Optically pumped alkali atomic beam frequency standard

[57] ABSTRACT

The frequency standard comprises an oven producing a beam of Rb⁸⁵ and Rb⁸⁷, a lamp using Rb⁸⁵ for enriching the level F = 1 of the fundamental state of the atoms of Rb⁸⁷, a hyperfrequency cavity equalizing the population of the levels F = 1, m_f- = 0 and F — 2, m_r = 0 of this state, a lamp using Rb⁸⁷ or natural Rb filtered by a vat containing Rb⁸⁵ for producing transitions between the levels F = 1 of the fundamental state and an excited level, and a detector completed by an electronic unit coupling a quartz oscillator to the atomic resonance.

Claims, 12 Drawing Figures

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PATENTED may 3 ο I9?z

3,667, 066

SHEET 1 GF 4

13

DETECTOR

113

FREQUENCY 33

CONTROL DEVICE

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AMPLIFIER \-8

7a

FREQUENCY SYNTHESIS DEVICE

PHASE

7b

LOW FREQUENCYX

MODULATOR

FREQUENCY MULTIPLIER

QUARTZ OSCILLATOR

5Mh

OJWf

<img file="US3667066A_D0003.tif" />

PATENTED MAY 3 Ο 1972

3,667,066

SHEET 2 OF 4

<img file="US3667066A_D0004.tif" />

<img file="US3667066A_D0005.tif" />

<img file="US3667066A_D0006.tif" />

PATENTED MAY 3 Ο 1972

3,667,066

SHEET 3 OF 4

<img file="US3667066A_D0007.tif" />

<img file="US3667066A_D0008.tif" />

PATENTED «ΛΤ 3 Ο 1973

3,667,066

SHEET 4 OF 4

<img file="US3667066A_D0009.tif" />

<img file="US3667066A_D0010.tif" />

3,667,066

OPTICALLY PUMPED ALKALI ATOMIC BEAM FREQUENCY STANDARD

This invention relates to atomic clocks or frequency standards using a beam of atoms; it is more especially concerned with clocks or frequency standards using a beam of alkali atoms and more particularly rubidium.

An object of this invention is to provide a standard or clock having a very great stability of frequency, especially in the long term, and constituting a primary or absolute standard of frequency, its resonance frequency being very near to the Bohr frequency of the free atom.

In accordance with this invention, an atomic clock or frequency standard, which uses a beam of atoms, in particular alkali atoms and more particularly still rubidium, comprising at least three levels of progressively increasing energy, namely two levels E, and E2 in the fundamental state and one level £3 in the excited state, is characterized by the fact that this beam of atoms passes, in a vacuum, successively through a zone of optical pumping in which it is illuminated by a source of nonpolarized radiation at a frequency corresponding to the interval of energy between one of the fundamental levels Ej or 1¾ and the excited state E₃, a radiofrequency cavity in which it is subjected to a magnetic field of frequency corresponding to the interval of energy between the levels E, and Ej of the fundamental state, and a zone of optical detection in which it is illuminated by a source of non-polarized radiation at a frequency corresponding to the interval of energy between the other level of the fundamental state 1¾ or E, and the excited level E3.

The invention will be well understood with the aid of the following complementary description and the accompanying drawings, which are, of course, given merely by way of example and other features and advantages will be apparent therefrom.

IN THE DRAWINGS

FIG. 1 represents schematically an atomic frequency standard or clock using a beam of rubidium, constructed according to this invention;

FIG. 2 is a longitudinal axial section through the rubidium oven of the clock of FIG. 1;

FIGS. 3 and 4 are cross-sectional views, respectively along lines III—III and IV—IV of FIG. 2 in the directions of the arrows;

FIG. 5 represents the energy levels of an atom of rubidium 87;

FIG. 6 represents the lines (or transitions) of atoms of rubidium 85 and rubidium 87 between the two levels of the fundamental state and a level of the excited state;

FIG. 7 illustrates the lines (or transitions) used in the rubidium clocks of the prior art;

FIG. 8 illustrates the lines (or transitions) used in the rubidium clock of FIG. 1;

FIGS. 9 to 11 illustrate the lines (or transitions) which can be used in three variants of the clock of FIG. 1, these variants also being constructed according to this invention; and

FIG. 12 represents the derivative signal obtained experimentally in the clock according to FIG. 1 with two separate radiofrequency cavities and with only a single radiofrequency cavity.

Before describing in detail a preferred embodiment of an atomic clock according to this invention, two known types of atomic clocks using alkali atoms will be discussed, namely the Rabi type atomic clock using a cesium beam and the clock using rubidium 87 vapor, as well as the physical principles which form the basis of these clocks of known type and of the atomic clocks according to this invention.

