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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 16 — Aug. 2, 2010
  • pp: 17020–17026
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Enhanced frequency up-conversion in Rb vapor

A. Vernier, S. Franke-Arnold, E. Riis, and A. S. Arnold  »View Author Affiliations


Optics Express, Vol. 18, Issue 16, pp. 17020-17026 (2010)
http://dx.doi.org/10.1364/OE.18.017020


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Abstract

We demonstrate highly efficient generation of coherent 420nm light via up-conversion of near-infrared lasers in a hot rubidium vapor cell. By optimizing pump polarizations and frequencies we achieve a single-pass conversion efficiency of 260% per Watt, significantly higher than in previous experiments. A full exploration of the coherent light generation and fluorescence as a function of both pump frequencies reveals that coherent blue light is generated close to 85Rb two-photon resonances, as predicted by theory, but at high vapor pressure is suppressed in spectral regions that do not support phase matching or exhibit single-photon Kerr refraction. Favorable scaling of our current 1mW blue beam power with additional pump power is predicted.

© 2010 Optical Society of America

Nonlinear optical processes can be greatly enhanced for quasi-resonant atomic and molecular systems, allowing phenomena like efficient frequency up-conversion, four-wave mixing, slow light or image storage to be studied at low light intensities. On resonance, absorption hinders the build-up of strong coherences; this can be counteracted by excitation via two-photon resonances and in particular by using electromagnetically induced transparency (EIT). Here we report the generation of 1.1mW of 420nm blue light by enhanced frequency up-conversion in a hot rubidium vapor. This is made possible by long lived two-photon coherences at frequencies that allow propagation under phase-matching conditions. Depending on the polarization of the pump lasers, up-conversion can be enhanced or almost completely suppressed.

Alkali metal vapors are versatile tools for spectroscopy and nonlinear optics in atomic physics and have long been used for studies of 2-photon spectroscopy [1

1. F. Nez, F. Biraben, R. Felder, and Y. Millerioux, “Optical frequency determination of the hyperfine components of the 5S1/2–5D3/2 two-photon transitions in rubidium,” Opt. Commun. 102, 432–438 (1993). [CrossRef]

, 2

2. M. J. Snadden, A. S. Bell, E. Riis, and A. I. Ferguson, “Two-photon spectroscopy of laser-cooled Rb using a mode-locked laser,” Opt. Commun. 125, 70–76 (1996). [CrossRef]

, 3

3. A. J. Olson, E. J. Carlson, and S. K. Mayer, “Two-photon spectroscopy of rubidium using a grating-feedback diode laser,” Am. J. Phys. 74, 218–223 (2006). [CrossRef]

], dispersion [4

4. M. Xiao, Y. Q. Li, S. Z. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995). [CrossRef] [PubMed]

] and EIT [4

4. M. Xiao, Y. Q. Li, S. Z. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995). [CrossRef] [PubMed]

, 5

5. S. D. Badger, I. G. Hughes, and C. S. Adams, “Hyperfine effects in electromagnetically induced transparency,” J. Phys. B 34, L749–L756 (2000). [CrossRef]

]. In both isotopes of rubidium, the 5S1/2–5P3/2 (780nm) and 5P3/2–5D5/2 (776nm) transitions (Fig. 1a) are easily accessible with simple diode laser systems [6

6. A. S. Arnold, J. S. Wilson, and M. G. Boshier, “A simple extended-cavity diode laser,” Rev. Sci. Instrum. 69, 1236–1239 (1998). [CrossRef]

]. The extremely strong dipole moment of the infrared 6P3/2–5D5/2 transition (Fig. 1b) means that two-photon pumping with 776 and 780nm light facilitates three-photon coherence between ground state and the 6P3/2 level. Excitation and decay via other levels (5P1/2, 6P1/2, 5D3/2) is excluded by large detuning and selection rules. Similar alkali metal transitions have proven ideal for studies of amplified spontaneous emission versus four-wave mixing [7

