Novel frequency comb vacuum-ultraviolet light sources and associated nuclear-referenced clocks

Abstract

A vacuum-ultraviolet laser source for generating a frequency comb includes a laser operating at a high repetition rate for generating a regular train of pulses with high peak power. The train of pulses is separated into a frequency upconversion path and a fundamental frequency path. The frequency upconversion path generates an upconverted frequency at least three times the frequency of the train of pulses from the laser. The upconverted pulses are combined with the fundamental frequency pulses and a gas-filled waveguide effects a χ(3) upconversion process on the combination, generating a vacuum-ultraviolet spectral region frequency comb. This frequency comb is useful in generating a nuclear clock signal.

Description

[0001] NOVEL FREQUENCY COMB VACUUM-ULTRAVIOLET LIGHT SOURCES AND ASSOCIATED NUCLEAR-REFERENCED CLOCKS

[0002] BACKGROUND OF THE INVENTION

[0003] This application claims the benefit of the filing date of U.S. pat. app. 63 / 608,601 , filed 11 December 2023, which is incorporated herein by reference.

[0004] FIELD OF THE INVENTION

[0005] The present invention relates to frequency comb vacuum-ultraviolet light sources and associated high-precision nuclear-referenced optical clocks.

[0006] DISCUSSION OF RELATED ART

[0007] Optical clock technology has advanced tremendously in recent years. The current state of the art in clock technology uses optical transitions in ions such as AI+ and Ca+, or in atoms such as Sr and Yb, as a frequency reference. By trapping and cooling these atoms to reduce transition linewidths, and by isolating the atoms from external perturbations, optical clocks have obtained the extraordinary accuracy that is observed today. For example, work at NIST / JILA has compared timing accuracy of three different clock technologies, implemented at scattered locations in Boulder, CO. They demonstrated a consistency between the clocks at the <10‘17level.

[0008] A key component of optical clock technology is the femtosecond laser frequency comb. “Optical” frequencies refer to electromagnetic wave frequencies generated by lasers, at frequencies typically ~1014Hz or greater — an oscillation frequency too fast count directly using electronics. In the 1990’s, co-inventors Kapteyn and Murnane demonstrated a new generation of femtosecond lasers with pulse durations of just a few optical cycles; i.e. 10’14seconds (10 femtoseconds). These very short pulses correspond to a broad emission spectrum, where the entire spectrum is temporally coherent, meaning that the phase relationship between the individual mode frequencies that constitute the laser spectrum all maintain a deterministic phase relationship over an unprecedented >100 nm spectral bandwidth (@ A-800 nm). These “mode-locked” lasers generate these short pulses at a regular interval set by the optical configuration of the laser, with the pulse repetition-rate generally in the range of 108Hz to109Hz or more — a pulse rate that can be counted using electronic circuits.

[0009] This very broad coherent spectrum enabled further spectral broadening using nonlinear fiber optics, and made it possible for the first time to generate an octavespanning (i.e. A / AA<2) coherent spectrum at visible / near-IR wavelengths. This capability makes it possible to implement the frequency comb laser source by frequency doubling the red part of the spectrum from such a source, and beating it against the blue part of the spectrum. This beating corresponds to the carrier envelope offset parameter for the laser, and can be feedback controlled, making it possible to stabilize the mode frequencies that constitute the laser spectrum (Figure 1)-

[0010] Figures 1A and 1 B (Prior Art) show the basic principle of the femtosecond laserbased frequency comb. Modelocked lasers, by virtue of their pulse-locked nature, intrinsically exhibit a spectrum with uniformly- space frequency “comb” lines, with frequencies spaced at the pulse repetition-rate. The “offset” frequency (fo here) ingeneral is not fixed; however, it can be measured and stabilized as needed, by using an octave spanning spectrum and interfering the frequency-doubled red side with the blue side of this spectrum — the oscillation frequency of this interference signal is fo, and is necessarily less than the laser pulse repetition-rate frep. Thus it can be measured using a suitable spectrally-filtered optical detector. Stabilization of fo can be accomplished by feedback through a number of means including slight changes in laser power, or by slight tilting of one of the mirrors in the laser cavity. Stabilizing fo allows the optical comb frequencies of the laser spectrum to be directly related to the pulse repetition-rate of the laser. The first such fo-stabilized laser was implemented using the laser design developed by several of the current inventors.

[0011] This exact fractional frequency division of optical frequencies is the basis for an optically- referenced clock. The optical “comb” frequencies now relate to the repetition rate of the laser. Since this repetition rate can easily be recorded by electronics, the result is a frequency divider that can — in one step — divide-down an optical frequency (~1014-1015Hz) to an electronically-countable (~108-109Hz) frequency. By referencing, “locking,” a single comb line to a narrow-bandwidth optical transition, the repetition-rate of the laser is locked to a fixed value with extraordinary precision, resulting in an “optical clock.”