It is known that an atom, in particular an alkali atom, has a fundamental state S and excited states P, D, ... of increasing energy. For alkali atoms, the level of the fundamental state is called the level S_1Z2 and the first excited state has two levels P_1Z2 and P_3Z2 because of the fine structure which explains the double lines of the alkali atoms (such as the double line of sodium corresponding to the transitions between the levels P_1Z2 and P_3Z2 on the one hand, and the level S_1Z2 on the other hand). Moreover, due to the nuclear moment I of the atoms, the level S_1Z2 of the fundamental state and the level P_1Z2 are each divided into two levels of hyperfine structure F = I -½. and 7=/+½. whereas the level P_3Z2 is divided into four levels of hyperfine structure I — 3/2, / — Vt, 1 + ^/ + 3/2. Furthermore, in a continuous magnetic field H, of constant intensity H„, the different levels of energy are subdivided into Zeeman sublevels whose spacing is proportional to H_o in a weak field.

FIG. 5, which represents the energy levels of rubidium 87 (Rb⁸⁷), shows:

the fundamental state S_1Z2 which is in this case a state 5 ²S_1Z2, with its two levels 7=1 and 7 = 2, for the nuclear moment / of Rb⁸⁷ is equal to 3/2;

the first two excited levels 5 ²P1Z2 and 5 ²P3Z2 which are divided respectively into two levels 7= 2 and 7= 1 and into four levels 7= 0,7= 1,7= 2,7= 3;

the doublet (double line) 7,800 A, 7,947.6 A between the levels 5 ²P3Z2 and 5 ²SiZ2, on the one hand, and between the levels 5 ²P1Z2 and 5 ²S1Z2, on the other hand, respectively;

the hyperfine spacing, corresponding to the frequency of 6,834.6 MHz, between the levels 7=2 and 7 = 1 of the fundamental state;

and, on the right-hand side of the vertical broken lines, the separation into Zeeman sublevels m_F when a magnetic field H„ of non-zero intensity H„ is applied to resolve the degeneracy by splitting the levels.

In the equilibrium state the different energy levels are occupied in accordance with a Boltzman distribution, the occupation of the levels decreasing progressively as their energy increases; nevertheless at ordinary temperatures the population decreases very slowly from one level to the next higher level.

A system of atoms is capable of absorbing and of emitting energy at a frequency/= (E_s — Ε_Ζ)/(Λ), where E_a and E_t are an upper level and a lower level between which a transition is possible (for a possible transition, the azimuthal and magnetic quantum numbers vary by one unit, whereas the principal and spin quantum numbers remain unchanged) and h is Planck’s constant. In the state of equilibrium, only absorption is possible, this absorption having the effect of making more atoms pass from the state E_t to the state of E_a than from the state E_ato the state E₍. Einstein showed that the absorption of energy is compensated by two types of emission: spontaneous emission according to which incoherent radiation is emitted by the falling back of atoms after a characteristic length of time in the upper excited state and stimulated emission according to which coherent radiation is emitted by the falling back of atoms under the effect of irradiation by energy at the frequency /, this stimulated emission forming the basis of the operation of masers and lasers.

In atomic clocks using an alkali metal, both in accordance with the prior art and in accordance with this invention, the magnetic transition between the two levels 7=2 and 7 = 1 of the fundamental state S_1Z2, for m_F = 0, is used to obtain a frequency standard, since this transition is not very sensitive to the effects of the magnetic field.

Thus in the case of known clocks using rubidium vapor, of which the principle will be considered below, the frequency of the magnetic transition between the following two levels of rubidium 87 is used as the frequency standard: 5 ²Si_Z2, 7 = 2, m_F= 0

5²S_1Z2, 7= l,m_f = 0 whose frequency/=/) + 573 IP (in hertz), with f, (frequency in a zero magnetic field) equal to 6,834,682,614 Hz and H equal to the mean value of the magnetic field in gauss.

Similarly, in known clocks using a cesium beam, the magnetic transition between the energy levels 7 = 4, m_F = 0 and 7= 3, m_F = 0 of the fundamental state is used, whose frequency 7 is given by 7 = F_o + 427 /7 (in hertz) with 7₀ equal to 9,192,631,770 Hz.

For an alkali atom, the following designations will be used in the description which follows:

3,667,066

Ei for the lower level of the fundamental state, as well as for the energy of this level,

E₂ for the higher level of the fundamental state, as well as for the energy of this level (E₂&gt;E,),

E₃ for an excited level, as well as for the energy of this excited level, the level £3 being constituted practically by the levels P_3/2, P_1/2.

In the case of rubidium 87, £^ — E, = 6834.6 MHz and Ej = E₂ or E₃ — E,»E₂ — E, is about 7,800-7,950 A.

