Measurement by means of atomic interferometry with multiple species of atoms

Abstract

Disclosed is a method for measuring an external parameter by atomic interferometry using two sets of atoms that belong to different species. Two measurements are taken simultaneously at the same location, but independently from one another, in order to obtain two measurement results. Constant phase shifts that appear in the atomic interferences for the two atom sets are quadrature-adjusted in order to ensure that one of the two measurements provides a value for the external parameter with satisfactory accuracy.

Claims

1. Method of measurement by atomic interferometry, in which each session of measurements is executed with at least two sets of atoms (11, 12) each subjected to conditions of formation of atomic interference, the atoms of each set of atoms (11, 12) being of a species dedicated to said set of atoms and different from the species of atoms of each other set of atoms, method in which, for each session of measurements, said conditions are produced for each set of atoms (11, 12) throughout a volume that is associated with said set of atoms and that contains at least one point in common with the volume associated with each other set of atoms, and are produced between a start time point and an end time point respectively before and after an intermediate time point common to all the sets of atoms, and in which a measurement result (P.sub.11, P.sub.12) is obtained in each session of measurements independently for each set of atoms (11, 12), each measurement result varying according to a first function of a total phase shift that appeared for the corresponding set of atoms during formation of the atomic interference, said total phase shift comprising a sum of a second function of an external parameter (a) a value of which is sought and of a constant phase shift that is undergone by the corresponding set of atoms during said formation of the atomic interference, the method being comprising the following steps: /1/ during a session of measurements, applying a value for at least one operating parameter, called internal parameter and making it possible to control a difference between the constant phase shifts to which the two sets of atoms are respectively subjected, the value applied for said at least one internal parameter being such that a difference between the total phase shifts that the two sets of atoms (11, 12) undergo, respectively, is between /4 and 3/4 in absolute value and modulo ; /2/ for each measurement result (P.sub.11, P.sub.12) obtained for one of the sets of atoms (11, 12) in said session of measurements, determining a derivative value of said measurement result with respect to the external parameter (a), said derivative being evaluated for said measurement result; /3/ selecting that one of the sets of atoms (11, 12) for which the derivative value determined in step /2/ is largest in absolute value; and /4/ calculating the value of the external parameter (a) from the measurement result (P.sub.11, P.sub.12) obtained in step /2/ for the set of atoms selected in step /3/.

2. Method according to claim 1, in which said at least one internal parameter comprises at least one amplitude of a phase jump introduced between two pulses of laser radiation that are used to form the atomic interference for one of the sets of atoms (11, 12), at least one rate of variation of a frequency of laser radiation that is used to form the atomic interference for one of the sets of atoms, or an intensity and a gradient of a magnetic field that is applied to the sets of atoms during the formation of the atomic interferences, or a combination of several among said at least one amplitude of phase jump, said at least one rate of variation of frequency of laser radiation and said magnetic field intensity and gradient.

3. Method according to claim 1, in which the value applied for said at least one internal parameter is such that the difference between the total phase shifts that the two sets of atoms (11, 12) undergo, respectively, is between 15/32 and 17/32, in absolute value and modulo , and in which, for that one of the sets of atoms (11, 12) that is selected in step /3/, the first function is replaced with an affine function of the total phase shift that appeared during the formation of the atomic interference for the selected set of atoms, in a whole interval of values having a length of interval greater than or equal to 3/8, and which contains said total phase shift that appeared during the formation of the atomic interference.

4. Method according to claim 1, in which the first function has the expression P=P.sub.0.Math.[1Ccos(.sub.tot)] for each set of atoms (11, 12), where P denotes the measurement result, .sub.tot is the total phase shift that appeared during the formation of the atomic interference for said set of atoms, and P.sub.0 and C are two non-zero numbers.

5. Method according to claim 1, in which said at least one internal parameter comprises an amplitude of a phase jump introduced between two pulses of laser radiation that are used to form the atomic interference for one of the sets of atoms (11, 12), and the constant phase shift that is undergone by said set of atoms comprises a term proportional to the amplitude of the phase jump.

6. Method according to claim 1, in which said at least one internal parameter comprises a rate of variation of frequency of laser radiation that is used to form the atomic interference for one of the sets of atoms (11, 12), and the constant phase shift that is undergone by said set of atoms comprises the term 2T.sup.2 where T is a base time for a sequence of interactions between the atoms and photons that is implemented to form the atomic interference of said set of atoms, and is the rate of variation of frequency of the laser radiation.

