**HAL Id: jpa-00221737**

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### Submitted on 1 Jan 1981

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**PRECISE DETERMINATION OF 135Ba+ AND** **137Ba+ HYPERFINE STRUCTURE**

### W. Becker, R. Blatt, G. Werth

**To cite this version:**

### W. Becker, R. Blatt, G. Werth. PRECISE DETERMINATION OF 135Ba+ AND 137Ba+

### HYPERFINE STRUCTURE. Journal de Physique Colloques, 1981, 42 (C8), pp.C8-339-C8-346.

### �10.1051/jphyscol:1981841�. �jpa-00221737�

**JOURNAL ***DE *

**PHYSIQUE **

*CoZZoque C8, suppZe'ment au n *

*'1 2,*

*Tome *

*4 2 ,*

*de'cembre 1981 * *page * C8-339

### 135 + ^{137 } +

**P R E C I S E D E T E R M I N A T I O N O F **

### Ba **AND ** Ba

**H Y P E R F I N E STRUCTURE**

**W.**

**Becker, R .**

**Blatt and G .**

**Werth**

*Institub * *fiir * *Phhysik, Universit8t Mainz, *

*6500*

*Mainz, *

*F.R.G.*

### Abstract.- We performed an optical double resonance experiment on the ground state of 137 and 135 ~ a + ions. About 10 particles **5 ** were confined in an rf quadrupole trap for many hours. Hfs state selection by pulsed laser optical pumping was followed by micro- wave transition, which were observed via change in the ionic fluorescence intensity. Linewidth of the order of the laser re- petition frequency (1-20 Hz) and a complicated line structure were observed in the "field independent" F=l, m=o - ^{F=2, } ^{m=o }

^{F=2, }

### transitions. The statistical uncertainty of the line center was below .1 Hz. The results for the hyperfine separations, in- cluding corrections to zero magnetic and electric field, are

**Av **

### (137 Ba+) = 8 037 741 667.69 (.37) Hz

**Av **

### (135 Ba+)

= 7### 183 340 234.35 **( . 4 7 ) ** Hz

### Since the succesful demonstration of "optical sideband cooling" of trapped ions at the University of Heidelberg/l/ and the National Bureau of Standards, Boulder/2/, the ion storage technique is very seriously considered for new ultrastable frequency standards in the microwave as well as in the optical region/3/. Among the candidates for microwave standards, based

**oh**

### ground state hygerfine transitions, the choice relies on

### (1) the existence of resonance transitions in the reach of available dye lasers,

### (2) a large hyperfine separation for high relative accuracy at a given Linewidth,

### (3) a heavy mass to minimize the second order Doppler shift for limited ion cooling,

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981841

JOURNAL **DE **PHYSIQUE

**( 4 ) **

### a small nuclear spin to limit the number of Zeeman sublevels for

### signal-to-noise reasons,

### (5) the easy availability of the ions.

### According to these criteria the first choice would be one of the odd ~ g + isotopes as soon as tunable laser radiation below 200 nm is available. With the present techniques the Ra ions with mass 135 and +

### 137, nuclear spin 3/2 and hyperfine separations of 7.18 and 8.04 GHz, respectively, may be considered as a possibility, which might yield high accuracy even without ion cooling.

### We performed an optical double resonance experiment on both stable odd Ra isotopes. Preliminary results have been published

### recently/4,5/. The ions were created by surface ionisation of a sample of isotope separated Ba on a hot Pt filament placed close to an end- cap of an rf quadrupole ion trap, whose operation is described in detail in the literature/6,7/. At 10-~mbar of He background pressure about 2

%### of the total ions emitted from the fila~ent are trapped and remain inside the trap for many hours. At typical operating conditions

### (Vdc=8V, Vac=750V, 0/2r=500 kHz, ro=20 **mrn) ** the trap formed a pseudo- potential vally of about 30 eV depth. The ions maintained at a tempe- rature, which corresponds to LO

% ### of the potential well depth/8/.

### Fig. 1 shows a setup of the experiment. Ground state population

tat.

,f-

### Fig. 1: Setup of the experi-

### men t

### inversion was achieved by optical pumpinq with an linear polarized

### pulsed dye laser, tuned to one of the hyperfine components of the

### 6SlI2 - 6PlI2 transition at 493,4 nm (fiq. 2). The laser spectral

### width (1 GHz) and the optical Doppler width (3 GAz) was small compared

### to the hyperfine splitting. Taking into account, that the excited

### PlI2 state partially decays into the metastable 5D3/2 state, whose

### radiative decay time is as long as 17.5 s/9/, we achieved almost com-

### plete population inversion after 10-15 laser pulses, which were well

### above saturation intensity.

### Fig. 2: Relevant energy levels of 137~aS. For 135~a+

### the ground state hyperfine separation is 7.18 GHz

### To induce the hyperfine transition microwaves were coupled into the trap by a hairpin antenna, placed betweed the ring and one of the endcap electrodes. The microwaves were created by a temperature stabilized klystron and phase locked to a harmonic of a quarz oscil- lator, referenced to a Rb atomic clock. Resonance between the

