Repumping and spectroscopy of laser-cooled Sr atoms using the (5s5p)3P2 - (5s4d)3D2 transition
P. G. Mickelson, Y. N. Martinez de Escobar, P. Anzel, B. J. DeSalvo, S. B. Nagel, A. J. Traverso, M. Yan, T. C. Killian
aa r X i v : . [ phy s i c s . a t o m - ph ] J u l Repumping and spectroscopy of laser-cooled Sr atoms using the (5 s p ) P - (5 s d ) D transition P. G. Mickelson, Y. N. Martinez de Escobar, P. Anzel, B. J. DeSalvo, S. B. Nagel, A. J. Traverso, M. Yan, T. C. Killian
Rice University, Department of Physics and Astronomy, Houston, Texas, 77251 (Dated: November 3, 2018)We describe repumping and spectroscopy of laser-cooled strontium (Sr) atoms using the (5 s p ) P - (5 s d ) D transition. Atom number in a magneto-optical trap is enhanced by driving this transitionbecause Sr atoms that have decayed into the (5 s p ) P dark state are repumped back into the(5 s ) S ground state. Spectroscopy of Sr, Sr, Sr, and Sr improves the value of the (5 s p ) P - (5 s d ) D transition frequency for Sr and determines the isotope shifts for the transition.
Cold atom experiments require cycling transitions forefficient laser cooling and trapping. Depending on thelevel structure, atoms may be shelved into dark statesduring laser cooling, which removes them from the cool-ing cycle and can cause them to be lost from the trap.By applying laser light of the appropriate frequency toshelved atoms, it is possible to return these atoms to thecycling transition [1, 2]. This repumping process can in-crease atom number and density, which improves signal-to-noise ratios for most measurements, enables study ofcollisional processes, and is crucial for achieving quantumdegeneracy [3].In experiments with alkali-metal atoms, the dark statesare ground state hyperfine levels, and repumping laserscan be generated with acousto-optic or electro-optic mod-ulators from the laser used for cooling. In alkaline-earth-metal atoms such as strontium (Sr), however, atom pop-ulation is trapped in highly excited metastable levels andindependent lasers are necessary. Despite requiring ad-ditional lasers, alkaline-earth-metal atoms are interestingto study because they offer the possibility of an all-opticalpath to quantum degeneracy [4, 5], possess narrow op-tical transitions that can be used for optical frequencystandards [6], and provide fine control of atomic interac-tions via optical Feshbach resonances [7].For Sr, the principal cycling transition for laser coolingoperates between the (5 s ) S and the (5 s p ) P states(Fig. 1). Decay via the (5 s p ) P - (5 s d ) D transi-tion [8] allows atoms to escape the cycling transition, andfurther decay from the (5 s d ) D state results in atomsin the (5 s p ) P and (5 s p ) P states (henceforth P j ). P atoms return to the ground state and are recapturedin the MOT, but P atoms are shelved because of the17 min lifetime of the P state [9].Here, we describe a repumping scheme for Sr using the P - (5 s d ) D transition at 3012 nm which has a his-torically difficult-to-reach wavelength in the mid-infrared(MIR). Lasers of this frequency based on optical para-metric oscillators have recently become available due toadvances in nonlinear optics and fiber lasers. Amongthe advantages this transition offers is the simplicity itbrings in comparison to repumping schemes like the onedescribed in [10] or [11]. Similar transitions have beenused to create a calcium MOT [12] operating on the 1978nm P - D cycling transition and in another Sr exper- FIG. 1: Wavelengths and decay rates for selected Sr transi-tions. The OPO laser enables the repumping scheme outlinedin the text by pumping atoms that have leaked from the P to the P state