According to a law of Einstein, the probability that an atom in a higher energy level, such as E^, will make a transition into a lower energy level, such as E,, is equal to the probability that an atom in the level E, will make a transition into the level E₂. In order to be able to detect an appreciable absorption or emission of energy between two levels E, and E₂, it is accordingly necessary to produce a population inequality between these two levels which is greater than the Boltzman statistical inequality at normal temperature. It is thus necessary either to populate further the lower level with respect to the higher level, or on the contrary to realize a veritable population inversion by overpopulating the higher level with respect to the lowerjevel. This is why different methods have been used for producing this appreciable difference of population between the energy levels E, and E₂.

For example in the case of an atomic clock using a beam of cesium 133 of the conventional Rabi type (and also using a beam of thallium of a more recent type), a first magnet (SternGerlach) is used for separating the atoms of the level F — 4 and of the level F = 3 (whose magnetic moments are of opposite signs) of a beam of atoms of cesium 133 coming from an oven; the atoms of the level F= 3 are deviated, whereas the atoms of the level F = 4 move towards the axis and pass through a cavity or rather a pair of cavities in which they undergo a hyperfine transition between the levels F₄ and F₃, a certain number of atoms falling back to the level F₃. After having undergone this hyperfine transition, the atoms in the two states F = 3 and F = 4 are subjected to the influence of a second magnet which focuses the particles in one of the states onto a detector of the surface ionization type constituted by a tungsten wire heated to 1,000° K, the output current of this detector being a function of the excitation frequency of a cavity with a maximum at the hyperfine resonance of cesium.

In the case of a clock using rubidium vapor, some rubidium 87 is disposed in a cell, this cell being placed in a hyperfrequency cavity. Three levels are used, as illustrated in FIG. 7, namely a level £, which is the level F= 1 of the fundamental state of FIG. S, a level E₂ which is the level F= 2 of the fundamental state of FIG. 5, and finally a third level E₃ which represents the whole of the excited state P_V2 and P_3/2 of FIG. 5.

In order to obtain a sufficient difference of population between the levels E₂ and E_t, the optical pumping method of one of the inventors, namely Mr. Alfred Kastler, is used between the levels E, and E₃. It is then necessary to irradiate the vapor of rubidium 87 of the cell by radiation of frequency /13 = (E₃ ~ Now in fact the frequency/_I3 is very near to the frequency/₂₃ = (E₃ —Ε₂)/(Λ); it is thus difficult if not impossible to separate the lines /₁₃ and by means of ordinary interference-type filters; it has been proposed to take advantage of the natural coincidence between the optical lines of the two isotopes rubidium 85 and rubidium 87 (the lines f_i3 of these two isotopes are distinct). For this purpose, the rubidium 87 of the cell is lit by means of a Rb⁸⁷ resonance light source through a filter constituted by a vat containing Rb⁸⁵which only allows the frequency/_{13 me} i_mt E, is thus impoverished while enriching the level E₃ according to the arrow f_l3 of FIG. 7. By spontaneous emission, some atoms of the level E₃ fall back to the levels E₂ and E, (arrows/» and/j₂); the result is an enrichment of the level E₂ with respect to the level E_u that is to say of the higher energy level F = 2 to the detriment of the population of the atoms of the lower level F= 1. When the frequency of the oscillator exciting the cavity in which the Rb⁸⁷ cell is housed corresponds to the hyperfine frequency of Rb⁸⁷ (6,834.6 MHz), the irradiation at hyperfrequency has the effect of establishing the equality of the populations of the levels E_t and E₂ (arrow /₂₁), which is manifested by an absorption of the light passing through the cell and a reduction of the emerging light which is received by a photoelectric detector which indicates the resonance.

Although many of these known clocks have been constructed and operate in relatively satisfactory conditions (the clock using a cesium beam has even served as the primary standard of frequency for defining the atomic time scale called ATI), they nevertheless have a certain number of disadvantages.

In particular, in a clock using a cesium beam, it is necessary to use permanent magnets having a relatively small air gap in order to create sufficiently intense magnetic fields (from 4,000 to 8,000 gauss) for deviating the atoms. This reduces the effective cross-section of the usable atom beams and consequently reduces the signal/noise ratio at the detector, with, as a consequence, less precision at the resonance frequency (the ability to pick out a resonance line is proportional to the signal/noise ratio with which the line is observed).

Furthermore it is necessary to establish, in the region of hyperfrequency interaction, a uniform continuous magnetic field, for example of about 50 milligauss to resolve the degeneracy by splitting the levels, which necessitates shielding the magnets very effectively in order to avoid leakage fields that are too great. Now these shields, and the resulting parasitic magnetizations, are sources of errors in the determination of the absolute frequency of the atom of cesium.

Another factor which contributes to the precision of the apparatus is connected with the width of the resonance line. In the apparatus previously described, Ramsey’s method of separate fields is used (instead of a single cavity, two cavities are used, separated by a certain distance and supplied in phase); in this case the width of the resonance line is given approximately by v/L where v is the mean speed of the atoms in the beam

L is the distance between the hyperfrequency cavities.

