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Appl. Phys. B 68, 1109–1116 (1999) / DOI 10.1007/s003409901498

Applied Physics B Lasers and Optics  Springer-Verlag 1999

Electrical conductivity of glass and sapphire cells exposed to dry cesium vapor M.A. Bouchiat1 , J. Gu´ena1 , Ph. Jacquier1 , M. Lintz1 , A.V. Papoyan2 1 Laboratoire Kastler Brossel∗ , D´ epartement de Physique de l’Ecole Normale Sup´erieure, 24 Rue Lhomond, F-75231 Paris Cedex 05, France (Fax: +33-1/45-35-00-76, E-mail: [email protected]) 2 Institute for Physical Researches, Ashtarak-2, 378410, Armenia

Received: 4 November 1998/Published online: 7 April 1999

Abstract. We demonstrate that the walls of glass cells become electrically conductive when exposed to a dry cesium vapor, glasses of different compositions leading to similar effects. We find dramatically different results for monocrystalline sapphire cells, which exhibit typical resistances of a few GΩ, nearly five orders of magnitude larger than glass cells in similar conditions. In spectroscopy experiments requiring the application of an electric field, low cell resistances imply leakage currents generating stray magnetic fields. The latter, at the origin of harmful effects in precise tests of the fundamental laws of physics performed in cesium cells, will thus be suppressed in sapphire cells. Moreover, with such cells it becomes possible to place the electrodes outside. A tentative interpretation of the surface electrical conductivity of glass cells is propounded by establishing a connection with the surface coverage by cesium atoms physically adsorbed on the glass surface. This results from the observed dependences of the cell conductance versus Cs vapor density in the mtorr range and versus the wall temperature up to 200 ◦ C, which indicates an activation energy of 0.66 ± 0.05 eV. In the sapphire cell, where there is no hint of surface effects, the conductivity looks instead attributable to collisional processes occuring inside the vapor for Cs number densities & 1014 at/ cm3 . PACS: 35; 42.80; 32.60 S; 73.25 Alkali atoms, and more particularly cesium and rubidium, have always been of large use in atomic and laser physics experiments and are of considerable interest in experiments for precise tests of the fundamental laws of physics [1–3]. To improve the sensitivity of such experiments, one has to push the technology to the limit. At the moment there are two different experimental approaches, one using atomic beams [4] and the other a vapor inside a glass cell [5, 6]. Whereas the first has the advantage of dealing with an ensemble of atoms ∗ Laboratoire

de l’Universit´e Pierre et Marie Curie et de l’ENS, associ´e au CNRS (URA18)

essentially free from wall interactions, the second gives access to very high atomic densities and total numbers, otherwise unachievable in beam or even trap experiments. Consequently the understanding and reduction of wall effects remains a problem of actuality. One of the most troublesome but also most intriguing features of the interaction of an alkali vapor with a glass wall is the fact that the walls exposed to such vapors become electrically conductive. In all experiments that make use of a dc electric field, this cell conductivity gives rise to leakage currents, and hence stray magnetic fields, the directions of which reverse with the applied electric field [6, 7]. This is a source of systematics difficult to control. In the present work, we study the conductivity of cells filled with cesium vapor without a buffer gas. The Cs reservoir side arm is maintained at a temperature TR lower than the wall temperature TW of the main body of the cell (TW − TR ≥ 15 ◦ C). Hence there is no condensation of cesium on the walls, which are exposed only to the dry cesium vapor. This implies that the “cesiated” walls and the vapor are in thermodynamical equilibrium. It is known that substantial amounts of the alkali can be adsorbed inside the glass, even at room temperature. At 300 ◦ C the rapid appearance of a brownish coloration is characteristic of the irreversible reduction of silicon dioxide by the alkali which produces a thin layer of silicon [8]. However, for the measurements reported here, we always kept the temperature below 200 ◦ C where no change in the appearance of the cell could be noticed. To measure the conductivity, we have implemented a simple method using capacitive coupling between the outer and the inner walls, which can be applied in any cell, not just those specially designed for this purpose. In this paper we present the results obtained for glasses of different origin and composition which have actually shown up great similarity. We have also studied the effect of the temperatures TR and TW in the range 150 ◦ C < TW < 200 ◦ C. The most interesting results of our work are those concerning monocrystalline sapphire cells filled with rubidium or cesium. In the same temperature range we observe results drastically different from those obtained in glass cells: the electric conductivity is reduced by nearly five orders of magnitude. We believe that