7. Method according to claim 1, in which said at least one internal parameter comprises an intensity and a gradient of a magnetic field that is applied to the sets of atoms (11, 12) during the formation of the atomic interferences, and the constant phase shift that is undergone by each set of atoms comprises the term (A.sub.at/M.sub.at)B.sub.0B.sub.1k T.sup.2, where B.sub.0 and B.sub.1 are the intensity and the gradient of the magnetic field respectively, T is a base time for a sequence of interactions between the atoms and photons that is implemented to form the atomic interference for said set of atoms, k is a modulus of a momentum received or transferred by one of the atoms during each interaction between the atoms and the photons, divided by =h/(2) where h is Planck's constant, and A.sub.at/M.sub.at is a coefficient that depends on the species of atoms.

8. Apparatus for measurement by atomic interferometry comprising: a source of atoms (100) suitable for producing at least two sets of atoms (11, 12), with the atoms of each set of atoms that are of a species dedicated to said set of atoms and different from the species of atoms of each other set of atoms; means (101-103) suitable for producing conditions of atomic interference for each set of atoms (11, 12), so that said conditions are produced for each set of atoms throughout a volume that is associated with said set of atoms and that contains at least one point in common with the volume associated with each other set of atoms, and produced between a start time point and an end time point respectively before and after an intermediate time point that is common to all the sets of atoms, so as to constitute a session of measurements; a detection device arranged for providing measurement results (P.sub.11, P.sub.12) respectively and independently for all the sets of atoms (11, 12) of each session of measurements; and an analysis unit suitable for calculating at least one value of an external parameter (a) from each measurement result (P.sub.11, P.sub.12), in which each measurement result (P.sub.11, P.sub.12) varies according to a first function of a total phase shift that appeared for the corresponding set of atoms during the formation of the atomic interference, said total phase shift comprising a sum of a second function of the external parameter (a) the value of which is sought and of a constant phase shift that is undergone by the corresponding set of atoms during said formation of the atomic interference, the apparatus being applying, during each session of measurements, a value for at least one operating parameter, called an internal parameter and making it possible to control a difference between the constant phase shifts that the two sets of atoms (11, 12) undergo, respectively, so that a difference between the total phase shifts to which the two sets of atoms are subjected respectively, is between /4 and 3/4, in absolute value and modulo ; and the analysis unit is suitable for executing steps /2/ to /4/ of a method of measurement by atomic interferometry according to claim 1.

9. Apparatus according to claim 8, in which, for each session of measurements, the conditions of atomic interferences are produced for all the sets of atoms (11, 12) using a single laser source assembly (102, 103), common to said sets of atoms.

10. Apparatus according to claim 8, forming an accelerometer, a gravimeter or a gyrometer.

11. Method according to claim 2, in which the value applied for said at least one internal parameter is such that the difference between the total phase shifts that the two sets of atoms (11, 12) undergo, respectively, is between 15/32 and 17/32, in absolute value and modulo , and in which, for that one of the sets of atoms (11, 12) that is selected in step /3/, the first function is replaced with an affine function of the total phase shift that appeared during the formation of the atomic interference for the selected set of atoms, in a whole interval of values having a length of interval greater than or equal to 3/8, and which contains said total phase shift that appeared during the formation of the atomic interference.

12. Method according to claim 2, in which the first function has the expression P=P.sub.0.Math.[1Ccos(.sub.tot)] for each set of atoms (11, 12), where P denotes the measurement result, .sub.tot is the total phase shift that appeared during the formation of the atomic interference for said set of atoms, and P.sub.0 and C are two non-zero numbers.

13. Method according to claim 3, in which the first function has the expression P=P.sub.0.Math.[1Ccos(.sub.tot)] for each set of atoms (11, 12), where P denotes the measurement result, .sub.tot is the total phase shift that appeared during the formation of the atomic interference for said set of atoms, and P.sub.0 and C are two non-zero numbers.

14. Method according to claim 2, in which said at least one internal parameter comprises an amplitude of a phase jump introduced between two pulses of laser radiation that are used to form the atomic interference for one of the sets of atoms (11, 12), and the constant phase shift that is undergone by said set of atoms comprises a term proportional to the amplitude of the phase jump.

15. Method according to claim 3, in which said at least one internal parameter comprises an amplitude of a phase jump introduced between two pulses of laser radiation that are used to form the atomic interference for one of the sets of atoms (11, 12), and the constant phase shift that is undergone by said set of atoms comprises a term proportional to the amplitude of the phase jump.