up to the D state, thus allowing decay tothe P state and subsequent return to the S ground state.The main cycling transition operates on the S to P tran-sition, and time-of-flight absorption imaging of ground stateatoms is performed using 461 nm light. iment [13] that uses the (5 s d ) D for the upper level,with a transition wavelength of 496 nm, to repump atomsout of the P state.We also determine an improved value of the transi-tion frequency and perform spectroscopy of the P -(5 s d ) D transition for Sr, Sr, Sr, and Sr. Us-ing these spectra, we assign isotope shifts for the Sr, Sr, and Sr transition relative to the Sr transition.Our experiment begins similarly to previously pub-lished work [10, 14, 15]. As many as 50 x 10
Sr atomsare trapped in a magneto-optical trap (MOT) operat-ing on the 461 nm cycling transition between the S and the P states. The MOT beams, red-detuned by60 MHz from resonance and with intensity-per-beam I =2.3 mW/cm , yield atom samples with a temperature ofabout 2 mK, a density on the order of 10 cm − , anda 1 /e radius of about 1 mm. For spectroscopy, we alsotrap other Sr isotopes [16], Sr ( < atoms), Sr(10 x 10 atoms), and Sr (5 x 10 atoms). Light at 461nm is produced by frequency doubling via KNbO in alinear enhancement cavity [17]. Time-of-flight absorptionimaging is also performed using the S - P transition.We produce 3 µ m light for repumping and spectroscopyusing a laser based on optical parametric oscillation A t o m N u m b e r [ ] Sr Without 3 µ m Repumper LaserWith 3 µ m Repumper LaserTwo−Body FitsOne−Body Fits Sr FIG. 2: Here we show the number of Sr and Sr (inset)atoms trapped as a function of time with and without appli-cation of mid-infrared (MIR) laser light at 3 µ m. Without theMIR light, atoms excited by the cooling laser that decay tothe metastable P state are lost from the trap, which limitsthe maximum number. The MIR laser pumps the metastableatoms to a state that decays back to the ground state so thatthey are not lost. Using the model described in the text, wedetermine that two-body collisions are limiting the maximumnumber of Sr atoms when the repumping laser is on; a one-body fit to early-time data (dashed line) overestimates thefinal number when the repumper is on, whereas it is a goodfit when the repumper is off. Only 300,000 Sr atoms are ob-served without the repumper because the natural abundanceof Sr (0.56%) is very low. The enhancement of Sr due tothe repumper is larger than that of Sr primarily because ofimproved vacuum conditions during the Sr experiment. (OPO) which is seeded by a fiber laser at 1.06 µ m[18]. Our experiments only require a minimal amountof power, typically about 4 mW incident on the atoms,and the beam has a 1 /e radius of about 3 mm. Wefrequency-stabilize the laser to 0.002 cm − precision us-ing a calibrated wavemeter.As described earlier, the cycling transition used for theMOT is not closed because of leakage from the P state,leading to shelving of atoms in the P state. Figure 2shows the number of atoms as a function of the MOTloading time with and without the repumping laser ap-plied. Absent the repumping laser, the atom number issignificantly lower than when the repumping laser enablesa return path to the ground state.We examine the enhancement the repumping laserbrings to the steady-state number of atoms using thetime-dependent number equation for MOT loading:˙ N = L N − Γ N − β ′ N . (1)Here, N is the number of atoms, L N is the loading rateof atoms into the MOT, Γ is the one-body loss rate, and β ′ = β/ (2 √ V ), where β is the two-body loss constantand V = R d re − r σ is the effective volume for two-bodyprocesses ( σ is the 1/ √ e radius and r is position). The solution to this differential equation is N ( t ) = N ss (1 − e − γt )(1 + χe − γt ) , (2)with γ = Γ + 2 β ′ N ss , N ss the steady state number ofatoms, and χ the measure of the relative contributions ofthe one- and two-body loss coefficients: N ss = − Γ + p Γ + 4 β ′ L β ′ (3)and χ = β ′ N ss β ′ N ss + Γ . (4)Using this model, we determine the fits shown in Fig.2. Without the repumping laser, a one-body fit (dashedline), with β ′ = 0 and Γ = 10.7 ± − is consistent withoptical pumping of atoms to the P state by the MOTlaser [19]. A two-body fit, with β = 6 ± × − cm /sand Γ = 2.4 ± − , fits the data when the repumpinglaser is on. A one-body fit to the first 0.5 s of this data(dashed line), overestimates the steady state number ofatoms. This value of β is only approximate, as care wasnot taken to accurately measure the sample volume, V,but it indicates that two-body processes are limiting thenumber of atoms loaded into the MOT. β is slightly lowerthan the value found in [19] which is reasonable given thelarger detuning of our MOT laser frequency and the lowerintensity of our MOT beams.Using the repumping of atoms, we performed spec-troscopy of the P - D transition for all the stableisotopes of Sr. For this study, we observe the repumpingenhancement in the steady-state number of MOT atoms,although trapping of P atoms in the magnetic trapformed by the quadrupole magnets of the MOT [10] canaffect the results. Scanning the laser across the resonancefrequency of the repumping transition changes the num-ber of atoms imaged (Fig. 3). The structure of the evenisotopes, Sr, Sr, and Sr, is simpler than that of theodd isotope, Sr, because the even isotopes have nuclearspin equal to zero.At low repumping laser intensity, the spectra of Srand Sr (see inset of Fig. 3) reveal structure arising fromZeeman splitting due to the 50 G/cm magnetic field gra-dient of the MOT magnetic coils. The detailed dynamicsof the repumping process are beyond the scope of thispaper. We suspect that at the low repumper intensitiesused for these isotopes, the repumping is slow enoughthat atoms escape the region of the MOT unless they arein the m j = 2 and m j = 1 sublevels and are magneticallytrapped [10], and m j = 2 is more populated because itis trapped more strongly. The double peaks we observeare likely due to transitions from the m=2 state of P to the m=2 and m=1 states in the D manifold. Theobserved splitting matches what one would expect fromthe known magnetic moments of the upper and lower lev-els, the magnetic field gradient, and the temperature of −2500 −1500 −500 0 500 15000.811.21.41.61.82 Detuning from Sr Transition [MHz] N u m b e r o f A t o m s [ S ca l e d ] DP 7/25/2 5/25/2 9/27/2 7/27/2 11/29/2 5/27/2 9/29/213/211/2 7/29/2 11/211/2 9/211/2 13/213/2 11/213/2DP 7/25/2 5/25/2 9/27/2 7/27/2 11/29/2 5/27/2 9/29/213/211/2 7/29/2 11/211/2 9/211/2 13/213/2 11/213/2DP 7/25/2 5/25/2 9/27/2 7/27/2 11/29/2 5/27/2 9/29/213/211/2 7/29/2 11/211/2 9/211/2 13/213/2 11/213/2DP 7/25/2 5/25/2 9/27/2 7/27/2 11/29/2 5/27/2 9/29/213/211/2 7/29/2 11/211/2 9/211/2 13/213/2 11/213/2DP 7/25/2 5/25/2 9/27/2 7/27/2 11/29/2 5/27/2 9/29/213/211/2 7/29/2 11/211/2 9/211/2 13/213/2 11/213/2DP 7/25/2 5/25/2 9/27/2 7/27/2 11/29/2 5/27/2 9/29/213/211/2 7/29/2 11/211/2 9/211/2 13/213/2 11/213/2DP 7/25/2 5/25/2 9/27/2 7/27/2 11/29/2 5/27/2 9/29/213/211/2 7/29/2 11/211/2 9/211/2 13/213/2 11/213/2DP 7/25/2 5/25/2 9/27/2 7/27/2 11/29/2 5/27/2 9/29/213/211/2 7/29/2 11/211/2 9/211/2 13/213/2 11/213/2DP 7/25/2 5/25/2 9/27/2 7/27/2 11/29/2 5/27/2 9/29/213/211/2 7/29/2 11/211/2 9/211/2 13/213/2 11/213/2DP 7/25/2 5/25/2 9/27/2 7/27/2 11/29/2 