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such results will prove of considerable importance for all the experiments in which leakage currents have been for a long time the source of a serious trouble. 1 Manifestation of the electrical conductivity We first encountered the problem with cesium cells having electrical feedthroughs to internal electrodes [9]. With such cells one can measure the resistance very easily, simply by using an ohmmeter. We have used, for example, cylindrical glass cells1 (50 mm diameter) with ring electrodes held in place by a multitude of small springs made from a metallic mesh (see Fig. 1 and [9]), which increase their surface of contact with the walls. The electrode-to-wall contact resistance was then particularly low. The resistance measured between the springs of two adjacent ring electrodes, 6 mm apart, was only 2 kΩ at TR = 150 ◦ C and TW = 185 ◦ C (temperatures used in our current PV experiment [5]). We note that the resistance between the extreme electrodes was very close to the sum of the successive interelectrode resistances. The higher the vapor pressure is, the lower the resistance becomes. By contrast, if the electrodes have no other contact with the glass wall than the feedthrough itself (without springs), the measured resistance is typically one order of magnitude higher. Therefore, despite its dependence on Cs pressure, the low resistance between two multicontact electrodes cannot be attributed to the vapor itself, but rather to a surface process taking place on the cesiated glass wall. Knowing the geometry, we can determine the square resistance of the cesiated glass wall, typically R2 ≈ 40 kΩ.

Fig. 1. View of the cell providing a longitudinal electric field for the PV experiment

2 A simple method of measurement Our primary goal was to search for a material having a very low surface conductivity in the presence of cesium. In order to perform many trials with different materials it was important to find a method of measurement that is rapid, inexpensive and convenient, in particular one which does not require internal electrodes. The idea consisted in capacitively coupling the outer side of the cell to the inner side. The inner surface whose resistance is to be determined can thus be inserted in an electronic circuit whose Bode diagram (i.e. impedance versus frequency) we measure. The capacitive coupling has been realized in two different ways. The first consists of applying a thin layer of silver paste on two delimited areas of the outer cylindrical surface of the cell, which serve as electrodes facing each other (Fig. 2a). In the second we wrap tightly around the tube two metallic ribbons about 5 mm wide separated by one to several centimeters (Fig. 2b). (A thin mesh of stainless steel was found to be convenient to use and easily removable, in contrast to the silver paste which stuck to the glass after a few hours at about 200 ◦ C). Both methods, although they correspond to quite different geometries, led to similar conductivity results. The equivalent circuit is schematized in Fig. 3. The two capacitors in series which connect the electrodes to the inner surface are replaced by the single capacitance CW , while 1 The chosen borosilicate glass, Schott 8250, has the advantage that it can be directly soldered to molybdenum rods conveniently used as feedthroughs.

Fig. 2a,b. Schematic views of the two types of capacitively coupled cells used in the conductivity measurements. Potentials are applied a on two patches of silver paste; b on two external rings of stainless steel mesh

Ci represents the interelectrode capacitance, typically 3 < CW /Ci < 20. The resistance, RCs , in parallel with Ci , receives two contributions: the resistance of the inner wall, RW , and the resistance of the Cs vapor, Rvap . Hence we write: −1 −1 −1 RCs = RW + Rvap .

