Hyperfine measurement of 6\text{P}_{1/2} state in ^{87}\text{Rb} using double resonance on blue and IR transition
Elijah Ogaro Nyakang'o, Dangka Shylla, Vasant Natarajan, Kanhaiya Pandey
HHyperfine measurement of P / state in Rb using double resonance on blue and IRtransition
Elijah Ogaro Nyakang’o, Dangka Shylla, Vasant Natarajan, and Kanhaiya Pandey ∗ Department of Physics, Indian Institute of Technology Guwahati, Guwahati, Assam 781039, India Department of Physics, Indian Institute of Science, Bangalore, 560012, India (Dated: January 19, 2021)In this paper, we present the spectroscopy of 6P / state in Rb using double resonance techniqueat 780 nm and 421 nm. The double resonance technique is implemented using electromagneticallyinduced transparency (EIT) and optical pumping methods. Using these spectroscopy methods, wehave measured the hyperfine splitting of 6P / state with precision of <
400 kHz which agrees wellwith other spectroscopy methods such as electrical discharge and saturated absorption spectroscopyat 421 nm.
PACS numbers:
I. INTRODUCTION
Precise measurements of the hyperfine structure of var-ious lines in an atom provide key information about theproperties of the nucleus such as the electric and mag-netic moments. Rb is one of the most widely investigatedelements in atomic physics for the spectroscopy both ex-perimentally [1–6] and theoretically [7]. This providegreat opportunities to verify different methods of the-oretical many-body calculations [8, 9]. Hyperfine split-ting measurements are good sources of input for studyingsubjects at the interface of atomic and nuclear physicssuch as atomic parity violation [10]. Experimentally, hy-perfine structures of 5P / , 5D / and 7S / have beenmeasured using single-photon transition 5S / → / at780 nm [1–3], and two-photon transitions 5S / → / at 778 nm [4] and 5S / → / at 760 nm [2, 5, 6]respectively.Besides verifying theoretical calculations, the above re-ferred transitions are used as low cost optical frequencystandards. For example, the precisely measured transi-tion 5S / → / at 780 nm is used as an optical refer-ence for measuring unkown transitions [3]. All these tran-sitions fall in IR region; however, the weak and narrowlinewidth (2 π × .
27 MHz [11]) transition in the blue re-gion (i.e. at 421 nm) has the advantage of high precisionfor frequency standards [12, 13] and is a promising can-didate for metrology. Measuring the hyperfine splittingof 6P / adds important input to theoretical calculations[7]. The hyperfine splitting measurement of 6P stateshas been carried out using saturated absorption [14] forboth 6P / and 6P / states, or fluorescence spectroscopy[15] for 6P / state on 5S / → / / transition andusing RF transition with electrical discharge [16].The direct detection of absorption of 421 nm on5S / → / transition requires heating of Rb vaporcell upto 80 − ◦ C [14, 17] and using a photodiode with ∗ Electronic address: [email protected] blue enhanced sensitivity. The spectroscopy at 421 nmcan also be done using double-resonance spectroscopy[18–22] which does not require heating of Rb vapor cell.The double resonance method can be of electromagnet-ically induced transparency (EIT) type in a V-system[23–27] a technique which is known as coherent controlspectroscopy (CCS). We have also added optical pumpingtechnique for the same double resonance spectroscopy.The precise measurement of the hyperfine interval of6P / state in Rb is carried out using the two doubleresonance spectroscopy methods. Although the methodbased upon electrical discharge in reference [16] providesgreat precision, it is important to measure hyperfine split-ting with different methods to avoid systematic shiftsin the experiment due to ion-atom and atom-atom colli-sions. Similarly heating the Rb cell also increases atom-atom collision and can cause collisional/pressure shift [28]which can contribute to systematic shift in the hyperfinemeasurement.
