We have examined the frequency spectrum of the blue light generated via
four-wave mixing in a rubidium vapor cell inside a ring cavity. At high atomic
density and input laser power, two distinct frequency components separated by
$116 \pm 4$ MHz are observed, indicating alternate four-wave mixing channels
through the $6p_{3/2}$ hyperfine states. The dependence of the generated light
on excitation intensity and atomic density are explored, and indicate the
primary process has saturated. This saturation results when the excitation rate
through the 6p state becomes equal to the rate through the 5p state, giving no
further gain with atomic density while a quadratic intensity dependence
remains

Brekke, E.

Swan, N.

English

arXiv

We have examined the frequency spectrum of the blue light generated via four-wave mixing in a rubidium vapor cell inside a ring cavity. At high atomic density and input laser power, two distinct frequency components separated by 116±4  MHz are observed, indicating alternate four-wave mixing channels through the 6p3/2 hyperfine states. The dependence of the generated light on excitation intensity and atomic density are explored, and they indicate that the primary process has saturated. This saturation results when the excitation rate through the 6p state becomes equal to the rate through the 5p state, giving no further gain with atomic density while a quadratic intensity dependence remains.https://digitalcommons.snc.edu/faculty_staff_works/1019/thumbnail.jp

Brekke, Erik

Swan, Noah

St. Norbert College

St. Norbert CollegeDigital Commons @ St. Norbert CollegeFaculty Creative and Scholarly Works2-1-2019Saturation and alternate pathways in four-wavemixing in rubidiumErik BrekkeSt. Norbert College, erik.brekke@snc.eduNoah SwanSt. Norbert CollegeFollow this and additional works at: https://digitalcommons.snc.edu/faculty_staff_worksPart of the Physics CommonsThis Article is brought to you for free and open access by Digital Commons @ St. Norbert College. It has been accepted for inclusion in FacultyCreative and Scholarly Works by an authorized administrator of Digital Commons @ St. Norbert College. For more information, please contactsarah.titus@snc.edu.Recommended CitationBrekke, Erik and Swan, Noah, "Saturation and alternate pathways in four-wave mixing in rubidium" (2019). Faculty Creative andScholarly Works. 20.https://digitalcommons.snc.edu/faculty_staff_works/20Saturation and competing pathways in four-wave mixing in rubidiumE. Brekke∗ and N. SwanSt. Norbert College, Department of Physics, De Pere, WI 54115(Dated: August 28, 2018)We have examined the frequency spectrum of the blue light generated via four-wave mixing in arubidium vapor cell inside a ring cavity. At high atomic density and input laser power, two distinctfrequency components separated by 116±4 MHz are observed, indicating competing four-wave mix-ing channels through the 6p3/2 hyperfine states. The dependence of the generated light on excitationintensity and atomic density are explored, and indicate the primary process has saturated. Thissaturation results when the excitation rate through the 6p state becomes equal to the rate throughthe 5p state, giving no further gain with atomic density while a quadratic intensity dependenceremains.I. INTRODUCTIONNonlinear optical processes can result in a wide rangeof phenomena in atomic media. Four-wave mixing inparticular has drawn considerable interest in the areas ofsingle photon sources [1], quantum information and slowlight [2, 3], Rydberg states [4, 5], the transfer of orbitalangular momentum [6, 7], and frequency up-conversion.Frequency up-conversion through parametric four-wave mixing has now been demonstrated in a numberof environments, including near resonant cw excitationin rubidium [8–11] and cesium [12], and pulsed or cwexcitation far detuned from the intermediate state [13–15]. Extensive work has been done to understand the fre-quency characteristics [16–18], observe the infrared emis-sion [19, 20], and examine competing