Transit Ramsey EIT resonances in a Rb vacuum cell
Ravn M. Jenkins Eugeniy E. Mikhailov Irina Novikova

	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	College of William & Mary, Williamsburg, VA. 23185, USA
	
	
	
	[]eemikh@wm.edu
	
	
	
	College of William & Mary, Williamsburg, VA. 23185, USA
	
	
	[ixnovi@wm.edu]
	
	
	
	College of William & Mary, Williamsburg, VA. 23185, USA
	
	
	
	
	
		We investigate a dual-channel arrangement for electromagnetically-induced transparency in a vacuum Rb vapor cell, and report the observation of a transient spectral feature due to the atoms traversing both beams while preserving their ground-state spin coherence. Despite a relatively small fraction of atoms participating in this process, their contribution to the overall lineshape is not negligible. By adjusting the path difference between the two optical beams, the differential intensity measurement can produce an error signal for the microwave frequency stabilization as strong as a single-channel measurement, but it provides a much higher signal-to-noise ratio due to the cancellation of intensity noise, dominating the signal channel detection. 
	
	
	
	
	
	
	
	
	Transit Ramsey EIT resonances in a Rb vacuum cell
    Irina Novikova
    December 30, 2023
=================================================


	
	

§ INTRODUCTION

	
	Two-photon Raman resonances in Rb atoms provide an all-optical access to long-lived spin coherences and thus enables observation in spectrally narrow optical transmission and absorption resonances, widely used for atomic clocks <cit.>, magnetometers <cit.>, and other metrological applications. Since the intrinsic spin decoherence rate is negligible, the spectral width of such features is typically limited by the environmental disturbances, such as dephasing collisions or external field gradients. For the thermal atomic ensembles, the limited interaction time of moving atoms with the laser beam becomes a leading limiting factor <cit.>, as the consequent depolarizing wall collisions completely dephase any light-induced spin coherence, unless a special anti-relaxation coating is applied <cit.>. Often an inert buffer gas is introduced to increase the interaction time as atoms slowly diffuse through the laser beam <cit.>, and this approach has been successfully used to reduce the electromagnetically induced transparency (EIT) resonance linewidth down to a few tens of Hz <cit.>. However, collisions with the buffer gas also perturb the transitions, increasing the environmental sensitivity. Plus, some two-photon resonances are degraded by the strong collisional depolarization of the optical excited state, thus making the use of buffer gas impractical. 
	
	
	
	Here we explore the ballistic motion of Rb atoms between two identical illuminated regions in a Rb vapor cell with no anti-relaxation wall coating and no additional buffer gas to produce an additional narrow structure within a usual EIT resonance, as shown in Fig. <ref>. Each beam consists of two optical fields near the two-photon EIT resonant conditions, shown in Fig. <ref>(a). While the majority of atoms interact only once with one of the laser beams before hitting the cell wall, there is a group of atoms, depicted in Fig. <ref>(b), that traverses both beams without decohering. For these atoms the conditions of the original Ramsey experiment <cit.> are recreated, as they experience two consecutive interactions, separated by the free evolution region. Such an arrangement is also a spatial equivalent of Raman-Ramsey CPT experiments <cit.>, as the spin superposition state, prepared in the first beam, is allowed to evolve in the dark before interacting with the second beam.  The spectral narrowing associated with such multi-zone interactions has been investigated in the case of degenerate Hanle magneto-optical resonances <cit.>.  With the use of a bichromatic optical field to produce a coherent superposition of two ground-state levels, we observe an additional interference-like feature on top of the regular single-channel EIT resonance, shown in Fig. <ref>(c,d). While the signal can be clearly observed in direct optical transmission, it is more convenient to analyze it using a phase-sensitive lock-in detection with improved signal-to-noise ratio (SNR). 
	
	This transit Ramsey EIT (TREIT) effect provides an additional way of reducing the width of the EIT feature in the situation when addition of buffer gas or antirelaxation coating is impossible, for example in ultra thin vapor cells <cit.>. It is also somewhat surprising that even though only a small fraction of atoms traverse both laser beams, their contribution to the resonance slope is comparable with the single-channel resonance amplitude. Moreover, the possibility of such spin coherence transfer may need to be accounted for in multiplexed experimental arrangements, commonly used in quantum optics <cit.>. 
	