### possible AF=1, Amlo,

**t**

### 1 transition was monitored via the change in fluorescence intensity perpendicular to the primary light **be= **

### either at 493,4 nn or 649,6 nm. In spite of the low quantum efficiency of our photomultiplier in the red

**( s**

### 1%) we decided for the P-D

### transition to be independent of any laser stray light. Among the possible transitions the **F=2, ** m=o - **F=l, ** m=o line depends only in second order on the magnetic field. At field levels of about 100 mG inhomogenieties do not represent a significant contribution to line broadeninq effects. The remaining field dependent AF=l, Am=o,

**t**

### 1 transitions were used to determine the magnetic field strength. The lineshape of the "field independent" transition is dominated by the pulsed laser excitation sheme. If T is the time between two.conse- cutive laser pulses, the well known theory for a two level system predicts for the transition probability

### where

**w**

### is the microwave frequency , uo the transition frequency and

**y **

### the transition rate, depending on the microwave power. In our case

### however the diameter of the ion cloud, which assumes a Gaussian

### density distribution/8/, is about 10 mm, smaller than the laser beam

*C8-342 * JOURNAL **DE PHYSIQUE **

**diameter (4 mm). Thus there is a chance for an ion to escape one or ** even more laser pulses and extend his free interaction time with the microwave field to multiples of T. Consequently the total transition probability is given by

### The constants ak become rapidly smaller with increasing k and are determined only by geometry. Throuqhout our analysis of the observed transitions we found that n= 5 was sufficient to fit all the data.

### Normalising to .Eak=l we found al=0.781, a2=0.156, a =0.039, **3 **

### a4=0.016, a =0.008. These values were held constant throughout the 5 whole analysis. In addition we had to add a small term

### 2 2 b

**exp**

### {-(w-wo) /

**y**

### >

### to the transition probability to account for spatial variation of the microwave power over the trap volume. Finally ion loss was assumed to be linear, since the storage times of many hours far exceeded the averaging time of a few minutes for one line. With this lineshape formula we found excellent agreement to all the observed transitions within our limits of error. Fiq. 3 shows an example of a 137 l 3 a ' line which was taken with high spectral resolution (.6 Hz per point) at a

### laser repetition rate of 16 Hz.

**8 ****037 ****741 ****982 ****HZ **

**Frequency **(Hz)

### Fig. 3: F=1, m=o - F=2, m=o Hyperfine transition in 137~a+. Laser

### repetition rate was 16.6 s -1 , averaging time 15 s per point,

### microwave frequency steps .6 Hz. The full line represents

### the theoretical lineshape according to the formula given in

### the text. Statistical uncertainty of the line center (one

### standard deviation) is .07 Hz

### The width of the central maximum depends linear on the laser repeti- tion rate. Even at repetition rates of 1 Hz we found a FWHM of 0.87 Hz in the "field independent" transition (fig. 4) and no indication of relaxation broadening.

**voo **= **7 183 340 594.908 **

**(0,013) ****HZ **

### Fig. 4: "field independent" transition in 135 ~ a + . Laser repetition rate 1 ,-I, averaging time 30 s per channel, microwave steps

### .1 HZ

**LL **

**0 ** **80 160 ****240 ****120 **
**7 ****163 140 ****594 ****Nz **

**Frequency ****(HZ) **

### The limitations in accuracy in our experiment were mainly given by the applied fields and the available equipment. We varied the magnetic field between .2 and 2.5 G. To obtain a decent rate of

### information we operated the laser typically at 10-20 Hz, thus limiting the spectral resolution of the transition. The extrapolation to zero maqnetic field according to the Rreit-Rabi-Formula (fig. 5) shows an uncertainy of .23 Hz for 137 Ba+ and .40 Hz for 135 Ba+. Variation of the electric field changes the potential depth of the trap and

### Fig. 5: Magnetic field dependence of the F-1, m=o -

^{F = 2 , }### m=o transition in 137 ~ a - . The magnetic field was determined by several AF=l, Am=o,

**2**### 1 transi- tion. Full line: Breit Rabi Formula fitted to the experimental points.

**Magnetic fleld (lW4Tesla) **

### C8-344 JOURNAL DE PHYSIQUE

### accordingly the ion temperature. This leads to a shift from the second order Doppler effect combined with a possible Stark shift. The contribution of the latter however is assumed to be very small.

### Experimentally we found fluctuations of the transition frequency at different operding points, which exeeded the expected statistical variations (fiq. 6) .

