Two-photon optical frequency reference system with auxiliary laser for light-shift cancellation

Abstract

An optical frequency generation system (100), comprising: - reference atoms (7) in a gas phase, - an interrogation laser source (1) configured to emit an interrogation signal (101) comprising a first optical frequency suitable for exciting a two-photon transition in said reference atoms (7), said interrogation signal (101) being configured to interact with said reference atoms (7) in a Doppler-free scheme; - optical frequency modulation means (31, 31a, 31b) configured to adjust said first optical frequency and to modulate said first optical frequency at a first modulation frequency f1; - an optical sensor (9) configured to detect a fluorescence signal (110) from said reference atoms (7); - a first control loop (10) configured to lock said first optical frequency to a resonance frequency of said two-photon transition, said fluorescence signal (110) being input into the first control loop (10); - a mitigation laser source (2) configured to emit a mitigation signal (102) comprising a second optical frequency selected to produce a light-shift of said two-photon transition of opposite sign of the light-shift produced by the interrogation signal (101); characterized in that the optical frequency generation system (100) further comprises: - optical amplitude modulation means (5) configured to modulate the amplitude of the interrogation signal (101) and of the mitigation signal (102) at a second modulation frequency f2, and - a second control loop (20) configured to adjust the relative amplitude of the mitigation signal (102) with respect to the interrogation signal (101) such as to cancel the effective light-shift of the combined interrogation (101) and mitigation (102) signals.

Description

[0001] Two-photon optical frequency reference system with auxiliary laser for light-shift cancellation

[0002] Technical Field

[0003] The invention is in the field of optical atomic clocks. More specifically it concerns optical atomic clocks based on a Doppler-free atomic transition interrogation.

[0004] In particular, the invention relates to a frequency generation system based on an optical transition driven by a first laser source (interrogation laser) with a Doppler-free scheme. The system further comprises an auxiliary laser, non-resonant with the optical transition, configured to actively cancel the light shift of the optical transition caused by the interrogation laser.

[0005] The invention also relates to a method of operating such frequency generation system.

[0006] State of the art

[0007] High stability clocks are increasingly needed for everyday applications such as navigation and telecommunications, as well as for high-end instrumentation.

[0008] In US10684591 B1 , and the related scientific publication Martin et al. “Compact Optical Atomic Clock Based on a Two-Photon Transition in Rubidium”, PHYSICAL REVIEW APPLIED 9, 014019 (2018), hereinafter referred to as “Martin2018”, an optical atomic clock based on an optical two-photon transition of Rubidium interrogated with a Doppler-free scheme is disclosed. This system presents a convenient compromise between size, complexity, and frequency stability. Two-photon transitions are attractive because they enable Doppler-free excitation of an optical atomic transition in an atomic vapor cell, leading to a high resonance quality factor Q, provided by two counter-propagating laser beams. Moreover, the two- photon transition can be observed via a fluorescence signal which can be spectrally separated from the probe laser.

[0009] One of the major sources of instability in atomic clocks comes from the AC Stark shift affecting the transition frequency of the atoms, resulting from the optical field of the interrogation laser itself. Power variations of the interrogation laser generate fluctuations of the energy of the reference transition, producing thus instability in the clock frequency. This is commonly referred to as light-shift instability.

[0010] Several approaches to mitigate the light shift instability are discussed in Martin et al. “Frequency shifts due to Stark effects on a rubidium two- photon transition”, PHYSICAL REVIEW A 100, 023417 (2019), hereinafter referred to as “Martin2019”.

[0011] One of them is the stabilization of the laser power. This most obvious approach is however limited by the technical possibilities to stabilize the laser power at the required level. For example, Martin et al. estimate that the optical power must be stabilized to 2.1 pW to achieve 1 E-15 clock instability (Matin2018). Just measuring such minor power fluctuations is already a significant technical challenge. Also, beyond that problem, the drift of the detector and voltage reference will ultimately result in the drift of the clock frequency.

[0012] Another approach is based on a two-color excitation of the transition, but this leads to residual Doppler broadening, because the k vectors of the excitation photons no longer match.

