Patent Publication Number: US-2019181611-A1

Title: Common mode noise suppression of optical frequency combs for optical clock applications

Description:
PRIORITY CLAIM AND CROSS-REFERENCE TO RELATED APPLICATION 
     This patent document claims the priority of U.S. Provisional Application No. 62/596,712, entitled “Common Mode Noise Suppression of Optical Frequency Combs for Optical Clock Applications,” filed on Dec. 8, 2017, the entire disclosure of which is incorporated by reference herein. 
    
    
     FIELD OF THE DISCLOSURE 
     Various aspects of the disclosure relate to optical metrological devices. More specifically, aspects of the disclosure relate to methods and apparatus for optical clocks and in particular to stabilizing optical frequency combs for optical clock applications. 
     BACKGROUND 
     Stabilized optical comb oscillators can be useful in a variety of metrological applications, including optical atomic clocks. Realization of a completely stabilized equidistant frequency comb oscillator may involve two-point stabilization to stabilize both the center frequency and the free spectral range of the optical comb. This may be characterized, in the time domain, as stabilization of the carrier envelop offset frequency of the comb and the repletion rate of the comb. Often, a first aspect of two-point stabilization involves locking the comb center frequency to an external reference, such as a stabilized cavity or an atomic transition in an optical clock, and the second aspect of the two-point stabilization involves self-locking. Self-locking may be based on a procedure in which the frequency of one of the comb harmonics is coherently multiplied by some number, using a nonlinear optical frequency multiplier, and then compared to another harmonic that is at (or near) the frequency of the multiplied value. Examples of this technique are may be referred to as f-2f and 2f-3f self-referencing. This type of self-referencing may involve generation of broad optical frequency combs covering either an octave (e.g. f-2f self-locking) or ⅔ of an octave (e.g. 2f-3f self-locking). Producing such a comb can be technically complex. Furthermore, spectrally broad frequency combs often consume a lot of power, which is undesirable. It is possible to generate spectrally narrow frequency combs, covering, for example, 1/10 of an octave or less. However, self-referencing does not work very well in such cases. It is also possible to lock two different comb lines to two different atomic clocks. However, the result of such locking may not be optimal. In this regard, the two clocks are often characterized with independent drifts, which are additive if the two harmonics of the comb are locked to the clocks. As a result, the stability of the locked comb can become compromised. 
     Herein, methods and apparatus are provided to address these or other problems. 
     SUMMARY 
     This document provides, among other features, methods and apparatus that provide two-point locking of frequency combs for use with, e.g., optical atomic clocks. 
     In one aspect, an apparatus includes: an optical reference sample with first and second optical transitions at different wavelengths; a coherent light source configured to provide polychromatic coherent light, coherent light source optically coupled to the optical reference sample; and a stabilization system configured to provide stabilization of the polychromatic coherent light based on the first and second optical transitions of the reference sample. 
     In another aspect, a method for generating polychromatic coherent light using a coherent light source; coupling a portion of the polychromatic coherent light into an optical reference sample having first and second optical transitions at different wavelengths; and stabilizing the polychromatic coherent light based on the first and second optical transitions of the reference sample. 
     In yet another aspect, an apparatus includes: means for generating polychromatic coherent light using a coherent light source; means for coupling a portion of the polychromatic coherent light into an optical reference sample having first and second optical transitions at different wavelengths; and means for stabilizing the polychromatic coherent light based on the first and second optical transitions of the reference sample. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows an example of an atomic clock system providing two-point locking of a frequency comb based on the D 1  and D 2  optical transitions of rubidium (Rb) atoms confined within a vapor cell. 
         FIG. 2  shows another example of an atomic clock system providing two-point locking based on optical transitions of Rb atoms confined within a vapor cell. 
         FIG. 3  illustrates an exemplary method for generating an atomic clock signal while implementing two-point locking. 
         FIG. 4  summarizes components of an exemplary optical apparatus. 
         FIG. 5  summarizes further components of an exemplary optical apparatus. 
         FIG. 6  summarizes an exemplary method according to aspects of the present disclosure. 
         FIGS. 7A and 7B  summarize further aspects of an exemplary method according to the present disclosure. 
         FIG. 8  illustrates an exemplary processing system that includes an optical atomic clock with two-point locking, such as for use in a portable navigation system. 
         FIG. 9  summarizes an exemplary general method in accordance with aspects of the present disclosure. 
         FIG. 10  summarizes an exemplary general apparatus in accordance with aspects of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     In the following description, specific details are given to provide a thorough understanding of the various aspects of the disclosure. However, it will be understood by one of ordinary skill in the art that the aspects may be practiced without these specific details. For example, circuits may be shown in block diagrams in order to avoid obscuring the aspects in unnecessary detail. In other instances, well-known circuits, structures and techniques may not be shown in detail in order not to obscure the aspects of the disclosure. In the figures, elements may each have a same reference number or a different reference number to suggest that the elements represented could be different and/or similar. However, an element may be flexible enough to have different implementations and work with some or all of the systems shown or described herein. The various elements shown in the figures may be the same or different and, which one is referred to as a first element and which is called a second element is arbitrary. 
