Method and a device for the frequency control of an atomic or molecular beam frequency standard

The method realizes the frequency control of a frequency standard including an atomic or molecular beam resonance apparatus with two microwave cavities, to which an electromagnetic field is fed, whose frequency is modulated in time with a sinewave signal about an interrogation frequency near to the characteristic resonance frequency of a selected transition of the atoms or molecules of the beam. In the resonance device a current is generated, proportional to the number of atoms or molecules of the beam which have undergone said transition as an effect of their passing through the cavities. The method includes the step of extracting from said current the component whose frequency is an odd harmonic of the modulation frequency of an order higher than the first, in particular the third. Said component is coherently demodulated, in amplitude and sign, to generate a control signal which is used to steer the frequency of said electromagnetic field, in such a way as to minimize the difference between the interrogation frequency and the characteristic resonance frequency of the atomic or molecular transition.

The present invention relates to a method for the frequency control of a 
frequency standard including an atomic or molecular beam device with two 
microwave cavities, to which an electromagnetic field is fed, whose 
frequency is modulated in time with a sinewave signal about an 
interrogation frequency near to the characteristic resonance frequency of 
a selected transition of the atoms or molecules of the beam, and in which 
a current is generated, proportional to the number of atoms or molecules 
of the beam which have undergone said transition as an effect of their 
passage through the cavities; the method including the steps of: 
generating a control signal as a function of a selected characteristic 
detected in said current, and 
modifying the frequency of said field as a function of said control signal, 
in such a way as to minimize the difference between the interrogation 
frequency and said characteristic resonance frequency. 
Such a procedure is currently implemented in Cesium beam devices as 
disclosed for example in U.S. Pat. Nos. 2,972,115 and 3,354,307. 
In FIG. 1 of the enclosed drawings such a device is shown. Said device 
includes a source 1 (oven) which generates a Cesium atomic beam 2 and 
sends it through a first pair of deflecting magnetic polepieces 3a and 3b, 
which generate a strongly dishomogeneous magnetic field. Said magnetic 
field spatially separates the atoms which are in the energetic state 
having a given direction of the magnetic moment from the atoms which have 
the opposite direction of the magnetic moment. 
The selected atoms 2a subsequently interact in two successive resonant 
microwave cavities 4a, 4b, with an electromagnetic radiation of a 
frequency .nu. near to the frequency capable of causing the transition or 
change of state (inversion of the direction of the "spin" magnetic moment) 
of said atoms. 
The nearer is the frequency of said radiation to the Cesium transition 
characteristic frequency (9,192,631,770 Hz), the greater is the number of 
atoms which invert their magnetic moment, that is which change state. 
A second pair of deflecting magnetic polepieces 5a, 5b affect the atoms 2a 
which emerge from the second cavity 4b, in such a way that only the atoms 
2b which have undergone the magnetic moment inversion can reach a detector 
6. 
The detector produces, in a known way, a current I proportional to the 
number of incoming atoms. 
From a functional point of view, the Cesium beam device of FIG. 1 can be 
considered for the following description as a "block" D (FIG. 2) 
characterised by a known transfer function which relates the output 
current I to the input interrogating frequency .nu.. 
Said transfer function is well known and will be further described in the 
following. 
In FIG. 3 a frequency standard is illustrated, including a Cesium tube D of 
the type described with reference to FIGS. 1 and 2. 
In FIG. 3 a phase modulator 10 is shown, which modulates the frequency (for 
example 5 MHz) of the signal fed thereto by a voltage controlled 
oscillator (VCO). The frequency of VCO 11 is thus modulated in time by a 
sinewave having a frequency fm obtained starting from a square wave 
oscillator 12 at frequency 2 fm. 
The output of this oscillator drives two frequency dividers 13, 14, which 
half the input frequency and emit thus at the output a square wave signal 
at frequency fm. The output of divider 13 is fed to a low-pass filter 15, 
whose output provides a practically sinusoidal signal at frequency fm for 
the modulator 10. 
The frequency-modulated signal produced by modulator 10 is elevated in 
frequency for example by means of a frequency multiplier 16, which 
provides the Cesium tube D with a signal whose frequency is sinusoidally 
modulated in time about an interrogation frequency near to the 
characteristic resonance frequency of Cesium. 
The current I generated by the detector 6 is fed to a selective amplifier 
17, which extracts and amplifies from said current only the sinewave 
component whose frequency is the first harmonic of the modulating 
frequency fed into modulator 10, that is the frequency fm. 