16. Method according to claim 4, in which said at least one internal parameter comprises an amplitude of a phase jump introduced between two pulses of laser radiation that are used to form the atomic interference for one of the sets of atoms (11, 12), and the constant phase shift that is undergone by said set of atoms comprises a term proportional to the amplitude of the phase jump.

17. Method according to claim 2, in which said at least one internal parameter comprises a rate of variation of frequency of laser radiation that is used to form the atomic interference for one of the sets of atoms (11, 12), and the constant phase shift that is undergone by said set of atoms comprises the term 2T.sup.2, where T is a base time for a sequence of interactions between the atoms and photons that is implemented to form the atomic interference of said set of atoms, and is the rate of variation of frequency of the laser radiation.

18. Method according to claim 3, in which said at least one internal parameter comprises a rate of variation of frequency of laser radiation that is used to form the atomic interference for one of the sets of atoms (11, 12), and the constant phase shift that is undergone by said set of atoms comprises the term 2T.sup.2, where T is a base time for a sequence of interactions between the atoms and photons that is implemented to form the atomic interference of said set of atoms, and is the rate of variation of frequency of the laser radiation.

19. Method according to claim 4, in which said at least one internal parameter comprises a rate of variation of frequency of laser radiation that is used to form the atomic interference for one of the sets of atoms (11, 12), and the constant phase shift that is undergone by said set of atoms comprises the term 2T.sup.2, where T is a base time for a sequence of interactions between the atoms and photons that is implemented to form the atomic interference of said set of atoms, and is the rate of variation of frequency of the laser radiation.

20. Method according to claim 5, in which said at least one internal parameter comprises a rate of variation of frequency of laser radiation that is used to form the atomic interference for one of the sets of atoms (11, 12), and the constant phase shift that is undergone by said set of atoms comprises the term 2T.sup.2, where T is a base time for a sequence of interactions between the atoms and photons that is implemented to form the atomic interference of said set of atoms, and is the rate of variation of frequency of the laser radiation.

Description

(1) Other particular features and advantages of the present invention will become apparent from the following description of non-limitative implementation examples, with reference to the attached drawings, in which:

(2) FIG. 1 is a principle diagram of an apparatus for measurement by atomic interferometry according to the present invention;

(3) FIG. 2 shows steps of a session of measurements carried out using the apparatus according to FIG. 1;

(4) FIG. 3 shows a particular sequence of interactions for creating an atomic interference, which can be used for implementing the invention;

(5) FIG. 4a is a diagram showing how a value for an external parameter is obtained using a method according to the invention; and

(6) FIG. 4b is a simplified version of the diagram in FIG. 4a, proposed for certain implementations of the invention.

(7) For sake of clarity, the dimensions of the elements that are shown in these figures do not correspond to real dimensions or to proportions of real dimensions. Moreover, identical references that are indicated in different figures denote elements that are identical or that have identical functions.

(8) As shown in FIGS. 1 and 2, an apparatus according to the invention comprises a source of atoms 100 that is used for producing two sets of cold atoms 11 and 12, corresponding to step 1 in FIG. 2. Preferably, the atoms of set 11 may be .sup.85Rb atoms, and those of set 12 may be .sup.87Rb atoms. The source 100 has the function of trapping the atoms of each set 11, 12 and cooling them to a specified temperature. It may have one of the structures known to a person skilled in the art, such as a magneto-optical trap. Such a trap comprises a pair of coils (not shown) in anti-Helmholtz configuration, which are supplied with electric current during a first phase of operation of the trap in order to create a magnetic field gradient at the location in which each set of atoms is held. Three pairs of laser beams cross at this location, propagating in opposite directions for two beams of one and same pair. Thus, beams F.sub.1 and F.sub.2 propagate in opposite directions along the z axis, beams F.sub.3 and F.sub.4 along the x axis and beams F.sub.5 and F.sub.6 along the y axis. Different methods of forming beams F.sub.1-F.sub.6, in particular using reflecting mirrors such as mirror 101 in order to reduce the number of laser sources that are required, are so well known that it is not necessary to repeat them. In a second phase of operation of the magneto-optical trap, the magnetic field gradient is suppressed and the radiation frequencies of the laser beams are detuned in order to obtain the sets of cold atoms 11 and 12, called molasses.