     Overview 
     Herein, among other aspects, methods and apparatus are described for utilizing a single sample atomic reference for two-point stabilization of an optical frequency comb oscillator for realization of an atomic clock. In an illustrative method, two different optical clock transitions of the same sample of reference atoms or molecules are simultaneously interrogated using two different lasers. Since the reference transitions belong to the same sample, they are influenced by environmental factors in a common manner. As the result, the stability of the relative frequencies of the transitions, expressed as a linear combination m*f1-n*f2 (where m and n are some numbers, and f1 and f2 are the transition frequencies) can be better than the frequency of each transition (f1 and f2) measured separately. Hence, the frequency difference between two optical frequency comb lines that are locked to the two transitions can be stabilized more effectively as compared to locking the frequency comb to two optical sources stabilized to optical transitions produced by two different (e.g. separated in space and/or time) samples of the reference atoms. (Note that, when using the techniques disclosed herein, more than two different optical clock transitions of the same sample of reference atoms/molecules can be interrogated simultaneously to further improve lock quality.) 
     In the following, to provide concrete examples of these procedures, various atomic clock examples are provided. It should be understood that these are exemplary only, and the general principles described herein may be exploited in a wide variety of methods and apparatus to provide, e.g., for stabilization of polychromatic coherent light. Generally speaking, the beams of the polychromatic coherent light, occupying the same spatial mode volume or separated in space, and having frequencies in the vicinity of the clock transitions of the reference sample, are used to interrogate the resonances of a reference sample that is characterized by two or more optical clock transitions with different wavelengths. Interrogation signals obtained using phase/frequency/amplitude spectroscopy or other techniques may then be used to stabilize the frequency harmonics of the polychromatic coherent light. If the harmonics belong to the same coherent frequency comb, the entire comb becomes stabilized using this procedure. 
     Atomic Clock Applications 
     The development of portable navigation and communication devices has been impeded by a lack of availability of reliable miniature high-performance clocks. 
     Atomic clocks can operate based on a comparison of the frequency of a local oscillator with a “constant” frequency that corresponds to a transition between two atomic energy levels. Since all atoms of a given species are the same, the same “constant” frequency in a given pair of transitions provides for similar outputs between two clocks made with the same atomic system and architecture. However, atomic transition frequencies are sensitive to local environmental perturbations. For example, atomic clocks based on a transition between hyperfine levels are readily perturbed by an ambient magnetic field, unless adequately shielded. Since the sensitivity to most perturbations encountered by atoms in a vapor cell (or an electrodynamic trap) decrease with increasing transition frequency, optical transitions, with much higher frequency compared to hyperfine transitions, offer greatly reduced sensitivity to perturbations due to collisions, ambient fields, density variations, etc. With the advent of optical frequency combs that relate optical frequencies to radio-frequency (RF) or microwave frequencies, the attributes of optical transitions have been exploited, and optical clocks can provide stable and accurate atomic-based clocks with stabilities and accuracies extending beyond the 10 −18  level. This high level of stability and accuracy is achieved, in part, by isolating the atoms undergoing the clock transition and by reducing the sensitivity to perturbations by using techniques such as laser cooling and trapping. 
     A frequency comb can be used to relate the optical frequency to a countable RF or microwave frequency for use in implementing an optical clock. Optical frequency combs for clock applications may be produced with a mode-locked femtosecond (fs) laser. The repetition frequency (f rep ) and the carrier envelope offset frequency (f ceo ) of the comb should be stabilized for use as a link between the optical and RF frequencies. Since both the laser frequency (e.g. the center frequency of the comb) and the pulse repetition rate are determined by the same mode-locked laser cavity, they both should be simultaneously stabilized. In other words, the stability of a frequency comb (at least a conventional comb) depends on simultaneously stabilizing the cavity length (⊗r, where r is the cavity length) and the mismatch between the group and phase velocity within the cavity that is caused by dispersion (⊗n, where n is the dispersion). Note that the (electrical) length of the cavity can also depend on the dispersion in the cavity. 
     Two-point stabilization of the fs mode lock laser can be accomplished by stabilizing the laser frequency to an external laser (itself stabilized to an external cavity and locked to a reference atomic transition) and by implementing so-called 1f to 2f stabilization. (Stabilization of the center frequency of the comb often requires locking it to a stand-alone reference laser; stabilization with the 1f to 2f scheme often requires an octave-spanning comb.) 
     Despite advances in the realization of ruggedized optical combs based on an fs laser, this style of stabilized comb (involving high enough laser power to generate an octave, a reference laser, and the auxiliary optics and electronics for generation and locking of the 1f to 2f frequency) cannot be easily miniaturized for use in a small atomic clock. However, in the last few years Kerr comb generators based on optical whispering gallery mode (WGM) resonators have become available and are small enough for use in miniature optical clocks. 
     In the approach described herein, an optical atomic clock is provided by implementing a two-point locking system for stabilization of a frequency comb oscillator and to achieve stabilization of the comb repetition frequency in the microwave domain to the optical frequency. The two-point lock can be implemented, as described herein, using two optical transitions, for example, D 1  and D 2 , in rubidium (Rb) atoms confined within the same vapor cell. The use of optical transitions reduces the sensitivity to ambient magnetic fields. The clock sensitivity to ambient perturbations is further reduced since lasers locked to D 1  and D 2  frequency lines of Rb serve to interrogate Rb atoms held in the same vapor cell. 