pathways and pro-cesses [21–23].In this paper we examine the parametric four-wavemixing process in the regime where saturation of the pri-mary channel occurs due to interference between alter-nate excitation pathways. This results in a limit to the ef-fectiveness of higher atomic densities and a reduced gainwith input intensity. In addition, the saturation of theprimary channel leads to four-wave mixing on an alter-nate pathway through different excited hyperfine states,resulting in two distinct frequency peaks in the blue lightseparated by 116 ± 4 MHz in 87Rb. The onset of satu-ration and its dependence on excitation parameters canplay a large role in the resulting frequency convertedlight.II. EXPERIMENTAL METHOD AND SETUPOur experimental setup is schematically illustrated inFig. 1. A single extended cavity diode laser (ECDL) at778 nm excites the two photon 5s1/2 → 5d5/2 transitionin rubidium. The frequency control and tapered amplifiersystem have been described previously [15]. Amplifiedspontaneous emission and four-wave mixing in rubidium∗ erik.brekke@snc.eduresult in generated beams at 5.23 µm and 420 nm. Therelevant energy levels are shown in Fig. 2.TaperedAmplifier778nm ECDL PBSTo SpectroscopyRb-87 CellPiezoInput CouplerOutgoing 420nm Lightf = 40 cmlensPhotodiodeFIG. 1. A simplified version of the experimental setup. Asingle ECDL laser on the 5s1/2 → 5d5/2 transition is ampli-fied and focused through a Rb cell inside a ring cavity. Theresulting 420 nm light is sent into a 1.5 GHz FSR Fabry-Perotcavity.The use of a ring cavity as described in [24] allows us toattain blue powers in excess of 100 µW. At these powerlevels saturation, power broadening, and competition be-tween four-wave mixing pathways should play a signifi-cant role. An amplified photodiode measures blue powergenerated, while a scanning Fabry-Perot cavity with FSR1.5 GHz is used to examine the frequency characteristicsof the resulting blue light.III. COMPETING TRANSITIONDuring the excitation process, the excitation laser istypically locked to the 5s1/2 F = 2 → 5d5/2 F=4 tran-sition, which has the highest coupling strength amongthe 5d5/2 hyperfine states. Only one 420 nm frequencymode is observed at low excitation rates and atomic den-sities, corresponding to four-wave mixing along the 5d5/2F=4→ 6p3/2 F=3→ 5s1/2 F=2 path. However, as thegenerated power increases, a second frequency mode isobserved in the 420 nm light, as shown in Fig. 3.25dF=1F=4F=3F=229 MHz16 MHz23 MHzF=3F=2F=16p 87 MHz51 MHz24 MHzF=05s     F=2Compeng FWM Path⁄⁄⁄5p⁄DPrimary FWM Path0 1 2 3 FIG. 2. Energy levels involved in the four-wave mixing pro-cess in 87Rb. Two-photon excitation is accomplished using asingle 778 nm ECDL on the 5s1/2 → 5d5/2 transition detuned1 THz from the 5p state. The resulting process produces co-herent and collimated beams at 5.23 µm and 420 nm. Theprimary four-wave mixing path goes through the 6p3/2 F=3state, with a competing path through the 6p3/2F=2 state.We have examined the dependence of this secondarypeak on atomic density, excitation intensity, and detun-ing. The spectrum of the 420 nm light in the Fabry-Perotinterferometer is shown in Fig. 3a for a variety of atomicdensities. Here excitation occurs on resonance with a cir-culating intensity of 2x1014 Wm2 . As density increases, theprimary peak ceases to increase in power, while a secondpeak appears and continues to grow, changing the rela-tive size of the peaks. At high densities, the power at theprimary peak even decreases, suggesting the importanceof absorption inside the cell.In order to minimize the effect of absorption, the bluespectrum were taken while the excitation process wasdetuned -600 MHz from the 5s1/2 F = 2 → 5d5/2 F=4transition. As has been shown previously [18], this resultsin the detuning of the 420 nm beam. Figure 3b shows theresulting spectra for a variety of densities. Here the samegeneral trends are confirmed, with growth of the primarypeak slowing relative to the secondary peak, while theeffect of absorption is