In principle, there is also the bulk resistance of the glass and the resistance of the external surface of the cell connecting directly the output to the input of the circuit. However, this was measured to be higher than 100 GΩ and will be omitted here. The general expression for the impedance of our circuit is: Z=

1 + jωRCs (CW + Ci ) . jωCW (1 + jωRCs Ci )

When the frequency is increased we can distinguish three regimes, clearly apparent on the expected Bode diagram,

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Fig. 3. Circuit diagram equivalent to the cell for conductivity measurements. The resistances and capacitances involved are defined in Sect. 2

shown on Fig. 4a: (i) At low frequencies (ω  1/RCs CW ) both capacitors block. The circuit behaves nearly like the capacitor CW alone. Then Z ≈ 1/jωCW . (ii) At intermediate frequencies (1/RCs CW . ω . 1/RCs Ci ), the capacitor CW passes while Ci still blocks, the circuit behaves nearly like the pure resistance RCs . In particular, if this domain is sufficiently wide the phase almost cancels. (iii) At high frequencies (ω  1/RCs Ci ), both capacitors pass and the resistance is short-circuited by Ci . The circuit is again equivalent to a pure capacitor, but now has the impedance Z ≈ 1/jωCi + 1/jωCW . In order to measure the impedance, the circuit is driven by a generator tunable between 1 Hz and 6 MHz with 10 V rms voltage output. The frequency range where there is a clear manifestation of RCs is such that ωRCs CW ≈ 1, with CW ' 5pF, that is: 5 kΩ . RCs . 30 GΩ . This turns out to coincide with the interesting domain for studying our cesium cells. For detection we use a lock-in amplifier (EG&G model 5206) operating up to 20 kHz. At higher frequencies, measurements were performed using a digital oscilloscope in averaging mode. In order to avoid stray capacitances all the leads were kept short, far apart, and far from other conducting bodies. In addition, we avoided the use of coaxial cables. We were also careful to make the oven sufficiently large in order to avoid stray capacitances between the cesium cell and the metallic parts of the oven. A typical Bode diagram obtained for a glass cell is shown on Fig. 4b, together with the best theoretical fit. With Schott 8250 glass, we were able to compare the square resistance obtained by capacitive coupling in cells without internal electrodes (42 kΩ), to that measured with an ohmmeter (39 kΩ) for a cell with internal electrodes. The good agreement validates the method of measurement based on capacitive coupling. 3 Results: high electrical conductivity of glass cells 3.1 Comparison between different materials We first compared the conductivity results obtained in cells made of different kinds of glass, the Schott 8250 glass, Pyrex, and fused silica (Heraeus, both standard Suprasil and Suprasil 300 whose OH− content is 1000 times less). Once the equilibrium value of RCs was reached, which required more or less

Fig. 4. a Theoretical Bode diagram (modulus of the impedance Z vs. frequency ω/2π in log coordinates) for the circuit represented in Fig. 3 with values of the parameters: RCs = 1 MΩ, Ci = 1 pF, CW = 50 pF. b Example of an experimental Bode diagram for a glass (Suprasil 300) cell with cesium recorded at TR = 317 K, TW = 451 K. Experimental points (black diamonds) and best fit (solid line) with fitted values RCs = 430 kΩ, Ci = 1.4 pF, CW = 9 pF

time depending on the nature of the glass, the results obtained in all cells at TR = 150 ◦ C and TW = 180 ◦ C were found to be quite similar. We also tried a glass cell coated with a sol-geldeposited silica coating2, but did not notice any difference. 3.2 Dependence on TR and TW We have performed two kinds of studies. We have varied the wall temperature TW at a constant value of the reservoir temperature TR and varied TR at a constant wall temperature. In the latter case the cesium number density, NCs , in the upper part is a well-known function of TR [10]. Moreover, according to the law of mass action, the density of dimers varies quadratically with NCs as long as TW is kept constant. We describe first the influence of the wall temperature at a fixed value of TR . Figure 5a presents the conductance of a Suprasil 300 cesium cell. The very fast decrease observed 2

We are grateful to J.Cl. Plenet and his collaborators (DPM, Universit´e Claude Bernard, Lyon I) for preparing this coating.