In a beam of atoms, ν' is conditioned by a Maxwellian distribution; in order to avoid excessive lengths L, atoms must be selected which have slow speeds; this selection of speeds is made by displacing the source and the detector with respect to the axis of the clock. Unfortunately this reduces the solid angle of the atoms entering the magnets, which reduces the signal/noise ratio at the detector. A compromise must be accepted in the choice of V and L, which reduces the performance of the apparatus.

In the case of a clock using a rubidium vapor cell, the width of the resonance line is decreased and the effectiveness of the optical pumping is increased by introducing into the cell, in addition to the rubidium 87, an inert gas such as helium, nitrogen, neon or argon. However the collisions of the atoms of Rb⁸⁷ with molecules of the buffer gas produce a considerable frequency shift, which is dependent on the nature and the pressure of the buffer gas, sensitive to the temperature and also sensitive to the intensity of the pumping light. The result is that the resonance frequency of the cell must be determined by calibration. The apparatus can therefore only serve as a secondary frequency standard.

Having given this explanation of the prior art atomic clocks using alkali metals, a preferred embodiment, in accordance with the present invention, of an atomic clock using a beam of rubidium, will now be described with reference to FIGS. 1 to 4, and its operation will be discussed with reference to FIGS. 5,8 and 12.

The clock essentially comprises (FIG. 1):

an evacuated elongated container 1;

an oven 2 (which will be described in more detail below with reference to FIGS. 2 to 4) disposed in the lower portion of this container and containing natural rubidium (constituted by 75% of Rb⁸⁵ atoms and 25% of Rb⁸⁷atoms), this oven producing an atom beam 3 with a proportion of 75% of Rb⁸⁵ and 25% of Rb⁸⁷; at the outlet of the oven there is, for the atoms of Rb⁸⁷, an approximative equality of population in the two levels F= 1 and F— 2 of

3,667,066 the fundamental state, i.e., the energy levels E, and E₂ (in fact there are very slightly more atoms in the lower level F= 1 than in the higher level F= 2);

optical pumping means, constituted by an annular, Rb⁸⁵resonance lamp 4 or two Rb⁸⁵ resonance lamps and lenses 5, this pumping (which will be explained below in detail) having the effect of enriching the energy level E, (F= 1) with respect to the energy level E₂ (F= 2), especially for the Rb⁸⁷ atoms having the slowest speeds due to the fact that the effectiveness of the optical pumping is greatest for slow atoms, which remain longer in the zone lit by the lamp 4, than for the rapid atoms;

a zone 6 in which the atoms of the beam of rubidium, after having undergone the optical pumping, are subjected to irradiation of radio or hyperfrequency corresponding to the hyperfine spacing between the energy levels E_t and E₂, namely 6,834.6 MHz, by means of a Ό-shaped cavity 7 through the two branches Ία and 76 of which passes the beam 3; this zone 6 is subjected to a continuous magnetic field H_o of weak constant intensity H_o (about 50 milligauss) to resolve the degeneracy by splitting the levels F = 1 and F = 2; magnetic shielding 8 isolates this zone 6 from external magnetic fields; this continuous field H_o is parallel to the direction of the hyperfrequency magnetic field, and perpendicular to the direction of the beam of atoms in order to avoid a widening of the resonance lines due to the Doppler effect. The field H„ is produced by four longitudinal wires 34 through which passes a direct current of constant intensity;

detection means comprising a Rb⁸⁷ resonance lamp 9 (or a lamp using natural rubidium), a vat 10 containing Rb⁸⁵and an inert gas at high pressure (for example neon at 50 torr), this vat having the role of stopping the component of frequency f₂₃ while allowing the frequency f_i3 of the Rb⁸⁷ to pass (as explained in more detail hereafter with reference to FIG. 6), a collimation lens 11, a lens 12 for collecting the light which is not absorbed by the beam of atoms and a detector 13, advantageously constituted by a photomultiplier, on which is concentrated, by the lens 12, the light which has passed through the beam;

an electronic unit 14, annexed to the atomic clock proper and comprising a quartz oscillator which is coupled to the clock, this unit being described in more detail below.

The structure and the operation of the various parts of the clock proper and of the electronic unit will now be considered in detail.

The oven 2 (FIGS. 2, 3, 4) comprises a base 15 constituted by an insulating disc made of steatite, a body 16 comprising a foot 17 fixed on the disc, an ejector 18 carried by the neck 19 of the body 16 and a sleeve 20 screwed on the neck 19. The body 16 comprises a blind axial bore 21 for the rubidium and peripheral channels 22 in which heating resistances (not shown) are housed. The ejector 18 is traversed by a series of longitudinal channels constituted by nickel tubes 23 having a cross-section of about a square millimeter. Into the central bore 21 is introduced some natural rubidium, which is covered by octane. When current is passed through the resistances of the channels 22, the octane evaporates, then the rubidium, the temperature being about 180° C.; the atoms of Rb⁸⁵ and Rb⁸⁷pass through the tubes 23 of the ejector 18 and thus form at the outlet of this ejector a true beam 3.