     Note that, for convenience herein, frequencies may be occasionally referred to in terms of their corresponding wavelengths. For example, a laser beam within an atomic clock might be referred to as having a frequency of 795 nm. It is meant, of course, that the frequency corresponds to a wavelength of 795 nm. The actual frequency may be expressed in terra Hz (THz). For example, the frequency that corresponds to 795 nm is about 377 THz. The frequency that corresponds to 780 nm is about 384 THz. 
     Exemplary Embodiments 
       FIG. 1  illustrates an exemplary optical atomic clock  100  for generating an RF clock signal where the optical clock is configured to implement a two-point locking system to stabilization of its frequency comb oscillator. 
     In the example of  FIG. 1 , the optical clock includes a 795 nm semiconductor laser (laser #1)  102  that is self-injection locked to a high-Q crystalline whispering gallery mode (WGM) resonator  104  via an optical coupler  106  and is also locked via a Pound-Drever-Hall (PDH) arrangement or sub-system to the D 1  line of Rb held in a vapor cell  112 . More specifically, for the D 1  PDH locking, a portion of a main output beam  103  from the 795 nm laser  102  is split off from beam  103  using a beamsplitter  105  as a secondary beam  107  that is directed via a polarization beam splitter (PBS)  108  and a λ/4 plate  110  into a vapor cell  112  that holds one or more Rb atoms, where the beam  107  interrogates the atoms and causes at least some to absorb light at resonant frequency D 1  (which has a corresponding wavelength at or near 795 nm). 
     A mirror  114  reflects unabsorbed portions of the beam back through the vapor cell  112  to pass through the vapor cell  112  a second time. The reflected beam (showing absorption at frequency D 1 ) then passes back through a λ/4 plate  110  and PBS  108  to a photodetector  115 . (The λ/4 plate  110  and the PBS  108  operate in combination to discriminate between the two directions of light travel, i.e. into and out of the vapor cell  112 .) The output electrical signal of the photodetector  115  is applied as feedback to the 795 nm laser  102  via a lock #1 controller  116 , which controls and/or modulates the laser  102  based on a D 1  spectroscopic absorption pattern or signal detected by the photodetector  115 . In this regard, phase/frequency/amplitude spectroscopy or other suitable spectroscopic techniques may be employed. 
     The optical clock  100  also includes a 780 nm semiconductor laser (laser #2)  120  that is concurrently locked via PDH to the D 2  line of the Rb held in the vapor cell  106 . That is, for the D 2  PDH, a portion of a main output beam  121  from the 780 nm laser  120  is split off from beam  121  using a beamsplitter  123  as a secondary beam  125  that is directed via a PBS  126  and a λ/4 plate  128  into the same vapor cell  112 , where the beam interrogates the atoms in the sample and causes at least some to absorb light at resonant frequency D 2  (which is at or near a corresponding wavelength of 780 nm). The mirror  114  again reflects unabsorbed portions of the beam back through the vapor cell  112  to pass through the vapor cell  112  a second time. The reflected beam (showing absorption at frequency D 2 ) then passes back through a λ/4 plate  128  and PBS  126  to a photodetector  130 . The output electrical signal of the photodetector  130  is applied as feedback to the 780 nm laser  102  via a lock #2 controller  132 , which controls and/or modulates the laser  102  based on a D 1  spectroscopic absorption pattern or signal detected by the photodetector  130 . 
     As noted, the 795 nm semiconductor laser (laser #1)  102  is also injection locked to the WGM resonator  104  via an optical coupler  106 . More specifically, the main portion  103  of the output beam from the 795 nm laser  102  passes through beamsplitter  105  and a portion of beam  103  is then captured by the WGM  104  via coupler  106  (which may be, for example, a prism). The portion of beam  103  captured by the WGM  104  forms propagating waves that resonate therein at frequencies set by a lock #3 controller  134 , which controls and/or modulates the WGM  104  using, for example, a lead zirconate titanate (PZT) piezoelectric transducer or actuator component  136  formed within (or on or adjacent to) the WGM  104 . The lock #3 controller  134  is controlled by a signal from a photodetector  138  that receives the main portion  121  of the output signal from 780 nm laser  120  that is not split off by beamsplitter  123 . As shown, a reflector  142  may be provided to direct the output beam  121  to the photodetector  138 . In the illustrative example, the temperature of WGM  104  is set via lock #3 controller  134  and PZT  136  to control the WGM  104 . In other examples, the WGM  104  may be controlled and/or modulated by application of an electrical potential and/or mechanical pressure using other types of transducers and/or actuators. 
     A portion of light from beam  103  that is captured by the WGM  104  then emerges from the WGM as an optical comb. That is, the interaction of the laser  102  and the WGM  104  serves to generate or produce an optical comb within beam  103 . (In other examples, the laser  102  may be configured to generate the comb on its own). The optical frequency comb is illustrated in  FIG. 1  as comb  144 , which is shown adjacent to beam  103  to visually illustrate the polychromatic comb features of beam  103 . The comb  144  includes a harmonic  150  at 780 nm and a center frequency  151  with a wavelength corresponding to 795 nm (as well as other harmonics not specifically labeled). In  FIG. 1 , beam  121  of laser  120  is shown aligned with harmonic  150  to illustrate that the frequency of beam  121  is set to that particular harmonic. One or more periodic beats arise within the optical comb due to interactions between the various frequencies of the comb, such as between the 780 nm harmonic and the 795 nm center line. 