[0013] Finally, a last alternative is proposed where a second laser, off-resonance from the virtual and intermediate states of the two-photon transition, is directed to the atomic vapor. The wavelength of this second laser, in the following referred to as the “mitigation laser”, is chosen such that the AC Stark shift generated by this field is opposite in sign to that of the interrogation laser. The optical powers of the interrogation and mitigation lasers can then be adjusted to a ratio where the resulting light shift is effectively cancelled. This approach allows stabilizing the laser powers with respect to each other, thus reducing the requirements on detector sensitivities and drift, as well as eliminating a need for a precise voltage reference. However, frequency drifts in the mitigation laser would cause the variation of the Stark-shift cancelling power ratio, imposing a new requirement of frequency stabilization of the mitigation laser. The solution to this problem proposed in Martin2019 is to implement a Volume Bragg grating stabilized laser, as those developed for Raman spectroscopy experiments (mitigation laser principle proposed but not validated by experimental results in this reference paper). Unfortunately, even if those lasers offer improved frequency stability as compared to standard laser diodes, they are also subject to long term drifts, for example driven by temperature fluctuations.

[0014] In general, any attempts to stabilize the interrogation and mitigation lasers upstream and independently of the probed two-photon transition will result in added complexity to the system and will always be limited by long-term drifts of the stabilization loops.

[0015] In a recently published Dissertation from the University of Arizona (Seth E. Erickson, “An Optical Atomic Clock Based On Frequency Comb Spectroscopy”; https: / / repository.arizona.edu / handle / 10150 / 671250 available since July 21 , 2024) an approach is disclosed, implementing interrogation and mitigation lasers, with a control loop aiming to adjust their relative powers to cancel the light shift, based on a direct measurement of said light shift at a provided modulation frequency. As mentioned by the author, the implementation of the disclosed system resulted in a degradation of the stability performance for reasons which the author was not able to identify.

[0016] There is thus a need for one such system where the cancellation of the light-shift does not entirely depend on the stabilization of the interrogation and mitigation lasers at pre-determined ideal values which can drift away from the optimal performance.

[0017] Disclosure of the invention

[0018] It is an aim of the present invention to propose a frequency generation system, based on a Doppler-free two-photon atomic transition with active light-shift cancellation, wherein said light-shift cancellation does not entirely rely upon pre-determined operating values which can drift away from the optimal performance.

[0019] According to the present invention, the power of the mitigation laser is adjusted in a feedback loop, to cancel the DC light-shift, by directly sensing the light shift of the reference atomic transition at a modulation frequency.

[0020] A system according to the invention is defined by claim 1 .

[0021] Several embodiments of the system are defined by dependent claims 2 to 16.

[0022] A clock according to the invention is defined by claim 17.

[0023] An operating method according to the invention is defined by claims 18 to 21.

[0024] Brief description of the drawings Figure 1 shows a schematic representation of a system according to a first embodiment of the invention.

[0025] Figure 2 shows a schematic representation of a second embodiment of a system according to the invention.

[0026] Figure 3 shows a qualitative representation of the relation between the total intensity of the optical beams interacting with the atoms and the energy of the two-photon atomic transition for different ratios of combined interrogation and mitigation signals.

[0027] Embodiments of the invention

[0028] The following paragraphs can be understood with reference to either figure 1 or 2, unless it is explicitly indicated that a paragraph refers to specific aspects which differ between the two represented embodiments.

[0029] A first embodiment of a system 200 for the control, adjustment or certification of timepieces is described hereafter with reference to figure 1 . For example, the system allows to obtain an accurate measure the rate of timepieces, notably an accurate measure of the daily rate of timepieces.

[0030] The system 200 includes an optical atomic clock 300 which includes an optical frequency generation system 100.

[0031] The optical frequency generation system 100 comprises:

[0032] - an interrogation laser source 1 ,

[0033] - a mitigation laser source 2,

[0034] - optical amplitude modulation means 5,

[0035] - reference atoms 7 in a gas phase,

[0036] - an optical sensor 9,

[0037] - a first control loop 10 for controlling an optical frequency modulation means 31 that supplies power to the interrogation laser source 1 , and

[0038] - a second control loop 20 for controlling the optical amplitude modulation means 5 and a power modulation means 32 that supplies power to the mitigation laser source 2.

[0039] The first control loop 10 comprises:

[0040] - a first RF source 11 ,

[0041] - a first mixer 13,

[0042] - a low pass filter 15, and

[0043] - a first PID controller 17.

[0044] In the first embodiment, the first control loop 10 further comprises a summing-circuit 19.