This beam, as indicated previously, is made up of 75% of Rb⁸⁵ atoms and 25% of Rb⁸⁷ atoms. In the preferred embodiment, only the atoms of Rb⁸⁷ in the beam will be used, this beam traveling from the bottom towards the top in the elongated container 2. Among these atoms of Rb⁸⁷ of the beam 3 coming out of the oven 2, there are, as indicated above, practically the same number of atoms in the state E, (5 ²S1/2, F= 1, mF = 0) as in the state E2 (5 ²S1/2, F = 2, m_F — 0) represented in FIGS. 5 and 8.

In order to explain how the optical pumping is realized, reference will be made to FIGS. 5 and 6. FIG. 5 shows in detail the lowest energy levels of Rb⁸⁷. The optical resonance line is a double line D,, D₂ comprising the two components of fine structure D, (5 ²S1/2 - 5 ²P1/2) and D₂ (5 ²S„2 - 5 ²P3/2) represented by the double arrows at 7,947.6 A and 7,800 A respectively. The hyperfine structures of the first excited state 5 ²P are in general smaller than the Doppler width and will thus be neglected, as will the difference between D, and D2, whereas the hyperfine structure of the fundamental state 5 ²S1Z2 is in general greater than the Doppler width. The lines D, and D₂ thus each separate into two hyperfine components due to the structure of the fundamental state. In general, in the mode of optical pumping used here, the effects of the lines D, and D₂ are additive. Considering therefore only one or the other of the lines D, and D₂, the lines of resonance of the mixture of atoms of Rb⁸⁵ and Rb⁸⁷ thus comprise four principal components A and B for Rb⁸⁵ and a and 6 for Rb⁸⁷; as can be seen in FIG. 6, the optical lines A of Rb⁸⁵ and a of Rb⁸⁷ are practically coincident whereas the optical lines B of Rb⁸⁵ and b of Rb⁸⁷ are distinct, and this is true for both D, and D₂.

Use is made of this fact for realizing the optical pumping from the level E₂ (5 ²5V2, F= 2, mF = 0) to the level E3 (first excited state P) by illuminating the atoms of Rb⁸⁷ of the atom beam 3 by a Rb⁸⁵ resonance lamp 4. Accordingly only the component A of Rb⁸⁵, which has the same frequency as the component a of Rb⁸⁷, will have an effect: it will excite more particularly the atoms of the level E2 (F = 2) thus bringing them to the excited level ²P (arrow fa of FIG. 8); the atoms remain there for a mean time equal to the life-time of this excited state (of the order of 10“⁸ second), then fall back into the fundamental state while being divided between the two levels E, (F= 1) and E₂ (F= 2) as represented by the arrows f₃, and /₃₂ shown in broken lines. Finally the optical pumping has the effect of transferring part of the atoms from the level E₂ to the level E, thus enriching this latter level and impoverishing the level E₂.

In the absence of a hyperfrequency field in the zone 6, the beam arrives in the detection zone 25 (before its condensation at 24) with a level E, enriched with respect to the level E₂. The resonance lamp 9 using natural Rb or Rb⁸⁷ emits the four components A, B, a, b; the vat 10 containing Rb⁸⁵ only allows the components B and 6 to pass, but only the component b is active which has just the frequency (E3 - E,)/(.h) which permits it to be absorbed by the atoms of Rb⁸⁷ of the beam which are in the level E, (arrow f13 of FIG. 8): the result of this absorption is finally a repopulation of the level E₂ by the falling back from the excited level E₃ into the levels E₂ and E, of the fundamental state (arrows f₃₂ and f_3l in broken lines in FIG. 6). The optical pumping in the bottom of the beam 3 which enriches the level E, produces an increase of the absorption of the component 6 in the top of the beam (zone 15), hence a reduction of the light received by the detector 13.

If there is now applied to the cavity 7 a voltage at the frequency (E₂ - E,)l(h) = 6,834.6 MHz in order to create in the zone 6 a hyperfrequency field at 6,834.6 MHz, the result is the saturation of the transition Ep— E₂ of the atoms of Rb⁸⁷ of the beam, that is to say the equality of the populations of the levels E, and E2 by raising a certain number of atoms of Rb⁸⁷from the level E, to the level E2 (arrow/₁₂) thus cancelling the effect of the prior optical pumping. The beam of rubidium, which thus arrives in the zone 25 with as many atoms of Rb⁸⁷in the level E₂ as in the level E,, absorbs less of component 6 from the system 9,10 than if there had not been saturation by the hyperfrequency field. Consequently the current delivered by the detector 13 is increased when the hyperfrequency field is applied; more precisely, the current delivered by the detector 13 passes through a maximum when the frequency of the field produced by the double cavity 7 reaches the value 6,834.6 MHz.