[0012] One significant enabler for useful frequency combs is the implementation of the frequency comb source at the highest possible repetition rates. The spectral output of a modelocked laser consists of a series of uniformly-spaced frequency modes — with a frequency spacing corresponding to the repetition rate of the laser source. A higher repetition rate means that that total power output of the source is split between a smaller number of more-broadly spaced comb lines. Many comb sources operate at repetition rates of 100 MHz-10 GHz, corresponding to optical cavity lengths of a few cm to a few meters. The important parametric relationship for implementing an optical clock is that the comb mode spacing (i.e. frep) be larger than the spectral linewidth of the reference transition, so that a single comb line predominantly interacts with the reference transition. Indeed, it was the development of very short-pulse modelocked lasers with megawatt-scale peak power at these very high repetition-rates that allows for spectral broadening and frequency comb implementation.

[0013] Further advances in the accuracy and stability of optical clocks depend on improving the stability of the reference wavelength. Current systems employ long-lived atomic (i.e. electronic) transitions in atoms or ions as the reference, with current research efforts toward increased accuracy to use an optical lattice to trap a large number of atoms (e.g. tens to thousands). The reference frequency then corresponds to averaging over a large ensemble of atoms, increasing clock stability. However, this approach is technically complex, requiring a large number of lasers for producing, cooling, and individually trapping a large number of isolated, non-interacting atoms. This optical trap requires interferometric stability with multiple ultranarrow linewidth lasers.

[0014] Another, possibly much simpler-to-implement, reference transition would be to employ a nuclear rather than atomic transition as a frequency reference. Nuclear isomer transitions can emit and absorb photons, and these transitions have much longer lifetime, narrower spectral linewidth — and are expected to be much more immune to external perturbations compared with atomic transitions. Employing nuclear rather than atomic / electronic transitions is broadly acknowledged to represent a next great leap in clock precision. This extremely narrow linewidth of nuclear transitions is most-dramatically manifested in the well-known Mossbauer effect, as illustrated in Figure 2, where57Fe in a crystalline matrix exhibits linewidths corresponding to very small (mm / sec) Doppler shifts between the emitted and absorbed x-rays.

[0015] Figure 2 (Prior Art) is a diagram of Mossbauer resonance fluorescence spectrum of57Fe. Splitting of the spectral line due to individual nuclear spin transitions is resolved with a resolution corresponding to a Doppler shift of <1 mm / sec, or 10'8eV at 14.4 keV — an intrinsic linewidth — obtained simply by cooling an Fe crystal to LN2 temperatures — of A ~1012.

[0016] These data also illustrate a huge potential advantage of nuclear-based clocks: nuclear transitions are relatively insensitive to chemical environment, making it possible to “trap” the reference nuclei within a crystalline solid. Furthermore, the recoil “kick” due to emission of a photon is taken-up by the solid lattice as a whole rather than by an individual atom, essentially eliminating recoil effects. This is the origin of the Mossbauer effect, and can make it possible to substitute the complex optical lattice or atom cooling setups used for atomic clocks with a simple solid reference sample.

[0017] Figures 3A (Prior art) and 3B (Prior art) illustrate nuclear isomer decay of229Th. Figure 3A (Prior art) shows Gamma ray spectroscopy of decay of233U to229Th. This decay, which is the primary method for producing229Th, shows a doublet structure with a 2% yield of this decay to an isomeric excited state, displaced from the ground state of229Th by ~8 eV.

[0018] These data were taken using a high resolution cryogenic microcalorimeter with E / AE -3000 and clearly show an asymmetry in the line. Other measurements of electrons ejected through internal conversion decay of this state also clearly show a transition energy of -8 eV. Figure 3B (Prior Art) is a diagram illustrating direct observation of VUV emission from CaF2 ion- implanted with229Rn, which then undergoes a p decay chain producing229Th isomer, with subsequent VUV emission. The 148.4 nm wavelength is well matched to the 7th harmonic of Yb-based lasers (-1039 nm), with a (half -life) lifetime estimate of 670 seconds.

[0019] The 14.4 keV photon energy of the57Fe transition is not yet a frequency range that is accessible to laser-based frequency combs; however, lower-energy nuclear transitions exist. Specifically,229Th has a nuclear transition at around -8.34 eV. This is the lowest-known energy of a nuclear isomer transition, and its energy was initially determined indirectly through a difference in high-energy transition energies (Figure 3) and through electron internal conversion. However, the transition has very recently been directly measured by Kraemer et al through VUV emission from ion- implanted CaF2 crystals through a nuclear decay chain. The229Th transition, with a lifetime of -103s, has a potential fractional linewidth of A / AA-1018. Although this linewidth is not unprecedented compared with atomic transitions, its insensitivity to external fields not-only can provide unprecedented clock performance, but if229Th in a solid matrix indeed is subject to the Mossbauer effect, implementation of this clock promises to be dramatically simpler than for cold-atom references. More recent measurements have used direct laser excitation of the transition providing more accuracy.

