Radiative deflection of a BaF molecular beam from the optical cycling
We demonstrate a quasi optical cycling for the transition and a radiative force induced deflection on the buffer-gas cooled BaF molecular beam. The laser induced fluorescence enhancement with additional sidebands and a polarization modulation scheme indicates that the hyperfine states and the Zeeman sublevels are closed. The quasi optical cycling by repumping the leads to a 0.8 mm deflection of the beam via scattering 150 photons per molecule, in good agreement with the predictions from our multi-level rate equation model. Further improvement by closing the leakage and state allows scattering thousands of photons, and laser cooling and slowing of BaF.
Laser cooling and trapping Chu (1998) using the light scattering force have led to lots of fundamental breakthroughs in atomic and quantum physics, especially the frequency standard for precision measurement Ludlow et al. (2015) and the applications of the degenerate quantum gases Bloch et al. (2008); Giorgini et al. (2008). Over the last decade, great efforts have been spared into extending the techniques for control and cooling neutral atoms to polar molecules Carr et al. (2009); Moses et al. (2017) due to the additional vibrational, rotational degrees of freedom, which provide potential novel applications in many-body physics Wang et al. (2006); Buchler et al. (2007), cold controlled chemistry Krems (2008); Ospelkaus et al. (2010), and quantum simulation and computation DeMille (2002); Rabl et al. (2006); Andre et al. (2006). While high phase space density has been achieved in closed-shell bi-alkali molecules by external association and adiabatic transferring techniques Ni et al. (2008); Moses et al. (2015), producing a degenerate open-shell molecular sample, such as alkali-alkaline-earth system, is still under exploration Hara et al. (2011); Pasquiou et al. (2013). Besides, another type of open-shell molecule, alkaline-earth-metal monohydride and monofluoride, first proposed by Di Rosa Di Rosa (2004), can be directly laser-cooled Shuman et al. (2010), which has received quite great interests in recent years.
In fact, for molecules, it is difficult to find a perfect closed optical cycling channel to provide successive photon-molecule interactions required by laser-cooling because of the additional complexities. Fortunately, molecules like alkaline-earth-metal monohydride and monofluoride have special internal level structures, leading to nearly diagonal distribution of the Franck-Condon factors (FCFs), which results in a much simpler repumping process Di Rosa (2004), making laser cooling feasible. The earlier experimental demonstrations of laser cooling such molecules (SrF Shuman et al. (2009, 2010) and YO Hummon et al. (2013)) were implemented by DeMille group and Ye group respectively, following which the magneto-optical trapping of these two molecules was achieved short time later Barry et al. (2014); Yeo et al. (2015); Norrgard et al. (2016). Till now, on one hand, the temperature of the trapped molecule samples has been achieved lower and lower, and recently a three-dimensional molasses of sub-Doppler temperature (K) was produced for CaF molecule Truppe et al. (2017a). On the other hand, increasing the density of the molecular samples is urgent for further experiments, like evaporative cooling or sympathetical cooling. Molecular densities of Truppe et al. (2017a) and Anderegg et al. (2017) are achieved by Hinds group and Doyle group respectively. Besides these significant advances, laser cooling exploration on other molecules has sprung up over the world, including YbF Tarbutt et al. (2013), MgF Xu et al. (2016) and BaH Iwata et al. (2017); and now even sub-Doppler cooling of polyatomic molecule (SrOH) has been achieved Kozyryev et al. (2017).
Besides the above, the heavier BaF molecule is another candidate for direct laser cooling and trapping experiments due to the similar level structures and the good transition wavelength ( 900 nm) which can be easily achieved with external cavity diode lasers Bu et al. (2016). Besides, the effective buffer-gas cooling of BaF to the science rovibrational levels required by laser cooling has already been demonstrated Bu et al. (2017). Recently, a rovibrational cooling of a supersonic BaF beam to a rotational temperature of 6K with broadband laser sources has also been reported Cournol et al. (2017), which provides another possible approach for preparing the cold molecular source.
In this paper, we experimentally demonstrate the quasi-cycling transition and further observe the light scattering force induced deflection on the buffer-gas cooled BaF molecular beam. We use electronic transition (with the linewidth of MHz Berg et al. (1998)), which has the required highly diagonalized FCFs, to close the vibrational branching. The cycling scheme has been described in detail in Ref.Chen et al. (2016). The rotational transition is employed to eliminate the rotational branching, and a sideband modulation scheme to generate four frequency branches to cover the hyperfine levels. In current experiment, we have not taken the leakage channel from the state into account yet. The contents are organized as following. Section II describes the experimental details. In Sec.III, we present the enhancement of the laser induced fluorescence (LIF) by introducing the repump laser, the sideband modulation and the polarization modulation of the light. Furthermore, we show the deflection of the molecular beam induced by the quasi-cycling photon scattering. The last section gives a brief conclusion and outlook.