The outputs of amplifier 17 and frequency divider 14 are both connected to 
a coherent phase demodulator 18, of a known type, whose output is fed to 
an integrator amplifier 19, in turn connected to the control input of VCO 
11. 
In FIG. 4 of the annexed drawings a series of waveforms is shown to explain 
the operation of both a Cesium beam frequency standard of known type, and 
a standard realized according to the present invention. 
In particular in FIG. 4 the curve of I shown as a function of the frequency 
of f is the so-called Ramsey curve (pattern), which is the transfer 
function of a Cesium beam tube. 
Said curve features a central peak at frequency f.sub.cs, which is 
9,192,631,770 Hz for the transition between the F=3,m.sub.F =0 and the 
F=4,m.sub.F =0 Zeeman sublevels. 
Above and below the Ramsey curve in FIG. 4 are two graphs illustrating the 
time variation of the modulated frequency fed to the Cesium tube D. 
In the graph below the Ramsey curve are shown two different sinusoidal 
variation of .nu., labelled .nu..sub.(1) and .nu..sub.(3) : in both cases 
the time variation of .nu. is centered about f.sub.cs. Supposing that the 
frequency of the signal fed to the Cesium tube D be modulated according to 
.nu..sub.(1) or .nu..sub.(3) of the lower graph of FIG. 4, the current I 
generated by detector 6 will have, as a function of time t, the waveforms 
shown by curves I.sub.(1) and I.sub.(3) of FIG. 4 respectively. 
It can be seen that, if the modulated frequency is perfectly centered about 
the central peak of the Ramsey curve, the current produced by the detector 
of the Cesium tube contains only even harmonics of the modulation 
frequency fm. As a consequence in such a case the selective amplifier 17 
has ideally zero output signal and the frequency of VCO 11 is not 
modified. 
On the contrary if the modulated frequency .nu. is not centered about the 
central peak of the Ramsey pattern, as it is shown in the graph above the 
Ramsey curve in FIG. 4, the detector of the Cesium tube will yield a 
current with the waveforms shown by curves I'.sub.(1) and I'.sub.(3) in 
FIG. 4 respectively. 
Curves I'.sub.(1) and I'.sub.(3) of FIG. 4 show that, if the modulated 
frequency is not centered on the central Ramsey peak, the current produced 
by the detector has a content of odd harmonics of the modulation 
frequency. In particular I'.sub.(1) shows mostly a first harmonic content. 
In this case the selective amplifier 17 of FIG. 3 is tuned to extract from 
current I the component at frequency fm, which is then demodulated in 
amplitude and sign by the coherent phase demodulator 18. 
At the output of the latter appears then a signal at frequency 2 fm, which 
is basically a doublewave rectified sinewave of frequency fm. This signal 
is amplified and integrated in amplifier 19 and is then used to steer the 
frequency of VCO 11. 
However the above described way of operation of the standard shown in FIG. 
3 is somewhat idealized since the effect of the Cesium transitions 
adjacent to those at frequency f.sub.cs has not been taken into account. 
FIG. 5 shows the so-called Rabi curves which illustrate the output current 
I from the tube D as a function of the frequency f on the abscissae, for 
the three central transitions of Cesium atoms. The central Rabi line, 
centered on frequency f.sub.cs corresponds to the transitions between the 
above indicated Zeeman sublevels. 
The curve on the left instead corresponds to the transition between the 
F=4,m.sub.F =-1 and the F=3,m.sub.F =-1 sublevels, whereas the curve on 
the right corresponds to the transition between the F=4,m.sub.F =1 and the 
F=3,m.sub.F =1 sublevels. 
In the ideal case these two side curves are equal and symmetric about the 
central curve, and in the frequency interval F centered about the center 
Ramsey peak the "wings" or "tails" of the side curves (which in that 
interval can be well approximated by a straight segment) add up, giving as 
a result a horizontal straight segment, labelled R in FIG. 5. 
However in the real case the tails of said curves corresponding to the 
adjacent transitions add up giving as a result in the interval F a 
straight segment R' with a finite slope, generally different from zero. 
In the ideal case the effect of the adjacent transitions gives no problem: 
as already pointed out their combined transfer function is given by a 
horizontal straight segment, which does not change the harmonic content of 
the tube's output current. 