     Thus, with the overall arrangement of  FIG. 1 , an electrical signal derived from the 780 nm laser  120  (via photodetector  138 ) is used to control the characteristics of the WGM  104  (via PZT  136 ) to modulate the injection locking of the 795 nm laser  102  to stabilize a selected periodic beat in the optical comb  141  of beam  103 , where a periodicity of the beat is based, e.g., on a difference in frequency between the harmonic  150  and the center frequency  151  of the comb  144  (or between any other two harmonics). The beat in beam  103  is detected by a fast photodetector  148 , which outputs an RF clock signal based on the beat. Although not shown in  FIG. 1 , additional circuitry may be provided to convert (e.g. rectify) the output from the photodetector  148 , which may be sinusoidal, into a clock signal with sharp rising and falling clock pulse edges. 
     Hence, a signal derived from beam  121  (which is PDH locked to the D 2  line of the Rb and hence to the harmonic  150  of the optical comb  144 ) is used to stabilize a beat within the optical comb  141  of beam  103  (which is PDH locked to the D 1  line of the Rb and hence to the center frequency  151  of the optical comb  144 ). Thus, two-point locking of the comb is provided (via D 1  and D 2  of the Rb atomic reference sample) to stabilize the optical comb  144  and thus also stabilize the final clock signal  146 . 
     In this manner, two beams of the light (from the first and second lasers) that occupy the same spatial mode volume (or are separated in space) and have frequencies in the vicinity of the clock transitions of the reference sample are used to interrogate the resonances of the reference sample. The interrogation signals obtained with phase/frequency/amplitude spectroscopy or other spectroscopy techniques are used to stabilize the frequency harmonics of the light. If the harmonics belong to the same coherent frequency comb, the entire comb becomes stabilized because of this procedure. 
     Note that, as shown in  FIG. 1 , the 780 nm laser  120  may include, or be coupled to, a WGM microcavity  152  (which is separate from the WGM  104 ) that provides self injection locking of laser  120 . The WGM microcavity  152  may include a piezo element (not separately shown) that is controlled based on the signal from the lock #2 controller  122 . The WGM microcavity  152  may be configured to provide low residual amplitude modulation and linewidth reduction of the 780 nm laser  120 . 
     Note also that some resonant Rayleigh scattering occurs in the WGM resonator  104  due, e.g., to surface and volumetric inhomogeneities, which is reflected back to 795 nm laser  102 , as indicated by backscattered beam  154 . In this regard, some amount of light reflects back into the laser  102  when the frequency of the emitted light coincides with the frequency of a resonator mode of WGM  104 , providing optical feedback, which can lead to a reduction of laser linewidth of the 795 nm laser  102 . Similar Rayleigh scattering may occur in the WGM microcavity  152  to provide a backscattered beam (not shown) to the 780 nm laser to provide similar optical feedback. 
     The following paragraphs highlight and discuss other notable features of the apparatus and configuration of  FIG. 1 . 
     The PDH locks of lasers  102  and  120  to the D 1  and D 2  lines, respectively, are primarily accomplished by modulating, controlling or adjusting the corresponding WGM resonator ( 104  or  152 ) via a suitable piezo element, and not the laser current. This modulation scheme can provide quite low (e.g. −80 dB) relative amplitude modulation (RAM) since it produces pure frequency modulated signals. As a consequence, the lasers  102  and  120  can be locked to the Rb lines to achieve long-term stability better than, e.g.,  10   −13 . This stabilization scheme can also feature ultra-narrow linewidths because of the injection locking to, e.g., the high-Q crystalline resonator  104 . 
     The laser stabilization to the D 1  Rb line serves to stabilize the f n =N frep +f ceo  harmonic of the frequency comb  144 , and the second laser  120  locked to the D 2  line stabilizes the f m =M frep +f ceo  of the comb. Since integer M is known, by utilizing the lock D 1 , the apparatus of  FIG. 1  thus stabilizes both f rep  and f ceo . 
     Stabilization to the D 1  and D 2  lines of Rb held in the same cell may serve to ensure that the relative stability of the two locks can be as high as, e.g., 10 −15 , since all perturbations to the atoms held in the cell, at least to first order, are the same for both transitions. This is because of near equality of collision cross sections, magnetic sensitivity, and quadratic Stark shift of energy levels for D 1  and D 2  transitions, as they originate in the same ground state, and the excited state transition energies (frequencies) are very close. 
     Generation of the optical comb  144  (which may be a normal group velocity dispersion (GVD) Kerr frequency comb) may exploit an ultra-high Q crystalline (CaF 2 ) resonator for use as WGM  104 . Since the threshold for comb generation is related to the inverse square of the Q of the resonator, power requirements can be quite modest. Combs with as little as 5 milliWatt (mW) may be generated in this manner at 795 nm. As such, the optical clock  100  may have modest power requirements for operation. 
     The configuration of  FIG. 1  also allows for generating a comparably spectrally narrow frequency comb that spreads from 795 nm to 780 nm. As such, there is no need to reach octave spreading of the frequency comb (which might be challenging at these wavelengths, where the GVD is normal). 
     The optical clock  100  can be readily packaged in a miniature package for a wide variety of practical applications. 