[0020] The Kraemer et al. work has deduced that in ion implantation of MgF2, a significant fraction of the ion implanted population is incorporated into lattice sites that allow for predominant photon emission decay rather than internal conversion electronic excitation — a situation that is encouraging for very narrow linewidth laser excitation and subsequent fluorescence decay detection. Optical clocks typically operate by slightly varying the excitation laser wavelength across the absorption transition, referencing to both shoulders of the transition line through excitation followed by detection of fluorescence. By, for example, balancing the fluorescence intensity at the two half-maximum points of the transition line by steering the center wavelength, slow drifts of a frequency comb referenced to a low-noise reference cavity can be corrected. Variations of this locking method, based on the coherence of the transition, have been used with optical clocks and can be used here also. This results in a clock with excellent short- and long- term stability and accuracy.

[0021] A photon energy of 8.34 eV, or a wavelength A = 148.38 nm corresponds to the Vacuum Ultraviolet (VUV, hv~7-20 eV) spectral region. Light-matter interactions are strongest in the VUV, making laser and frequency-comb sources in this spectral region of particular interest for a broad range of applications. The ionization energies of nearly all molecules and materials lie in this energy range, enabling a number of novel probes of physical and chemical processes: Photoionization mass spectrometry (PI MS) is used for identifying molecules and molecular isomers in reaction products, while photoemission spectroscopies (PES) can probe the band structure of materials and surfaces.

[0022] However, this very strong light-matter interaction has also made this spectral region extremely difficult to work with, limiting experimental access. VUV light has a photon energy just above what is accessible with conventional laser technology. Nonlinear optics (NLO) upconversion in crystals can be used to generate coherent light only up to photon energies ~6-7 eV due to phase matching and photoabsorption limitations. Upconversion in gasses (i.e. high harmonic generation, HHG) can be used to generate light from the VUV all the way into the x-ray spectral regions, but its very high peak-power requirements make the high repetition rates necessary for useful frequency combs difficult. Resonant build-up cavities for HHG are possible but suffer from materials, thermal, plasma dynamics, contamination, and other technical issues related to the very high stored optical powers. Thus, these sources are less-than- ideal for routine, long-term use.

[0023] SUMMARY OF THE INVENTION

[0024] A vacuum-ultraviolet laser source includes a laser operating at a high repetition rate for generating a regular train of pulses with high peak power. A separator separates the train of pulses into a frequency upconversion path and a fundamental frequency path. The train of pulses in the frequency upconversion path is upconverted to a frequency greater than three times the frequency of the train of pulses from the laser. Next, a recombiner for combines the frequency upconverted beam with a beam from the fundamental frequency path to form a combined beam. This combined beam is applied to a x(3)element configured to effect a x(3)upconversion process on the combined beam and generate vacuum-ultraviolet spectral region pulses.

[0025] In many embodiments, it is useful for the laser source repetition rate to be sufficiently high to use its output as a frequency comb. E.g. the repetition rate could be over 10 kHz, over 100 kHz, or even over 1 MHz. The laser source may generate light pulses over 100 fs, and the peak power may be over 10 MW.

[0026] In some embodiments, the frequency upconversion element comprises a series of twoX(2)crystals resulting in an upconverted frequency four times the frequency of the train of pulses from the laser. Then, the x(3)element may be configured to generate a degenerate four-wave process resulting in a frequency comb having a frequency seven times the frequency of the train of pulses from the laser.

[0027] TheX(3)element might be gas-filled waveguide such as a structured waveguide.

[0028] One especially useful implementation of the laser source is to provide a frequency comb as an input to a clock. The clock apparatus interrogates an optical frequency reference to generate a stabilized clock signal. The optical frequency reference falls within the frequency band of the vacuum-ultraviolet spectral region pulses. In some embodiments, an optical frequency reference transition is a nuclear transition, such as a229Thorium transition.

[0029] BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figures 1A and 1 B (Prior Art) are schematic diagrams showing the basic principle of the femtosecond laser-based frequency comb.

[0031] Figure 2 (Prior Art) is a diagram of Mossbauer resonance fluorescence spectrum of 57Fe.

[0032] Figure 3A (Prior Art) is a diagram illustrating gamma ray spectroscopy of decay of 233U to229Th. Figure 3B (Prior Art) is a diagram illustrating direct observation of VUV emission from CaF2 ion- implanted with229Rn, which then undergoes a ft decay chain producing229Th isomer, with subsequent VUV emission.

[0033] Figure 4 is a plot illustrating calculations of nonlinear upconversion in hollow optical fibers through direct and cascaded four-wave mixing processes.

[0034] Figure 5 is a schematic diagram of a vacuum-ultraviolet (VUV) laser source including a high repetition-rate laser and frequency upconversion for providing a VUV frequency comb.

[0035] Figure 6 is a schematic diagram of a nuclear referenced clock using a VUV frequency comb.

[0036] Figure 7 is a schematic diagram showing a four-wave mixing process.

[0037] Figure 8 is a flow diagram showing an example process of four-wave mixing.