7. M. S. Malcuit, D. J. Gauthier, and R. W. Boyd, “Suppression of amplified spontaneous emission by the four-wave mixing process,” Phys. Rev. Lett. 55, 1086–1089 (1985). [CrossRef] [PubMed]

, 8

8. S. M. Hamadani, J. A. D. Stockdale, R. N. Compton, and M. S. Pindzola, “Two-photon resonant four-wave mixing and multiphoton ionization of cesium in a heat-pipe oven,” Phys. Rev. A 34, 1938–1943 (1986). [CrossRef] [PubMed]

], superfluorescence [11

11. A. I. Lvovsky, S. R. Hartmann, and F. Moshary, “Omnidirectional superfluorescence,” Phys. Rev. Lett. 82, 4420–4423 (1999). [CrossRef]

], multi-photon ionization processes [8

8. S. M. Hamadani, J. A. D. Stockdale, R. N. Compton, and M. S. Pindzola, “Two-photon resonant four-wave mixing and multiphoton ionization of cesium in a heat-pipe oven,” Phys. Rev. A 34, 1938–1943 (1986). [CrossRef] [PubMed]

], and sensitive atomic imaging [9

9. D. V. Sheludko, Simon C. Bell, R. Anderson, C. S. Hofmann, E. J. D. Vredenbregt, and R. E. Scholten, “State-selective imaging of cold atoms,” Phys. Rev. A 77, 033401 (2008). [CrossRef]

, 10

10. H. Ohadi, M. Himsworth, A. Xuereb, and T. Freegarde, “Magneto-optical trapping and background-free imaging for atoms near nanostructured surfaces,” Opt. Express 17, 23003–23009 (2009). [CrossRef]

].

Recent papers [12

12. A. S. Zibrov, M. D. Lukin, L. Hollberg, and M. O. Scully, “Efficient frequency up-conversion in resonant coherent media,” Phys. Rev. A 65, 051801 (2002). [CrossRef]

, 13

13. T. Meijer, J. D. White, B. Smeets, M. Jeppesen, and R. E. Scholten, “Blue five-level frequency-upconversion system in rubidium,” Opt. Lett. 31, 1002–1004 (2006). [CrossRef] [PubMed]

, 14

14. A. M. Akulshin, R. J. McLean, A. I. Sidorov, and P. Hannaford, “Coherent and collimated blue light generated by four-wave mixing in Rb vapour,” Opt. Express 17, 22861–22870 (2009). [CrossRef]

] have reported the generation of tens of µWatts of coherent 420nm blue light by pumping the Rb 5S–5P–5D transition. In our experiment we obtained up to 1.1mW of coherent blue light for similar input pump powers. We have studied and optimized blue light generation for a variety of experimental parameters, namely input beam polarization and frequency, and Rb vapor pressure. In our system we have measured a maximum of 1.1mW of coherent blue light close to two-photon resonance of the input lasers at Δ780 = −Δ776≅1.6GHz. Optimal conditions include a Rb vapor pressure of 10−3 mbar and cocircularly polarized input beams at maximum available powers of 17mW at 776nm and 25mW at 780nm. This corresponds to a conversion efficiency of η = P 420/(P 776 P 780) ~ 260%/W.

Fig. 1. a) The Rb energy level scheme. b) Relevant Rb transition parameters [15]. c) Experimental image showing how co-propagating focussed 780 and 776nm laser beams create a coherent 420nm (and invisible 5.2µm) beam.
Fig. 2. a) Experimental schematic, abbreviations used are: PD (photodiode), VC (vapor cell) N/PBS (non/polarizing beamsplitter) and ECDL (external cavity diode laser). b) Power in the coherent 420nm beam as a function of 780nm (red) and 776nm (black) input power. For each trace the power of the other input beam was maximal and detunings and polarization were optimized, see text.

The essence of the experimental setup is shown in Fig. 1c), with a more detailed view in Fig. 2a). Laser beams from Faraday-isolated 776nm and 780nm extended-cavity diode lasers are overlapped on a non-polarizing beamsplitter and focussed into a 75mm long Rb vapor cell. The pump beams have maximum powers of 17mW and 25mW respectively which for elliptical beams with waists of 0.6mm × 1.1mm yield an estimated focal intensity of ≈ 2×106W/m2 each. Note that the 780nm beam area after the cell varies with frequency, differing by more than an order of magnitude due to Kerr lensing.