II. MEASUREMENT SCHEMESA. Coherent Control Scheme
The energy level diagram for coherent control schemeis given in Fig. 1a and the experimental setup is as shownin Fig. 2. The 780 nm probe laser is locked to resonanceon 5S / (F = 2) → / (F (cid:48) = 3) cycling transitionand its absorption is monitored as the co-propagating421 nm control laser beam scans 5S / (F = 2) → / transitions. As soon as the 421 nm scanning controllaser comes to resonance (i.e. when both laser beamsare addressing zero velocity group atoms), absorptionof the 780 nm probe laser is reduced giving rise toa Doppler-free dip. There are two reasons for reduc-tion of the 780 nm probe laser absorption. One is dueto coherent effect i.e. V system EIT [24, 27] and an-other is optical pumping to other ground hyperfine level,5S / (F = 1) [29–31] via 5S / (F = 2) → / exci-tation and 6P / → / (F = 1) decay channels. The a r X i v : . [ phy s i c s . a t o m - ph ] J a n P P S (b)(a) GHzMHz MHz266.652(78)
F' F1 F"1 C on t r o l l a s e r . m F21
MHz265.12(7)
F"216 P S GHz6.835(90) P r ob e l a s e r . m P r ob e l a s e r . m C on t r o l l a s e r . m P MHz266.652(78)156.947(70)72.218(40)
F'3210
Figure 1: (Color online). Schematic of a multilevel atomicsystem interacting with two laser beams in (a) V-type schemeand (b) optical pumping scheme in Rb. transparency spectrum is shown in Fig. 3a.Besides the two hyperfine peaks due to zero velocitygroup atoms, there are other extra peaks outside themain spectrum. The extra peaks are caused by atomsmoving with velocities 208 m/s and 330 m/s respectively.Atoms moving with velocity 208 m/s will see the 780 nmprobe laser to be on resonance with 5S / (F = 2) → / (F (cid:48) = 2) transition. The corresponding two extrapeaks are separated by hyperfine interval of 6P / andlocated at 494 MHz from the main peaks respectively.Similarly, atoms moving with velocity 330 m/s will beresonant for 5S / (F = 2) → / (F (cid:48) = 1) transitionand another two fold of extra peaks are located at 783MHz from the main peaks. The theoretical plot in Fig.3 is generated using density matrix calculation for seven-level system in Doppler-broadened Rb atomic vapors atroom temperature (300 K). Due to non-linearity in thescan of the laser, there is a mismatch between experi-ment and theory in the position of the extra peaks. Thelinewidth of the experimental spectrum ranges between29 and 31 MHz and the theoretical simulation curve hasa linewidth of 26 MHz. However, this linewidth is largerthan the natural linewidth (6 .
065 + 1 .
27 MHz). This iscaused by Doppler mismatch between the 780 nm and421 nm lasers [32].
B. Optical Pumping Scheme
Fig. 1b is the energy level diagram for optical pump-ing scheme and the experimental setup is also given inFig. 2. The 780 nm probe laser is locked to resonanceon 5S / (F = 2) → / (F (cid:48) = 3) cycling transitionand its absorption is monitored as the co-propagating421 nm control laser beam scans around the 6P / hy-perfine levels on 5S / (F = 1) → / transition in-stead of 5S / (F = 2) → / transition. The 421 nmscanning control laser beam, partially transfers popula-tion from the lower ground hyperfine level (5S / (F = 1)) to the upper ground hyperfine level (5S / (F = 2)) via5S / (F = 1) → / excitation and 6P / → / (F =2) decay channels. Thus, optical pumping of zero ve-locity group atoms to the upper ground hyperfine level[29–31] and coherence dephasing rate of the ground hy-perfine levels [33–35] increase absorption of the probegiving rise to Doppler-free peaks. The absorption spec-trum is shown in Fig. 3b. Since all velocity group atomsare optically pumped from 5S / (F = 1) to 5S / (F = 2)ground hyperfine level, extra peaks are formed outsidethe main spectrum as explained in the previous section.The linewidth of the experimental spectrum ranges be-tween 29 and 34 MHz and linewidth for theoretical sim-ulation curve is 23 and 34 MHz. III. EXPERIMENTAL DETAILSA. Setup and Results
The 780 nm beam is generated from (thorlab laserdiode L785H1) a home-assembled extended cavity diodelaser (ECDL) with typical linewidth of 500 kHz. Theerror signal for locking the 780 nm laser is generated byfrequency modulation using the current of ECDL at 50kHz. The error is fed to the piezo using a home-madeanalog PID controller for locking to the particular tran-sition. The 421 nm beam is generated from commer-cial available ECDL from TOPTICA with model no. DLPRO HP with output power of 70 mW and linewidth of <
200 kHz. In the experimental setup given in Fig. 2, the421 nm laser beam addressing 6P / hyperfine level is di-vided into two laser beams. The first laser beam is passeddirectly through the Rb vapor cell and co-propagateswith one of the 780 nm probe laser. The second 421 nmlaser beam is passed through the acousto-optic modulator(AOM) twice and its frequency is shifted to be approx-imately the hyperfine interval value. The double-passAOM configuration has the advantage of preserving thedirection of propagation of the laser beam as the fre-quency of AOM is changed [36]. The AOM frequency inour double-pass setup is shifted between 130 −
136 MHz.The double passed AOM beam, again passes through thesame Rb vapor cell where it co-propagate with the sec-ond 780 nm probe laser. The two sets of co-propgating421 nm and 780 nm laser are around 12 mm apart in thesame cell. The single-mode operation of the 421 nm laseris monitored using Confocal Fabry Perot Interferometerwith free spectral range of 150 MHz. The beam diame-ter of the 780 nm probe laser is 2 × µ W (or intensity, I = 1 .