[0038] Figure 9 is a plot demonstrating upconversion to a desired region with narrow spectral linewidth.

[0039] DETAILED DESCRIPTION OF THE INVENTION

[0040] The recent demonstration by the inventors of the process of highly cascaded harmonic generation (HCHG) presents a fundamental new enabler for implementing frequency comb sources in the VUV spectral range. HCHG uses two-color upconversion in gasses, often using newly-developed antiresonant hollow waveguides to confine the light, enabling relatively efficient upconversion into the VUV. HCHG greatly reduces peak-power requirements for upconversion compared with HHG, allowing implementation at MHz or higher repetition-rates. See U.S. Pat. No. 11 ,209,717, issued 28 December 2021 and incorporated herein by reference. Furthermore, the 8.34 eV photon energy for229Th is comfortably within the tuning range for a straightforward upconversion of light from a Yb-based laser, including Yb-fiber which is a high-power laser technology compatible with frequency combs. Thus, a new, compact and practical nuclear optical clock technology with unprecedented performance is possible. A frequency-comb source of light in the 8.34 eV spectral region allows for a resonant excitation of229Th with a single frequency from the comb line.

[0041] HCHG relies on a phase-matched four-wave mixing process in gasses, which can be highly efficient in upconverting light to shorter wavelengths in a non-resonant (i.e. wavelength-agnostic) phase-matched two-color mixing process: 2 ■ 2M - M = 3M. This process was first demonstrated by some of the inventors in the 1990’s, and results from the fact that phase matching conditions for this process are favorable in normally dispersive media — atomic gasses such as xenon are normally dispersive up to 8.4 eV.

[0042] For a frequency comb source, comb-line brightness scales with both higher source repetition-rate, and inverse to the linewidth of the upconverted VUV spectral line. Light from a 1 MHz repetition-rate comb source at 8.4 eV, with a spectral line width of -20-40 meV, will consist of many (>106) comb lines, one of which will ideally excite the229Th transition.

[0043] Likewise, the spectral brightness of the light may depend on the number of nonlinear steps used in the gas-phase upconversion process. 8.34 eV can be generated as the 7th harmonic of the Yb laser output. The simplest implementation of HCHG frequency doubles light at -1040 nm to 520 nm, then injects the two colors into the gas filled hollow waveguide. Upconversion then requires a multi-step cascaded process: 2 ■ 2M - M = 3<D; 2M + 3M - M = 4a>; 4M + 2M - M = 5M; 5M + 2M - M = 6M 6M + 2M - M = 7M, or 2 ■ 2M - M = 3M 2M + 3M - M = 4M; 2 ■ 4M - M = 7M. This can be reduced to 2 steps in the gas-filled waveguide by doing third-harmonic upconversion in conventional nonlinear crystals (typically, 2 crystals) before the gas- filled waveguide: 2 ■ 3M - M = 5M; 3M + 5 - M = 7M. Third harmonic upconversion in a crystal can be done with good efficiency and with higher resulting 3M pulse energies, likely increasing the flux. Frequency quadrupling in a nonlinear optical crystal reduces the gas-phase NLO interaction to a single-step 4-wave mixing process, 2 ■ 4M - M = 7M. Highly efficient (i.e. >10%) nonlinear upconversion of Yb- laser pulses to the 4th harmonic at 260 nm using BBO, LBO, BiBO, CLBO, and similar crystals is routine. Figure 4 is a plot illustrating calculations of nonlinear upconversion in hollow optical fibers through direct and cascaded four-wave mixing processes. The solid line shows the spectrum of emission for the case of starting with 1040 nm and 520 nm — the fundamental and second harmonic of a Yb-based ultrafast (200 fs) laser. The predicted spectrum extends to >15 eV, consistent with experimental results. The dotted curve corresponds to using 260 nm and 1040 nm — the fundamental and fourth harmonic — injected into the gas-filled waveguide, starting with the same pulse energy at 1040 nm from the laser (20 pJ), but first frequency quadrupling the light to 260 nm. Note that the predicted flux at 8.4 eV is >30 dB higher for the latter case, single-step to 8.4 eV, case than for the cascaded four-wave mixing case, with a conversion efficiency of close to 5% of the 260 nm converted to 149 nm.

[0044] Figure 4 illustrates the potential enhancement of the latter scheme for generating high power frequency combs around 8.3 eV. These spectra are generated by Luna.jl, an open-source solver of the unidirectional pulse propagation equation (UPPE) with a constant (i.e. non-resonantly-enhanced) x(3)nonlinearity, and compare two cases. The first — solid line— is the case of injection of the fundamental 1 .2 eV (-1040 nm) and second harmonic 2.4 eV (-520 nm) into the waveguide. This calculation shows results consistent with experiments to-date, with excellent qualitative agreement and showing generation of a comb of cascaded harmonics. Here the pulses were assumed to be 200 fs in duration, with a pulse energy of 3 pJ in both the fundamental and the second harmonic, similar to the energies successfully used in experiment.