We have measured the conversion efficiency as a function of the 776 and 780nm input power (Fig. 2b), with all other parameters fixed at their optimum values stated above. We note that conversion efficiency depends on the Rabi frequencies and detunings of the pump beams, so that for low pump powers the chosen detunings are not ideal. The pump power was varied by rotating half wave plates in the individual input beams, and monitored via the polarizing beamsplitter (PBS) shown in the dashed region of Fig. 2a). Although the blue light begins to saturate with 780nm input power, it is linear in 776nm input power in the regions accessible by our diode lasers, promising a further increase in blue light power for stronger 776nm pumping.

The atomic density and associated vapor temperature were measured to high resolution via absorption spectroscopy of a low power (5µW) 780nm probe beam [16

16. P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B 41, 155004 (2008). [CrossRef]

]. This avoided any inaccuracy due to the inhomogeneity of the external cell temperature. For our setup optimal blue light generation occurs at a temperature of 120±1°C, corresponding to a Rb vapor pressure of 9×10−4 mbar, nearly 4 orders of magnitude higher than at room temperature. While higher temperatures, and therefore atomic densities, facilitate the nonlinear up-conversion process, they also increase absorption of the pump and output beams. Overall, the system is fairly robust: more than half of the maximum blue beam efficiency could be achieved over a temperature range of 104–131°C corresponding to a factor of 5 in Rb pressure, and focussing the nearinfrared light from 0.4 to 4 times the optimal free-space focal intensity yielded similar (> 75% of optimal) conversion efficiency.

In order to investigate the up-conversion process we have measured fluorescent and coherent blue light generation over a wide range of input beam frequencies, see Fig. 3c)–f). Data was taken for low and high Rb temperatures of 90°C and 120°C respectively, corresponding to vapor pressures of 1×10−4 mbar and 9×10−4 mbar. The frequency of the 780nm beam was measured via saturated absorption spectroscopy in a room temperature Rb cell, and that of the 776nm beam by monitoring the two-photon absorption of a weak 776nm probe beam counterpropagating through the hot cell (Fig. 2a).

We have modeled fluorescence and coherent light generation (Fig. 3a) and b) from optical Bloch equations for the 5 atomic levels, using a similar model to Ref. [13

13. T. Meijer, J. D. White, B. Smeets, M. Jeppesen, and R. E. Scholten, “Blue five-level frequency-upconversion system in rubidium,” Opt. Lett. 31, 1002–1004 (2006). [CrossRef] [PubMed]

], evaluated with Doppler broadening (FWHM~580MHz for the 776 and 780nm light at ~100°C) and for Rabi frequencies (Ω780 = 1.4GHz, Ω776 = 0.4GHz, ΩIR = 30MHz, Ω420 = 20MHz) similar to the estimated experimental focal values in the low pressure cell. The model does not explicitly include propagation, and neglects the hyperfine structure of the upper states. Nevertheless, numerical solutions for the steady state of the optical Bloch equations allowed us to interpret many of the observed features. Fluorescence (top row of Fig. 3) arises from a transfer of population to the 5D level and subsequent fast decay to the 6P level. Our model shows that this happens mainly when the system is pumped at two-photon resonance between the Stark-shifted atomic levels, and to a lesser extent, for resonant driving of the 776nm transition. The model (Fig. 3a) describes the observed fluorescence well (Figs. 3c and e), even though it does not account for propagation effects or 780nm pump Kerr lensing which increase at higher temperature.