The electronic unit 14 comprises an audiofrequency amplifier 26 amplifying the output from the photomultiplier 13, a quartz oscillator 27, a system 28 automatically servo-coupling the frequency of the oscillator 27 to the frequency of the atomic resonance at 6,834.6 MHz and a frequency synthesizing device 29 which permits shifting from the frequency of the

3,667,066 oscillator (which is a frequency at a sub-multiple of 6,834,682,614 Hz) to a frequency at a round number such as 5 MHz, as well as to the usual frequencies of 1 and 0.1 MHz.

The servo-control system 28 comprises:

a frequency multiplier 30 which multiplies the frequency of 5 the oscillator 27 (about 5 MHz) by a number such that the multiple frequency is equal to 6,834.6 MHz;

a modulator 31 at very low frequency (at 30 Hz for example) which frequency-modulates the output of the multiplier 30 in order to scan the resonance line in the cavity 1θ 7, which is translated as an amplitude modulation at the same very low frequency of the luminous beam striking the detector 13 and hence of the current I delivered by the amplifier 26 (this point will be discussed later with reference to FIG. 12); 15 a phase detector 32 which determines the phase difference between the applied modulation (at 30 Hz) and the reestablished modulation (that of the current I) and constitutes the error signal which controls the frequency of ₂θ the quartz oscillator 27 by means of the frequency device 33.

With reference now to FIG. 12, an explanation will be given, on the one hand, of the advantage of using a double hyperfrequency cavity 7, in the shape of a U, with two ₂5 branches 7α and 7b, and on the other hand, of how the modulation at low frequency permits an error signal to be obtained.

The curves I, and I₂ represent the variation of the amplitude of the current I as a function of the frequency of the signal applied to the cavity 7 in the case in which this cavity is a single 3Q cavity (having a length equal to the length through which the atom beam passes in a single branch) and a U-shaped cavity (as illustrated) respectively. It can be seen that the width of the resonance line is much narrower in the second case: in fact the width is inversely proportional to the total length of the 35 single cavity in the first case or of the distance between the cavities in the second case. (A single cavity of great length cannot be used for, in view of the dimensions of the wavelength corresponding to the frequency 6,834.6 MHz, the same phase cannot be achieved along the entire length of such 40 a cavity.) The width of the resonance line is in fact equal to v/L; by using the present invention, the slow atoms are given an advantage, and hence the resonance line is reduced further.

The modulation of the phase of the oscillator at very low frequency and the use of synchronous detection (phase detection) of the very low frequency signal delivered by the detector 13 result in the derivative curve Γ, of I, and Γ₂ of I₂ respectively. The slope of Γ₂ in the neighborhood of 6,834.6 MHz is much greater than the slope of I',; the error signal which is proportional to this slope is thus greater in the case of a double cavity: for a frequency variation of df the error signal is di. Thus a positive or negative error signal is obtained according as the frequency is on one side or the other of the resonance frequency. This error signal serves, in the servo-control 55 system, for holding the frequency of the quartz oscillator at the frequency of the hyperfine resonance of Rb⁸⁷ (6,834.6 MHz).

In order to increase the output signal of the photomultiplier 13, the detection light produced by the system 9,10,11 can be ₆q made to pass several times through the beam, for example by using mirrors. Nevertheless it is necessary to avoid an excess of detection light for an excess of such a light could have a tendency to depopulate the level E, more rapidly than the pumping by the system 4, 5 can populate this level, which would 65 lead to the disappearance of a sharp maximum of current I at the resonance and hence a decrease of the signal/noise ratio.

The rubidium beam atomic clock which has just been described with reference to FIGS. 1 to 6, 8 and 12 has numerous advantages with respect to the prior art cesium beam 70 clocks or rubidium vapor clocks whose principles have been explained above.

1. The clock according to this invention gives a primary frequency standard or absolute frequency standard, in the sense that the frequency of the resonance is very close to 75 the Bohr frequency of the free atom. In particular, since the atoms of Rb travel in a vacuum, there are no frequency shifts due to collisions of the atoms of Rb with the molecules of the buffer gas as in the clocks using alkali vapor cells. For the same reason, the effect of temperature is minimized.

Moreover, in the beam of Rb, the regions of optical pumping and of optical detection are clearly separated from the regions of interaction of the hyperfrequency fields, and accordingly, frequency shifts due to the virtual transitions induced by the pumping light are avoided; this effect is particularly troublesome and difficult to eliminate in the case of clocks using alkali vapor cells; here, it is possible, by careful construction, to avoid leakage of the pumping light or of the detection light in the region of interaction of the fields of high frequency.

2. Due to the fact that no focusing or deflection magnets are used, it is easy to shield the apparatus magnetically and thus to reduce the effects of frequency shifts due to the magnetic field.

3. Since the aperture angle of the beam of atoms is not limited by the air gaps of focusing or deflection magnets, relatively intense atom beams can be used which thus considerably increases the signal/noise ratio during detection.