[0045] The second — dotted line — corresponds to injection of 1.2 eV and 4.8 eV (-260 nm) into the waveguide, splitting the energy of the fundamental laser into roughly 1.5 pJ of 4.8 eV and 5 pJ of 1 .2 eV. Here, the comb of harmonics is sparser. The first upconversion step to 7<z> shows a conversion efficiency of several percent, significantly higher compared with generation of 7<D through the a>, 2a> cascaded process. In the case of 1 MHz repetition- rate, the power injected into the waveguide would be 2W — a feasible power level based on inventor experiments — while the output power at 8.4 eV is predicted to be several tens of mW — an unprecedented average power for such a vacuum-ultraviolet laser source. Furthermore, the Luna.jl calculation shows a conversion efficiency for the first upconversion step comparable for the 2 ■ 4M - <D = 7 t case vs the 2 ■ 2M - M = 3M case. In experiments, the 2 ■ 2M - M = 3c upconversion step yielded a power at 3.6 eV of 230 mW with a total injection power of 7 W; comparable power at 8.4 eV may thus be possible, even in early experiments. Given the very high power capabilities of Yb-fiber laser technology, driving this process with much higher repetition rates, yielding VUV powers at the watt level or higher, are a possibility.

[0046] Embodiments use guided wave propagation in hollow-core fibers to confine the light with lower loss, increasing interaction length and allowing for phase matching through a balance of waveguide and gas dispersion, particularly in the four-wave difference frequency mixing process. For the HCHG work to-date, the use of structured hollow waveguides — in-particular, antiresonant structured hollow core fibers designed specifically for ultralow loss at the fundamental (-1040 nm) wavelength have proven particularly useful in obtaining the highest possible conversion efficiency with the lowest possible driving pulse energy. This enables conversion at high repetition-rates enabling the implementation of a VUV source with usable frequency-comb structure. However, the use of simple capillary (hollow tube) waveguides or even free-space four-wave mixing interactions for the VUV generation may also be possible.

[0047] The model of Figure 4 includes a (non-resonant) field-resolved / (3)nonlinear optical process, as well as the inclusion of self-steepening effects. The strong four-wave mixing process is enhanced by the very rapid beating of the two waves driving the four-wave mixing process, creating something approximating an attosecond pulse train. The fast timescale modulation in the intensity of the driving field, combined with self-steepening effects, results in an EM waveform distorted at time-scales very close to the optical cycle timescale.

[0048] This distortion of the EM field indeed corresponds to the generation of new harmonic frequencies. This is a new regime of nonlinear optics, distinct from high-order harmonic generation in that it does not rely on ionization, but rather on complex modulation of bound-electron wave functions. Figure 5 is a schematic diagram of a vacuum-ultraviolet (VUV) laser source 100 including a high repetition-rate laser 110 and frequency upconversion 120 for providing a VUV frequency comb 150. A repetitively pulse laser 110 operating at a high repetition-rate »1 kHz, generally in the near infrared spectral region, generates regular train of pulses 112 with high peak power. This beam is split into two parts using a beamsplitter 115. One of these beams 116 is directed into a setup for multi- step frequency upconversion, 120, the simplest manifestation of which is a sequence of two frequency-doubling steps 122, 124, which can convert a portion of the laser power from the near infrared into the deep-ultraviolet, using well- establishedX(2)laser frequency upconversion techniques employing nonlinear optical crystals such as BBO. This creates a train of deep-ultraviolet pulses 126. The light emerging from this step is then manipulated using optics such as one or more lenses 128, and then recombined with the near infrared beam 118 in a modematching recombiner 130 via mirror 132 and optics 134. The combined beams 138 focus into a gas-filled waveguide 140 to effect a x(3)upconversion process into the vacuum-ultraviolet spectral region. This allows the generation of high-flux radiation 150 in the vacuum-ultraviolet region otherwise not directly accessible to upconversion using nonlinear-optical crystals.

[0049] Variations in this upconversion setup include separate tuning of the infrared beam 118 wavelength and the deep ultraviolet 126 wavelength through more-advanced frequency upconversion or downconversion techniques, or using separate lasers with temporal synchronization. An aspect of this setup is operation of the laser at repetition-rates » 1kHz up to 100 MHz that allow for the frequency-comb structure of the spectrum of the emission to be resolvable. This upconversion at very high repetition-rates is facilitated by the use of guiding of the two colors to increase the interaction strength. The use of a continuous-wave (CW) laser in this scheme is also possible- in the context of this work, a CW laser corresponds to a pulsed laser operating at a very high repetition-rate with transform-limited bandwidth, such that the frequency comb structure of the light consists of a single comb line.