5/27/2 9/29/213/211/2 7/29/2 11/211/2 9/211/2 13/213/2 11/213/2DP 7/25/2 5/25/2 9/27/2 7/27/2 11/29/2 5/27/2 9/29/213/211/2 7/29/2 11/211/2 9/211/2 13/213/2 11/213/2DP 7/25/2 5/25/2 9/27/2 7/27/2 11/29/2 5/27/2 9/29/213/211/2 7/29/2 11/211/2 9/211/2 13/213/2 11/213/2DP 7/25/2 5/25/2 9/27/2 7/27/2 11/29/2 5/27/2 9/29/213/211/2 7/29/2 11/211/2 9/211/2 13/213/2 11/213/2 −600 −400 −200 0 Sr Sr Sr Sr FIG. 3: Spectroscopy of the P - D transition. Shifts aremeasured relative to the zero of the Sr spectrum. For Sr, Sr, and Sr, the number is normalized to the number ob-served without the repumping laser. For Sr, the scaling isarbitrary because large repumping efficiency is necessary toobserve a spectrum. Structure in the Sr spectrum is dueto the hyperfine interaction: the fermionic isotope of Sr hasnuclear spin I equal to 9/2. Level assignments (arrows) canbe made for all of the observed peaks, and the isotope shift of Sr is determined by the shift of the centroid of the energylevel manifold from the Sr zero. Inset: the arrow in theinset shows the position of the centroid for the Sr hyper-fine levels. The structure observed in the Sr and Sr linesis due to Zeeman splitting caused by the 50 G/cm magneticfield gradient of the MOT magnetic field. The gradient alsocontributes some broadening to the lines. Structure is notresolved for Sr and Sr because the spectra are observedonly at high laser power, which washes out the structure. atoms in the MOT [10]. This simple model allows usto determine the position of the unperturbed resonances(Fig. 3 inset). For Sr and Sr, all the repumping laserpower is necessary to achieve signal because of the lownatural abundance of Sr (0.56 %) and the poor repump-ing efficiency of Sr, and no structure is observed. Forthese isotopes, the unperturbed resonances are taken asthe center of the line.The Sr spectrum shows hyperfine structure becauseit has a nuclear spin of I =9/2, but since the spectraare taken at high repumping laser intensity, no magneticsublevels are observed. We calculate the positions of thehyperfine states using the Casimir formula:∆ E F = A K B (cid:20) / K ( K + 1) − I ( I + 1) J ( J + 1) I (2 I − J (2 J − (cid:21) , (5)with K = F ( F + 1) − J ( J + 1) − I ( I + 1) and the valuesof the magnetic dipole and electric quadrupole factors( A and B , respectively) taken from [20] for the D leveland from [21] for the P level. For this transition J = 2and I = 9 /
2, and the total angular momentum, F , variesfrom 5 / / −1 ] A mm on i a A b s o r p t i on [ A r b . U n i t s ] DataFit
FIG. 4: Absorption spectroscopy of ammonia for waveme-ter calibration. We fit the peaks using a multiple Gaussianline shape and compare the center frequency of the strongestline to data from [22] to determine the systematic error ofour wavemeter readings. The uncertainty of our fit to thesefrequencies is about 0.0015 cm − to the calculated positions.To calibrate the wavemeter absolutely, we perform ab-sorption spectroscopy of ammonia in a gas cell at roomtemperature and ∼ − P - D transition in Sr to be 3320.226 ± − , which is a small shift and improvement over thepreviously available value of 3320.232 cm − [24]. Our un-certainty arises from statistical uncertainty in fitting thelines in Fig. 4 and from drifts in the wavemeter calibra-tion. TABLE I: Wavemeter calibration with ammonia absorptionline. Observed Level [cm − ] Ref. [22] Level [cm − ]3333.3928(15) 3333.3975(10)TABLE II: Isotope shifts and uncertainties of the P - D transition at λ =3012 nm in Sr.Isotope Pair Isotope Shift [MHz] at λ −1 0 1 2 3 4 5x 10 Sr Sr Sr δ ν M for S − (2S+1) P [MHz amu] δ ν M f o r P − D [ M H z a m u ] S − P S − P Fit