Figure 1(a) shows the diagram of the deflection experiment. We demonstrate the cycling scheme based on the buffer-gas cooled molecular beam of BaF produced with the laser ablation. Different from our previous study of the cold collisions between BaF and He Bu et al. (2017), the He buffer gas here flows into the cell at a rate of 2 sccm (standard cubic centimeters per minute). The effectively thermalized ( 4K) mixture of He and BaF forms a beam via a 3 mm exit aperture of the cell. Another 3 mm aperture lying at 20 cm downstream from the cell filters out the molecules with higher transverse velocity, and collimate the beam. To deflect the molecules, we apply several laser beams along the direction, perpendicular to the beam propagation. The molecule-light interaction time is controlled just by varying the pass number of the beams, and the maximum pass number can be tuned to 8 in our experiment. The pump (860 nm) and repump (896 nm) lasers, see Fig.1(b), are spatially overlapped with a diameter of 2 mm and powers of 160 mW and 100 mW respectively. To make all passes along the same direction, the laser beams are circularly reflected around the vacuum chamber Shuman et al. (2009). The LIF from the transition is collected by an avalanche photo diode (APD), which focuses on the first laser beam in the 10 cm long interaction region. The deflection probe region locates 35 cm away from the interaction region, and between them a clean-up laser (896 nm) with a diameter of 8 mm and power of 50 mW hits the molecular beam to pump the molecules from the state back to the state. The BaF molecular beam profiles, including the width and position, are recorded by imaging LIF from a retroreflected laser beam (only 860 nm) on a CCD camera in probe region. The zoom ratio of the image system is . A band-pass filter of nm is used to decrease the background noise from the ablation laser and other stray lights.
To eliminate the hyperfine dark state, both the pump and repump lasers should cover all four hyperfine levels of the states; see Fig.1(c). Recalling the analysis in Ref.Chen et al. (2016), a resonant-type electro-optic modulator (EOM) with a modulation frequency of 38 MHz is employed in our experiment, and a modulation depth of 2.6 results in the first and second sidebands with equal amplitude, nearly matching the four hyperfine transitions in . On the other hand, the Zeeman dark state could be remixed by applying either an angled magnetic field or time-dependent polarization modulation Berkeland and Boshier (2002). Here we use a pockel cell to implement the polarization switching scheme and the modulation frequency is set as 1 MHz. Additionally, both the clean-up and the deflection probe beams are sideband modulated and polarization modulated as well.
Iii Results and discussion
iii.1 Quasi optical cycling
Figure 2 shows the time of flight (ToF) LIF signals from the main pump transition monitored by the APD with the toggle technique applied. From Fig.2(a), by introducing the 38 MHz sideband modulation to the pump laser to address the hyperfine sublevels, the LIF signal is enhanced in comparison with that when only one single-frequency pump laser resonant with the sublevel applied. This can be easily understood since much more sublevels are excited by the additional sidebands, leading to more scattering photons before the molecules populate the Zeeman dark states and state. On the other hand, the ToF signal tells us the time window of the detection. The peak LIF signal appears at 1.7 ms, while the ablation laser fires at 0 ms and the distance between the cell and the interaction region is 35 cm, indicating the most probable velocity is 200 m/s. This means that the time window of the APD is about .
The addition of the time-dependent 1 MHz polarization modulation to the pump laser increases the LIF signal by a factor of 1.5; see Fig.2(b). We find that the enhancement seems insensitive to the modulation frequency, and a 5 MHz modulation also leads to a similar result. However, our 4+13 multi-level rate equation (MLRE) model with the experimental parameters in Sec.II indicates about enhancement of the scattering photon number per molecule within interaction time; see Appendix.A for details. Due to the strong pump laser intensity (the saturation factor for each sideband is 300), interaction time of is enough to pump the molecule to dark state, and the model shows that each molecule scatters about 18 photons, which is close to the predicted value of and Chen et al. (2016) is the FCF for the transition. Consequently, the LIF enhancement with polarization switching indicates that about 18/1.5 = 12 photons are scattered when no switching scheme applied. This might resort to the earth’s magnetic field which can also remix the Zeeman sublevels, since from the 4+13 model we expect only 6 photons are scattered before the molecule populates the Zeeman dark states or state without any remixing technique involved.