[0050] A fiber-based narrow linewidth optical frequency comb is generated, by frequency upconversion using one of the techniques described above, in this embodiment using upconversion from 1040 nm to 260 nm in 2 nonlinear optical crystals, followed by nonresonant 2 ■ 4M - M = 7 M upconversion in a suitable gas-filled hollow core fiber. The fiber-laser based comb reference could be derived from modelocked lasers operating anywhere in near-IR region (i.e. Yb or Er fiber lasers) since the comb is very broadband. The pulse repetition rate and duration of the comb pulses amplified for upconversion is optimized depending on application, but will likely fall in the range of frep~1 MHz (+ / - factor of 10-100) and a pulse duration of 100 fs-100 ps. The laser is tuned to center on the 8.34 eV229Th transition, with one comb line serving to excite the transition. The transition can be monitored through fluorescence induced by the laser, most-likely alternating excitation and fluorescence detection to avoid scattering background. Dithering the frequency comb can allow for sampling of the transition frequency on both sides of the lineshape. Standard “optical clock” methods — optical heterodyning, etc. can be used then to translate this frequency reference into a clock signature. Many auxiliary techniques commonly used in optical clocks, such as the use of an isolated reference cavity — which can exhibit excellent ultranarrow linewidth but is subject to frequency drift — can also be incorporated into an optical clock system. The229Th atoms will ideally be confined inside an optically transparent crystal (i.e. CaF2, MgF2 or similar) but also could be confined in an optical lattice or ion trap. The very long excited state lifetime of the229Th transition means that a useful function of this transition is as a long- term stable, environmentally insensitive reference for a clock that already exhibits the excellent short- term stability necessary to probe this narrow linewidth transition.

[0051] Figure 6 is a schematic diagram of a nuclear referenced clock 400 system based on a VUV frequency comb 150. Similar reference numbers are used for similar elements in Figure 5 for clarity, though those skilled in the art will appreciate that many variations are possible. An infrared laser 110 with a sufficiently high pulsed repetition rate frep> 1 kHz is stabilized in both repetition rate and carrier envelope offset frequency by feedback electronics 300 to emit pulses 112 regular in time 202 and discrete frequency lines 201 . In this specific example, the laser 110 frequency has a central wavelength 7 times that of the relevant nuclear transition (here around 1039 nm). The laser light 112 is split into two independent paths via beam splitter 115; in path 116 via mirror 114, the laser light is frequency quadrupled, here with a series of two X(2)crystals 120, to a wavelength of 259.7 nm (the fourth harmonic). The fourth harmonic is recombined with the fundamental infrared light 118 via mirror 132 and beam splitter 136 and the combined beams 138 are injected into a gas-filled hollow waveguide 140 and undergo a x(3)degenerate four-wave process (i.e. 4w + 4w - w - > 7w). The output 150 of this light is now an upconverted frequency comb centered at the 7th harmonic of the fundamental (148.4 nm) with a locked pulse train in the temporal domain 206, and discrete VUV lines in the frequency domain 205. Beam splitter 219 diverts signal 224 to photodiode 225, generating counter 260 for clock 400. Beam splitter 219 passes along signal 226 to apparatus 220.

[0052] Tuning frepand fcEo of the frequency comb 226 varies the individual frequencies of the frequency comb lines, allowing one comb line to “lock” to the nuclear transition frequency (dashed line 202 in 205). In apparatus 220, the229Th-doped sample 221 is interrogated by the VUV frequency comb 226. When the VUV laser is sufficiently locked to the nuclear reference, fluorescent light 228 is emitted and collected by optics 222 and sent to a VUV detector 223. The fluorescence signal 250 is sent to locking feedback electronics 300 where a control loop controls fcEo (via A fcEo 302) and frep (via A frep304) to keep the frequency comb 226 locked to the nuclear transition.

[0053] Photodiode 225 is used to detect the frequency comb signal, where frepand fcEo can be read out by RF electronics and used as a counter 260 for a clock 400.

[0054] Note that this configuration is similar to a “standard” optical clock configuration- the novel aspect is in using a VUV frequency comb source 100 that employed four-wave mixing upconversion at a repetition rate high enough to resolve the linewidth of the nuclear transition reference, allowing the use of the frequency comb structure of the source.

[0055] The net result of implementation of a clock 400 based on a solid-state nuclear reference 221 is that ultra- precision optical clock technology may be much more amenable to a compact and straightforward implementation, for example for deployment in the field, for GPS-denied navigation applications, or in space. Wattlevel Yb lasers can be extremely compact systems, as can other components - the hollow-fiber upconversion, fluorescence detection, and passive cavity reference.

[0056] One possible difference between a VUV-referenced clock 400, and contemporary optical clocks is that generally in optical clock technology, the frequency comb has not been used as the direct excitation source for the clock transition, but rather is used as the frequency divider. A CW laser is locked to the frequency comb through a beat note between the comb and the laser. This allows for higher power at a single wavelength, which is advantageous when the clock transition wavelength is accessible using single-wavelength lasers. In the229Th case, it is likely that CW laser radiation will be inconvenient to generate. Direct amplification and then upconversion of a spectral “slice” from the frequency comb is likely to be the simplest implementation. The spectral band to be amplified can be selected through the use of a fiber Bragg grating (which can select passbands «1 nm wide, and which is often used in the chirped-pulse amplification of picosecond and femtosecond pulses in fiber), etalons, and other spectral filtering techniques. Alternatively, however, one could lock a single frequency source within the Yb spectral band (based on fiber or other materials) to a frequency comb, then amplify this light in either a pulsed or a CW mode to drive the upconversion process.