	

§ EXPERIMENTAL ARRANGEMENTS

	
	The schematic of the experimental setup is shown in Fig. <ref>. To create the two optical fields for  the EIT resonance, we used a vertical cavity surface-emitting diode laser (VCSEL) operating at the Rb D_1 line (794.7 nm), current-modulated at the frequency of the ^87Rb ground state hyperfine splitting Δ_HFS≃ 6.834 GHz. We locked the carrier frequency of the laser to the 5S_1/2F=2→ 5P_1/2F'=1 optical transition with dichroic atomic vapor laser lock (DAVLL), so that the +1 modulation sideband, containing ≈ 20% of the total laser power, became resonant with the 5S_1/2F=1→ 5P_1/2F'=1 transition, forming a Λ system, shown in Fig. <ref>(a). A detailed description of the VCSEL current modulation and DAVLL arrangements can be found in Ref. <cit.>. 
	
	
	
	After passing through the optical diode (OD), the VCSEL output with a maximum total power of 300 μW was  split into two beams using a non-polarizing beam splitter (BS). While the transmitted beam (Ch1) passed directly forward, the reflected beam (Ch2) was directed toward a delay line, consisting of a retroreflecting  prism mounted on a translation stage, before being reflected by a mirror to travel parallel to the first beam at a separation of ≈ 5 mm. Moving the prism allowed us to adjust the relative phase between the zeroth and the first modulation sidebands inside the Rb cell in the second channel:
	
    ϕ_HF=2πΔ z/λ_RF,

	where Δ z is the additional path length in the delay stage, and λ_RF=c/Δ_HFS is the wavelength of the resonant frequency between the two hyperfine states. For this experiment we used the lin||lin EIT configuration <cit.>, and a polarizing beam splitter (PBS) placed before the Rb cell ensured the identical linear polarization of all optical fields in both channels. Half-wave plates (HWP) and a quarter-wave plate (QWP) before and after the non-polarizing beam splitter allowed us to precisely balance the laser power in two channels. At the cell location, both laser beams had almost identical slightly elliptical Gaussian profiles: the measured 1/e^2 radii in the first channel were 0.72 mm and 0.75 mm, and in the second channel 0.74 mm and .72 mm. 
	
	Both beams then passed through an evacuated cylindrical Pyrex cell (length 75mm, diameter 22mm) containing isotopically enriched ^87Rb vapor, heated to 44.5^∘ C. Then, the transmitted light intensities in both channels were detected using two identical photodiodes, PD1 and PD2, that can be operated in the differential mode. We have also recorded the output of the lock-in amplifier by superimposing an additional 10 kHz frequency modulation on the 6.834 GHz VCSEL RF modulation signal.  
	
	

§ TRANSIENT RAMSEY RESONANCE OBSERVATION

	
	To understand the TREIT lineshape one needs to consider the relative phase between the two optical fields, forming a two-photon EIT resonance (in our case, the carrier and the first modulation sidebands of the VCSEL laser, as shown in Fig. <ref>(a)). While locally the two optical fields are nearly perfectly phase coherent, the value of their relative phase changes as the beams propagate thanks to their frequency mismatch, at a rate given by Eq.(<ref>). Thus, if the two beams travel unequal paths before entering the cell, the exact expressions for the atomic dark state in each beam will reflect the acquired phase difference, as illustrated in Fig. <ref>(b). For example, if we set the relative phase between two EIT fields as zero in the first beam and Δϕ_HF in the second beam, we can write the expressions for the unperturbed EIT dark states independently formed in each channel: 
	
    |D_1⟩(t=0)    =    (Ω_1 |b⟩ -Ω_0 |c⟩)/Ω,  
    
    	|D_2⟩(t=0)    =    (Ω_1 |b⟩ -e^i ϕ_HFΩ_0 |c⟩)/Ω,

	where Ω_0 and Ω_1 are the absolute values of Rabi frequencies for the two EIT transitions, and Ω=√(Ω_0^2+Ω_1^2) is the normalization coefficient. In the case of zero two-photon detuning δ = 0 the optical response of the atoms, prepared in the dark state in one beam and then probed by another, is symmetric for both beams. However, a small two-photon detuning δ breaks this symmetry, since during the transit time τ between the two interactions the relative phases of the both dark states evolve by the same amount δ·τ:
	
    |D_1⟩(t=τ)    =    (Ω_1 |b⟩ -e^i δ·τΩ_0 |c⟩)/Ω,  
    
    	|D_2⟩(t=τ)    =    (Ω_1 |b⟩ -e^i ϕ_HF+ i δ·τΩ_0 |c⟩)/Ω,

	causing the difference in optical responses depending on with which beam the atoms first interacted.
	