[0045] The second control loop 20 comprises:

[0046] - a second RF source 21 ,

[0047] - a band pass filter 22,

[0048] - a second mixer 23,

[0049] - a low pass filter 25, and

[0050] - a second PID controller 27.

[0051] In a preferred embodiment, the reference atoms 7 of the frequency generation system 100 are Rubidium atoms in gas phase. Conveniently, the transition 5SI / 2 5Ds / 2 can be excited by a two-photon absorption of an optical signal at 778.1 nm. This wavelength can be easily obtained from currently available laser sources as will be discussed later with reference to the interrogation laser source 1 of the system.

[0052] The reference atoms 7 in gas phase are preferably contained in a sealed and thermally stabilized vapor cell containing no other gas, or controlled buffer gases. On the other hand, the invention could also be implemented with reference atoms 7 provided as an atomic jet or fountain, as known from the prior art.

[0053] The interrogation laser source 1 is a continuous wave laser (cw-laser), which emits the interrogation signal 101. The specific nature of this interrogation source 1 is mainly determined by the atomic species 7 and the transition to be probed, which defines the target wavelength.

[0054] For example, the transition 5SI / 2 5Ds / 2 of Rb can be excited by two- photon absorption of an optical signal 101 at 778.1 nm. This optical signal can be obtained directly from a laser diode with primary output at this wavelength or from second harmonic generation (SHG) from a primary laser source at 1556.2 nm. Conveniently, this 1556.2nm wavelength falls within the telecommunication C-band and can be procured from mature laser technologies including stable laser diodes and Er-doped fiber amplifiers, which can generate a high-power signal for efficient SHG.

[0055] Not represented in the figures, the interaction between the reference atoms 7 and the interrogation signal 101 can be advantageously configured in a Doppler free scheme as described, for example, in Martin2018. In this case, the interrogation signal 101 is directed across the transparent windows of the vapor cell containing the reference atoms 7 and is retroreflected by a cat’s-eye reflector in precise antiparallel direction across the same path through the vapor cell. The two-photon transition involving counter-propagating photons is Doppler-insensitive and highly advantageous compared to the two-photon transition resulting from the absorption of two photons having the right energy according to the Doppler shift of the moving atoms. As a result, the absorption line is mostly unaffected by Doppler broadening, leading to a narrow resonance and a high quality factor. The detector 9 can be any photodetector suitable for detecting the fluorescence of the reference atoms 7 after excitation of the two-photon transition. For example, the transition 5SI / 2 5Ds / 2 of Rb produces fluorescence at a wavelength around 420 nm. Advantageously, the photodetector 9 can comprise an optical filter adapted to block scattered light, particularly at the wavelengths of the interrogation signal 101 and mitigation signal 102. Preferably, such optical filter comprises a band-pass filter allowing the transmission of a narrow optical band corresponding to the fluorescence band of the reference atoms 7, such as to remove any scattered and background light from the detected signal.

[0056] Importantly, the photodetector 9 must present a response bandwidth in the range, or preferably higher than the first modulation frequency f1 of the system 100. This frequency f1 can be comprised between 1 kHz and 10 MHz, preferably between 10 kHz and 1 MHz.

[0057] Suitable detectors 9 include photodiodes or photomultiplier tubes, or avalanche photodiodes.

[0058] The optical frequency of the interrogation signal is modulated at a first modulation frequency f1 , as required for the stabilization scheme that will be described in the following paragraphs. Different means 31 , 31 a, 31 b for producing said frequency modulation can be provided. Those means may be integrated in the interrogation laser source 1 (31 , 31 a), or be provided by an external device 31 b, downstream of the laser source 1 (as represented in figure 2). Such external device 31 b may be an Electro-optic Modulator (EOM).

[0059] For example, if the interrogation laser source 1 is a laser diode, the optical frequency can be modulated directly at the source by acting on the current injected to the diode. This integrated actuator 31 is suitable for both a low- bandwidth adjustment of the optical frequency, and an RF modulation at the first modulation frequency f1 , up to hundreds of kHz or even MHz.

[0060] Alternatively, or in combination with the injection current, the optical frequency of the interrogation signal 101 could be adjusted at the laser source 1 by acting on the temperature of the laser diode. This type of actuator 31 can be rapid enough to maintain the low-bandwidth optical frequency stability (up to a few kHz), but would not be suitable for introducing the necessary modulation at the first modulation frequency f1 . In that case, a temperature actuation 31 a, could be combined with another source-integrated fast actuator (e.g. injection current), or more advantageously, with an independent downstream actuator 31 b, such as an EOM, which can provide frequency-modulation with bandwidths up to the GHz range.

