γ*denotes the diffusion-induced spin wave decay. Finally,

_{D}*γ*

_{sp}denotes the rate of the single atom spontaneous emission which depends linearly on the light power

*I*and has a contribution from the collisions with the buffer gas — pressure broadening of the excited state. As a single atom effect

_{w}*γ*

_{sp}should be independent from spin wave periodicity i.e. |

*K*|. In Fig. 4(b) we present measured growth rate

*κ*as a function of angle

*θ*between the write beam and Stokes photon. We also mark the predicted contribution of the diffusion-induced spin wave decay

*γ*inferred from the previous measurement.

_{D}26. S. Manz, T. Fernholz, J. Schmiedmayer, and J.-W. Pan, “Collisional decoherence during writing and reading quantum states,” Phys. Rev. A **75**, 040101 (2007). [CrossRef]

*γ*

_{sp}which results from the loss of phase coherence of the excited state. As seen in Fig. 3(b) and Fig. 4(b) for 0.5 an 1 Torr Krypton one can trade slower diffusion for faster growth.

### Intensity correlations

*μ*s respectively. The frame shows the speckle pattern of both the Stokes and the anti-Stokes scattering with the highest intensity around the driving beam directions. The pattern is produced due to the boson amplification of initially random fields in many spatial modes, just as it happens in spontaneous parametric down-conversion [31

31. B. M. Jost, A. V. Sergienko, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Spatial correlations of spontaneously down-converted photon pairs detected with a single-photon-sensitive CCD camera,” Opt. Express **3**, 81–88 (1998). [CrossRef] [PubMed]

32. A. Perrin, H. Chang, V. Krachmalnicoff, M. Schellekens, D. Boiron, A. Aspect, and C. I. Westbrook, “Observation of atom pairs in spontaneous four-wave mixing of two colliding Bose-Einstein condensates,” Phys. Rev. Lett. **99**, 150405 (2007). [CrossRef] [PubMed]

*K*| are washed off before the readout.

*C*(

_{ij}*θ*,

_{x}*θ*;

_{y}*θ*′

*,*

_{x}*θ*′

*). It is defined using deviations of the actual photon number from the mean value Δ*

_{y}*n*(

_{i}*θ*,

_{x}*θ*) =

_{y}*n*(

_{i}*θ*,

_{x}*θ*) − 〈

_{y}*n*(

_{i}*θ*,

_{x}*θ*)〉,

_{y}*i*=

*s*,

*a*as follows: We depict

*C*(

_{is}*θ*,

_{x}*θ*;

_{y}*θ*′

*,*

_{x}*θ*′

*) with fixed reference direction*

_{y}*θ*′

*,*

_{x}*θ*′

*in the Stokes as a function of*

_{y}*θ*,

_{x}*θ*for both the Stokes–Stokes

_{y}*C*and anti-Stokes–Stokes

_{ss}*C*type of correlations.

_{as}*C*for the reference direction along the write beam

_{as}*θ*′

*= 0 and at an angle of*

_{x}*θ*′

*= 0.7 mrad to it. Initial width of the correlation function with respect to*

_{x}*θ*equals 1 mrad regardless of the reference direction

_{y}*θ*′

*. It shrinks first slowly and then quite abruptly for long storage times due to diffusional damping of high-*

_{x}*K*spin waves. In Fig. 8(c) we can see correlation of the Stokes field with itself

*C*. It also has 1 mrad width regardless of the reference direction.

_{ss}**86**, 013818 (2012). [CrossRef]

*N*can be approximated as a number of speckle spots that fit into the solid angle occupied by the scattered light. We take

*N*= 2(

*w*

_{avg}/

*w*)

_{C}^{2}, where

*w*

_{avg}and

*w*are 1/

_{C}*e*

^{2}radius of the average intensity of the Scattered light and correlation function respectively. The numerical factor arises from the fact that the correlation function is square in the intensity. Its value is confirmed by considering a simple model, in which the registered intensity is a sum of randomly populated modes of a width

*w*

_{speckle}. It is found that the width of the correlation function is

*N*for the Stokes field. From the Gaussian fits we find the angular radius of the average intensity

*w*

_{avg}= 2.8 mrad as depicted in Fig. 6 and Stokes-Stokes correlation function

*w*= 1 mrad, giving a total number of modes

_{C}*N*≃ 15.7. These numbers allow us to assess the fundamental mode angular spread

*N*is expected to be the Fresnel number of the write beam [14

**86**, 013818 (2012). [CrossRef]

*F*= |

*k*|

_{s}*w*

^{2}/(2

*πL*) = 15 in our case, which is consistent with the experimental results. Let us note that in experiments by Boyer

*et al.*[11

11. V. Boyer, A. Marino, and P. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. **100**, 143601 (2008). [CrossRef] [PubMed]

*F*= 120. Therefore we conclude that the relation between number of modes and Fresnel number of the excited portion of the sample can be used for designing future experiments.