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when the wall temperature increases is typical of the desorption of the Cs atoms on the walls. Physical adsorption is characterized by the fact that during the process the adsorbed atom and the adsorbant retain their individuality. When an atom gets near the wall, its motion is determined by longdistance attractive forces and electrostatic repulsive forces. This determines its dwell time on the wall, τS . One can show that τS = τ0 exp(E a /kTW ), where τ0 is of the same order of magnitude as the time of vibration of the atoms of the adsorbant and E a is the adsorption energy [11]. One sees that τS decreases when TW increases, and hence so does the fraction θ of the surface covered with adsorbed atoms. The rapid −1 simultaneous decrease of RCs suggests a possible connec−1 tion between RCs and θ. For this reason we examined the possibility of a proportionality relationship between the sur-

Fig. 5a,b. Glass cell (Suprasil 300) filled with cesium. Variations of the −1 measured conductance RCs a vs. wall temperature TW at fixed reservoir temperature TR = 368 K; b vs. cesium vapor pressure (variation of TR ) at fixed wall temperature TW = 465 K. Due to the geometry, the square resistance is ≈ 4.35 times the measured resistance. In a black squares are the experimental points and the solid line is the fit √ by the sum of a term following the law expected from (1), exp(E a /kTW )/ TW , and a small off−1 set = 0.006 kΩ . In b squares and triangles are the experimental points obtained at increasing and decreasing pressures, respectively. A hysteresis effect is conspicuous. The solid and dotted lines represent fits by expresPCs /P1 sions of the type: a 1+P /P + bPCs (bi-Langmuir isotherm [15]) Cs

1

face conductivity and the number of atoms adsorbed per unit area [11]: n ads =

1 NCs (TR , TW )hv(TW )iτ0 exp(E a /kTW ), 4

(1)

where hv(TW )i is the average Cs atom velocity in the vapor. Note that (1) is based on the assumption that θ  1 and that E a is uniform over the whole surface. Figure 5a represents the results of the conductance measurements together with the TW dependence predicted by the right-hand side of (1). We find that the latter actually matches the experimental data nicely. The solid line is the best fit obtained with E a = 0.66 ± 0.05 eV, a fairly large, though not unreasonable value3 . Measurements performed at a lower reservoir temperature (TR = 333 K) have led to quite similar results. One can note in Fig. 5a that, at the highest tempera−1 tures explored, RCs tends to become independent of TW . This is why we allow for a slight offset in the fitting curve (fitted −1 = 0.006 kΩ−1 ), whose possible origin will be disvalue RCs cussed below. We have to remark here that, strictly speaking, the value of E a extracted from the fit represents the activation −1 , not of n ads ; the electrical conduction process energy of RCs might possibly involve an additional activation energy not affecting the adsorption process. Let us now consider the adsorption isotherms presented on Fig. 5b where the measured conductance is plotted versus the vapor pressure PCs at TW = 465 K. We first note that there is a hysteresis: the isotherm observed at decreasing PCs clearly lies above that taken at increasing PCs . This is so in spite of the long period of time allowed between two measurements (at least a few hours). We also observe a noticeable departure from a linear regime at the very low pressures with a concave curvature. This is expected in the case of heterogeneous adsorbants, characterized by the presence of sites having different adsorption energies [11]. If there are active sites with a larger adsorption energy, even in small proportions, these are occupied preferentially since the trapping time is locally the longest. They influence the shape of the adsorption isotherms at lower densities by adding a second contribution on the right-hand side of (1) which presents a rapid saturation versus PCs [15]. In addition, the atoms trapped in those sites might be responsible for the slight offset noticed in Fig. 5a: even when the walls are heated up those atoms cannot desorb easily. As for the observed hysteresis, it may result from the fact that a certain amount of cesium penetrates inside the glass and dissolves into the material beneath the surface. This process, known as swelling, is frequently met for porous media and is known to occur for cesium adsorbed on inorganic surfaces [11]4 . Because the diffusion constant inside the solid is very low and pressure-dependent, the time constants required for the atoms to reach an equilibrium distribution can be very long and are longer for desorption than for adsorption [15]. 3

For comparison a measurement of the adsorption energy of cesium on Pyrex using an optical method has given 0.53 ± 0.03 eV [12]. By contrast, for optically oriented rubidium atoms colliding on paraffin wall coatings an adsorption energy of 0.1 eV was extracted from the temperature dependence of the spin relaxation time [13]. 4 In organic substances swelling effects can be much stronger, as has been spectacularly demonstrated for silane-coated cells filled with different alkali vapors [14].