[0061] Another advantageous implementation of the integrated frequency actuator 31 , 31 a can be a piezo-electric actuator configured to modify the effective laser cavity length, for example, in an external-cavity diode laser or in a fiber Bragg grating laser. The advantage of such implementation is that in this case there is almost no coupling between the frequency actuation and any amplitude modulation. Depending on the actuation bandwidth of such piezo-system, the actuator could be used for both optical frequency-correction and modulation at f 1 , or be used in combination with the external actuator 31 b as represented on figure 2.

[0062] The modulation of the optical frequency of the interrogation signal 101 results in a modulation of the two-photon absorption efficiency by the reference atoms 7 and consequently, of the fluorescence signal detected by the detector 9. This modulated fluorescence signal 110 is used as input of a first control loop 10, configured to lock the optical frequency of the interrogation signal 101 to the two-photon atomic transition. Not shown in the figures, the frequency-locked interrogation signal 101 can be used as reference optical signal for stabilizing a frequency comb to provide an RF output of the optical atomic clock 300. Frequency division from an optical frequency reference to an RF output by means of a frequency comb stabilized on said optical frequency reference is a well- known procedure in the field of time and frequency metrology.

[0063] Two possible embodiments of the first control loop 10 are represented in figures 1 and 2. In both cases, there is an RF source 11 , providing an electronic signal 111 at the first modulation frequency f1 . As mentioned earlier, f1 can be comprised between 1 kHz and 10 MHz, preferably between 10 kHz and 1 MHz. The mixer 13, receives the modulated fluorescence signal 110 and demodulates it by mixing with the modulation signal 111. The output signal 113 of the mixer 13 is cleaned from residual modulations by the low-pass filter 15 with cut-off frequency (fcut-15) below the first modulation frequency f1 and below the second modulation frequency f2 (fcut-15 < f2 < f1 ). The filtered signal 115 is provided to the Proportional-Integral-Derivative (PID) controller 17 to generate a low- frequency correction signal 117 adapted to adjust the mean optical frequency of the interrogation signal 101 , locking it to the atomic transition.

[0064] The way in which the correction signal 117 and the modulation signal 111 actuate on the interrogation signal 101 differs between figures 1 and 2. In figure 1 , the correction signal 117 is added to the modulation signal 111 , using for example the summing-circuit 19. The resulting mixed signal 119 is provided to the source-integrated frequency modulation means 31 of the laser source 1 . This configuration is well adapted for example, when the frequency modulation means 31 is the injection current of a laser diode with large modulation bandwidth. By contrast, in figure 2, only the low-bandwidth correction signal 117 is provided to the source-integrated frequency modulation means 31 a. The frequency modulation 111 is introduced in the interrogation signal 101 downstream, through the additional actuator 31 b. This configuration can be implemented for example, by using the temperature control of the laser diode as integrated actuator 31 a, and an external EOM as fast downstream actuator 31 b. Thus, in the second embodiment, there is no summing-circuit 19 as in the first control loop of the first embodiment.

[0065] The mitigation laser source 2 is also a cw-laser which must be selected according to the specific reference atoms 7. The wavelength of the mitigation signal 102 must be selected to produce a light-shift of opposite sign to the light shift induced by the interrogation signal 101 . For example, if the interrogation signal addresses the transition 5SI / 2 5Ds / 2 of Rb, with a wavelength of 778.1 nm, a suitable mitigation signal can be provided at a wavelength of 785 nm, or at a wavelength of 1556.2 nm, which are known to produce a light shift of opposite sign of that of the 778.1 nm light.

[0066] In this example, using a wavelength of 1556.2 nm as mitigation signal 102 can be particularly practical if the interrogation signal is also obtained from SHG from the same laser source. This means that in practice only one laser source would be necessary to provide both the interrogation 101 and mitigation 102 signals in another embodiment (not represented).