33. A. Gorshkov, A. André, M. Lukin, and A. Sørensen, “Photon storage in Λ-type optically dense atomic media. III. Effects of inhomogeneous broadening,” Phys. Rev. A **76**, 033806 (2007). [CrossRef]

## 5. Conclusion

**86**, 013818 (2012). [CrossRef]

16. A. Marino, V. Boyer, R. Pooser, P. Lett, K. Lemons, and K. Jones, “Delocalized correlations in twin light beams with orbital angular momentum,” Phys. Rev. Lett. **101**, 093602 (2008). [CrossRef] [PubMed]

**100**, 143601 (2008). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature |

2. | J. Appel, E. Figueroa, D. Korystov, M. Lobino, and A. Lvovsky, “Quantum memory for squeezed light,” Phys. Rev. Lett. |

3. | K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Storage and retrieval of a squeezed vacuum,” Phys. Rev. Lett. |

4. | K. Hammerer, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. |

5. | K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik, “Quantum memory for entangled continuous-variable states,” Nature Phys. |

6. | J. Nunn, K. Reim, K. C. Lee, V. O. Lorenz, B. J. Sussman, I. A. Walmsley, and D. Jaksch, “Multimode memories in atomic ensembles,” Phys. Rev. Lett. |

7. | D. V. Vasilyev, I. V. Sokolov, and E. S. Polzik, “Quantum volume hologram,” Phys. Rev. A |

8. | 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 |

9. | D. Higginbottom, B. Sparkes, M. Rancic, O. Pinel, M. Hosseini, P. Lam, and B. Buchler, “Spatial-mode storage in a gradient-echo memory,” Phys. Rev. A |

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

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

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

13. | M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A |

14. | J. Kołodyński, J. Chwedeńczuk, and W. Wasilewski, “Eigenmode description of Raman scattering in atomic vapors in the presence of decoherence,” Phys. Rev. A |

15. | P. H. S. Ribeiro, C. H. Monken, and G. A. Barbosa, “Measurement of coherence area in parametric downconversion luminescence,” Appl. Opt. |

16. | A. Marino, V. Boyer, R. Pooser, P. Lett, K. Lemons, and K. Jones, “Delocalized correlations in twin light beams with orbital angular momentum,” Phys. Rev. Lett. |

17. | F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. |

18. | A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein-Podolsky-Rosen entanglement,” Nature |

19. | C. Chou, S. Polyakov, A. Kuzmich, and H. Kimble, “Single-photon generation from stored excitation in an atomic ensemble,” Phys. Rev. Lett. |

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

21. | K. Wagner, J. Janousek, V. Delaubert, H. Zou, C. Harb, N. Treps, J. F. Morizur, P. K. Lam, and H. A. Bachor, “Entangling the spatial properties of laser beams.” Science |

22. | J. Janousek, K. Wagner, J.-F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H.-A. Bachor, “Optical entanglement of co-propagating modes,” Nature Photon. |

23. | B. Chalopin, F. Scazza, C. Fabre, and N. Treps, “Direct generation of a multi-transverse mode non-classical state of light,” Opt. Express |

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

25. | Y.-W. Cho, J.-E. Oh, and Y.-H. Kim, “Storage and retrieval of ghost images in hot atomic vapor,” Opt. Express |

26. | S. Manz, T. Fernholz, J. Schmiedmayer, and J.-W. Pan, “Collisional decoherence during writing and reading quantum states,” Phys. Rev. A |

27. | K. Gibble and A. Gallagher, “Measurements of velocity-changing collision kernels,” Phys. Rev. A |

28. | O. Firstenberg, P. London, M. Shuker, A. Ron, and N. Davidson, “Elimination, reversal and directional bias of optical diffraction,” Nature Phys. |

29. | M. Shuker, O. Firstenberg, R. Pugatch, A. Ben-Kish, A. Ron, and N. Davidson, “Angular dependence of Dicke-narrowed electromagnetically induced transparency resonances,” Phys. Rev. A |

30. | O. Firstenberg, M. Shuker, A. Ron, and N. Davidson, “Coherent diffusion of polaritons in atomic media,” Pre-print arXiv:1207.6748 (2012). |

31. | B. M. Jost, A. V. Sergienko, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Spatial correlations of spontaneously down-converted photon pairs detected with a single-photon-sensitive CCD camera,” Opt. Express |

32. | A. Perrin, H. Chang, V. Krachmalnicoff, M. Schellekens, D. Boiron, A. Aspect, and C. I. Westbrook, “Observation of atom pairs in spontaneous four-wave mixing of two colliding Bose-Einstein condensates,” Phys. Rev. Lett. |

33. | A. Gorshkov, A. André, M. Lukin, and A. Sørensen, “Photon storage in Λ-type optically dense atomic media. III. Effects of inhomogeneous broadening,” Phys. Rev. A |

**OCIS Codes**

(020.0020) Atomic and molecular physics : Atomic and molecular physics

(030.4070) Coherence and statistical optics : Modes

(270.6630) Quantum optics : Superradiance, superfluorescence

(290.5910) Scattering : Scattering, stimulated Raman

**ToC Category:**

Atomic and Molecular Physics

**History**

Original Manuscript: October 31, 2012

Revised Manuscript: December 7, 2012

Manuscript Accepted: December 9, 2012

Published: December 19, 2012

**Citation**

Radosław Chrapkiewicz and Wojciech Wasilewski, "Generation and delayed retrieval of spatially multimode Raman scattering in warm rubidium vapors," Opt. Express **20**, 29540-29552 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-28-29540

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### References

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