The generation of coherent blue light requires coherences between the ground state 5S hyperfine levels and the 6P level. While the detuning of the blue (and IR) light is experimentally unknown, our simulations suggest that coherent blue light conversion occurs at three-photon resonance. For the (relatively) small blue light and IR intensities in the experiment the 6P level is unshifted, so three-photon resonance coincides with two-photon resonance. Phase-matching is a prerequisite of efficient coherent light generation. Our model shows that phase-matching Δk = n 780 k 780+n 776 k 776nIRkIRn 420 k 420≈0 is satisfied along most of the three-photon resonances. We model blue light generation (Fig. 3b) as Doppler-broadened coherences adjusted to account for Kerr lensing and absorption of the 780nm pump beam. This is an approximation to a full analysis which would require the study of field and density matrix propagation for non-collinear beams. At lower vapor pressure, we observe coherent blue light over a range of detunings near two-photon resonance (Fig. 3d), reminiscent of observations in Ref. [13

13. T. Meijer, J. D. White, B. Smeets, M. Jeppesen, and R. E. Scholten, “Blue five-level frequency-upconversion system in rubidium,” Opt. Lett. 31, 1002–1004 (2006). [CrossRef] [PubMed]

, 14

14. A. M. Akulshin, R. J. McLean, A. I. Sidorov, and P. Hannaford, “Coherent and collimated blue light generated by four-wave mixing in Rb vapour,” Opt. Express 17, 22861–22870 (2009). [CrossRef]

]. Strikingly, when the Rb pressure in the cell is high, the experiment shows an increase of blue beam generation by 1.5 orders of magnitude, however only over a restricted range of input detunings (Fig. 3f), with highest conversion efficiency for two-photon (and three-photon) resonance at Δ780 = −Δ776 = 1.6GHz. We attribute the suppression of blue light generation outside this region to Kerr-lensing of the 780nm input beam. Furthermore, absorption of 780nm light contributes to the absence of light generation from the 87Rb isotope.

Fig. 3. Relative blue fluorescence (top row) and blue beam (bottom row) power as a function of 780 and 776nm light detuning. Theoretical simulations of the 5-level Bloch equations are shown in a) and b). Graph a) shows the Doppler-broadened population in the 6P level corresponding to blue fluorescence. Fig. b) shows the Doppler-broadened coherences between ground and the 6P level, corresponding to coherent blue light generation. The blue coherences are adjusted to account for Kerr lensing and absorption of the 780nm pump beam. Graphs c) and d) show measurements at a cell temperature of 90°C, and e) and f) at 120°C. At low pressure, coherent light is generated over a range of detunings at twophoton resonance. At high pressure Kerr-lensing of the pump beams and phase-matching become more pronounced, restricting blue light generation to a narrow frequency window. The backdrops show 780nm saturated absorption in a cold cell.

A scan (Fig. 4) of the 780nm input frequency, keeping the 776nm detuning constant at the optimized value of Δ776 = −1.6GHz, shows clearly the strong frequency dependence of fluorescence and blue light generation. The theoretical model (Fig. 4a) of blue fluorescence accompanied by 776nm absorption agrees well with the experiment (Fig. 4c). Coherences on the 420nm transition between the 5S level and 6P level are present at two-photon resonance for the two hyperfine ground levels of 85Rb and 87Rb, and mark out four frequency regions of potential blue light generation, Fig. 4b). Kerr-lensing depletes and deflects the 780nm pump laser at three of these resonances, so that only the coherence at Δ780 = 1.6GHz survives. The same detuning also exhibits a local minimum of absorption of the 780nm input laser. We note that Kerr lensing will change beam direction and hence also modify the phase-matching condition. Increasing the atomic density and hence the optical path length, makes propagation effects and phase-matching more critical and adds further complexity as more 5µm and 420nm fields are generated. Experimentally, the strongest blue light generation was observed near a minimum of lensing for the 780nm beam, Fig. 4d).

Fig. 4. Coherent and fluorescent blue light as a function of Δ780 for Δ776 = −1.6GHz. Graph a) shows theoretical blue fluorescence (420F, blue) as well as transmission of the 776nm (776T, black) pump beam, including Doppler-broadening. Graph b) shows the blue beam coherences (420B, blue), as well as the Doppler-broadened theoretical transmission (780T, red) and Kerr-lensing ( 780n2Δn780ΔI780 intensity-dependent refraction, black) of the 780nm beam, which favors the coherence at 1.6GHz. Measurements of blue fluorescence accompanied by 776nm absorption c), and blue beam generation d) are shown for different input polarizations: counter-circular (red), crossed-linear (green), co-linear (blue) and co-circular (purple). Vertical lines indicate 85Rb and 87Rb 780nm resonances.