[0067] On the other hand, using a wavelength of 785 nm provided from the independent mitigation source 2, has the advantage of enabling independent control of the power and frequency of each laser source 1 , 2. Also, the proximity of the interrogation and mitigation wavelengths facilitates their mixing and guiding through the optical setup, as well as the implementation of amplitude modulation means providing an equivalent modulation on both signals 101 , 102. The interrogation signal 101 and the mitigation signal 102, must overlap in the volume where the interaction with the reference atoms 7 occurs. The spatial combination of the interrogation and mitigation signals may be conveniently performed prior to their modulation by the optical amplitude modulation means 5. Advantageously, the combination may be implemented in fiber using for example:

[0068] • Fused Fiber Wavelength Division Multiplexers (WDMs), also known as wavelength combiners / splitters, or

[0069] • Fiber polarization combiners, or

[0070] • Fused fiber splitter / combiner.

[0071] Alternatively, the laser signals can also be combined in free space, using for example:

[0072] • dichroic mirror, or

[0073] • polarized beam splitter, or

[0074] • Free-space beam splitter / combiner.

[0075] Amplitude modulation means 5 are provided in the system to produce a modulation of the total light-shift at a second modulation frequency f2. The principle of this modulation is explained with reference to figure 3. In the qualitative graphic of this figure, the vertical axis represents the energy of the two-photon atomic transition. The horizontal axis represents the total intensity of the optical beams interacting with the atoms. A first line I, represents the situation where the light shift of the interrogation signal dominates, i.e. the mitigation signal is too weak. In this case the modulation of the overall power (AP) at frequency f2 will produce a modulation of the transition energy of positive sign (i.e. in phase with the power modulation). A second line M represents the situation where the light shift of the mitigation signal dominates, i.e. the mitigation signal is too strong. In this case the modulation of the overall power (AP) at frequency f2 will produce a modulation of the transition energy of negative sign (i.e. in counter-phase with the power modulation). A third line C, represents the ideal situation where the light-shift of the interrogation signal is cancelled by the light shift of the mitigation signal. In this case, the modulation of the overall power (AP) at frequency f2 will produce no modulation of the transition energy. In this ideal situation, the amplitude noise at any frequency of either the interrogation or mitigation signals have no (or minimum) influence on the transition frequency of the atoms.

[0076] The second control loop 20 of the system 100 is configured to adjust the optical power of the mitigation signal 102 to operate in this ideal situation of light-shift cancellation. In other words, the second control loop 20 is configured to adjust the amplitude of the mitigation signal such as to cancel the effective light-shift of the combined interrogation 101 and mitigation 102 signals. Alternatively or complementarily, the second control loop 20 could be configured to adjust the amplitude of the interrogation signal such as to cancel the effective light-shift of the combined interrogation 101 and mitigation 102 signals, since the effective light-shift of the combined interrogation 101 and mitigation 102 signals can be canceled by an adjustment of the relative amplitude of the mitigation signal (102) with respect to the interrogation signal (101 )

[0077] The amplitude modulation means 5 can be implemented using for example an AOM (acousto-optic modulator) or a VOA (variable optical attenuator) such as a MEMS VOA or a liquid crystal modulator.

[0078] An RF source 21 provides the modulation signal 121 at the second modulation frequency f2. As mentioned earlier, f2 should be smaller than the first modulation frequency f1 by a factor of at least 1000, preferably at least 10’000. The amplitude modulation of the interrogation signal 101 , responsible for the atomic transition will result in an amplitude modulation at the same frequency f2 of the fluorescence signal 110. Since this modulation is at a frequency much lower than f1 , the mixer 13 of the first control loop 10 will reject that near-DC component. On the other hand, if the light-shift of the system is not cancelled (regimes I or M in figure 3), the resulting modulation of the transition energy, will be mixed with the modulation of the optical frequency of the interrogation signal 101 , and produce a modulation component of the fluorescence signal 110 at frequency f1 + f2. This will result in a component at frequency f2 of the signal 113 at the output of the mixer 13.

[0079] Clearly, this component at frequency f2 reflecting the regime of the light shift induced by the second modulation, must be rejected from the first control loop 10 which adjusts the optical frequency of the interrogation signal 101. This is why the filter 15 was described before as having a cutoff frequency (fcut-15) below the first modulation frequency f1 and below the second modulation frequency f2 (fcut-15 < f2 < f1 ). This is where the rejection of the component at frequency f2 happens in the first control loop 10. One alternative to this approach, which is not explicitly represented in the figures, is that the filter 15 comprises a low-pass filter with cut-off frequency (fcut-15) below the first modulation frequency f1 (i.e., f2 < fcut-15 < f1 ) and an additional band-stop filter to remove the f2 component from the first control loop 10.