(9) Actually, the source 100 may comprise two injectors of atoms, of .sup.85Rb and of .sup.87Rb respectively, and the magneto-optical trap is controlled in order to produce two entangled trapping structures, that are intended for the .sup.85Rb atoms and the .sup.87Rb atoms respectively. The source 100 is adjusted so that the two sets 11 and 12 are available at the same time and at the same location, for each to be subjected to a sequence of interactions with photons independently of the other set of atoms.

(10) The sequences of interactions with the photons are then produced simultaneously for the two sets of atoms 11 and 12, corresponding to steps 2.sub.1 and 2.sub.2, in order to produce an atomic interference for each of these sets independently of the other set. Each sequence may comprise a series of laser pulses in order to cause stimulated transitions between two states of the atoms of set 11 or 12 to which the sequence is dedicated. Several sequences of pulses may be used alternately, including that which is usually called Mach-Zehnder and is described in the article entitled Atomic interferometry using stimulated Raman transitions, by M. Kasevich et al., Phys. Rev. Lett. 67, pp. 181-184 (1991) and which is recalled now: a first pulse, called /2 pulse and having a splitting function for the wave function of the initial set of atoms, in order to produce two atomic wave packets; a second pulse, called and having an atomic mirror function for each atomic wave packet; and then a third pulse, again /2 and having a function of recombination of the atomic wave packets.

(11) This sequence of interactions is shown in FIG. 3, in which t denotes time, and A, B, C and D denote the interactions that a part of the set of atoms in question is subjected to each time. k denotes the moduli of the wave vector k.sub.11 and k.sub.12 alternately, which are defined just afterwards for the sets of atoms 11 or 12 respectively, and similarly for T, which denotes the base times T.sub.11 and T.sub.12 alternately.

(12) Each interaction of one of the laser pulses with an atom of one of the sets 11/12 is generally of the multiphoton type, and uses the two laser beams F.sub.1 and F.sub.2, which propagate in opposite directions in parallel with a common direction (see FIG. 1). The modulus of the wave vector k.sub.11/12 then corresponds to the total momentum p.sub.tot that is transferred to the atomi.e. received or lost by the atomduring such multiphoton interaction: k.sub.11/12=2P.sub.tot/h=N.sub.11/12k.sub.laser=N.sub.11/122/.sub.laser, where h is Planck's constant, k.sub.laser and .sub.laser are respectively the modulus of the wave vector and the wavelength of the laser radiation constituting beams F.sub.1 and F.sub.2 (k.sub.laser=2/.sub.laser), and N.sub.11 and N.sub.12 denote the numbers of photons that are involved in each multiphoton interaction, for an atom of set 11 or for an atom of set 12, respectively. The two numbers N.sub.11 and N.sub.12 can be selected independently of one another, from the conditions of formation of the atomic interference for the set of atoms in question. Thus, these conditions determine the types of multiphoton interactions that are generated and the number N.sub.11/12 of photons that are involved in each interaction. For example, each multiphoton interaction may be a diffraction of the atoms by optical gratings that are formed with beams F.sub.1 and F.sub.2, in Bragg mode or in Bloch oscillation mode with atomic transitions without internal change of state for the atoms. The article entitled 102k Large Area Atom Interferometers by S-w. Chiow, T. Kovachy, H-C. Chien and M. A. Kasevich, Phys. Rev. Lett. 107, 130403 (2011), describes employing multiphoton Bragg interactions by producing each pulse of radiation of the sequence that forms the atomic interference in the form of a series of base subpulses. Alternatively, each multiphoton interaction may be a Raman transition, or a double diffraction by an optical grating, i.e. atomic transitions that are accompanied by changes of the internal state of the atom.

(13) T.sub.11/12 is the base time that separates the successive laser pulses in the sequence of interactions between the atoms of the set 11/12 and the photons. In the Mach-Zehnder sequence pulses described above, T.sub.11/12 is the length of time that separates the first pulse with a splitting function from the second pulse with a mirror function, and that also separates this second pulse from the third pulse with a recombination function. T.sub.11 thus relates to the sequence of pulses that is used to form the atomic interference of the set of atoms 11, and T.sub.12 relates to the sequence of pulses that is used to form the atomic interference of the set of atoms 12. For example, the base times T.sub.11 and T.sub.12 may be between 50 ms (millisecond) and 150 ms.

(14) In general, the two sequences of interactions, the types of the interactions between the atoms and the laser radiation and the base times that are used separately for the two sets of atoms, may be identical or different.