[0057] Similarly, a simple embodiment of this clock is to implement a single high-power Yb- based source at 7*148.38 nm = 1038.7 nm. However, once a frequency comb source is implemented, there is flexibility to implement more than one amplifier to optimize upconversion to 148.38 nm. For example, the xenon 2-photon resonances are at wavelength 252-260 nm. One could run one amplifier at, for example 1020 nm for 4(L> DUV generation, to get closer to the Xenon 2-photon resonance — still within the bandwidth of Yb-fiber sources and well-matched to materials such as Yb:YLF. The IR wave in this case would tune to shorter wavelengths — for 1020 nm, the idler is 894 nm, which may require a more complex source to implement — for example a parametric amplifier or thsapphire amplifier. Another example using the 2-photon resonance at 259.1 nm (fourth harmonic of 1036.5 nm) could combine with an idler wavelength of 1021 .3 nm to generate VUV light at 148.4 nm. Figure 7 is a schematic diagram showing a four-wave mixing process. The fundamental harmonic 118 and fourth harmonic 126 are injected into a gas-filled waveguide 140 and the 7th harmonic 150 is generated by a degenerate four-wave mixing process, where 4® (4.77 eV)+ 4® (4.77 eV) - co (1.19 eV) -> 7® (8.35 eV).

[0058] Figure 8 is a flow diagram showing one specific example of how four-wave mixing in a gas-filled waveguide can be used to generate light on the229Th transition at 148.4 nm. The driving laser is a Yb laser 100 with a fundamental wavelength of 7 times the nuclear transition wavelength (1038.7 nm). The light is split into two arms; in arm 116, the light is frequency quadrupled in a series of x(2) crystals 122, 124, first to its second harmonic (519.3 nm) and then its fourth harmonic (259.7 nm). The fundamental 118 and fourth harmonic 126 are then combined and mixed in a gas- filled waveguide 140. In this waveguide, the light undergoes degenerate four-wave mixing (DFWM) where the output light is determined by 4w + 4w - w -> 7w. The output light, the 7th harmonic of the fundamental driving laser, has a central wavelength of 148.4 nm, in line with the nuclear transition in229Th.

[0059] Figure 9 is a plot showing data experimentally demonstrating upconversion to a desired region with narrow spectral linewidth. This graph demonstrates the feasibility of the proposed approach, in that by using a laser operating at 1 MHz repetition-rate, we have demonstrated upconversion of light from 1.03 pm to 147 nm (hv=8.44 eV)- the spectral region very close to the229Th transition- with a relatively narrow spectral linewidth. The narrow linewidth of 25.8 milli-eV corresponds to a fractional spectral resolution of -300 (i.e. hv^\hv~300)- excellent (likely unprecedented) spectral purity for a laser source in the VUV. Note that the discrepancy between the 147 nm center wavelength of this demonstrated source and the required 148.4 nm is not significant in terms of a feasibility demonstration, but rather reflects the fact that the laser we used (Light Conversion Pharos) had a fixed wavelength of 1.03 pm. The upconversion process that we used does not rely on a resonant phase-matched process and will tune to 148.4 nm when driven with a laser source at 1039 nm, and 1039 nm is a wavelength that can easily be obtained from Yb-based lasers, including Yb-fiber lasers. Measurements done using the laser operating at 1 kHz repetition-rate show upconversion with relatively narrow spectral bandwidth. Furthermore, at reduced repetition rates (reduced for technical reasons, to accurately measure power), a pulse energy of 15 nJ and a conversion efficiency slightly less than 0.1 % was measured.

[0060] Experimental results demonstrate that the new single-four-wave-mixing-step approach to generating light around 8.4 eV enables an efficiency improvement of up to 4 orders of magnitude. The pulse energy measurement seems to bear this out. At 1 MHz repetition-rate, the average power - 6 mW - and power per comb mode - 1 nW - is on-par with the power levels expected.

[0061] While the exemplary preferred embodiments of the present invention are described herein with particularity, those skilled in the art will appreciate various changes, additions, and applications other than those specifically mentioned, which are within the spirit of this invention. For example, using gas mixtures for the nonlinear optical medium. Mixing Xenon, for example, with Helium gas, may suppress ionization, or quench any excited states created incidentally. Careful selection of the gas type may to avoid multiphoton absorption of the generated VUV light at the Th transition.