As shown in Fig.2(c), the addition of the repump laser further makes the LIF signal enhanced. This indicates that the scattering photon number within increases to , which is consistent with the predicted value from the 4+25 MLRE model with polarization switching scheme (see Fig.6 in Appendix). Till now, the quasi optical cycling has been implemented by applying the 38 MHz sideband modulation, the 1 MHz polarization switching scheme and the repump laser to close the hyperfine, the Zeeman and the first vibrational dark states respectively. The observed LIF enhancement agrees well with the predictions from our theoretical models.
Another important issue for the deflection experiment is the frequency of the pump and repump lasers. Because of the different excitation rates for each hyperfine sublevel in , we scan the frequency within several hundreds of MHz to find an optimal position to lock the frequency of the two lasers respectively. Figure 3 illustrates the dependence of the LIF signal intensity (the peak value of the ToF signal) on the laser frequency with the 38 MHz sideband modulation. For the pump laser, the fit tells us that the lock point should be +270 MHz, corresponding to (identical to the value resolved from the in-cell spectroscopy Bu et al. (2017)); while for the repump laser, the best point is +30 MHz, corresponding to . The clean-up laser and probe laser in Fig.1 are also locked at these two frequency points respectively Bu et al. (2016).
iii.2 Radiative deflection
The LIF enhancement for a single pass of the deflection beam in the interaction region indicates a significant radiative force on the molecules once the pass number increases. Figure 4 shows the resolved molecular beam deflection along the direction monitored by the CCD camera for the pass number . The shapes of the deflected and the unperturbed beams in the probe region are illustrated as Fig.4(a) and (b) respectively. An integration of the unperturbed image along the axis resolves the transverse width of the BaF molecular beam, about 3 cm, as shown in Fig.4(c). The addition of the deflection beam and clean-up beam leads to a mm shift in the direction while the beam width remains about 3 cm; see the normalized signals in Fig.4(d). We have also tested the effect of the repump laser and clean-up laser, without which only 10% molecules remain in state after suffering the pump in the interaction region. Putting the repump and clean-up laser into the system again recovers the molecular signal to 80%, which indicates effective optical pumping and repumping. The 20% loss is due to the leakage and the channels Chen et al. (2016).
Let us make an estimation of the scattering photon number from the deflection length . The time required for the molecular beam propagating from the interaction region to the probe region is , then the transverse velocity changes by . The photon recoil momentum is given by , where is Planck constant and nm is the wavelength of the main pump transition. The observed deflection length mm corresponds to a scattering photon number , here is the mass of the BaF molecule.
We have also measured the dependence of the scattered photon number on the interaction time , simply derived from deflection length versus the pass number of the deflection beam, as shown in Fig.5. Decrease of the pass number results in a linear decrease of the scattering photon number. The fit tells us the average scattering rate , which is only a little different from the numerical result (also plotted in Fig.5) predicted by the 4+25 MLRE model with switching scheme. On the other hand, the theoretical maximum scattering rate for a multi-level 4+24 system Truppe et al. (2017a) is given as . The unsaturated average scattering rate in our experiment might result from the detunings Chen et al. (2016) of the sidebands for the hyperfine transitions.
To summarize, we have clearly shown the evidence of the quasi optical cycling and further the radiative force from the scattering photons with only one additional repump. By applying the 38 MHz sideband modulation to the pump and repump lasers, the hyperfine dark states are eliminated. For Zeeman dark states, we have employed the 1 MHz polarization switching scheme to remix them to the cycling. Putting all these techniques together and increasing the pass number of the beam to achieve longer interaction time, we have observed a significant transverse deflection ( mm) of the BaF molecular beam, indicating a scattering rate of MHz, which agrees well with the theoretical prediction from our MLRE model.
By adjusting the detunings of the pump and repump lasers, retroreflecting the both laser beams and providing sufficient interaction length, the molecular beam should be transversely cooled. Furthermore, the scattering photon number required for loading the beam to a trap is about with a frequency-chirped or white light to longitudinal slow the beam, as a consequence, another transition, for example, , might be employed to improve the scattering rate Truppe et al. (2017b). To build a magneto-optical trapping (MOT) of BaF, the addition of repump laser should be required due to the calculated larger branching ratio of for Chen et al. (2016) than those of CaF Zhelyazkova et al. (2014) and SrF Shuman et al. (2009). Besides the RF-MOT with polarization switching Anderegg et al. (2017), our previously proposed microwave mediated MOT (-MOT) Xie et al. (2016) might be another candidate for our future laser cooling and trapping experiment.
Acknowledgements.We acknowledge the support from the National Natural Science Foundation of China under Grant No. 91636104, Zhejiang Provincial Natural Science Foundation under Grant No. LZ18A040001, the Fundamental Research Funds for the Central Universities Grant No. 2016QNA3007. We thank Yong Xia for useful discussions.