(15) In particular, the apparatus configuration that is described in the article A cold atom pyramidal gravimeter with a single laser beam, by Q. Bodart et al., Appl. Phys. Lett. 96, 134101 (2010), may be adopted. The magneto-optical trap and the means for producing the conditions of atomic interference are produced using a single laser source assembly, comprising the laser source 102 and the control unit 103. Such an apparatus configuration is simple, economical and very compact. Moreover, the same laser source assembly can be used for both sets of atoms 11 and 12, as described in the article entitled Simultaneous Dual-Species Matter-Wave Accelerometer, by A. Bonnin, N. Zahzam, Y. Bidel and A. Bresson, Phys. Rev. A 88, 043615 (2013), so that it has the following four functions: trapping and cooling the atoms of set 11; trapping and cooling the atoms of set 12; producing the pulses for creating the atomic wave interferences for the set of atoms 11; and producing the pulses for creating the atomic wave interferences for the set of atoms 12.

(16) Each interferometry measurement then proceeds by detection of the proportion of the atoms of the corresponding set that are in a specified state, for example one of two fundamental hyperfine states. Several different techniques are known to a person skilled in the art for carrying out such a detection. For example, it may be a measurement of light absorption, with pulses of radiation the wavelength of which is selected in order to cause absorption from just one of the hyperfine atomic states. Such detections are carried out independently for the two sets of atoms 11 and 12, according to steps 3.sub.1 and 3.sub.2 in FIG. 2. Suitable detection devices are also assumed to be known, and are not shown in FIG. 1 for the sake of clarity.

(17) A first measurement result, denoted P.sub.11, is thus obtained for the set of atoms 11, and a second measurement result, denoted P.sub.12, is also obtained for the set of atoms 12. The set of steps formed by the production of the two sets of atoms 11 and 12 (step 1), the production of the simultaneous sequences of interactions with photons, for the two sets of atoms respectively (steps 2.sub.1 and 2.sub.2), and the two detections of the proportions of atoms that are finally in a specified state for obtaining the measurement results P.sub.11 and P.sub.12 (steps 3.sub.1 and 3.sub.2), constitute a session of measurements. Such a session is characterized by the simultaneity of the sequences of interactions that produce the atomic interferences, and the co-localization of the sets of atoms during these sequences, whereas the atoms of the two sets are of different species.

(18) Under these conditions, the measurement result P.sub.11 is linked to the component a along the z axis of the acceleration a that the atoms of set 11 undergo, by the following two relationships:
P.sub.11=P.sub.0.Math.[1Ccos(.sub.tot|.sub.11)]
.sub.tot|.sub.11=.sub.11(a)+.sub.op|.sub.11
where P.sub.0 and C are two known non-zero numbers; .sub.tot|.sub.11 is the total phase shift undergone by the atoms of set 11 during the formation of the atomic interference that is intended for them; .sub.11(a) is the part of the total phase shift .sub.tot|.sub.11 that is caused by the acceleration component a. In particular, when the magnetic field is zero or uniform during formation of the atomic interference for the set of atoms 11:
.sub.11(a)=k.sub.11T.sub.11.sup.2a; and .sub.op|.sub.11 is the constant phase shift, which depends on the manner of producing the interference conditions for the set of atoms 11. The constant phase shift .sub.op|.sub.11 depends on operating conditions that are undergone reproducibly, and on parameters internal to the atomic interferometry apparatus, which are controlled for each measurement carried out with the set of atoms 11.

(19) In the same way, for the atoms of set 12, the measurement result P.sub.12 is linked to the same value of component a along the z axis of the acceleration a by the following two other relationships:
P.sub.12=P.sub.0.Math.[1Ccos(.sub.tot|.sub.12)]
.sub.tot|.sub.12=.sub.12(a)+.sub.op|.sub.12
where P.sub.0 and C are two known non-zero numbers, which may or may not be different from P.sub.0 and C; .sub.tot|.sub.12 is the total phase shift undergone by the atoms of set 12 during the formation of the atomic interference that is intended for them, .sub.12(a) is the part of the total phase shift .sub.tot|.sub.12 that is caused by the acceleration component a. Once again, in particular, when the magnetic field is zero or uniform during formation of the atomic interference for the set of atoms 12: .sub.12(a)=k.sub.12T.sub.12.sup.2a; and .sub.op|.sub.12 is the constant phase shift, which depends on the manner of producing the interference conditions for the set of atoms 12. It also depends on the operating conditions that are undergone reproducibly, and on internal parameters that are controlled for each measurement carried out with the set of atoms 12.