       FIG. 2  summarizes an optical atomic clock  200  with two-point locking. The clock may employ the various components of the exemplary apparatus of  FIG. 1  or may use other suitably-equipped devices or components. A 795 nm semiconductor laser  202  is coupled to a PDH sub-system  204  that is configured to operate based on the D 1  Rb transition of one or more rubidium atoms held within a vapor cell  206  (or other suitable containment system). A 780 nm semiconductor laser  208  is coupled to a separate PDH sub-system  210  that is configured to operate based on the D 2  Rb transition of the one or more rubidium atoms held within the same vapor cell  206 . The D 1  and D 2  PDH sub-systems  204  and  210  operate to lock respective lasers  202  and  208  (as described above). 
     The 795 nm laser  202  is also coupled via an optical coupler  212  to a high-Q crystalline WGM resonator  214  with adjustable/modulatable resonance frequencies. That is, a portion of a laser beam output from the 795 nm laser  202  is coupled into the WGM resonator  214 , and propagates and resonates therein, which serves to provide injection locking of the 795 nm laser  202  and also generates the optical comb. The 780 nm laser  208  is also coupled via a transducer/actuator  216  to the same high-Q WGM resonator  214  to adjust and/or modulate at least one of its resonance frequencies. Note that, whereas the coupling of the 795 nm laser beam into the WGM resonator  214  is an optical coupling via a prism or the like, the coupling of the 780 nm laser beam to the WGM resonator  214  is instead achieved, as described above, by deriving an electrical signal from the 780 nm laser beam, which is then used to control the transducer/actuator  216  (e.g. PZT) by applying mechanical, thermal, or electrical signals to the WGM resonator  214  to modulate one or more of its resonance frequencies. The effect of modulating the WGM resonator  214  using the 780 nm laser output is to stabilize beats with selected frequencies or periodicities within an optical comb emerging from the WGM  214 . A photodetector  218  or other suitable device detects the periodic beats within the optical comb and generates an RF clock signal  220  as output. 
       FIG. 3  illustrates a method  300  for generating an atomic clock signal while implementing a two-point locking and stabilization system. The method may employ the apparatus of  FIG. 1  or other suitably-equipped devices or apparatus. 
     Beginning at block  302  of  FIG. 3 , the optical clock apparatus generates a first laser beam using a 795 nm semiconductor laser. At block  304 , the optical clock apparatus locks the first beam using a PDH feedback sub-system to the D 1  transition of a rubidium (Rb) atomic sample in a vapor cell. Concurrently, beginning at block  306 , the optical clock apparatus generates a second laser beam using a 780 nm semiconductor laser and, at block  308 , locks the second beam using a separate PDH feedback system to the D 2  transition of the same Rb atomic sample. 
     At block  310 , the optical clock apparatus optically couples the first beam into an ultra-high Q crystalline (e.g. CaF 2 ) optical WGM resonator to self-injection lock the 795 nm laser and generate an optical comb having periodic beats between harmonics. At block  312 , the optical clock apparatus modulates a resonance frequency of the WGM resonator using a signal derived from the second laser beam to stabilize the periodic beats in the optical comb and complete the two-point locking of the optical comb. At block  314 , the optical clock apparatus converts the periodic beats within the beam emerging from the resonator into a RF clock signal using a fast photodetector. 
     Additional Embodiments 
       FIG. 4  summarizes features of an exemplary apparatus  400 . Briefly, a first coherent light source  402  is optically coupled to an optical reference sample  404  and modulated by a first optical transition of the optical reference sample  404 . The optical reference sample  404  has at least first and second optical clock transitions. A second coherent light source  406  is coupled to the same optical reference sample  404  and modulated by the second optical transition of the optical reference sample  404 . An optical resonator  408  is optically coupled to the first coherent light source  402  and configured to injection lock the first coherent light source  402 , with the optical resonator  408  controlled by a signal derived from a light beam from the second coherent light source  406 . In the example of  FIG. 4 , an output component  410  is also provided that is configured to output a clock signal generated based on one or more beats arising within an optical comb emerging from the optical resonator  408 . 
       FIG. 5  summarizes additional features of an exemplary optical clock apparatus  500  for generating a clock signal. The clock apparatus  500  includes a first semiconductor mode-locked laser  502  (or optical polychromatic frequency comb generator or Kerr frequency comb source) that is optically coupled via a first PDH or other locking system to an optical reference sample  504  and modulated by a first (D 1 ) transition of the sample. The optical reference sample  504  has at least first (D 1 ) and second (D 2 ) transitions, such as an Rb atomic vapor cell, electrodynamic atomic trap, optical atomic trap, solid state matrix doped with reference atoms or molecules, or other atomic or molecular manifolds. A second semiconductor laser  504  (or other coherent light source) is optically coupled via a second PDH or other locking system to the same reference sample  504  and modulated by the second (D 2 ) transition (or other suitable transition). 