Appendix A Multi-level rate equation model
The rate equations to describe the time evolution of the populated fraction in each sublevel for a multi-level system is given as Metcalf and Straten (1999)
where and are the populated fractions for the -th sublevel in the ground state and the -th sublevel in the excited state, is the spontaneous decay rate of the excited state, is the branching ratio for transitions (see the values in Ref.Chen et al. (2016)). is the excitation rate for transition from the -th laser beam Tarbutt (2015), and is the saturation factor and is the detuning. For the evaluation of with polarization switching scheme, we should take the selection rules into account, i.e., for when and when . The scattered photon number at time is evaluated from .
We firstly build a 4+13 model with linearly polarized laser applied, considering 4 excited states in and 12 sublevels in . The 13rd level is the assumed loss channel with a branching ratio of . For linearly polarized excitation, the sublevels are dark states. Our numerical calculation indicates that the molecule will loss to the 13rd level or populate the Zeeman dark states just after scattering photons; see Fig.6. By introducing the 1 MHz polarization modulation, the model shows that scattered photon number increases to , three times larger than that without switching, before the molecule entirely populates the dark states.
To close the loss channel, we add the repump laser to our model, i.e., 4+25 model. Besides the 4 excited states and 12 sublevels for and respectively, the other loss channels, for example, and states, are all labeled as the 25-th level with a total branching ratio . This model indicates that the molecule suffers from nearly successive photon scattering within 100 s (larger than the interaction time in our deflection experiment), and finally the scattering process terminates after 600 photons (close to the value of ) are scattered for an interaction time of about 1 ms. Figure 6 shows the scattering photon number as a function of the interaction time within 20 s. For 10 s interaction time, the addition of the repump laser only increases the scattering number by a factor of , which is consistent with our experimental observation. Finally, to achieve laser cooling of BaF, additions of repump laser and microwave remixing of channels Chen et al. (2016) are necessary to scatter thousands of photons.
- Chu (1998) S. Chu, Rev. Mod. Phys. 70, 685 (1998).
- Ludlow et al. (2015) A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, Rev. Mod. Phys. 87, 637 (2015).
- Bloch et al. (2008) I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. 80, 885 (2008).
- Giorgini et al. (2008) S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 80, 1215 (2008).
- Carr et al. (2009) L. D. Carr, D. DeMille, R. V. Krems, and J. Ye, New Journal of Physics 11, 055049 (2009).
- Moses et al. (2017) S. A. Moses, J. P. Covey, M. T. Miecnikowski, D. S. Jin, and J. Ye, Nat. Phys. 13, 13 (2017).
- Wang et al. (2006) D.-W. Wang, M. D. Lukin, and E. Demler, Phys. Rev. Lett. 97, 180413 (2006).
- Buchler et al. (2007) H. P. Buchler, A. Micheli, and P. Zoller, Nat. Phys. 3, 726 (2007).
- Krems (2008) R. V. Krems, Phys. Chem. Chem. Phys. 10, 4079 (2008).
- Ospelkaus et al. (2010) S. Ospelkaus, K.-K. Ni, D. Wang, M. H. G. de Miranda, B. Neyenhuis, G. Quéméner, P. S. Julienne, J. L. Bohn, D. S. Jin, and J. Ye, Science 327, 853 (2010).
- DeMille (2002) D. DeMille, Phys. Rev. Lett. 88, 067901 (2002).
- Rabl et al. (2006) P. Rabl, D. DeMille, J. M. Doyle, M. D. Lukin, R. J. Schoelkopf, and P. Zoller, Phys. Rev. Lett. 97, 033003 (2006).
- Andre et al. (2006) A. Andre, D. DeMille, J. M. Doyle, M. D. Lukin, S. E. Maxwell, P. Rabl, R. J. Schoelkopf, and P. Zoller, Nat. Phys. 2, 636 (2006).
- Ni et al. (2008) K.-K. Ni, S. Ospelkaus, M. H. G. de Miranda, A. Pe’er, B. Neyenhuis, J. J. Zirbel, S. Kotochigova, P. S. Julienne, D. S. Jin, and J. Ye, Science 322, 231 (2008).
- Moses et al. (2015) S. A. Moses, J. P. Covey, M. T. Miecnikowski, B. Yan, B. Gadway, J. Ye, and D. S. Jin, Science 350, 659 (2015).
- Hara et al. (2011) H. Hara, Y. Takasu, Y. Yamaoka, J. M. Doyle, and Y. Takahashi, Phys. Rev. Lett. 106, 205304 (2011).