(20) In connection with the terms that have been used in the general part of the present description: P.sub.11 as a function of .sub.tot|.sub.11 has been called first function, effective for the set of atoms 11; .sub.11 as a function of a, has been called second function, effective for the set of atoms 11; P.sub.12 as a function of .sub.tot|.sub.12 has also been called first function, but effective for the set of atoms 12; .sub.12 as a function of a, has also been called second function, but effective for the set of atoms 12; and a is the external parameter the value of which is sought.

(21) The external parameter a that is measured may be a component of an acceleration, for example due to a translational or rotational movement of a device carrying the apparatus for measurement by atomic interferometry, or may be a component of a gravitational field in which the apparatus is located.

(22) The first functions P.sub.11(.sub.tot|.sub.11) and P.sub.12(.sub.tot|.sub.12) are not necessarily identical for implementing the invention, but they will be assumed to be identical in the remainder of the present description, for the sake of simplicity.

(23) Similarly, the second functions .sub.11(a) and .sub.12(a) are not necessarily identical, in particular when the types of interactions of the atoms with the laser radiation, and/or the sequences of interactions are different for the two sets of atoms 11 and 12, and/or when a magnetic field gradient is applied to the sets of atoms 11 and 12 during formation of the atomic interferences.

(24) According to the invention, the conditions of formation of the atomic interferences for the sets of atoms 11 and 12 are selected so that the difference between the total phase shifts .sub.tot|.sub.11 and .sub.tot|.sub.12 is of the order of /2 in absolute value and modulo , for example equal to /2. This quadrature relationship ensures that the two cosines of the functions P.sub.11(.sub.tot|.sub.11) and P.sub.12(.sub.tot|.sub.12) are not equal to +1 or 1 simultaneously, so that one of the two sets of atoms 11 and 12, for which the value of the cosine is sufficiently different from +1 and 1, makes it possible to determine the acceleration component a with satisfactory accuracy. However, that one of the sets of atoms 11 or 12 that provides the value of the acceleration component a with the best accuracy may change as a function of the value of a that is finally obtained. However, the invention ensures that one or the other of the two sets of atoms provides the value of a with satisfactory accuracy.

(25) Moreover, the difference between the total phase shifts .sub.tot|.sub.11 and .sub.tot|.sub.12 may only be adjusted to the value /2 or close to this value, in absolute value and modulo , in a restricted interval around the real value of the acceleration component a. Indeed, as stated above, the two terms .sub.11(a) and .sub.12(a) of the total phase shifts .sub.tot|.sub.11 and .sub.tot12 may be different, so that a quadrature relationship that exists for one value of the acceleration component a no longer exists for another possible value of the acceleration component a. The quadrature relationship, exact or in an approximate extent, is therefore necessary for the value of the acceleration component a that is finally deduced from each session of measurements.

(26) A first implementation of the invention uses at least one phase jump between two pulses of laser radiation of the sequence that is used for the set of atoms 11. It may be assumed by way of example that this sequence is of the Mach-Zehnder type that was described above, and the respective phases of the laser radiation of the pulses are compared when they are referred to one and same time point and one and same point in space. The difference that appears under these conditions between the phases of the laser radiation of two pulses of the sequence is called the phase jump. In a known manner, such phase jump can easily be adjusted to any value, between 0 and 2, the zero value being possible, using microwave sources, in particular for laser radiation from Raman sources. Then the constant phase shift .sub.op|.sub.11 that is present in the wave function of the atoms of set 11 at the end of the atomic interference is: .sub.op|.sub.11=.sub.12.sub.2+.sub.3, where .sub.1, .sub.2 and .sub.3 denote the respective phases of the laser radiation of the three successive pulses of the Mach-Zehnder sequence, when these phases are brought to the same time point and to the same point in space. For example, when a phase jump of amplitude is introduced between the first pulse with the splitting function and the second pulse with the mirror function, and no phase jump is introduced between this second pulse and the third pulse with the recombination function, then: .sub.2=.sub.3=.sub.1+ and .sub.op|.sub.11 =+.sub.inv|.sub.11 where .sub.inv |.sub.11 is a phase shift of atomic interference which may exist unintentionally, for example owing to the apparatus used. In principle, the unintentional phase shift .sub.inv|.sub.11 is constant and reproducible for successive sessions of measurements. In general for a Mach-Zehnder sequence: .sub.op|.sub.11=.sub.2-3|.sub.11.sub.1-2|.sub.11, where .sub.1-2|.sub.11 is the amplitude of the phase jump between the first pulse and the second for the set of atoms 11, and .sub.2-3|.sub.11 is the amplitude of the phase jump between the second pulse and the third for the same set of atoms. By controlling the amplitudes of the phase jumps for the two sets of atoms 11 and 12 separately, each in the way that has just been described for the set of atoms 11, the difference between the total phase shifts .sub.tot|.sub.11 and .sub.tot|.sub.12 can be adjusted to /2 modulo , whatever the unintentional phase shifts .sub.tot|.sub.11 and .sub.tot|.sub.12 that may exist for the two sets of atoms 11 and 12 respectively.