	We can experimentally verify the significance of the EIT phase difference between the two beams by controlling the beam path for the second channel using a delay stage. Fig. <ref>(a) shows the differential lock-in signal for the different delays. It is easy to see that it is possible to adjust the relative delay to almost perfectly match the EIT resonances in each channel (the small residual signal is due to small laser beam disbalance in two channels). However, by changing the delay one can maximize the contrast of the TREIT signal between the two channels.
	
	
	
	We can qualitatively confirm such behavior using a repeated interaction model developed in Refs.<cit.> to describe the optical response of atoms after two consecutive interactions under EIT conditions. Generalizing this expression for the two regions with identical absolute values but different in phase EIT fields, we can describe the differential signal for a given travel time between the two beams τ as:
	
    Δ I(δ)   ∝   |Ω|^2/δ^2+Γ^2e^-2Γ t_trsinϕ_HF×
       ×   sin [ δ(2t_tr+τ)+tan^-1(δ/Γ)],

	where Γ is the power-broadened single-channel EIT linewidth and t_tr is the transit time of an atom through the interaction region. Here we neglect the intrinsic ground-state decoherence rate. 
	
	Fig. <ref>(b) shows the results of numerical simulations for the differential lock-in signal, averaged over the transverse Maxwell-Boltzmann velocity distribution of atoms, moving between the two beams. Despite many simplifications of the model (optically-thin medium, absence of Doppler broadening of optical transitions and the longitudinal motion of the atoms), the general features of the model predictions nicely match the experiment: we observe the maximum lock-in differential signal at zero two-photon detuning for ϕ_HF = ±π/2, and the TREIT feature disappears for ϕ_HF=0.
	
	

§ SIGNAL-TO-NOISE ANALYSIS

	
	Many EIT-based measurements suffer from the residual intensity noise, especially if broad-band lasers, such as VCSELs, are used to excite optical transitions <cit.>. Several differential EIT schemes, e.g., based on magneto-optical rotation <cit.> or polarization selection rules <cit.>, have been proposed recently to suppress the common-mode intensity noise while maintaining high-contrast EIT resonant features. 
	
	Our observations suggest that the TREIT signal may also be applied to reduce the intensity noise and thus boost the signal to noise ratio. Simple visual comparison of a single-channel EIT and TREIT signals in Fig. <ref>(d) shows a strong noise suppression in the differential signal. To quantify this observation we measured the slope of each lock-in signal near zero two-photon detuning at the point where it crosses zero, as this slope determines the strength of the feedback error signal if the resonance is used for frequency stabilization. The measured slope as a function of laser power is plotted in Fig. <ref>(a). It is easy to see that both EIT schemes give comparable results. A single-channel EIT performs better at lower laser power, likely due to the reduced power broadening. Higher laser power, however, improves the optical pumping of atoms into the dark state, thus increasing the number of atoms contributing to the two-beam interactions. In addition, the Ramsey interrogation schemes are known to be less sensitive to the power broadening during the evolution in the dark period <cit.>. Thus, not surprisingly, the measured slope of the TREIT signal surpasses that of the single-channel EIT at higher laser powers.  
	
	
	
	At the same time, the comparison of the measured noise levels, shown in Fig. <ref>(b), clearly demonstrate the advantage of the differential detection, as we see more than an order of magnitude noise reduction for the differential TREIT signal. In fact, we were unable to accurately measure the TREIT noise for the lowest laser powers, as it fell below the technical noises of our detector. 
	
	The resulting signal-to-noise ratio (SNR) for both schemes is shown in Fig. <ref>(c). Note, that while the SNR for the single-channel EIT has a clear maximum at approximately 30 μW of laser power due to the known saturation of the EIT amplitude at higher powers <cit.>, the TREIT SNR remains relatively constant at high laser powers, which may be an attractive feature for some applications. 
	
	
	

§ CONCLUSIONS

	
	We have demonstrated a possibility to obtain a narrow differential signal on top of a regular EIT resonance taking advantage of the ballistic motion of coherently prepared atoms between two spatially separated identical optical channels in a vacuum Rb vapor cell. This feature is based on the consecutive Ramsey-like repeated interactions of atoms as they fly through both beams. We demonstrated that it is possible either to cancel or to produce a strong differential optical signal by controlling the relative phase between the two EIT fields in two regions, i.e setting the phases of the EIT dark states in the two channels. Moreover, we demonstrate that such differential detection may offer significant advantages for metrology, as it allows the subtraction of common intensity noise without sacrificing the strength of the feedback error signal.   
	