[0080] The signal 113 is sampled as input signal 120 of the second control loop 20 before removing the f2 component. The band-pass filter 22 may be advantageously provided to remove noise around the f2 component, which is the useful part of the input signal 120 for the second control loop 20. The filtered signal 122 is combined in the mixer 23 with the modulation signal 121 to provide a correction signal 123, adapted to adjust the optical power of the mitigation laser source 2 to actively force the system into the lightshift cancelled regime (regime C in figure 3). This signal 123 can advantageously be filtered to remove residual f2 modulation, for example with the low pass filter 25 having a cut-off frequency fcut-25 below the second modulation frequency f2. The additional PID controller 27 may further adapt the correction signal to provide the output 127 which is fed to the power modulation means 32 of the mitigation laser source 2.

[0081] The power modulation means 32 may simply be a control on the injection current of a laser diode, or an attenuator of any form. Bandwidth concerns are negligible in this case, since the correction is made at very low frequency (below f2). A possible shift of the optical frequency of the mitigation laser 2 is also not a concern. Indeed, this would have an influence on the power-ratio of the lasers but the cancelling of the light-shift is still ensured. This system is not controlled to achieve a pre-determined power ratio. On the contrary, this system directly senses the light-shift at the second modulation frequency f2 and adapts the power ratio to cancel said light-shift, whichever power ratio is needed.

[0082] Whatever the embodiment or the variant:

[0083] - the interrogation laser source 1 is configured to emit an interrogation signal 101 comprising a first optical frequency suitable for exciting a two- photon transition in the reference atoms 7, said interrogation signal 101 being configured to interact with said reference atoms 7 in a Doppler-free scheme;

[0084] - the optical frequency modulation means 31 are configured to adjust said first optical frequency and to modulate said first optical frequency at the first modulation frequency f1 ;

[0085] - the optical sensor 9 is configured to detect a fluorescence signal 110 from said reference atoms 7;

[0086] - the first control loop 10 is configured to lock said first optical frequency to a resonance frequency of said two-photon transition, said fluorescence signal 110 being input into the first control loop 10;

[0087] - the mitigation laser source 2 is configured to emit the mitigation signal 102 comprising a second optical frequency selected to produce a light-shift of said two-photon transition of opposite sign of the light-shift produced by the interrogation signal 101 ; the optical amplitude modulation means 5 are configured to modulate the amplitude of the interrogation signal 101 and of the mitigation signal 102 at the second modulation frequency f2; and

[0088] - the second control loop 20 is configured to adjust the relative amplitude of the mitigation signal 102 with respect to the interrogation signal 101 such as to cancel the effective light-shift of the combined interrogation 101 and mitigation 102 signals.

[0089] As a consequence of the above-disclosed systems and operations, the invention also relates to a method for operating the above-disclosed system 100 or the above-disclosed system 200 or the above-disclosed optical atomic clock 300. The method comprises the following steps:

[0090] - providing an interrogation signal 101 at a first optical frequency and interacting with said reference atoms 7 in a Doppler-free scheme,

[0091] - modulating said first optical frequency at a first modulation frequency f1 ,

[0092] - detecting a fluorescence signal 110 from said reference atoms 7,

[0093] - demodulating said fluorescence signal 110 at the first modulation frequency f1 for obtaining a first demodulated signal 113 and using said first demodulated signal 113 to adjust said first optical frequency, locking it to a two-photon transition of said reference atoms 7,

[0094] - providing a mitigation signal 102 suitable for producing a light-shift of said two-photon transition of opposite sign of the light-shift produced by the interrogation signal 101 ,

[0095] - modulating the amplitude of the interrogation 101 and mitigation 102 signals together at a second modulation frequency f2, - further demodulating the first demodulated signal 113 at the second modulation frequency f2, to produce a second demodulated signal 123, and

[0096] - using said second demodulated signal 123 for adjusting the relative amplitude of the mitigation signal 102 with respect to the interrogation signal 101 such as to cancel the effective light-shift of the combined interrogation 101 and mitigation 102 signals.