We finally report the crucial effect of input polarization on blue light generation, shown in Fig. 4c) and d). For these experiments the PBS in the dashed region of Fig. 2a) had to be removed. We simultaneously monitored the blue beam power (PDB), the blue fluorescence in the cell (PDF), absorption of the 776nm beam (PD776), and the detuning of the 780nm laser (PDSAS). Measurements were taken for four different relative input polarizations of the 776nm and 780nm input beams: co-linear, crossed-linear, co-circular and counter-circular. Care was taken to compensate for grating polarization-dependence in the 776nm pump beam measured at PD776. By analyzing the 776nm laser absorption (Fig. 4c), we can estimate that it is possible to create a coherent 420nm photon for every six 776nm photons absorbed. Note that the blue beam generation is suppressed by a factor of 500 when counter-circular polarization is used, although there is still a similar amount of blue fluorescence and 776nm beam absorption, indicating that the transfer of population to levels 5D5/2 and 6P3/2 is not forbidden by two- and three-photon absorption selection rules. This implies that the excitation of three-photon coherences between the 5S1/2 ground state and the 6P3/2 state depend crucially on polarization. Optical pumping favors blue light generation for the case of co-circularly polarized pump beams, however, the inhibition of blue light generation for counter-circular polarization suggests an interference effect. This may be attributed to a cancelation of the coherences due to the phase of the atomic dipoles. One can envisage that this property will be useful for applications in optical switching, where flipping 780nm (or 776nm)pump polarization would switch the blue beam power.

As our system is not saturating with pump power, increasing the pump power or using a build-up cavity could generate tens of mW of blue light. By accessing higher lying D 5/2 levels one should be able to generate similar powers at UV wavelengths by transitions via the corresponding P 3/2 levels. It is interesting to consider the application of such light sources for laser cooling where the narrower linewidth on these blue/UV transitions will lead to much lower Doppler temperatures [17

17. J. L. Hall, M. Zhu, and P. Buch, “Prospects for using laser-prepared atomic fountains for optical frequency standards applications,” J. Opt. Soc. Am. B 6, 2194–2205 (1989). [CrossRef]

]. In initial experiments we have observed 420nm linewidths of less than 8MHz, at the resolution limit of our etalon. The scheme should generalize to all alkali metals, and has recently been realized in cesium [20

20. J. T. Schultz, S. Abend, D. Döring, J. E. Debs, P. A. Altin, J. D. White, N. P. Robins, and J. D. Close, “Coherent 455nm beam production in cesium vapor,” Opt. Lett. 342321–2323 (2009). [CrossRef] [PubMed]

].

Acknowledgements

Thanks to N. Paterson, S. Clark and N. Houston for experimental contributions. We gratefully acknowledge discussions with P. Siddons and I. G. Hughes. SFA is a RCUK Research Fellow.

References and links

1.

F. Nez, F. Biraben, R. Felder, and Y. Millerioux, “Optical frequency determination of the hyperfine components of the 5S1/2–5D3/2 two-photon transitions in rubidium,” Opt. Commun. 102, 432–438 (1993). [CrossRef]

2.

M. J. Snadden, A. S. Bell, E. Riis, and A. I. Ferguson, “Two-photon spectroscopy of laser-cooled Rb using a mode-locked laser,” Opt. Commun. 125, 70–76 (1996). [CrossRef]

3.

A. J. Olson, E. J. Carlson, and S. K. Mayer, “Two-photon spectroscopy of rubidium using a grating-feedback diode laser,” Am. J. Phys. 74, 218–223 (2006). [CrossRef]

4.

M. Xiao, Y. Q. Li, S. Z. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995). [CrossRef] [PubMed]

5.