- Pasquiou et al. (2013) B. Pasquiou, A. Bayerle, S. M. Tzanova, S. Stellmer, J. Szczepkowski, M. Parigger, R. Grimm, and F. Schreck, Phys. Rev. A 88, 023601 (2013).
- Di Rosa (2004) M. D. Di Rosa, The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics 31, 395 (2004).
- Shuman et al. (2010) E. S. Shuman, J. F. Barry, and D. DeMille, Nature 467, 820 (2010).
- Shuman et al. (2009) E. S. Shuman, J. F. Barry, D. R. Glenn, and D. DeMille, Phys. Rev. Lett. 103, 223001 (2009).
- Hummon et al. (2013) M. T. Hummon, M. Yeo, B. K. Stuhl, A. L. Collopy, Y. Xia, and J. Ye, Phys. Rev. Lett. 110, 143001 (2013).
- Barry et al. (2014) J. F. Barry, D. J. McCarron, E. B. Norrgard, M. H. Steinecker, and D. DeMille, Nature 512, 286 (2014).
- Yeo et al. (2015) M. Yeo, M. T. Hummon, A. L. Collopy, B. Yan, B. Hemmerling, E. Chae, J. M. Doyle, and J. Ye, Phys. Rev. Lett. 114, 223003 (2015).
- Norrgard et al. (2016) E. B. Norrgard, D. J. McCarron, M. H. Steinecker, M. R. Tarbutt, and D. DeMille, Phys. Rev. Lett. 116, 063004 (2016).
- Truppe et al. (2017a) S. Truppe, H. J. Williams, M. Hambach, L. Caldwell, N. J. Fitch, E. A. Hinds, B. E. Sauer, and M. R. Tarbutt, Nat. Phys. advance online publication (2017a).
- Anderegg et al. (2017) L. Anderegg, B. L. Augenbraun, E. Chae, B. Hemmerling, N. R. Hutzler, A. Ravi, A. Collopy, J. Ye, W. Ketterle, and J. M. Doyle, Phys. Rev. Lett. 119, 103201 (2017).
- Tarbutt et al. (2013) M. R. Tarbutt, B. E. Sauer, J. J. Hudson, and E. A. Hinds, New Journal of Physics 15, 053034 (2013).
- Xu et al. (2016) L. Xu, Y. Yin, B. Wei, Y. Xia, and J. Yin, Phys. Rev. A 93, 013408 (2016).
- Iwata et al. (2017) G. Z. Iwata, R. L. McNally, and T. Zelevinsky, Phys. Rev. A 96, 022509 (2017).
- Kozyryev et al. (2017) I. Kozyryev, L. Baum, K. Matsuda, B. L. Augenbraun, L. Anderegg, A. P. Sedlack, and J. M. Doyle, Phys. Rev. Lett. 118, 173201 (2017).
- Bu et al. (2016) W. Bu, M. Liu, D. Xie, and B. Yan, Review of Scientific Instruments 87, 096102 (2016).
- Bu et al. (2017) W. Bu, T. Chen, G. Lv, and B. Yan, Phys. Rev. A 95, 032701 (2017).
- Cournol et al. (2017) A. Cournol, P. Pillet, H. Lignier, and D. Comparat, arXiv 1709.06797 (2017).
- Berg et al. (1998) L.-E. Berg, N. Gador, D. Husain, H. Ludwigs, and P. Royen, Chem. Phys. Lett. 287, 89 (1998).
- Chen et al. (2016) T. Chen, W. Bu, and B. Yan, Phys. Rev. A 94, 063415 (2016).
- Berkeland and Boshier (2002) D. J. Berkeland and M. G. Boshier, Phys. Rev. A 65, 033413 (2002).
- Truppe et al. (2017b) S. Truppe, H. J. Williams, N. J. Fitch, M. Hambach, T. E. Wall, E. A. Hinds, B. E. Sauer, and M. R. Tarbutt, New Journal of Physics 19, 022001 (2017b).
- Zhelyazkova et al. (2014) V. Zhelyazkova, A. Cournol, T. E. Wall, A. Matsushima, J. J. Hudson, E. A. Hinds, M. R. Tarbutt, and B. E. Sauer, Phys. Rev. A 89, 053416 (2014).
- Xie et al. (2016) D. Xie, W. Bu, and B. Yan, Chin. Phys. B 25, 053701 (2016).
- Metcalf and Straten (1999) H. J. Metcalf and P. Straten, Laser cooling and trapping (Springer, 1999).
- Tarbutt (2015) M. R. Tarbutt, New J. Phys. 17, 015007 (2015).