	

§ ACKNOWLEDGMENTS

	We would like to thank Kelly Roman for the original exploratory work with two-beam EIT configuration, and Hana Warner and Kangning Yang for their help with the initial experiment construction. This research was supported by the National Science Foundation grant PHY-308281. RMJ acknowledges the support of the DeWilde research fellowship.
	


32
fxundefined [1]
 ifx#1

fnum [1]
 #1firstoftwo
 secondoftwo
 
fx [1]
 #1firstoftwo
 secondoftwo
 





noop [0]secondoftwo

ref[1]@startlink#1@href
href[1]#1@endlink
anitize@url [0]`
12`$12`&12`#12`1̂2`_12`%12
startlink[1]
endlink[0]

rl [1]href #1












@bib@innerbibempty

[Vanier and Audoin(1989)]vanier_book
  author author J. Vanier and author C. Audoin, @noop  title The Quantum Phisics of
  Atomic Frequency Standards, Vol. volume 1 (publisher Adam Hilger; Philadelphia, year 1989)NoStop
[Vanier.(2005)]vanier05apb
  author author J. Vanier., 10.1007/s00340-005-1905-3 journal journal Applied Physics B: Lasers and Optics  volume 81, pages 421 (year
  2005)NoStop
[Shah and Kitching(2010)]Shah201021
  author author V. Shah and author J. Kitching, in http://dx.doi.org/10.1016/S1049-250X(10)59002-5 booktitle
  Advances in Atomic, Molecular, and Optical Physics, series
  Advances In Atomic, Molecular, and Optical Physics, Vol. volume
  59, editor edited by editor P. B. E. Arimondo and editor C. Lin (publisher Academic Press, year 2010) pp. pages 21 – 74NoStop
[Budker and Kimball(2013)]budker_optmagn_book
  editor D. Budker and editor D. F. J. Kimball, eds.,  @noop  title Optical Magnetometry (publisher Cambridge University Press, address Cambridge,
  UK, year 2013)NoStop
[Stahler et al.(2001)Stahler, Knappe, Affolderbach,
  Kemp, and Wynands]stahler01eurlett
  author author M. Stahler, author S. Knappe,
  author C. Affolderbach, author W. Kemp,  and author
  R. Wynands, @noop  journal journal Europhysics Lett. volume 54, pages 323 (year 2001)NoStop
[Budker and Romalis(2007)]romalis2007natphys
  author author D. Budker and author M. Romalis, 10.1038/nphys566 journal
  journal Nature Physics volume 3,  pages 227 (year 2007)NoStop
[Novikova et al.(2012)Novikova, Walsworth, and Xiao]novikovaLPR12
  author author I. Novikova, author R. L. Walsworth,  and author Y. Xiao, 10.1002/lpor.201100021 journal
  journal Laser & Photonics Reviews volume 6, pages 333 (year 2012)NoStop
[Budker et al.(1998)Budker,
  Yashchuk, and Zolotorev]budker'98
  author author D. Budker, author V. Yashchuk,   and author M. Zolotorev, http://link.aps.org/doi/10.1103/PhysRevLett.81.5788 journal
  journal Phys. Rev. Lett. volume
  81, pages 5788 (year 1998)NoStop
[Klein et al.(2011)Klein,
  Hohensee, Phillips, and Walsworth]klein2011pra_eit_coated_cells
  author author M. Klein, author M. Hohensee,
  author D. F. Phillips,  and  author R. L. Walsworth, 10.1103/PhysRevA.83.013826 journal journal Phys. Rev. A volume 83, pages 013826 (year 2011)NoStop
[Xiao(2009)]XiaoMPL09
  author author Y. Xiao, 10.1142/S0217984909019028 journal
  journal Modern Physics Letters B volume
  23, pages 661 (year 2009)NoStop
[Wynands and Nagel(1999)]wynands'99
  author author R. Wynands and author A. Nagel, @noop  journal journal Appl.  Phys. B volume 68, pages 1 
  (year 1999)NoStop
[Ramsey(1950)]RamseyPhysRev.78.695
  author author N. F. Ramsey, 10.1103/PhysRev.78.695 journal