S. D. Badger, I. G. Hughes, and C. S. Adams, “Hyperfine effects in electromagnetically induced transparency,” J. Phys. B 34, L749–L756 (2000). [CrossRef]

6.

A. S. Arnold, J. S. Wilson, and M. G. Boshier, “A simple extended-cavity diode laser,” Rev. Sci. Instrum. 69, 1236–1239 (1998). [CrossRef]

7.

M. S. Malcuit, D. J. Gauthier, and R. W. Boyd, “Suppression of amplified spontaneous emission by the four-wave mixing process,” Phys. Rev. Lett. 55, 1086–1089 (1985). [CrossRef] [PubMed]

8.

S. M. Hamadani, J. A. D. Stockdale, R. N. Compton, and M. S. Pindzola, “Two-photon resonant four-wave mixing and multiphoton ionization of cesium in a heat-pipe oven,” Phys. Rev. A 34, 1938–1943 (1986). [CrossRef] [PubMed]

9.

D. V. Sheludko, Simon C. Bell, R. Anderson, C. S. Hofmann, E. J. D. Vredenbregt, and R. E. Scholten, “State-selective imaging of cold atoms,” Phys. Rev. A 77, 033401 (2008). [CrossRef]

10.

H. Ohadi, M. Himsworth, A. Xuereb, and T. Freegarde, “Magneto-optical trapping and background-free imaging for atoms near nanostructured surfaces,” Opt. Express 17, 23003–23009 (2009). [CrossRef]

11.

A. I. Lvovsky, S. R. Hartmann, and F. Moshary, “Omnidirectional superfluorescence,” Phys. Rev. Lett. 82, 4420–4423 (1999). [CrossRef]

12.

A. S. Zibrov, M. D. Lukin, L. Hollberg, and M. O. Scully, “Efficient frequency up-conversion in resonant coherent media,” Phys. Rev. A 65, 051801 (2002). [CrossRef]

13.

T. Meijer, J. D. White, B. Smeets, M. Jeppesen, and R. E. Scholten, “Blue five-level frequency-upconversion system in rubidium,” Opt. Lett. 31, 1002–1004 (2006). [CrossRef] [PubMed]

14.

A. M. Akulshin, R. J. McLean, A. I. Sidorov, and P. Hannaford, “Coherent and collimated blue light generated by four-wave mixing in Rb vapour,” Opt. Express 17, 22861–22870 (2009). [CrossRef]

15.

Kurucz data, cfa-www.harvard.edu/amp/tools.html.

16.

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B 41, 155004 (2008). [CrossRef]

17.

J. L. Hall, M. Zhu, and P. Buch, “Prospects for using laser-prepared atomic fountains for optical frequency standards applications,” J. Opt. Soc. Am. B 6, 2194–2205 (1989). [CrossRef]

18.

G. Morigi, S. Franke-Arnold, and G.-L. Oppo, “Phase-dependent interaction in a four-level atomic configuration,” Phys. Rev. A 66, 053409 (2002). [CrossRef]

19.

S. Kajari-Schröder, G. Morigi, S. Franke-Arnold, and G.-L. Oppo, “Phase-dependent light propagation in atomic vapors,” Phys. Rev. A 75, 013816 (2007). [CrossRef]

20.

J. T. Schultz, S. Abend, D. Döring, J. E. Debs, P. A. Altin, J. D. White, N. P. Robins, and J. D. Close, “Coherent 455nm beam production in cesium vapor,” Opt. Lett. 342321–2323 (2009). [CrossRef] [PubMed]

OCIS Codes
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(270.1670) Quantum optics : Coherent optical effects

ToC Category:
Nonlinear Optics

History
Original Manuscript: May 10, 2010
Revised Manuscript: June 11, 2010
Manuscript Accepted: July 19, 2010
Published: July 27, 2010

Citation
A. Vernier, S. Franke-Arnold, E. Riis, and A. S. Arnold, "Enhanced frequency up-conversion in Rb vapor," Opt. Express 18, 17020-17026 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-16-17020