minimized.Fitting the Fabry-Perot peaks allowed us to determinethe width of the peaks and their separation. The separa-tion between the peaks was consistent for a large range ofdensities and intensities at 116±4 MHz. Our ring cavityhas a FSR of 500 MHz, so this spacing is not related tocavity modes. We hypothesize that the secondary peak iscaused by an alternate hyperfine path for the four-wavemixing process [9]. At the high temperatures of the cell,a large number of atoms would have the correct velocityto have the 5d5/2 F=3 state Doppler shifted into reso-nance. This state could then decay to the 6p3/2 F=2state, resulting in a different blue frequency during thefinal step. The relevant hyperfine levels are shown in1.00.80.60.40.20.0Normalized Intensity-300 -200 -100 0 100 200Frequency (Mhz) Excitation at D2=0 MHz 2.72x1014 cm-3 1.97x1014 cm-3 1.41x1014 cm-3 9.99x1013 cm-3 7.00x1013 cm-3 3.32x1013 cm-31.00.80.60.40.20.0Normalized Intensity -300 -200 -100 0 100 200Frequency (MHz) Excitation at D2=-600 MHz  2.72x1014 cm-3 1.97x1014 cm-3 1.41x1014 cm-3 9.99x1013 cm-3 7.00x1013 cm-3  3.32x1013 cm-3a)b)FIG. 3. Frequency spectrum of the 420 nm light for a varietyof atomic densities. a) Excitation on resonance with the 5s1/2F = 2 → 5d5/2 F=4 transition. b) Excitation detuned -600MHz from the 5s1/2 F = 2 → 5d5/2 F=4 transition. Theappearance of a second peak at -116 MHZ from the primarypeak becomes significant at high densities, and continues togrow while the primary peak growth slows.Fig. 2. In addition to the 87 MHz shift for the 6p hy-perfine states, there is a Doppler shift of generated light.In order to have the excitation light on resonance withthe 5d5/2 F=3 state, the 778 nm excitation laser mustDoppler shift 14.5 MHz. Since the Doppler shift of theblue is 1.85 times this [18], the total frequency shift ex-pected would result in a separation between the peaks of113.8 MHz.To verify the source of separation between the peaks,we replaced the 87Rb cell with a cell containing naturalisotope abundances, and examined the light generatedfrom 85Rb. Here we measured the separation betweenthe peaks to be 68 ± 11, where the separation was notas precisely determined as the peaks were more difficultto resolve. Using the same logic for Doppler shifted ex-citation of the 5s1/2 F = 3 → 5d5/2 F=4 transition anddecay through the 6p1/2 F=3 state, we would expect aseparation of 47.9 MHz.The theoretical values for the separation betweenpeaks is in good agreement with our experimental mea-surements for 87Rb, suggesting the origin of the sec-ondary peak is from competition along a different hy-perfine level path. For 85Rb, the separation betweenpeaks is smaller as expected, but the value here is notin agreement with theory and more precise data will beneeded. Additionally, the length of the 85Rb cell requireda non-ideal cell placement in the ring cavity, which mayhave resulted in increased absorption. Even for detunedexcitation, the effects of absorption in the cell are not3eliminated, and this may effect the perceived center ofthe blue peaks. It has been observed [25] that the orien-tation of the cell and reflected beams can play a crucialrole in the four-wave mixing process as well. The 5.23 µmbeam does not leave our cell, but in the future the ex-amination of the infrared spectrum could provide furtherinsight into the mechanism for the competing frequency.IV. SATURATION PROCESSThe dependence of the power in the primary peak onatomic density suggests the four-wave mixing process be-gins to saturate. To further consider the mechanism ofsaturation, the spectrum of the 420 nm light was alsomeasured for a variety of circulating intensities for a con-stant density of 2.7x1014 m−3, and shown in Fig. 4. Here,a different trend between the peaks is observed, as the rel-ative size of the secondary peak remains fairly consistentover a wide range of intensities. The power produced onthe primary peak continues to increase, revealing a dif-ferent dependence than that observed for atomic