[0062] What is claimed is:

Claims

CLAIMS1. A vacuum-ultraviolet laser source comprising: a laser operating at a high repetition rate for generating a regular train of pulses; a separator for separating the train of pulses into a frequency upconversion path and a fundamental frequency path; a frequency upconversion element configured to convert the train of pulses in the frequency upconversion path to a upconverted frequency greater than three times the frequency of the train of pulses from the laser; a recombiner for combining a beam from the frequency upconversion path and a beam from the fundamental frequency path to form a combined beam; and a x(3)element configured to effect a x(3)upconversion process on the combined beam and generate vacuum-ultraviolet spectral region pulses.

2. The laser source of claim 1 wherein the high repetition rate is sufficiently high to use as a frequency comb.

3. The laser source of claim 2 wherein the high repetition rate is over 10 kHz.

4. The laser source of claim 2 wherein the high repetition rate is over 100 KHz.

5. The laser source of claim 2 wherein the high repetition rate is over 1 MHz6. The laser source of claim 1 wherein the laser generates light pulses over 100 fs.

7. The laser source of claim 1 wherein the frequency upconversion element comprises a series of two x(2)crystals resulting in an upconverted frequency four times the frequency of the train of pulses from the laser.

8. The laser source of claim 1 wherein the x(3)element is configured to generate a degenerate four-wave process resulting in a frequency comb having a frequency seven times the frequency of the train of pulses from the laser.

9. The laser source of claim 1 wherein the x(3)element is a gas-filled waveguide.

10. The laser source of claim 9 wherein the x(3)element is a structured waveguide.11 . The laser source of claim 1 further comprising clock apparatus that interrogates an optical frequency reference to generate a stabilized clock signal.

12. The laser source of claim 11 wherein the optical frequency reference falls within the frequency band of the vacuum-ultraviolet spectral region pulses.

13. The laser source of claim 12 wherein an optical frequency reference transition is a nuclear transition.

14. The laser source of claim 13 wherein the optical frequency reference comprises229Thorium.

15. A vacuum-ultraviolet laser source comprising: a laser operating at a high repetition rate for generating a regular train of pulses; a separator for separating the train of pulses into a frequency upconversion path and a fundamental frequency path; a frequency upconversion element configured to convert the train of pulses in the frequency upconversion path to a upconverted frequency greater than three times the frequency of the train of pulses from the laser; a recombiner for combining a beam from the frequency upconversion path and a beam from the fundamental frequency path to form a combined beam; a x(3)element configured to effect a x(3)upconversion process on the combined beam and generate vacuum-ultraviolet spectral region pulses; and clock apparatus that interrogates an optical frequency reference to generate a stabilized clock signal.

16. The laser source of claim 15 wherein the optical frequency reference falls within the frequency band of the vacuum-ultraviolet spectral region pulses.

17. The laser source of claim 16 wherein an optical frequency reference transition is a nuclear transition.

18. The laser source of claim 17 wherein the optical frequency reference comprises229Thorium.

19. The laser source of claim 16 wherein the high repetition rate is sufficiently high to use as a frequency comb.

20. The laser source of claim 19 wherein the high repetition rate is over 10 kHz.

21. The laser source of claim 19 wherein the high repetition rate is over 100 KHz.

22. The laser source of claim 19 wherein the high repetition rate is over 1 MHz23. The laser source of claim 16 wherein the laser generates light pulses over100 fs.

24. The laser source of claim 16 wherein the frequency upconversion element comprises a series of two x(2)crystals resulting in an upconverted frequency four times the frequency of the train of pulses from the laser.

25. The laser source of claim 16 wherein the x(3)element is configured to generate a degenerate four-wave process resulting in a frequency comb having a frequency seven times the frequency of the train of pulses from the laser.

26. The laser source of claim 16 wherein the x(3)element is a gas-filled waveguide.

27. The laser source of claim 26 wherein the x(3)element is a structured waveguide.

28. The method of providing generate vacuum-ultraviolet spectral region pulses comprising the steps of: providing a regular train of laser pulses at a high repetition rate; separating the train of pulses into a frequency upconversion path and a fundamental frequency path;frequency upconverting the train of pulses in the frequency upconversion path to a upconverted frequency greater than three times the frequency of the train of pulses; combining a beam from the frequency upconversion path and a beam from the fundamental frequency path to form a combined beam; and effecting a x(3)upconversion process on the combined beam to generate the vacuum-ultraviolet spectral region pulses.

29. The method of claim 28 further including the step of interrogating an optical frequency reference to generate a stabilized clock signal.

30. The method of claim 28 wherein the optical frequency reference comprises229Thorium.31 . The method of claim 28 wherein the high repetition rate is over 10 kHz.

32. The method of claim 28 wherein the high repetition rate is over 100 KHz.

33. The method of claim 28 wherein the high repetition rate is over 1 MHz34. The method of claim 28 wherein the light pulses are over 100 fs.

35. The method ce of claim 28 wherein the frequency upconversion step includes series of two x(2)crystals resulting in an upconverted frequency four times the frequency of the train of pulses from the laser.

36. The method of claim 28 wherein x(3)upconversion process generates a degenerate four-wave process resulting in a frequency comb having a frequency seven times the frequency of the train of pulses from the laser.

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