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In order to interpret the shape of the isotherms of Fig. 5b we are finally led to assume that, in addition to the largely dominant contribution coming from low binding energy sites, responsible for both the rapid TW variation of Fig. 5a and the linear asymptotic variation of the isotherm, there is also a contribution coming from a small fraction of high binding energy sites. Their characteristic energy E a ≈ 0.85 eV can be roughly extracted from the curved region of the isotherms of Fig. 5b at the lowest PCs values explored. In all other TR and TW temperature ranges studied these sites have a near unit probability to be occupied and they provide a constant −1 as well. One can note a semicontribution to θ and to RCs quantitative agreement between the value at which the lin−1 early dependent contribution to RCs intercepts the vertical axis in Fig. 5b and the offset observed on Fig. 5a at the highest temperatures, about 0.006 kΩ−1, both representing the contribution of the high binding energy sites once saturated. 3.3 Discussion Our results indicate a proportionality of the electrical conductivity of the glass walls to the fraction θ of the surface covered by adsorbed Cs atoms. We now address the question of the orders of magnitude. First we give an estimate of the surface coverage θ, making the assumption that the empirically determined activation energy of the conductivity represents the adsorption energy. Then we attempt to relate the wall conductivity to θ. 3.3.1 Estimation of the surface coverage. The number of atoms adsorbed per unit area can be computed from (1) in which we substitute the values of the experimental parameters for TR = 368 K, and TW = 383 K: PCs = 0.41 mtorr, NCs = 1.0 × 1013 at/cm3 , hvi = (8 kTW /π m Cs )1/2 = 3.3 × 104 cm/s, and τ0 = 10−13 s (according to the prescription of [11]). We make use of the adsorption energy value, E a = 0.66 eV, deduced from the observed TW dependence. We thus obtain: n ads = 4.0 × 1012 at/cm2 .

(2)

This is to be compared to the surface density expected for complete coverage (θ = 1): n 0 = 1/1.57 d 2 = 2 × 1014 at/cm2 ,

(3)

where d is the atomic diameter (5.9 Å), and the numerical coefficient 1.57 corresponds to hexagonal close-packed arrangement [11]. We obtain: θ = n ads /n 0 = 2.0 × 10−2 . In fact taking into account the uncertainty in the determination of E a the result we can infer at TR = 368 K, TW = 383 K is: 5 × 10−3 . θ . 10−1 .

(4)

Keeping the central value, we see that the range of θ covered by varying TW from 373 K to 483 K is 10−3 to 2 × 10−2. 3.3.2 Theoretical estimate of the surface conductivity. Let us consider the electron gas constituted by the free electrons

present in the film of adsorbed Cs atoms. We shall adopt the usual description of the electrical conductivity given in textbooks [16]. Let us introduce the correlation time τ of the electron velocity. By the application of the field E for the time duration τ the incremental velocity acquired by the electrons in the E direction is v = −e E τ/m e . The current density can be written: j = −Ne e v, where Ne is the electron density. Therefore: j = Ne e2 τ E/m e

(5)

and the electrical conductivity σ follows from its definition, j = σE: σ = Ne e2 τ/m e .

(6)

This formula applies both for a Boltzmann and a Fermi distribution of electrons [16]. If we consider a square sheet of thickness d and side L its resistance is obtained from R2 = σ −1 L/Ld = 1/σd, hence: th R2 = m e /(e2 Ne d τ) .