density.1.00.80.60.40.20.0Normalized Intensity-300 -200 -100 0 100 200Frequency (Mhz)Excitation at ∆=-600 MHz 1.0x1010 W/m2 9.4x109 W/m2 8.6x109 W/m2 7.5x109 W/m2 6.9x109 W/m2FIG. 4. Frequency spectrum of the 420 nm light for a va-riety of excitation laser intensities for excitation -600 MHzdetuned from the 5s1/2 F = 2→ 5d5/2 F=4 transition. Herethe ratio between the primary and secondary peak remainsapproximately constant.To further understand the saturation process, we con-sider the interference of two alternate excitation path-ways [13]. As the blue and infrared fields grow, a secondtwo-photon pathway along the 5s1/2 → 6p3/2 → 5d5/2path interferes with the original four-wave mixing exci-tation. When the two excitation rates along these pathsbecome equal, the rate of blue production will be thesame as that of blue absorption, and blue light will nolonger increase as the density increases. This saturationpoint is given byΩ01Ω12∆1=Ω03Ω32∆3, (1)where Ωab is the Rabi frequency between two states,and ∆a is the detuning from state a. For the excita-tion scheme used here, the very large detuning from the5p state means that the process can approach saturationeven for µW level blue powers. The detuning from the 6pstate is not directly controlled in the parametric process,so the photons through the 6p state are near-resonance,and the two-photon excitation is limited by the width ofthe 6p state. The number of photons for the infrared andblue are identical, which allows the saturation conditionto be written in terms of the dipole moments, detunings,and wavelengths involved asP420 =√λ32λ03µ01µ12µ03µ32∆3∆1P778. (2)The saturation process would then still result in anincreased blue output as the input light increases. Thisis further shaped by the linewidth of the 5s1/2 → 6p3/2transition, as the 420 nm light produced in this processis sufficient to cause power broadening. In the limit of420 intensities much higher than the saturation intensity,the linewidth will go as√P420. Putting this into Eqn. 2,we see that the power at 420 nm is expected to scale asthe square of the input power in the saturated and powerbroadened regime.200150100500Blue Power (mW)12x1091110987Circulating Intensity (W/m2 )250200150100500Blue Power (mW)500x1012400300200100Density (cm-3)a)b)FIG. 5. a) The blue power is measured as a function of theatomic density in the cell, showing the output power reachesa maximum level as density continues to increase. b) Theblue power is measured as a function of the excitation laserintensity, showing a continued growth even in the high powerregime. Both of these are consistent with expectations in thesaturated regime.The light at the focus of the cavity inside the rubidiumcell has a waist of 22 µm, meaning that only 1 µW of bluepower would give a width of 3.4 MHz. For the powersobtained here, linewidths in the range of 20 to 50 MHzwere seen. These linewidths are dominated by powerbroadening, but when the blue light is near resonancethe linewidth is further shaped by the absorption of thislight through the cell. It has previously been observed4that the implementation of a ring cavity resonant withthe resulting blue light can both increase the generatedpower and dramatically reduce the linewidth below thepower broadened values. [26]The dependence of the generated 420 nm light on bothatomic density and excitation power is shown in Fig. 5.This can now be explained in terms of the saturation pro-cess. As the blue power generated increases, the rate ofblue generation via FWM can become equal to the rate ofabsorption of blue light for two photon excitation. Thiswould result in no further increase in generated blue lightwith increasing density, but a continued dependence onthe original excitation rate. In Fig. 5a the growth inblue power ceases at high densities, suggesting this sat-uration point has been reached. As Fig. 5b shows, bluepower continues to grow with input intensity. Both ofthese trends are consistent with expectations of gener-ated power in the regime where the