### Fiq . ^{6 }

^{: }

### "field independent"

### transition frequency

I

### at different values of trap potential well depth.

I

**10 ** **20 ** **30 ** **40 **

**Potentlol Depth ****(ev) **

### As a possible explanation we consider temperature chanqes of the ion cloud even at the pulsed laser operation (duty cycle 5.10-*), since in the course of the experiment the time for a run occasionally exeeded several hours and we had no control about the proper tuning of the unstabilized laser wavelenqth. Estimate of the possible effect qive significant tenperature chanqes after several hours and at reasonable laser mistuning/lO/. Experimentally we found

### 6v/v

= (### -2,s + 1.1) x ~ o ' ~ ~ * D , if

**D**

### is the depth of the trapping potential. Extrapolation to zero electric field results in an error of

### .27 Hz. We operated the trap at rest qas densities of about rrbar in order to trap a sufficient nunber of ions. Once the ions are trapped, the qas could have been revoved. IIowever, since a possible pressure shift of the hyperfine transition according to the known data/ll/ is 6v/v = 6 10-l3 and collisional relaxation rates between the Hfs levels obviously is smaller than 1 sec-' (corresponding

* IY * <

### 2.10-l6 cm 2

) ,### we maintained this pressure during our measurements,

### since it increased the siqnal to noise ratio by collisional deexcita- tion of the long living metastable D-state. The final results for both ~ a + isotopes are listed in table 1. Further improvement in accuracy is easily possible by more careful determination of the electric and maqnetic field dependence of the "field independent"

### line. Limitations in line-Q by collisional relaxation may be esti- mated from our measurements: Since at mbar we obtained about

### v/Au

=### one may easily gain 3 or 4 orders of magnitude by oper-

### ating at UHV pressures. Tde did not extend our measurements into that

### range, since the stability of our available crystal oscillators was

### to poor to obtain the required resolution.

### Tqble 1: Ground state hfs separation of Ra isotopes. All frequencies +

### are given in Hz.

**r **

### Isotope

### 13 7Ba+

### 1 3 5 ~ a +

### The short term frequency stability (Allan variance 6f/f) of this syster. operated in feedback rode as a frequency standard can be estimated. The optimum feedback siqnal is obtained if the frequency is chopped between the opposite points of maximum signal change of the resonance curve. For this case we have 6f/f

=### 3/4 1/Q . ^{l/SNR }

### where **Q is the quality factor wo/6w of the line and SNR the signal to ** noise ratio. Taking fig. 4 as an example, where we have SNR=100 at 30s averaqing time, we obtain 6f/f

= ### 5-10-l2 t-ll2. This is in the same reqion as the short-term stability of commercial available Cs stan- dards. Technical improvements on the siqnal to noise ratio are easily possible if one considers the poor solid angle of our optics of 2

%### and the quantum efficiency of our photomultiplier at 650 nm of about 1

%.### In addition the succesful demonstration of optical side- band cooling/7/ indicates that the main source of error, the second order Doppler effect, may he reduced by several orders of magnitude.

### This work was supported by the Deutsche Forschungsgemeinschaft.

### 2A

### 8 037 741 667.69 7 183 340 235.53

### References

### /1/ **W. ** Neuhauser, M. Hohenstatt, P. Toschek and H. Dehnelt.

### ~ p p l . ~ h y s . **17, ** 123 (1978)

**17,**

### /2/ D.J. Wineland, R.E. Drullinqer and F.L. Walls, Phys. Rev.Lett.

### 40, 1936 (1978)

### -

### /3/

D . J .### :Vineland, Proc. 2nd Conf . on Precision Measurements and

### Fundamental Constants, Gaithersburq, 1981 /4/ R. Rlatt and **G. ** Werth, Z.Phys. A 299, 93 (1981)

### /5/ w. Recker, R. Blatt and G. "Jerth, Proc. 2nd. Conf. on Precision Measurements and Fundamental Constants, Gaithersburg, 1981 /6/ H.G. Dehmelt, Adv.At. and Mol.Phys. *3 , * ^{5 3 } ^{(1976) }

^{5 3 }

### statistic.

### uncert. of line center

### c.1

### <.1

### error of magn. extra- polation

### .23 .

^{(0 }### error of pot.

### depth extrapo- lation

### .27 .25

### total error

### .37

**- 4 7**

JOURNAL DE PHYSIQUE

**/7/ ** **J.F.J. ** **Todd, **

**G.**

**Lawson and R.F. Ronner in: Quadrupole Mass Spec- ** **trometra (P ** **.H. ** **Dawson ed **

.) ### , **Elsewier, Amsterdam 1976 **

**/8/ H. ~ c h a a f , **

**U.**

**Schmeling and G. Werth, **

**b p p ~**

**.Phys. 25, 249 (1981) ** -

**/9/ R. Schneider and G. Werth, Z.Phys. ** **A ** **293, 183 (1979) ** **/lo/ **

**J.**