(7)

We now consider the case of an atomic monolayer of thickness d and coverage fraction θ. If θ is sufficiently close to 1, the valence electrons constitute a degenerate free electron gas so that we can write Ne = n ads /d = θ/(1.57 d 3). We can assume that the correlation time is τ = l/vF , where l = 1/(n ads )1/2 is the average distance between two adsorbed atoms and vF the Fermi velocity which we can express in the two-dimensional sheet as: vF = ( mhe )(2π n ads )1/2 . Finally we deduce: th R2 ≈ (2 π)1/2

h = 10.3 kΩ . e2

(8)

We note that this result does not involve the charge density, hence θ, as long as the electron gas is degenerate. In the submonolayer coverage regime, however, it is no longer correct to assume that the conduction electrons obey Fermi statistics, since they are, on average, too far apart. This means that for the small values of θ at which our measurements take place (7) does not provide a correct description. At the lowest TW values (largest θ) explored, the de Broglie wavelength of the electrons, λdB = 6 Å, is already smaller than the interatomic distance l ≈ 40 Å. The Cs atoms in the low binding energy sites can thus be considered as isolated. Even without making any definite assumptions on the origin of the conduction in this case, it is interesting to compare our experimental results with the prediction given by (7). −1 The proportionality of RCs to n ads , observed experimentally (Figs. 5a and 5b), means that the product Ne dτ is proportional to θ, as opposed to what occurs at θ ≈ 1. Hence it is very likely that for small values of θ the correlation time becomes θ-independent. If we make the assumption that we still have −1 Ne = n ads /d = θ/(1.57 d 3 ) then, from the value of R2 /θ observed in the range 373 K . TW . 473 K, corresponding to the coverage domain 10−3 . θ . 2 × 10−2, we deduce a velocity correlation time τ ≈ 4 × 10−14 s. In summary, the electrical conductivity of glass walls exposed to a dry Cs vapor does not result from an irreversible transformation of the walls but from a thermal equilibrium between the walls and the vapor, giving rise to the formation

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of a submonolayer of atoms and to a slow penetration of the alkali in the glass surface underneath. We can account for the observed conductivity if we assume the existence of a twodimensional gas of electrons having the density of adsorbed atoms and a velocity correlation time of about 4 × 10−14 s. To conclude we wish to note a striking similarity between the effect observed here and the photoelectric emission of cesium atoms adsorbed on salt surfaces [17]. In the latter case, for small θ, the photoelectric current has been found to increase linearly with θ and the emitted electrons come from isolated adsorbed Cs atoms. One possible interpretation is therefore that here the conduction electrons are produced by thermionic emission of the isolated adsorbed cesium atoms, whose ionization energy is known to be considerably lowered compared to free atoms [17]. The electrons can hop from one ion trapped on the surface to another. However, a collective conduction process can also be invoked. The thermally excited electrons could contribute to the conduction band of the glass which would behave as a doped semiconductor with a donor density linear in θ. 4 The ultra low conductivity of monocrystalline sapphire cells The sapphire cell used in our measurements, manufactured by the Institute for Physical Research in Ashtarak, Armenia, is a cylindrical tube of monocrystalline sapphire, closed by two YAG windows glued on the tube. This latter non-birefringent material was chosen with future applications in mind. The tube has diameters of 10 mm (internal) and 13 mm (external) and is 83 mm long. The internal surface of the tube was coarsely polished (roughness ≤ 20 µm). The side arm which contains the cesium is perpendicular to the main cell body and located midway along the length. The assembling techniques have been reported previously [18]. The behavior of cesium in this monocrystalline sapphire cell has been found to be in stark contrast with what happens with all glass cells: its Bode diagram, represented on Fig. 6, exhibits a point of inflexion at frequencies as low as 30 Hz, instead of the several MHz observed at similar temperatures TW and TR in the glass cells. Analysis of the data, assuming surface conductivity, yields a square resistance equal to 2 GΩ, i.e. nearly five orders of magnitude larger than the 8250 Schott glass cell resistance reported above. All data were reproducible over a long period (≈ one month). A similar result has been obtained in a monocrystalline sapphire cell filled with rubidium: at TR = 180 ◦ C and TW = 190 ◦ C we obtained 0.5 GΩ, instead of R2 ≈ 40 kΩ for a Pyrex cell of rubidium at the same temperatures. The electrical conductivity of the sapphire cesium cell is actually so low that it makes sense to wonder whether the remaining conductivity is indeed a surface effect or whether it arises instead from the electrical conductivity of the cesium vapor. At a fixed temperature of the upper walls, TW = 190 ◦ C, we have studied the variations of the −1 cell conductance RCs versus TR , hence versus the Cs number density, NCs , which was varied over one decade (see Fig. 7a). The results exhibit a rapid rise which can be fitted by a cubic law. −1 The dependence of RCs versus TW in the range 150 − ◦ 200 C has also been measured at a nearly constant cesium