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References

  1. F. Nez, F. Biraben, R. Felder and Y. Millerioux, “Optical frequency determination of the hyperfine components of the 5S1/2-5D3/2 two-photon transitions in rubidium,” Opt. Commun. 102, 432–438 (1993). [CrossRef]
  2. M. J. Snadden, A. S. Bell, E. Riis and A. I. Ferguson, “Two-photon spectroscopy of laser-cooled Rb using a mode-locked laser,” Opt. Commun. 125, 70–76 (1996). [CrossRef]
  3. A. J. Olson, E. J. Carlson and S. K. Mayer, “Two-photon spectroscopy of rubidium using a grating-feedback diode laser,” Am. J. Phys. 74, 218–223 (2006). [CrossRef]
  4. M. Xiao, Y. Q. Li, S. Z. Jin and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995). [CrossRef] [PubMed]
  5. S. D. Badger, I. G. Hughes and C. S. Adams, “Hyperfine effects in electromagnetically induced transparency,” J. Phys. B 34, L749–L756 (2000). [CrossRef]
  6. A. S. Arnold, J. S. Wilson and M. G. Boshier, “A simple extended-cavity diode laser,” Rev. Sci. Instrum. 69, 1236–1239 (1998). [CrossRef]
  7. M. S. Malcuit, D. J. Gauthier and R.W. Boyd, “Suppression of amplified spontaneous emission by the four-wave mixing process,” Phys. Rev. Lett. 55, 1086–1089 (1985). [CrossRef] [PubMed]
  8. S. M. Hamadani, J. A. D. Stockdale, R. N. Compton and M. S. Pindzola, “Two-photon resonant four-wave mixing and multiphoton ionization of cesium in a heat-pipe oven,” Phys. Rev. A 34, 1938–1943 (1986). [CrossRef] [PubMed]
  9. D. V. Sheludko, S. C. Bell, R. Anderson, C. S. Hofmann, E. J. D. Vredenbregt, and R. E. Scholten, “Stateselective imaging of cold atoms,” Phys. Rev. A 77, 033401 (2008). [CrossRef]
  10. H. Ohadi, M. Himsworth, A. Xuereb, and T. Freegarde, “Magneto-optical trapping and background-free imaging for atoms near nanostructured surfaces,” Opt. Express 17, 23003–23009 (2009). [CrossRef]
  11. A. I. Lvovsky, S. R. Hartmann and F. Moshary, “Omnidirectional superfluorescence,” Phys. Rev. Lett. 82, 4420–4423 (1999). [CrossRef]
  12. A. S. Zibrov, M. D. Lukin, L. Hollberg and M. O. Scully, “Efficient frequency up-conversion in resonant coherent media,” Phys. Rev. A 65, 051801 (2002). [CrossRef]
  13. T. Meijer, J. D. White, B. Smeets, M. Jeppesen, and R. E. Scholten, “Blue five-level frequency-upconversion system in rubidium,” Opt. Lett. 31, 1002–1004 (2006). [CrossRef] [PubMed]
  14. A. M. Akulshin, R. J. McLean, A. I. Sidorov, and P. Hannaford, “Coherent and collimated blue light generated by four-wave mixing in Rb vapour,” Opt. Express 17, 22861–22870 (2009). [CrossRef]
  15. Kurucz data, cfa-www.harvard.edu/amp/tools.html.
  16. P. Siddons, C. S. Adams, C. Ge and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B 41, 155004 (2008). [CrossRef]
  17. J. L. Hall, M. Zhu and P. Buch, “Prospects for using laser-prepared atomic fountains for optical frequency standards applications,” J. Opt. Soc. Am. B 6, 2194–2205 (1989). [CrossRef]
  18. G. Morigi, S. Franke-Arnold, and G.-L. Oppo, “Phase-dependent interaction in a four-level atomic configuration,” Phys. Rev. A 66, 053409 (2002). [CrossRef]
  19. S. Kajari-Schroder, G. Morigi, S. Franke-Arnold, and G.-L. Oppo, “Phase-dependent light propagation in atomic vapors,” Phys. Rev. A 75, 013816 (2007). [CrossRef]
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