     The clock apparatus  500  also includes a high-Q WGM optical micro-resonator  508  (or other resonator such as a monolithic dielectric resonator, micro-ring resonator, Bragg grating micro-resonator, or cavity integrated on a photonic integrated circuit platform) that is optically coupled to the first laser  502  via an evanescent field coupler (such as a prism, optical fiber, optical fiber taper, or optical grating) and configured to injection lock the first laser  502 , with the resonator  508  controlled via a transducer or actuator  510  by a signal derived from a light beam from the second laser  506 . That is, a transducer or actuator  510  is coupled to the WGM resonator  508  and configured to alter an optical property of the resonator by applying mechanical, thermal, and/or electrical signals to the WGM, where the transducer is controlled by a signal derived from a light beam from the second laser  506  and configured to adjust a frequency of light coupled out of the resonator  508  that provides injection locking of the first laser  502 . A photo-detector or other output component  512  is configured to output an RF or microwave clock signal based on one or more beats arising within an optical comb emerging from the WGM resonator  508  (which, as already explained, may arise between a center frequency and a harmonic of the optical comb or between two or more harmonics). 
       FIG. 6  summarizes features of an exemplary method  600  for generating a clock signal using an optical apparatus. Briefly, at block  602 , the apparatus generates a first beam of coherent light using a first coherent light source. At block  604 , the apparatus modulates the first beam using a first optical clock transition of an optical reference sample having first and second of optical clock transitions. At block  606 , the apparatus generates a second beam of coherent light using a second coherent light source. At block  608 , the apparatus modulates the second beam using the second optical clock transition of the same optical reference sample. At block  610 , the apparatus optically couples a portion of the first beam into an optical resonator configured to injection lock the first coherent light source. At block  612 , the apparatus modulates at least one resonance frequency of the optical resonator using a signal derived from the second beam of coherent light. At block  614 , the apparatus generates a clock signal from a beat within an optical comb light beam emerging from the optical resonator. 
     In at least some examples, means may be provided for performing the functions illustrated in  FIG. 6  and/or other functions illustrated or described herein. For example, the means may include one or more of: means, such as light source  402  of  FIG. 4 , for generating a first beam of coherent light using a first coherent light source; means, such as PDH sub-system  204  of  FIG. 2 , for modulating the first beam using a first optical transition of an optical reference sample having first and second of optical transitions; means, such as light source  406  of  FIG. 4 , for generating a second beam of coherent light using a second coherent light source; means, such as PDH sub-system  210  of  FIG. 2 , for modulating the second beam using the second optical clock transition of the same optical reference sample; means, such as optical coupler  212  of  FIG. 2 , for optically coupling a portion of the first beam into an optical resonator configured to injection lock the first coherent light source; means, such as transducer  216  of  FIG. 2 , for modulating at least one resonance frequency of the optical resonator using a signal derived from the second beam of coherent light; and means, such as photodetector  218 , for generating a clock signal from a beat within an optical comb light beam emerging from the optical resonator. 
       FIGS. 7A and 7B  illustrate additional features of an exemplary method for generating a clock signal using an apparatus. In particular, the exemplary method  700  of  FIGS. 7A and 7B  illustrates various more specific procedures and sub-procedures for use with an apparatus that includes a WGM resonator and an Rb sample. Beginning at block  702  of  FIG. 7A , the apparatus generates a first beam of coherent light using a first coherent light source with at least one optical frequency with a wavelength near 795 nm. At block  704 , the apparatus modulates the first beam by: applying the first beam to an optical reference sample that holds one or more rubidium atoms having first (D 1 ) and second (D 2 ) optical transitions; sensing an amount of absorption of the beam by the Rb sample at the first (D 1 ) optical transition; and modulating the first beam based, at least in part, on the amount of absorption of the first beam at the first (D 1 ) optical transition by passing a portion of the first beam through a first PDH apparatus. 
     Concurrently or simultaneously, beginning at block  706 , the apparatus generates a second beam of coherent light using a second coherent light source with at least one optical frequency with a wavelength near 780 nm. At block  708 , the apparatus modulates the second beam by: applying the second beam to the Rb sample; sensing an amount of absorption of the second beam by the Rb sample at the second (D 2 ) optical transition; and modulating the second beam based, at least in part, on the amount of absorption of the second beam at the second (D 2 ) optical transition by passing a portion of the second beam through a second PDH apparatus. 
     At block  710 , the apparatus optically couples a portion of the first beam into a high-Q WGM resonator configured to injection lock the first light source, where the WGM resonator and the first light source are modulated to generate an optical comb within a light beam emerging from the resonator, and where the optical comb has a center frequency with a wavelength near 795 nm and at least one harmonic near 780 nm so as to stabilize the entire comb (or where at least two harmonics of an equidistant coherent frequency comb are stabilized). 
     At block  712  of  FIG. 7B , the apparatus modulates at least one resonance frequency of the WGM resonator using a signal derived from the second beam of light by applying the derived signal to a transducer/actuator that is coupled to the resonator and configured to alter an optical property of the resonator to adjust a frequency of coherent light from the first coherent light source to stabilize a beat within the optical comb (where the beat may be based, e.g., on a difference between the 780 nm harmonic and the 795 nm center wavelength of the optical comb, i.e. the beat arises between at least two frequencies of the optical comb emerging from the optical resonator). At block  714 , the apparatus generates a clock signal from the beat by applying the optical comb that includes the beat to a photodetector to generate an output RF or microwave clock signal from the beat. 
     In at least some examples, means may be provided for performing the functions illustrated in  FIGS. 7A and 7B  and/or other functions illustrated or described herein. Exemplary apparatus or components corresponding to the various means are discussed and described above and will not be specifically listed in the following. The means may include one or more of: means for generating a first beam of coherent light using a first coherent light source with at least one optical frequency with a wavelength near 795 nm; means for modulating the first beam, including means for applying the first beam to an optical reference sample that holds one or more rubidium atoms having first and second optical transitions, means for sensing an amount of absorption of the beam by the Rb sample at the first optical transition, and means for modulating the first beam based, at least in part, on the amount of absorption of the first beam at the first (optical transition by passing a portion of the first beam through a first PDH apparatus. 