[0097] As a consequence of the above-disclosed systems and operations, the invention also relates to a system 200 for the control, adjustment or certification of timepieces comprising the above-disclosed optical atomic clock 300. Such a system 200 comprises means to measure the frequency signal and / or the rate of a timepiece or of several timepieces. Such means can be a device to measure the rate by recording and analyzing the acoustic signal emitted by the timepiece, notably the acoustic signal emitted through the function of the escapement and balance-spring oscillator in a mechanical timepiece. Alternatively or complementarily, such means can be a device to measure the rate by measuring optically the oscillation of a balance-spring oscillator in a mechanical timepiece. Alternatively or complementarily, such means can be a device to measure the rate through visual determination of the time indicated by the timepiece at at least two different instants, and comparison of the time interval as recorded by the timepiece with the time interval between the different instants recorded by a reference clock, such as the above-disclosed optical atomic clock or such as a timescale or clock ensemble which comprises the above-disclosed optical atomic clock.

Claims

Claims :1 . An optical frequency generation system (100), comprising:- reference atoms (7) in a gas phase,- an interrogation laser source (1 ) configured to emit an interrogation signal (101 ) comprising a first optical frequency suitable for exciting a two-photon transition in said reference atoms (7), said interrogation signal (101 ) being configured to interact with said reference atoms (7) in a Doppler-free scheme;- optical frequency modulation means (31 , 31a, 31 b) configured to adjust said first optical frequency and to modulate said first optical frequency at a first modulation frequency f1 ;- an optical sensor (9) configured to detect a fluorescence signal (110) from said reference atoms (7);- a first control loop (10) configured to lock said first optical frequency to a resonance frequency of said two-photon transition, said fluorescence signal (110) being input into the first control loop (10);- a mitigation laser source (2) configured to emit a mitigation signal (102) comprising a second optical frequency selected to produce a light-shift of said two-photon transition of opposite sign of the lightshift produced by the interrogation signal (101 ); characterized in that the optical frequency generation system (100) further comprises:- optical amplitude modulation means (5) configured to modulate the amplitude of the interrogation signal (101 ) and of the mitigation signal (102) at a second modulation frequency f2, and- a second control loop (20) configured to adjust the relative amplitude of the mitigation signal (102) with respect to the interrogation signal (101 ) such as to cancel the effective light-shift of the combined interrogation (101 ) and mitigation (102) signals.

2. The optical frequency generation system (100) according to claim 1 , characterized in that it comprises power modulation means (32) configured to control the power provided to the mitigation laser source (2), the power modulation means (32) being controlled by the second control loop (20), notably by a PID controller (27) of the second control loop (20).

3. The optical frequency generation system (100) according to one of the preceding claims, characterized in that the first modulation frequency f1 is comprised between 1 kHz and 10 MHz, preferably comprised between 10 kHz and 1 MHz.

4. The optical frequency generation system (100) according to one of the preceding claims, characterized in that the second modulation frequency f2 is smaller than the first modulation frequency f1 by a factor of at least 1000, preferably at least 10’000.

5. The optical frequency generation system (100) according to one of the preceding claims, characterized in that the reference atoms (7) are rubidium atoms.

6. The optical frequency generation system (100) according to the preceding claim, characterized in that the two-photon transition is the 5SI / 25Ds / 2 transition of rubidium.

7. The optical frequency generation system (100) according to one of the preceding claims, characterized in that the first control loop comprises:- a first RF source (11 ),- a first mixer (13),- a low pass filter (15),- a first PID controller (17), and- optionally, a summing-circuit (19).

8. The optical frequency generation system (100) according to one of the preceding claims, characterized in that the second control loop comprises:- a second RF source (21 ),- a band pass filter (22),- a second mixer (23),- a low pass filter (25), and- a second PID controller (27).

9. The optical frequency generation system (100) according to one of the preceding claims, characterized in that the optical frequency modulation means (31) comprises:- a current control, and / or,- a temperature control, and / or- a piezo-electric actuator, and / or- an electro-optic modulator.

10. The optical frequency generation system (100) according to one of the preceding claims, characterized in that the optical amplitude modulation means (5) comprises:- an acousto-optic modulator, or- a variable optical attenuator such as a MEMS variable optical attenuator, or- a liquid crystal modulator.

11. The optical frequency generation system (100) according to one of the preceding claims, characterized in that it comprises:- fused fiber wavelength division multiplexers (WDMs), or- fiber polarization combiners, or- fused fiber splitter / combiner, or- a dichroic mirror or- a polarized beam splitter, or- a free-space beam splitter / combiner, to combine the interrogation and mitigation signals.