Fig. 6. Example of an experimental Bode diagram for a sapphire cell with cesium registered at TR = 421 K, TW = 463 K. Experimental points (black diamonds) and best fit (solid line) with fitted values RCs = 3.3 GΩ, Ci = 0.34 pF, CW = 5.5 pF

density (NCs ≈ 1.0 × 1014 cm−3 ), as shown in Fig. 7b. It is clear that both curves in Fig. 7 differ markedly from the corresponding ones obtained for glass cells (Fig. 5), not only by the magnitude of the plotted conductances but also by their general appearance. For the sapphire cell, it seems very −1 versus TW as arisdifficult to interpret the variation of RCs ing from a decrease in the number of adsorbed Cs atoms on the walls when they are heated up, because the adsorption energy required to explain the observed effect would be much too large to be compatible with the drastic conductivity decrease observed between glass and sapphire. On the other hand, this behavior might be connected with the decrease in the density of dimers contained in the vapor under the effect of wall heating. We note that, at the highest TW values explored, heating becomes no longer effective despite the fact that the dimer density continues to decrease. Hence dimers cannot explain the dominant contribution to the electrical conductivity.We arrive at the conclusion that −1 the very rapid dependence of RCs versus TR is likely to be related to an atomic process taking place inside the vapor. Moreover, the (NCs )3 increase can be associated with the charge multiplication process which occurs in the well-known energy-pooling collisions [19]. Let us illustrate this for the kinds of collisions which, in the case of Cs have the largest probability: Cs(6S) + e → Cs(6P) + e Cs(6P) + Cs(6P) → Cs(6D) + Cs(6S) Cs(6D) + Cs(6P) → Cs+ + e + Cs(6S)

(9) (10) (11)

Several other similar processes have been reported. They involve the 7P, 8S, and 4F excited states instead of the 6D state [20]. According to the above scheme, and analogous ones, the liberation of one additional electron requires three successive interactions of a ground state Cs atom with three initial electrons: hence the associated multiplication rate grows proportionally to (NCs )3 . More experimental work will be necessary to reveal the exact origin of

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or parity violation measurements [6, 7], have used electrodes placed inside the cell, in spite of all the technical difficulties which must be overcome. The electrical conductivity of the cell is obviously the key parameter which prevents one from creating a dc electric field inside the vapor when the electrodes are placed outside: as is well known, it is not possible to create a static electric field inside a hollow conductor! In spite of its low conductivity described above even the monocrystalline sapphire cell cannot break this rule. A loophole exists, however, if instead of a steady electric field we now consider a repetitively pulsed one. Refering to the test cell of Fig. 2b, and its equivalent circuit (Fig. 3), the response of the voltage across the interelectrode capacity Ci to an input step voltage is characterized by the damping time constant τd = RCs (CW + Ci ). With typical values CW = 5.5 pF, Ci = 1 pF for a cell diameter of 10 mm and an electrode spacing of 10 mm we obtain τd = 60 ns for glass (RCs = 10 kΩ) but 5 ms for monocrystalline sapphire (RCs = 0.8 GΩ). For our own experiment which happens to require a pulsed field this makes a big difference. Indeed the laser excitation of the vapor during which the electric field needs to remain constant lasts only 18 ns [7]. With a glass cell this is is still too long to use external electrodes. With a sapphire cell, however, it now becomes possible to place electrodes on the outside. The Bode diagram of Fig. 6 indicates for instance that there will be no dropping of the interelectrode voltage and field when a squared voltage pulse is applied for 100 ns, a time interval exceeding the needed duration. Following this principle, a system of external electrodes is presently being assembled and will be soon employed in our parity violation experiment. 6 Conclusion