4. The optical detection is relatively simple with respect to the detection by surface ionization used in the clocks of the Rabi type, which (detection by surface ionization) often necessitates the use Of a mass spectrograph.

5. The optical techniques of pumping and of detection favor the slow atoms of the beam. If one works in the region where the optical effects are linear — which is practically the case with the intensities of the luminous sources available — the effectiveness of the optical pumping and the magnitude of the detection signal are each proportional to the length of time that the atoms remain in the illuminated region, namely to t = d/v, where d is the length of the illuminated path and v the speed of the atom. Since the law of distribution of speeds is a function of v’e-·* with a = m/2kT, a factor 1/v is introduced into the signal of the high frequency resonance when one works in the linear region far from saturation.

In the magnetic deflection method of the Rabi type, the effective mean speed is then given by / vdN f v^l-e~^av,dv 2 In 2 /2nkT S dN ft^-e^^dv nN a πν m

With the optical pumping and optical detection according to this invention, there is a supplementary factor 1/v for the pumping and a factor 1/vfor the detection, namely a factor 1/v²:

vdN S v-e-^dv 1 Ιπ__ 1 fr-rrkT J dN f e~^av*dv πν a π N m

A factor of 2 is thus gained in the fineness of the line with respect to the magnetic deflection methods.

The atomic clock of the type illustrated in FIGS. 1 to 4 can nevertheless consume more atoms of alkali metal than a clock of the Rabi type. In order to reduce the consumption, recirculation of the rubidium can be provided. It will be noticed that the system is symmetrical from the physical point of view: the condensed rubidium beam can be returned in the other direction by placing a rubidium oven in the zone 24 where the rubidium condenses and by collecting the rubidium in the region where the oven 2 is located in FIG. 1; the detector 13 would then be placed facing the Rb⁸⁵ lamp 4. In this case, the clock would operate as indicated in FIG. 9, the light from the system 9, 10, 11 pumping, by its component b, the atoms of Rb⁸⁷ of the beam from the level E, towards the level E₃ (arrow

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/.a), whence they would fall back towards the levels E, and £] (arrows/₃₁ and/^), thus enriching the level E₂ with respect to the level E_t. In this level E₂ the atoms of Rb⁸⁷ are apt to absorb preferentially the component A of the rubidium 85 lamp 4 (arrow /„), the resonant cavity 7 having the effect, as in the first case, of equalizing the populations of the two levels E, and E₂.

Hence the two schematic diagrams of FIGS. 8 and 9 are correct for the atoms of Rb⁸⁷.

The apparatus of FIGS. 1 to 4 could also operate by using the atoms of Rb⁸⁵ of the beam, the optical pumping being produced at the base by a Rb⁸⁵ lamp filtered by a vat of Rb⁸⁷, whereas the optical detection at the top of the beam would be effected by a non-filtered Rb⁸⁷ lamp, the frequency of excitation of the U-shaped hyperfrequency cavity now being 3,036 MHz, the hyperfine spacing between the levels E₂ (F = 3) and E_t (F= 2) of the fundamental state of Rb⁸⁵, as can be seen in FIG. 6.

FIG. 10 illustrates the use of such optical pumping and optical detection for the atoms of rubidium 85. The pumping at the base by the lamp of Rb⁸⁵ filtered by the Rb⁸⁷ has the effect of making the atoms of Rb⁸⁵ pass from the level E, to the excited level E3 (arrow f13), whence they fall back to the levels E2 and E, (arrows/32 and/]); thus the level E2 is enriched with respect to the level E,. The optical detection has the effect of making atoms of Rb⁸⁵ pass from the level E^ to the level E3 (arrow /₂₃). The saturation of the resonance line (E₂ - Ε,Ι/Οι) at 3,036 MHz by the hyperfrequency cavity has the effect of equalizing the population of the levels E, and E₂ and consequently of reducing the overpopulation of E₂ realized by the optical pumping, which leads to a reduction of the detection light from the Rb⁸⁷ lamp during passage of the beam. There is thus a maximum of the current delivered by the detector facing the Rb⁸⁷ detection lamp during the passage through the resonance.

Furthermore, while still using the atoms of Rb⁸⁵ of a beam, the variant illustrated in FIG. 11 can be adopted, in which the pumping is effected, according to the arrow fa, between the levels E2 and E3 by a non-filtered Rb⁸⁷ lamp, whereas the detection is effected, according to the arrow /13, by a lamp of Rb⁸⁵ filtered by a vat of Rb⁸⁷.

It will be noticed that the schematic diagrams of FIGS. 8, 9, 10 and 11, which represent this invention, are characterized by the fact that optical pumping is realized between one of the levels E₁ or E₂ of the fundamental state and the excited level E₃, and optical detection is realized between the other level (E₂ or E, respectively) of the fundamental state and the excited level E₃, the hyperfrequency cavity being supplied at the frequency corresponding to the spacing between the two levels E, and E₂ of the fundamental state.