  journal Phys. Rev. volume 78,  pages 695 (year 1950)NoStop
[Zanon et al.(2005)Zanon,
  Guerandel, de Clercq, Holleville, Dimarcq, and Clairon]ZanonPRL05
  author author T. Zanon, author S. Guerandel,
  author E. de Clercq, author D. Holleville, author
  N. Dimarcq,  and author
  A. Clairon, 10.1103/PhysRevLett.94.193002 journal journal
  Phys. Rev. Lett. volume 94, pages
  193002 (year 2005)NoStop
[Castagna et al.(2009)Castagna, Boudot, Guerandel, Clercq, Dimarcq, and Clairon]ClaironIEEE09
  author author N. Castagna, author R. Boudot,
  author S. Guerandel, author E. Clercq, author
  N. Dimarcq,  and author
  C. Clairon, 10.1109/TUFFC.2009.1033 journal journal
  Ultrasonics, Ferroelectrics, and Frequency Control, IEEE Transactions on  volume 56, pages 246 (year
  2009)NoStop
[Liu et al.(2013)Liu,
  Mérolla, Guérandel, de Clercq, and Boudot]Liu:13
  author author X. Liu, author J.-M. Mérolla, author S. Guérandel, author E. de Clercq,  and author R. Boudot, 10.1364/OE.21.012451 journal
  journal Opt. Express volume 21,  pages 12451 (year 2013)NoStop
[Failache et al.(2010)Failache, Lenci, and Lezama]LezamaPhysRevA.81.023801
  author author H. Failache, author L. Lenci,   and author A. Lezama, 10.1103/PhysRevA.81.023801 journal journal Phys. Rev. A volume 81, pages 023801 (year 2010)NoStop
[Radojičić et al.(2015)Radojičić, Radonjić, Lekić,
  Grujić, Lukić, and Jelenković]Radojicic:15
  author author I. S. Radojičić, author M. Radonjić, author M. M. Lekić, author Z. D. Grujić, author D. Lukić,  and author B. Jelenković, 10.1364/JOSAB.32.000426 journal journal J. Opt. Soc. Am. B volume 32, pages 426 (year 2015)NoStop
[Sargsyan et al.(2011)Sargsyan, Leroy, Pashayan-Leroy,
  Mirzoyan, Papoyan, and Sarkisyan]Sargsyan2011
  author author A. Sargsyan, author C. Leroy,
  author Y. Pashayan-Leroy,
  author R. Mirzoyan, author A. Papoyan,  and author D. Sarkisyan, 10.1007/s00340-011-4614-0 journal journal
  Applied Physics B volume 105, pages
  767 (year 2011)NoStop
[Sargsyan et al.(2015)Sargsyan, Leroy, Pashayan-Leroy,
  Cartaleva, and Sarkisyan]SargsyanJMO2015
  author author A. Sargsyan, author C. Leroy,
  author Y. Pashayan-Leroy,
  author S. Cartaleva,  and  author D. Sarkisyan, 10.1080/09500340.2015.1006699 journal journal Journal of Modern Optics volume 62,  pages 769 (year 2015)NoStop
[England et al.(2012)England, Michelberger, Champion,
  Reim, Lee, Sprague,
  Jin, Langford, Kolthammer,
  Nunn, and Walmsley]EnglandJPB2012
  author author D. G. England, author P. S. Michelberger, author T. F. M. Champion, author K. F. Reim,
  author K. C. Lee, author M. R. Sprague, author
  X.-M. Jin, author N. K. Langford, author W. S.  Kolthammer, author J. Nunn,  and author I. A.  Walmsley, http://stacks.iop.org/0953-4075/45/i=12/a=124008 journal
  journal Journal of Physics B: Atomic, Molecular and Optical
  Physics volume 45, pages 124008
  (year 2012)NoStop
[Higginbottom et al.(2015)Higginbottom, Geng, Campbell, Hosseini, Cao, Sparkes, Bernu, Robins, Lam, and Buchler]Higginbottom:15
  author author D. B. Higginbottom, author J. Geng,
  author G. T. Campbell, author M. Hosseini, author
  M. T. Cao, author B. M. Sparkes, author J. Bernu, author N. P.  Robins, author P. K.  Lam,  and author B. C.  Buchler, 10.1364/OE.23.024937 journal journal Opt. Express volume