(27) FIG. 4a shows such implementation of the invention. For the purposes of illustration, the following values were adopted for the constants: P.sub.0=P.sub.0=0.5 and C=C=1.0. In the diagram, the horizontal axis gives the values of the external parameter a in arbitrary units, and the vertical axis, generically denoted P, gives the values of the measurement results P.sub.11 and P.sub.12. The two curves denoted P.sub.11(a) and P.sub.12(a) correspond to the formulae that were given above. They therefore have a common period, equal to 2/(kT.sup.2), and are displaced from one another by /(2kT.sup.2), where k is the modulus of the wave vector that corresponds to the momentum transferred at each interaction between an atom and the laser radiation of a pulse, and T is the base time of the sequences of pulses. The values of k and T are assumed to be common to both sets of atoms 11 and 12, so that the second function of the acceleration component a, thus common to both sets of atoms, is .sub.11(a)=.sub.12(a)=kT.sup.2a. For a real value of the acceleration component a, the diagram shows the two measurement results that are obtained in one and the same session of measurements: P.sub.11meas(a) for the set of atoms 11 and P.sub.12meas(a) for the set of atoms 12. The value of the external parameter a that is deduced from each session of measurements is therefore the common abscissa value in the diagram in FIG. 4a, which solves the two equations P.sub.11(a)=P.sub.11meas and P.sub.12(a)=P.sub.12meas simultaneously. In the example shown, the measurement result P.sub.12meas is located close to an extremum (minimum in this case) of the curve P.sub.12(a). The derivative of P.sub.12(a) with respect to the acceleration component a, at this location on the curve is low in absolute value, so that deducing the value of the acceleration component a from this measurement result P.sub.12meas does not have good accuracy. In contrast, the derivative of P.sub.11(a) with respect to the acceleration component a, for the same value of the acceleration component a, is greater than that of P.sub.12(a), in absolute values. For this reason, the measurement result value P.sub.11meas makes it possible to deduce the value of the acceleration component (a) with better accuracy than is provided by the measurement result value P.sub.12meas . This analysis of the measurement results P.sub.11meas and P.sub.12meas for arriving at the value of the external parameter a corresponds to steps 4 and 5 in FIG. 2 and can be executed by an analysis unit (not shown) using a dedicated program. In FIG. 4a, the value for the acceleration component a that is thus obtained from one of the two curves P.sub.11(a) or P.sub.12(a), here P.sub.11(a) in the example shown, is denoted a.sub.obt.

(28) Based on these considerations, the diagram in FIG. 4b is deduced from that in FIG. 4a, only retaining, for each real value of the acceleration component a, the portion of that of the two curves P.sub.11(a) and P.sub.12(a) that provides the best accuracy. The relationship between the measurement results P.sub.11 and P.sub.12 on the one hand, and the value of the acceleration component a on the other hand, is then made up of segments that belong in turn to one or other of the two curves P.sub.11(a) and P.sub.12(a), changing the curve at each intersection between the latter. Moreover, the inventors found that each segment of curve thus identified could be replaced with a rectilinear segment joining the two points of intersection of curves P.sub.11(a) and P.sub.12(a), which define the ends of the segment in question. Each rectilinear segment then has a length equal to /(2kT.sup.2) in projection on the horizontal axis, corresponding to a length equal to /2 when it is expressed with respect to the total phase shifts.

(29) A second implementation of the invention uses at least one of the rates of variation of frequency of the laser radiation that is used to form the atomic interferences for the sets of atoms 11 and 12. If .sub.11 and .sub.12 denote these rates of variation of frequency of laser radiation, for the two sets of atoms 11 and 12 respectively, then .sub.op|.sub.11=2.sub.11T.sub.11.sup.2 and .sub.op|.sub.12=2.sub.12 T.sub.12.sup.2. Subject to the same hypotheses of identity of the interactions between atoms and radiation, of identity of the sequences of pulses between the two sets of atoms 11 and 12, and of identity of the base times, the diagrams in FIGS. 4a and 4b also apply to this second embodiment of the invention.