FIG. 5: A King plot of the modified isotope shifts, δν M , of the P - D transition versus the modified isotope shifts of the461 nm S - P [25] and 689 nm S - P [26] transitionsof Sr. Table II lists the isotope shifts relative to Sr. Theuncertainties reflect uncertainty in fitting and modeling the lines. Figure 5 compares our values for the isotopeshifts to previous isotope shift measurements on the S - P [25] and S - P [26] Sr lines with a King plot[27, 28] of the modified isotope shift ( δν M ), δν M = ( δν IS − δν NMS ) A A A − A , (6)where A and A are the mass numbers in atomic massunits (amu) of the isotopes, δν IS is the observed isotopeshift, and δν NMS = ( νm e /m p ) × ( A − A ) /A A is thenormal mass shift caused by the reduced mass of theatom ( ν is the frequency of the transition; m e and m p are electron and proton masses). Within the error, thisKing plot shows the expected linear relations betweenthe isotope shifts for the different transitions.In conclusion, we have shown repumping of all stableisotopes of Sr using the P - D transition. Addition-ally, we have measured the isotope shift of the P - D transition for Sr, Sr, and Sr and provided an im-proved value for the P - D transition wavelength of Sr. [1] W. Neuhauser, M. Hohenstatt, P. Toschek, andH. Dehmelt, Phys. Rev. Lett. , 233 (1978).[2] W. D. Phillips, J. V. Prodan, and H. J. Metcalf, J. Opt.Soc. Am. B , 1751 (1985).[3] W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, andD. E. Pritchard, Phys. Rev. Lett. , 2253 (1993).[4] H. Katori, T. Ido, Y. Isoya, and M. Kuwata-Gonokami,Phys. Rev. Lett. , 1116 (1999).[5] T. Ido, Y. Isoya, and H. Katori, Phys. Rev. A ,061403(R) (2000).[6] J. Ye, H. J. Kimble, and H. Katori, Science , 1734(2008).[7] R. Ciurylo, E. Tiesinga, and P. S. Julienne, Phys. Rev.A , 030701(R) (2005).[8] T. Loftus, J. R. Bochinski, and T. W. Mossberg, Phys.Rev. A , 013411 (2002).[9] A. Derevianko, Phys. Rev. Lett. , 023002 (2001).[10] S. B. Nagel, C. E. Simien, S. Laha, P. Gupta, V. S.Ashoka, and T. C. Killian, Phys. Rev. A , 011401(R)(2003).[11] X. Xu, T. H. Loftus, J. L. Hall, A. Gallagher, and J. Ye,J. Opt. Soc. Am. B , 968 (2003).[12] J. Gr¨unert and A. Hemmerich, Appl. Phys. B , 815(2001).[13] N. Poli, R. E. Drullinger, G. Ferrari, J. Leonard, F. Sor-rentino, and G. M. Tino, Phys. Rev. A , 061403(R)(2005).[14] S. B. Nagel, P. G. Mickelson, A. D. Saenz, Y. N. Mar-tinez, Y. C. Chen, T. C. Killian, P. Pellegrini, andR. Cˆot´e, Phys. Rev. Lett. , 083004 (2005).[15] P. G. Mickelson, Y. N. Martinez, A. D. Saenz, S. B. Nagel, Y. C. Chen, T. C. Killian, P. Pellegrini, andR. Cot´e, Phys. Rev. Lett. , 223002 (2005).[16] T. Kurosu and F. Shimizu, Jap. J. Appl. Phys , L2127(1990).[17] M. Bode, I. Freitag, A. T¨unnermann, and H. Welling,Opt. Lett. , 1220 (1997).[18] A. Henderson and R. Stafford, Opt. Express , 767(2006).[19] T. P. Dinneen, K. R. Vogel, E. Arimondo, J. L. Hall, andA. Gallagher, Phys. Rev. A , 1216 (1999).[20] B. A. Bushaw, H. J. Kluge, J. Lantzsch, R. Schwalbach,J. Stenner, H. Stevens, K. Wendt, and K. Zimmer, Z.Phys. D , 275 (1993).[21] S. M. Heider and G. O. Brink, Phys. Rev. A , 1371(1977).[22] G. Guelachvili, A. H. Abdullah, N. Tu, K. N. Rao,S. Urban, and D. Papousek, J. Mol. Spectrosc. , 345(1989).[23] P. F. Bernath, Spectra of Atoms and Molecules (OxfordUniversity Press, New York, 1995).[24] J. E. Sansonetti and W. C. Martin, J. Phys. Chem. Ref.Data , 1559 (2005).[25] B. A. Bushaw and W. N¨ortersh¨auser, Spectrochim. ActaB , 1679 (2000).[26] B. A. Bushaw and B. D. Cannon, Spectrochim. Acta B , 1839 (1997).[27] W. H. King, J. Opt. Soc. Am. , 638 (1963).[28] U. Dammalapati, S. De, K. Jungmann, and L. Willmann,Eur. Phys. J. D53