  23, pages 24937 (year 2015)NoStop
[Namazi et al.(2017)Namazi,
  Kupchak, Jordaan, Shahrokhshahi, and Figueroa]FigueroaPhysRevApplied.8.034023
  author author M. Namazi, author C. Kupchak,
  author B. Jordaan, author R. Shahrokhshahi,  and author E. Figueroa, 10.1103/PhysRevApplied.8.034023 journal journal
  Phys. Rev. Applied volume 8, pages
  034023 (year 2017)NoStop
[Mikhailov et al.(2010)Mikhailov, Horrom, Belcher, and  Novikova]mikhailov2010JOSAB_linparlin_clock
  author author E. E. Mikhailov, author T. Horrom,
  author N. Belcher,  and  author I. Novikova, 10.1364/JOSAB.27.000417 journal journal
  J. Opt. Soc. Am. B volume 27, pages
  417 (year 2010), http://arxiv.org/abs/0910.5881
  arXiv:0910.5881 NoStop
[Zibrov et al.(2010)Zibrov,
  Novikova, Phillips, Walsworth, Zibrov, Velichansky,
  Taichenachev, and Yudin]ZibrovPhysRevA.81.013833.2010
  author author S. A. Zibrov, author I. Novikova,
  author D. F. Phillips, author R. L. Walsworth, author
  A. S. Zibrov, author
  V. L. Velichansky, author
  A. V. Taichenachev,  and author V. I. Yudin, 10.1103/PhysRevA.81.013833 journal journal Phys.
  Rev. A volume 81, pages 013833
  (year 2010)NoStop
[Xiao et al.(2006)Xiao,
  Novikova, Phillips, and Walsworth]xiaoPRL06
  author author Y. Xiao, author I. Novikova,
  author D. F. Phillips,  and  author R. L. Walsworth, 10.1103/PhysRevLett.96.043601 journal journal Phys. Rev. Lett. volume 96, pages 043601 (year 2006)NoStop
[Xiao et al.(2008)Xiao,
  Novikova, Phillips, and Walsworth]XiaOE08
  author author Y. Xiao, author I. Novikova,
  author D. F. Phillips,  and  author R. L. Walsworth, 10.1364/OE.16.014128 journal journal
  Opt. Express volume 16, pages 14128
  (year 2008)NoStop
[Camparo and Coffer(1999)]CamparoPhysRevA.59.728
  author author J. C. Camparo and author J. G. Coffer, 10.1103/PhysRevA.59.728 journal
  journal Phys. Rev. A volume 59,  pages 728 (year 1999)NoStop
[Tan et al.(2015)Tan,
  Tian, Lin, Chen, and  Gu]SihongGu2015
  author author B. Tan, author Y. Tian, author H. Lin, author
  J. Chen,  and author
  S. Gu, 10.1364/OL.40.003703 journal journal Optics
  Letters volume 40, pages 3703
  (year 2015)NoStop
[Sun et al.(2016)Sun,
  Zhang, Cheng, Xu,
  Zhao, and Wang]SunOE16
  author author X. L. Sun, author J. W. Zhang,
  author P. Cheng, author C. Xu, author
  L. Zhao,  and author
  L. J. Wang, 10.1364/OE.24.004532 journal journal Opt.
  Express volume 24, pages 4532
  (year 2016)NoStop
[Guidry et al.(2017)Guidry,
  Kuchina, Novikova, and Mikhailov]Guidry:17
  author author M. A. Guidry, author E. Kuchina,
  author I. Novikova,  and  author E. E. Mikhailov, 10.1364/JOSAB.34.002244 journal journal
  J. Opt. Soc. Am. B volume 34, pages
  2244 (year 2017)NoStop
[Lin et al.(2017)Lin,
  Tian, Tan, and Gu]GuEPL2017
  author author H. Lin, author Y. Tian, author B. Tan,  and author
  S. Gu, http://stacks.iop.org/0295-5075/119/i=2/a=23001 journal
  journal EPL (Europhysics Letters) volume
  119, pages 23001 (year 2017)NoStop
[Gerginov et al.(2008)Gerginov, Knappe, Shah, Hollberg, and Kitching]kitchinIEEE2008
  author author V. Gerginov, author S. Knappe,
  author V. Shah, author
  L. Hollberg,  and author
  J. Kitching, 10.1109/TIM.2007.915123 journal journal IEEE
  Transactions on Instrumentation and Measurement volume
  57, pages 1357 (year 2008)NoStop