12. The optical frequency generation system (100) according to one of the preceding claims, characterized in that the mitigation laser source (2) wavelength is 785 nm.

13. The optical frequency generation system (100) according to one of the preceding claims, characterized in that the interrogation laser source (1) is a frequency-doubled laser, notably a frequency- doubled laser originating from the mitigation laser source (2).

14. The optical frequency generation system (100) according to one of the preceding claims and according to claim 7, characterized in that said first control loop (10) comprises:- the RF source (11 ) providing a modulation signal (111 ) at said first modulation frequency f1 ,- the mixer (13) receiving said fluorescence signal (110) and demodulating it by mixing with said modulation signal (111 ),- the low-pass filter (15) configured to clean, from residual modulations, an output signal (113) from said mixer (13), said low- pass filter (15) :-- having a cut-off frequency fCut-is below said first modulation frequency f1 and below said second modulation frequency f2, or -- comprising a low-pass filter with cut-off frequency below said first modulation frequency f1 and an additional band-stop filter adaptedto remove a component at said second modulation frequency f2, and- the Proportional-Integral-Derivative (PID) controller (17) receiving a filtered signal (115) from said low-pass filter (15), and configured to generate a low frequency correction signal (117) adapted to adjust the mean optical frequency of said interrogation signal (101 ), locking it to the atomic transition.

15. The optical frequency generation system (100) according to claim 14, characterized in that the output signal (113) is sampled as the input signal (120) of the second control loop (20) before removing the f2 component using said low-pass filter (15).

16. The optical frequency generation system (100) according to claim 15, characterized in that said second control loop (20) comprises a band-pass filter (22) receiving said input signal (120) and configured to remove noise around the f2 component of said input signal (120).

17. An optical atomic clock (300) comprising an optical frequency generation system (100) according to any of the preceding claims and further comprising an optical frequency comb stabilized on said optical frequency generation system (100).

18. An operating method of:- an optical frequency generation system (100) according to one of claims 1 to 16, and / or- an optical atomic clock (300) according to claim 17, the method comprising the following steps:- providing an interrogation signal (101 ) at a first optical frequency and interacting with said reference atoms (7) in a Doppler-free scheme,- modulating said first optical frequency at a first modulationfrequency f1 ,- detecting a fluorescence signal (110) from said reference atoms (7),- demodulating said fluorescence signal (110) at the first modulation frequency f1 for obtaining a first demodulated signal (113) and using said first demodulated signal (113) to adjust said first optical frequency, locking it to a two-photon transition of said reference atoms (7),- providing a mitigation signal (102) suitable for producing a light-shift of said two-photon transition of opposite sign of the light-shift produced by the interrogation signal (101 ),- modulating the amplitude of the interrogation (101 ) and mitigation (102) signals at a second modulation frequency f2,- further demodulating the first demodulated signal (113) at the second modulation frequency f2, to produce a second demodulated signal (123), and- using said second demodulated signal (123) for adjusting the relative amplitude of the mitigation signal (102) with respect to the interrogation signal (101 ) such as to cancel the effective light-shift of the combined interrogation (101 ) and mitigation (102) signals.

19. The operating method according to claim 18, characterized in that the method comprises the following steps:- an RF source (11 ) provides a modulation signal (111 ) at said first modulation frequency f1 ,- a mixer (13) receives said fluorescence signal (110) and demodulates it by mixing with said modulation signal (111 ),- a low-pass filter (15) cleans, from residual modulations, an output signal (113) from said mixer (13), said low-pass filter (15) :-- having a cut-off frequency fCut-is below said first modulation frequency f1 and below said second modulation frequency f2, or -- comprising a low-pass filter with cut-off frequency below said firstmodulation frequency f1 and an additional band-stop filter adapted to remove a component at said second modulation frequency f2, and - a Proportional-Integral-Derivative (PID) controller (17) receives a filtered signal (115) from said low-pass filter (15), and generates a low frequency correction signal (117) adapted to adjust the mean optical frequency of said interrogation signal (101 ), locking it to the atomic transition.

20. The operating method according to claim 19, characterized in that the output signal (113) is sampled as the input signal (120) of the second control loop (20) before removing the f2 component using said low-pass filter (15).

21. The operating method according to claim 20, characterized in that a band-pass filter (22) receives said input signal (120) and removes noise around the f2 component of said input signal (120).

Images