78 mW / cm andcorresponding Rabi frequency of 2 π × .
27 MHz). Thebeam diameter of the 421 nm control laser is 3 × .
945 mW and calculated inten-sity, I = 20 .
05 mW / cm . The intensity corresponds toRabi frequency of 2 π × .
17 MHz using the dipole momentin reference [11]The spectrum of 5S / (F = 2) → / or 5S / (F = PBSL DM PDPBS L780.241 nm λ/4λ/2 AOM λ/2 LLL PBS Rb vapormagnetic shield PDM MFP CavityDouble-Pass AOM λ/4 LPBS421.673 nm Control laser Probe laser
Figure 2: (Color online). Experimental setup for measuringhyperfine structure using coherent control and optical pump-ing schemes. L: Plano-convex lens; λ/
2: half-wave plate; λ/ → / weak transition driven by 421 nm laser shownin Fig. 3a and 3b respectively, is recorded using a pico-scope through the changes in the absorption spectrum of780 nm probe laser driving 5S / (F = 2) → / (F (cid:48) =3) strong transition. The red and black traces of ex-perimental spectrum in Fig. 4 corresponds to unshiftedand shifted AOM beams respectively. One of the tracesis deliberately inverted to see the matching of the twohyperfine peaks for the shifted and unshifted spectrum.The matching of the peaks is a measure of shifting thefrequency of the laser beam by exactly the hyperfine in-terval. The frequency difference (∆ diff ) between the twopeaks being matched is obtained by fitting the peaks witha Lorentzian line profile (see Fig. 4) and finding the dif-ference in the peaks location. Fig. 5 shows a plot offrequency shift (2 × AOM frequency) vs the frequencydifference between the two peaks (∆ diff ). The hyperfineinterval is obtained using a linear fit on the plot of fre-quency shift vs ∆ diff . The frequency shift correspondingto zero frequency difference (∆ diff = 0) in the linear fit isthe hyperfine interval ( V hfs ). This method removes theerror due to scan non-linearity and hence improves theprecision of measurement. From the linear fit the valueof V hfs = 265 . ± .
047 MHz in the case of the coherentcontrol scheme and V hfs = 265 . ± .
034 MHz for theoptical pumping scheme.
B. Errors
1. Systematic Errors
The main source of the systematic errors is the lightshift and stray magnetic field through Zeeman shift. Thesystematic error arising due to stray magnetic field isminimized using a µ -metal magnetic shield around theRb cell. The residual fields is below 1 mG which corre- -1000 -800 -600 -400 -200 0 200 400 600 800 1000 Frequency (MHz) of 421 nm laser P r ob e a b s o r p t i on ( a r b . un i t s ) P r ob e a b s o r p t i on -3 (2, 1) (1, 1); ( 2, 2)1 2 (a) Coherent control spectrum ExperimentTheory -1000 -800 -600 -400 -200 0 200 400 600 800 1000
Frequency (MHz) of 421 nm laser P r ob e a b s o r p t i on ( a r b . un i t s ) P r ob e a b s o r p t i on -3 (2, 1)(1, 1); ( 2, 2)(1, 2)1 2 (b) Optical pumping spectrum ExperimentTheory
Figure 3: (Color online). Theoretical and experimental spec-trum of 6P / . Extra peaks are caused by atoms moving withvelocity 208 m/s and 330 m/s which brings 780 nm and 421nm lasers to resonance on 5S / (F = 2) ↔ / (F (cid:48) = 1 , / (F = 1(2)) ↔ / (F (cid:48)(cid:48) = 1 ,
2) transi-tion (red color). sponds to errors less than 1 kHz. The light shift erroris due to presence of the hyperfine levels and the lasersdriving simultaneously many levels off resonance caus-ing the light shift of the levels driven resonantly. Thelocked probe laser 5S / (F = 2) → / (F (cid:48) = 3) cyclingtransition, also drives 5S / (F = 2) → / (F (cid:48) = 2(1))transitions off resonance causing the light shift to theground state 5S / (F = 2) upward and excited state5P / (F = 3) downwards. However, this shift does notcause any error for hyperfine interval because it willcause equal shift in the resonance for both the hyper-fine levels of 6P / . The scanning control laser is thesource of systematic error in the measurement of hy-perfine interval. This is because, when it is resonantto 5S / (F = 2) → / (F (cid:48)(cid:48) = 