In the real case the combined transfer function of the adjacent wings 
instead has generally a non-zero slope; therefore such transitions induce 
a first-harmonic content in the tube's output current I even when the 
modulated frequency .nu. is actually centered on the characteristic 
frequency of the excited transition. 
In general the transitions adjacent to the transition used as a reference 
introduce therefore a bias error in the frequency of the standard; since 
such bias may change with time, it may therefore limit both the accuracy 
and the long term stability of the standard. 
The object of the present invention is to allow the realization of 
frequency standards of higher accuracy, better repeatibility and long-term 
stability, and higher insensitivity to the environmental conditions. The 
latter may in fact affect the shape of the Rabi lines, for example through 
the power of the microwave field in the cavities. 
The said object is achieved according to the invention, with a method for 
the frequency control of a frequency standard of the above specified type, 
characterized by the fact that from said tube's output current a component 
is extracted, whose frequency is an odd harmonic higher than the first of 
the frequency fm modulating the interrogation frequency .nu., and that the 
control signal is generated by coherently demodulating said component, in 
amplitude and sign. Furthermore the invention relates to a device for the 
frequency control of a frequency standard of the above specified type, 
whose main features are summarized in the appended claims. 
Finally, the invention also relates to a frequency standard including such 
a control device.

In FIG. 6 parts already described with reference to FIG. 5 have been given 
the same reference numbers. 
In FIG. 6, between the oscillator 12 and the frequency divider 13 a further 
frequency divider 100 is inserted, which divides by 3 the frequency of the 
signal fed to its input. As a consequence divider 13 provides at its 
output a symmetric square wave at frequency fm/3. 
The filter 15 provides therefore modulator 10 with a sinewave modulating 
signal which is also at frequency fm/3. 
Also in this case the selective amplifier 17 connected to the output of the 
Cesium tube is tuned to extract the component at frequency fm. However, in 
this case, said frequency is the third harmonic of the modulating 
frequency. 
If the modulated frequency fed to the Cesium tube D is actually centered on 
the characteristic frequency f.sub.cs, the selective amplifier 17 yields 
at its output a signal which is practically zero. In fact the current I 
has a content of even harmonics only, which are rejected by the selective 
amplifier 17, plus a small component at the modulating frequency fm/3, 
caused by the adjacent transitions, which is also rejected by the 
selective amplifier 17. 
If on the contrary the modulated frequency fed to the tube D is not 
centered on frequency f.sub.cs, the current I has a waveform of the type 
shown by curve I'.sub.(3) in FIG. 4, with a strong component at the 
frequency fm corresponding to the third harmonic of the modulating 
frequency. This third harmonic component is coherently demodulated and 
integrated to generate the frequency control signal for VCO 11. Also in 
this case the contribution of the adjacent transitions gives no problem, 
because it is a component of current I at frequency fm/3 which is rejected 
by the selective amplifier 17. Therefore according to the invention it is 
possible to improve the accuracy and long-term stability by using coherent 
detection of the third harmonic of the frequency which modulates the 
microwave frequency fed to the cavities of the Cesium tube. 
Resorting to third harmonic detection to overcome the problems caused by a 
sloping background signal has been already proposed and realized for other 
applications, in particular for the frequency stabilization of lasers in 
saturated absorption spectroscopy. 
In the specific field of atomic beam frequency standards third harmonic 
detection not only was never proposed, but, on the contrary, was generally 
thought not to be viable, because it was believed that the amplitude of 
the detected third harmonic would be too much smaller than the amplitude 
of the detected fundamental frequency, and that as a consequence the loss 
in signal-to-noise ratio would be not acceptable. 
Such was the general opinion of the experts in the field, and in particular 
even of the inventors, as is reported for example in the paper "Pulling by 
neighbouring transitions and its effects on the performance of Cesium beam 
frequency standards", published in Metrologia, 20, 37-47 (1984). 
In critically reviewing such opinion, generally shared by the experts of 
the field, the inventors first derived analytically and then verified 
experimentally that the signal-to-noise ratio obtainable in a third 
harmonic loop is practically equal to that obtained in a first harmonic 
loop. 
FIG. 6, by comparison with FIG. 5, immediately suggests how existing 
frequency standards can be easily and quickly modified to include third 
harmonic detection and earn the advantages deriving therefrom. 
Naturally, the principle of the invention remaining the same, the 
embodiments and details of realisation may be varied widely with respect 
to those described and illustrated purely by way of non-limiting example, 
without thereby departing from the scope of the present invention.