(30) A third implementation of the invention uses a magnetic field gradient to which the two sets of atoms 11 and 12 are subjected during formation of the respective atomic interferences. For this, a component of the magnetic field B along the z axis may vary linearly as a function of the z coordinate (FIG. 1) as to follows: B(z)=B.sub.0+B.sub.1z, where B.sub.0 is the average intensity and B.sub.1 is the gradient of the magnetic field. Advantageously, the magnetic field B(z) may be produced by coils in anti-Helmholtz configuration of the magneto-optical trap. Then, the second function of the acceleration component a has an additional term, according to the following relationship for the set of atoms 11:
.sub.11(a)=k.sub.11T.sub.11.sup.2a+2A.sub.at|.sub.11B.sub.0B.sub.1T.sub.11.sup.3a
where A.sub.at|.sub.11=2 .sub.B.sup.2/(.sup.2G.sub.at|.sub.11), .sub.B denoting the Bohr magneton, G.sub.at|.sub.11 denoting the energy difference between the two hyperfine states of the Raman transition of the atoms of set 11, when such interaction between atoms and radiation is used, and being equal to h/(2) where h is Planck's constant. Simultaneously, the constant phase shift becomes:
.sub.op|.sub.11=A.sub.at|.sub.11B.sub.0B.sub.1k.sub.11T.sub.11.sup.2/M.sub.at|.sub.11+.sub.inv|.sub.11
where M.sub.at|.sub.11 denotes the mass of each atom of set 11.

(31) Similarly, the second function of the acceleration component a for the set of atoms 12 becomes, in the presence of the magnetic field gradient B:
.sub.12(a)=k.sub.12T.sub.12.sup.2a+2A.sub.at|.sub.12B.sub.0B.sub.1T.sub.12.sup.3a
and for the constant phase shift:
.sub.op|.sub.12=A.sub.at|.sub.12B.sub.0B.sub.1k.sub.12T.sub.12.sup.2/M.sub.at|.sub.12+.sub.inv12
where A.sub.at|.sub.12=2 .sub.B.sup.2/(.sup.2G.sub.at|.sub.12), G.sub.at|.sub.12 denoting the energy difference between the two hyperfine states of the Raman transition of the atoms of set 12, and M.sub.at|.sub.12 denoting the mass of each atom of set 12. For example, when the atoms of set 11 are the .sup.85Rb isotope: A.sub.at|.sub.11=2129010.sup.8 Hz/T.sup.2 and M.sub.at|.sub.1=1.41010.sup.25 kg, and when the atoms of set 12 are the .sup.87Rb isotope: A.sub.at|.sub.12=2 57310.sup.8 Hz/T.sup.2 and M.sub.at|.sub.12=1.44310.sup.25 kg. Thus, it is possible to select suitable values for the intensity B.sub.0 and the gradient B.sub.1 of the magnetic field, for which the difference between the total phase shifts .sub.tot|.sub.11 and .sub.tot|.sub.12 is once again equal to /2 modulo . Depending on the method used for producing the magnetic field, its intensity B.sub.0 and its gradient B.sub.1 may be proportional to one another. However, owing to the difference in value between the two coefficients A.sub.at|.sub.11 and A.sub.at|.sub.12, the periods of the two curves P.sub.11(a) and P.sub.12(a) are no longer identical even when k.sub.11=k.sub.12 and T.sub.11=T.sub.12, so that the quadrature relationship is only adjusted by the invention locally, around the value a.sub.obt of the acceleration component a.

(32) It is understood that the invention can be modified or adapted relative to the detailed description that has just been given. In particular, the pulse sequence that forms each atomic interference is not necessarily of the Mach-Zehnder type, but can be replaced with one of the other sequences known to a person skilled in the art for forming atomic interference.

(33) The three embodiments that have been described, using the phase jumps between successive pulses of the laser radiation, the rate of variation of the frequency of the laser radiation, and the magnetic field, can be combined. The contributions to the phase shifts that are accumulated during formation of each atomic interference are then added together.

(34) Finally, the type of each interaction between atoms and photons that is caused in each sequence can be varied, provided that the combination of the interactions of the sequence once again forms an atomic interference, and that the wave vectors associated with the total momenta that are transferred to the atoms during these interactions satisfy the present invention.