     The means may include one or more of: means for generating a second beam of coherent light using a second coherent light source with at least one optical freq. with a wavelength near 780 nm; means for modulating the second beam, including means for applying the second beam to the Rb sample, means for sensing an amount of absorption of the second beam by the Rb sample at the second optical transition, and means for modulating the second beam based, at least in part, on the amount of absorption of the second beam at the second optical transition by passing a portion of the second beam through a second PDH apparatus; means for optically coupling a portion of the first beam into a high-Q WGM resonator configured to injection lock the first light source, where the WGM resonator and the first light source are modulated to generate a polychromatic optical comb within a light beam emerging from the resonator; means for modulating at least one resonance frequency of the WGM resonator using a signal derived from the second beam of light to stabilize a beat within the optical comb (where the beat may be based, e.g., on a difference between the 780 nm harmonic and the 795 nm center wavelength of the optical comb); and means for generating a clock signal from the beat by applying the optical comb that includes the beat to a photodetector to generate an output RF or microwave clock signal from the beat. 
     In some examples, the clock may be a component of a processing system, such as the processing system of a portable navigation or communication device. 
     An exemplary processing system  800  of, e.g., a portable navigation or communication device is illustrated in  FIG. 8 . Briefly, the system  800  includes: an optical atomic clock  802  with two-point locking based on two optical transitions with different wavelengths in the same atomic/molecular reference sample, such as the optical clocks discussed above; a processor or processing circuit  804  (e.g., at least one processor, processing component, and/or other suitable circuitry); and a storage component  806  for storing data and/or programming instructions or other information. These components may communicate with one another via signaling busses or the like, not shown in  FIG. 8 . Note that other components, such as peripherals, voltage regulators, and power management circuits, may also be employed, though not shown. Also, other components of the portable navigation or communication device, such as suitable radio transceivers, antennae, etc., are not shown. 
     The storage medium  806  may be, for example, a computer-readable, machine-readable, and/or processor-readable device for storing programming, such as processor-executable code or instructions (e.g., software or firmware), electronic data, databases, or other digital information. The storage medium  806  may also be used for storing data used by the processing circuit  804  when executing programming. The storage medium  806  may be any available media accessible by a general purpose or special purpose processor, including portable or fixed storage devices, optical storage devices, and various other mediums capable of storing, containing or carrying programming. The storage medium  806  may include, e.g., a magnetic storage device (e.g., hard disk, floppy disk, magnetic strip), an optical disk (e.g., a compact disc (CD)), a smart card, a flash memory device, a random access memory (RAM), read only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), etc., or any other suitable medium for storing software and/or instructions. The storage medium  806  may be embodied in an article of manufacture (e.g., a computer program product). The computer program product may include a computer-readable medium in packaging materials. In some implementations, the storage medium  806  is a non-transitory (e.g., tangible) storage medium. For example, the storage medium  806  may be a non-transitory computer-readable medium storing computer-executable code, including code to perform various operations as described herein. Programming stored by the storage medium  806 , when executed by the processing circuit  804 , causes the processing circuit  804  to perform one or more of the various functions and/or process operations described herein. 
     The processing circuit  804  may be generally adapted or configured for executing programming stored on the storage medium  806 . As used herein, the terms “code” or “programming” include instructions, instruction sets, data, code, code segments, program code, programs, programming, subprograms, software modules, applications, software applications, software packages, routines, subroutines, objects, executables, threads of execution, procedures, functions, etc., whether referred to as software, firmware, microcode, hardware description language, or otherwise. 
     The processing circuit  804  may include circuitry configured to implement desired programming provided by appropriate media. For example, the processing circuit  804  may be implemented as one or more processors, one or more controllers, and/or other structure configured to execute executable programming. Examples of the processing circuit  804  may include a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), or other programmable logic component, etc., or any combination thereof designed to perform the functions described herein. A general-purpose processor may include a microprocessor, as well as any conventional processor, controller, microcontroller, or state machine. The processing circuit  804  may be implemented as a combination of computing components, such as a controller and a microprocessor, or other varying configurations. These examples are for illustration and other suitable configurations within the scope of the disclosure are also contemplated. The processing circuit  804  may be adapted to control or perform any or all of the features, processes, functions, operations and/or routines for any or all of the apparatuses or devices described herein. As used herein, the term “configured” in relation to the processing circuit  804  may refer to the processing circuit  804  being one or more of adapted, employed, implemented, and/or programmed to perform a particular process, function, operation and/or routine according to various features described herein. 
     Summary of General Features and Embodiments 
       FIG. 9  summarizes general features of an exemplary method  900  that may be used to, for example, stabilize a frequency comb oscillator using at least two optical transitions of the same atomic/molecular sample. Briefly, at block  902 , a suitably-equipped apparatus generates polychromatic coherent light using a coherent light source. At block  904 , the apparatus couples a portion of the polychromatic coherent light into an optical reference sample having first and second optical transitions at different wavelengths. At block  906 , the apparatus stabilizes the polychromatic coherent light based on the first and second optical transitions of the reference sample (wherein, for example, at least two frequency harmonics of the polychromatic coherent light are stabilized based on a correlation between the wavelengths of the first and second clock transitions with respect to any environmental perturbations). 