1), it also driving the5S / (F = 2) → / (F (cid:48)(cid:48) = 2) off resonance (neg-ative detuning equal to hyperfine interval, V hfs ) caus-ing the ground state 5S / (F = 2) to shift downwardsby Ω / V hfs . This effect causes resonant frequency for5S / (F = 2) → / (F (cid:48)(cid:48) = 1) to be shifted by+Ω / V hfs . Similarly, when the control laser is at res-onance on 5S / (F = 2) → / (F (cid:48)(cid:48) = 2) transition, itis also driving the 5S / (F = 2) → / (F (cid:48)(cid:48) = 1) tran-sition off resonance (positive detuning equal to hyperfineinterval) causing the ground state 5S / (F = 2) to shiftupwards by Ω / V hfs . This causes resonant frequency for -600 -400 -200 0 200 400 600 Frequency (MHz) of 421 nm laser P r ob e a b s o r p t i on ( a r b . un i t s ) Unshifted spectrumFitShifted spectrum
Figure 4: (Color online). Spectrum of shifted (black color)and unshifted (red color) beams fitted with a Lorentzian lineprofile (dashed green color) to obtain frequency difference(∆ diff ) between the matched peaks. / (F = 2) → / (F (cid:48)(cid:48) = 2) transition to be shiftedby − Ω / V hfs . The overall light shift error calculated us-ing the laser intensities in the previous section is 13 kHzand 6 kHz for the coherent control scheme and the opticalpumping scheme respectively.
2. Statistical Error
The above systematic error is much smaller than thestatistical error in the experiment. The non-linear scanof the laser is the main cause the statistical error. Thiserror is minimized by shifting AOM frequency within asmall range of frequencies around the neighboring hyper-fine level. To quantify the statistical error, two traces(shifted and unshifted spectrum) are recorded on two in-put channels of the picoscope with averaging of 20. Threesuch samples are taken for each AOM frequencies and thespread of the data (∆ diff ) is shown by the histogram inthe inset of Fig. 5. The spread of the data gives the sta-tistical error in the experiment and is extracted from thehistogram using a Gaussian fit. The extracted statisticalerror is 0 .
326 MHz for the coherent control scheme and0 .
337 MHz for the optical pumping scheme.
Table I: Hyperfine interval ( V hfs ) and magnetic dipole con-stant A for 6P / state in Rb. The number indicated innormal bracket is the statistical plus fitting error and in curlybracket is systematic error. V hfs (MHz) A (MHz) ReferenceCoherent control 265.134(373) { } { } In summary, the statistical error is dominating over systematic errors (light shift and stray magnetic field er-rors) and fitting error. The total error is 0 .
387 MHzand 0 .
378 MHz for the coherent control scheme and the -8 -6 -4 -2 0 2 4 6 8 10 diff (MHz) A O M f r e qu e n cy ( M H z ) Coherent controlOptical pumpingFit
Spread of data -2 0 202040
Figure 5: (Color online). A plot of frequency shift (2 × AOMfrequency) vs frequency difference (∆ diff ) for the two schemes.The inset shows the spread of data from the mean hyperfineinterval. optical pumping scheme respectively. Hence the hy-perfine interval in the case of coherent control schemeis V hfs = 265 . { } MHz and optical pumpingscheme is V hfs = 265 . { } MHz. The measuredhyperfine interval is related to the magnetic dipole hy-perfine constant, A = V hfs (F → F − / F. The valuesof A are 132 . . V hfs ) and magnetic dipole constant A with theearlier works is given in Tab. I. IV. CONCLUSIONS
We have presented two experimental schemes for pre-cision measurement of hyperfine interval of 6P / stateof Rb, namely coherent control and optical pumpingschemes using double resonance at 780 nm and 421 nm.Using an AOM, we have taken care of the scan non-linearity which is the dominant source of error in theexperiment. The measured hyperfine interval is consis-tent with two other techniques namely saturated absorp-tion and electrical discharge within the precision of ourmeasurement.
Acknowledgement
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