Although the present invention has been described more especially for Rb⁸⁷ or Rb⁸⁵, it can also be applied with few modifications for the other alkali atoms such as sodium, potassium or cesium.

However, with these atoms, hyperfine filtering by isotopes cannot be employed. In this case it is necessary to employ other methods such as the use of filters constituted by cells of alkali vapors placed in an intense magnetic field (which modifies the frequency by the Paschen-Back effect). For example, in the case of cesium, a cell containing some cesium vapor at 125° C. which is placed in a field of 8.3 kG can be used as the hyperfine filter. Semi-conductor lasers of the type Ga As.-j. Pj can also be used, of which the emitted frequency can be shifted by acting on the composition x and on the temperature. Such a laser has a frequency corresponding to one of the components of Cs¹³³.

An atomic clock or frequency standard in accordance with the present invention has numerous advantages with respect to the clocks or standards of the prior art, and among these advantages can be cited the following.

First of all it constitutes a primary standard of frequency, its frequency being very near to the frequency of the free atom.

It has very great stability of frequency, in particular in the long term.

It is relatively simple and does not require powerful magnets of complicated shape.

These advantages will be apparent from the following explanation of the two atomic clocks of the prior art which seem to be the most pertinent to the present invention.

1. Clock according to French Pat. No. 1,404,551.

The sequential system described in this patent establishes a program of actions, as a function of time, on atoms confined in the limited space of a cell. The alkali atoms are not in the form of a beam coming from an oven, but are present in the confined space of the cell in the form of vapor. This fundamental point leads to important consequences for the precision and the stability of the atomic clock or frequency standard. In particular:

a. In the case of a vapor, the interaction of the alkali atoms with the walls of the cell, or with the molecules of a buffer gas, if such a gas is used, causes, in general, frequency shifts which are difficult to predict theoretically and which are often unstable as a function of time. The result is that the frequency of a clock using a cell of alkali vapor can only be known by a preliminary measurement. In other words, these clocks operate as secondary standard of frequency, whereas one of the objects of the present invention is to provide a primary standard or absolute standard of frequency.

In a clock using a beam of alkali atoms, the atoms are emitted in a high vacuum and have very little interaction with the residual gases. Consequently, in these clocks, the resonance frequency is very near to the Bohr frequency, and the value can be obtained easily by making the corrections due to the continuous magnetic field. These clocks can thus be considered as primary standards of frequency.

Similarly, with an alkali vapor, it is necessary to operate at a relatively high temperature in order to obtain a density of atoms sufficient for a good signal/noise ratio during the detection. Under these conditions, with a cell, the fluctuations of operating temperature can influence the value of the resonance frequency. By contrast, with clocks using a beam of alkali atoms, in view of the little interaction of the atoms among themselves or with the walls of the vacuum container, the effects of temperature are much less marked.

b. Furthermore, although in the present invention the action of the light and of the radiofrequency field is also sequential in time, the different operations of optical pumping, of interaction with the radiofrequency field, and of optical detection, take place in different regions of space, in the vacuum container, and are produced by the movement of the atoms in space rather than by a square-wave modulation of the light or of the radiofrequency field. In the present invention, the pumping light or the detection light and the radiofrequency field are emitted in a continuous manner. The result is a simplification of the electronic excitation and servo-control systems.

c. The optical pumping of atoms in the form of an alkali vapor confined in a cell as in the aforementioned French patent, is quite different from the optical pumping of free atoms in a beam as in the present invention. In a cell, the alkali atoms are subjected for a longer time to the action of the pumping light, which can even be pulsed, and the effectiveness of the optical pumping can be great.

For the atoms in the form of a beam in a vacuum, the duration of the passage of the atoms in the region of illumination by the pumping light is very brief, about 0.2 milliseconds, and in order to obtain a good signal/noise ratio it is necessary to use intense beams with a wide opening, and this particular technique, which is absent in the alkali vapor cells is a feature of the present invention.

2. Atomic clock according to U.S. Pat. No. 3,328,633.

This patent is concerned with a thallium beam atomic clock of the conventional Rabi-Ramsey type. Although a beam of alkali atoms, in a vacuum, is used, the optical pumping and the optical detection which are features of the present invention are not mentioned.

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Π

In the beam magnets produce a separation between the alkali atoms belonging to different hyperfine levels, in order to preserve, for example, only the atoms of the higher energy level which are then focused onto an ionization detector. On the other hand in the present invention, the atoms are not separated, but, by the optical pumping, the populations of atoms in one of the hyperfine energy states is enriched. Similarly, the detection is made by an optical method which detects the change of populations produced by the radiofrequency.

Needless to say, the invention is not limited to the particular embodiments described hereinbefore; many modifications are possible without departing from the scope thereof as defined in the appended claims.