Fig. 7a,b. Sapphire cell filled with cesium. Variations of the measured con−1 ductance RCs a vs. the atomic number density of the vapor, NCs , at fixed wall temperature TW = 458 K; the solid line is a fit to the experimental points by the sum of a constant term, 1/(22 GΩ) = 0.045 GΩ−1 and a cubic term. b vs. wall temperature TW at fixed reservoir temperature TR = 409 K (NCs ≈ 1014 at/cm3 ); the solid line is a guide for the eyes. The resistance is measured for a cylinder of length L = 65 mm and diameter 10 mm in the geometry of Fig. 2b

the initial electrons (possibly thermionic emission, or ambient radioactivity). The noteworthy result is that in sapphire cells this density-dependent conductivity appears to mask that of the wall. The most likely interpretation is that the adsorption energy of the cesium atom on the monocrystalline sapphire walls is much smaller than it is on glass walls. At present, however, we cannot rule out that this may arise from a difference in the nature itself of the conduction processes for monocrystalline sapphire and glass walls.

5 Practical implications for applying a Stark field inside an alkali cell Up to now, experiments on alkali vapors requiring an electric field, such as searches for a static electric dipole moment

Our experimental results emphasize the drastic difference of behaviors exhibited by monocrystalline sapphire and glass cells exposed to a dry vapor of cesium or rubidium. For glass cells, we have been able to relate the temperature variations of the electrical surface conductivity of the cell to the presence of a submonolayer film of cesium atoms. The temperature variations of the conductivity have been used to obtain the activation energy ≈ 0.66 eV. By contrast in monocrystalline sapphire cells the electrical conductivity is smaller by up to five orders of magnitude in conditions typical of our PV experiment (TR = 150 ◦ C and TW = 180 ◦ C). In actual fact, we could find no indication whatsoever of wall conductivity. However, when the cesium density exceeds 1014 at/cm3 the resistance of the cell drops rapidly at a rate proportional to the cube of the cesium number density, this effect being attributable to conductivity of the vapor itself. Nevertheless, even if the variation is extrapolated to 1015 at/cm3 we are still left with a resistance in excess of 10 MΩ/cm, approximately 103 times larger than values typically encountered in glass cells. Several advantages of cesium cells made of sapphire have already been emphasized, in particular the very attractive possibility of controlling independently the number densities of the atoms and the dimers [21]. The additional advantage underlined here is also very important. For our Stark PV experiment in cesium using detection on a transmitted probe beam amplified by stimulated emission we need to operate

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at relatively large vapor pressures to take full benefit from the amplification of the probe intensity and the simultaneous amplification of the PV asymmetry [5]. Therefore, by suppressing the leakage currents circulating on the conductive glass walls, the sapphire cesium cells will provide a radical solution to the problem of the associated magnetic fields met with traditional glass cells and, what is even better, without requiring the complex construction of a sapphire cell with internal electrodes. Finally, we note that conductivity measurements open new perspectives for an experimental analysis of the alkalidielectric surface physics and for applications. Acknowledgements. We thank Dr. Daniel Bloch for the very helpful loan of a sapphire cell, and Romain Desrousseaux and Vincent Euzeby for their participation in the experiment. We are deeply grateful to Prof. David Sarkisyan and his group for the realization of sapphire cells of high quality. We gratefully acknowledge financial support from the DEPHY association, which made possible the visit to ENS of A.V. Papoyan, and from CNRS which allows us to pursue a collaboration.

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