     As discussed above, beams of the polychromatic coherent light, occupying the same spatial mode volume or separated in space, and having frequencies in the vicinity of the clock transitions of the reference sample, may be used to interrogate the resonances of the reference sample. Interrogation signals obtained using phase/frequency/amplitude spectroscopy or other techniques may then be used to stabilize the frequency harmonics of the light. If the harmonics belong to the same coherent frequency comb, the entire comb becomes stabilized using this procedure. 
     Detailed examples of the general method of  FIG. 9  are provided above. See, e.g., the various methods described above and shown in the other figures where the stabilization features of  FIG. 9  are exploited within optical atomic clocks or the like. 
       FIG. 10  summarizes general features of an exemplary apparatus  1000 . Briefly, a coherent light source  1002  is configured to provide polychromatic coherent light, with the coherent light source optically coupled to an optical reference sample  1004  that has first and second optical transitions at different wavelengths. The apparatus  1000  also includes a stabilization system  1006  configured to provide stabilization of the polychromatic coherent light based on the first and second optical transitions of the reference sample (where, for example, the stabilization system  1006  is configured to provide stabilization of at least two frequency harmonics of the polychromatic coherent light based on a correlation between the wavelengths of the first and second clock transitions with respect to any environmental perturbations, as already explained). 
     Detailed examples of the general apparatus of  FIG. 10  are provided above. See, e.g., the various embodiments described above and shown in the other figures where the stabilization system of  FIG. 10  includes components such as a WGM resonator and various PDH sub-systems. 
     In at least some examples, means may be provided for performing the functions illustrated in  FIGS. 9 and 10  and/or other functions illustrated or described herein. For example, the means may include one or more of: means, such as coherent light source  1002  of  FIG. 10 , for generating polychromatic coherent light using a coherent light source; means, such as optical coupler  212  of  FIG. 2 , for coupling a portion of the polychromatic coherent light into an optical reference sample, such as sample  1004  of  FIG. 10 , that has first and second optical transitions at different wavelengths; and means, such as stabilization system  1006  of  FIG. 10 , for stabilizing the polychromatic coherent light based on the first and second optical transitions of the reference sample. 
     Note that one or more of the components, steps, features, and/or functions illustrated in  FIGS. 1, 2, 3, 4, 5, 6, 7, 8, 9 , and/or  10  may be rearranged and/or combined into a single component, step, feature or function or embodied in several components, steps, or functions. Additional elements, components, steps, and/or functions may also be added without departing from the invention. 
     The word “exemplary” is used herein to mean “serving as an example, instance, or illustration.” Any implementation or aspect described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other aspects of the disclosure. Likewise, an aspect is an implementation or example. Reference in the specification to “an aspect,” “one aspect,” “some aspects,” “various aspects,” or “other aspects” means that a particular feature, structure, or characteristic described in connection with the aspects is included in at least some aspects, but not necessarily all aspects, of the present techniques. The various appearances of “an aspect,” “one aspect,” or “some aspects” are not necessarily all referring to the same aspects. Elements or aspects from an aspect can be combined with elements or aspects of another aspect. 
     The term “coupled” may mean that two or more elements are in direct physical or electrical contact. However, “coupled” may also mean that two or more elements are not in direct contact with each other, but yet still co-operate or interact with each other. 
     Not all components, features, structures, characteristics, etc. described and illustrated herein need be included in a particular aspect or aspects. If the specification states a component, feature, structure, or characteristic “may,” “might,” “can” or “could” be included, for example, that particular component, feature, structure, or characteristic is not required to be included. If the specification or claim refers to “a” or “an” element, that does not mean there is only one of the element. If the specification or claims refer to “an additional” element, that does not preclude there being more than one of the additional element. 
     Although some aspects have been described in reference to particular implementations, other implementations are possible. Additionally, the arrangement and/or order of elements or other features illustrated in the drawings and/or described herein need not be arranged in the particular way illustrated and described. Many other arrangements are possible according to some aspects. 
     Also, it is noted that the aspects of the present disclosure may be described as a process that is depicted as a flowchart, a flow diagram, a structure diagram, or a block diagram. Although a flowchart may describe the operations as a sequential process, many of the operations can be performed in parallel or concurrently. In addition, the order of the operations may be re-arranged. A process is terminated when its operations are completed. A process may correspond to a method, a function, a procedure, a subroutine, a subprogram, etc. When a process corresponds to a function, its termination corresponds to a return of the function to the calling function or the main function. 
     Those of skill in the art would further appreciate that the various illustrative logical blocks, modules, circuits, and algorithm steps described in connection with the aspects disclosed herein may be implemented as electronic hardware, computer software, or combinations of both. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, circuits, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the overall system. 
     The various features of the invention described herein can be implemented in different systems without departing from the invention. It should be noted that the foregoing aspects of the disclosure are merely examples and are not to be construed as limiting the invention. The description of the aspects of the present disclosure is intended to be illustrative, and not to limit the scope of the claims. As such, the present teachings can be readily applied to other types of apparatuses and many alternatives, modifications, and variations will be apparent to those skilled in the art.