excitation rate alongthe 6p path has become equal to the original excitationrate along the 5p path.V. DISCUSSION AND OUTLOOKWe have investigated the frequency spectrum and sat-uration characteristics of 420 nm light generated throughparametric four-wave mixing in rubidium vapor. Powerproduced along the primary pathway saturates when therate for excitation along the 5s1/2 → 6p3/2 → 5d5/2 be-comes comparable to the 5s1/2 → 5p3/2 → 5d5/2 path-way. For the two-photon excitation far detuned from the5p state, the rates along these two paths can becomeequal for µWs of blue light. At this point higher densi-ties do not result in further blue light production, thougha quadratic dependence on excitation intensity remains.Under low power conditions, the four-wave mixing pro-cess results in a single generated frequency, but as sat-uration approaches a second peak becomes increasinglysignificant. It is likely that though originally dominatedby excitation to the 5d5/2 F=4 state, an alternate fourwave mixing path through the 5d5/2 F=3→ 5p3/2 F=2becomes increasingly important as the primary transitionsaturates.The onset of saturation will be delayed by smaller de-tunings from the 5p state, such as in the near resonanttwo-step process. It could also be delayed by controllingthe detuning of the resulting light from the 6p state, per-haps by seeding the four-wave mixing process [22]. Carein the selection of excitation parameters is necessary tolimit the effects of competing channels and ensure thegeneration of single frequency beams in these systems.[1] F. Ripka, H. Kbler, R. Lw, and T. Pfau, arXiv (2018).[2] R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Nat.Photonics 3, 103 (2009).[3] A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D.Jenkins, A. Kuzmich, and T. A. B. Kennedy, Nat Phys6, 894 (2010).[4] N. R. de Melo and S. S. Vianna, J. Opt. Soc. Am. B 31,1735 (2014).[5] E. Brekke, J. O. Day, and T. G. Walker, Phys. Rev. A78, 063830 (2008).[6] A. M. Akulshin, I. Novikova, E. E. Mikhailov, S. A.Suslov, and R. J. McLean, Opt. Lett. 41, 1146 (2016).[7] R. F. Offer, D. Stulga, E. Riis, S. Franke-Arnold, andA. S. Arnold, arXiv (2018).[8] A. S. Zibrov, M. D. Lukin, L. Hollberg, and M. O. Scully,Phys. Rev. A 65, 051801 (2002).[9] T. Meijer, J. D. White, B. Smeets, M. Jeppesen, andR. E. Scholten, Opt. Lett. 31, 1002 (2006).[10] A. M. Akulshin, A. A. Orel, and R. J. McLean, J. Phys.B 45, 015401 (2012).[11] A. Vernier, S. Franke-Arnold, E. Riis, and A. S. Arnold,Opt. Express 18, 17020 (2010).[12] J. T. Schultz, S. Abend, D. Döring, J. E. Debs, P. A.Altin, J. D. White, N. P. Robins, and J. D. Close, Opt.Lett. 34, 2321 (2009).[13] R. K. Wunderlich, W. R. Garrett, R. C. Hart, M. A.Moore, and M. G. Payne, Phys. Rev. A 41, 6345 (1990).[14] J. P. Lopez, M. H. de Miranda, S. S. Vianna, andM. P. M. de Souza, arXiv (2016), 1605.00312.[15] E. Brekke and L. Alderson, Opt. Lett. 38, 2147 (2013).[16] A. Akulshin, C. Perrella, G.-W. Truong, R. McLean, andA. Luiten, J. Phys. B 45, 245503 (2012).[17] A. Akulshin, C. Perrella, G.-W. Truong, A. Luiten,D. Budker, and R. McLean, App. Phys. B 117, 203(2014).[18] E. Brekke and E. Herman, Opt. Lett. 40, 5674 (2015).[19] A. Akulshin, D. Budker, and R. McLean, Opt. Lett. 39,845 (2014).[20] J. F. Sell, M. A. Gearba, B. D. DePaola, and R. J. Knize,Opt. Lett. 39, 528 (2014).[21] A. M. Akulshin, R. J. McLean, E. E. Mikhailov, andI. Novikova, Opt. Lett. 40, 1109 (2015).[22] B. Gai, R. Cao, X. Xia, S. Hu, J. Liu, J. Guo, Y. Tan,W. Liu, Y. Jin, and F. Sang, Applied Physics B 122,165 (2016).[23] N. Prajapati, A. M. Akulshin, and I. Novikova, J. Opt.Soc. Am. B 35, 1133 (2018).[24] E. Brekke and S. Potier, Appl. Opt. 56, 46 (2017).[25] A. M. Akulshin, D. Budker, and R. J. McLean, J. Opt.Soc. Am. B 34, 1016 (2017).[26] R. F. Offer, J. W. C. Conway, E. Riis, S. Franke-Arnold,and A. S. Arnold, Opt. Lett. 41, 2177 (2016).

Saturation and alternate pathways in four-wave mixing in rubidium

Abstract

Similar works

Full text

Available Versions

St. Norbert College