Femtosecond Laser Frequency Comb Research Articles

International Comparisons of Femtosecond Laser Frequency Combs

Two types of international comparisons of femtosecond laser frequency combs have been performed in France and the USA. Five combs were involved in the comparisons. Three combs, of which two are transportable, employ nonlinear photonic crystal fiber (PCF) to obtain a wide spectrum covering a full optical octave. The other two are based on broadband femtosecond lasers and require no PCF. The comparisons were performed by counting the optical heterodyne beats between pairs of combs. The frequency agreement among three combs was at the subhertz level in the 563 THz part of the comb spectrum when the combs were referenced to a hydrogen maser. When the combs were referenced to an optical standard, the frequency agreement among four combs was much improved and found to be at the /spl sim/10/sup -19/ level in the spectral range of 333-473 THz. The fact that this result is obtained by five independent measurement systems (combs) strengthens the conclusion that no systematic effects are present at this level.

An Optical Frequency Standard Based on the Electric Octupole Transition in<tex>$^171rm Yb^+$</tex>

The frequency of the /sup 2/S/sub 1/2/(F=0,m/sub F/=0)-/sup 2/F/sub 7/2/(F=3,m/sub F/=0) transition in a single, trapped, laser cooled ion of /sup 171/Yb/sup +/ has been measured with an improved narrow probe laser and a femtosecond laser frequency comb generator. Our best estimate of the frequency is 642 121 496 772.3 /spl plusmn/ 0.6 kHz by comparison with earlier measurements. The uncertainty is limited by measurement statistics and by the ac Stark shift.

Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references

We use femtosecond laser frequency combs to convert optical frequency references to the microwave domain, where we demonstrate the synthesis of 10-GHz signals having a fractional frequency instability of < or =3.5 x 10(-15) at a 1-s averaging time, limited by the optical reference. The residual instability and phase noise of the femtosecond-laser-based frequency synthesizers are 6.5 x 10(-16) at 1 s and -98 dBc/Hz at a 1-Hz offset from the 10-GHz carrier, respectively. The timing jitter of the microwave signals is 3.3 fs.

Demonstration of a HeNe/CH_4-based optical molecular clock

We implement a simple optical clock based on the F2(2) [P(7), v3] optical transition in methane. A single femtosecond laser's frequency comb undergoes difference frequency generation to provide an IR comb at 3.39 microm with a null carrier-envelope offset. This IR comb provides a phase-coherent link between the 88-THz optical reference and the rf repetition rate. Comparison of the repetition rate signal with a second femtosecond comb stabilized to molecular iodine shows an instability of 1.2 x 10(-13) at 1 s, limited by microwave detection of the repetition rates. The single-sideband phase noise of the microwave signal, normalized to a carrier frequency of 1 GHz, is below -93 dBc/Hz at 1-Hz offset.

Deep-Ultraviolet Quantum Interference Metrology with Ultrashort Laser Pulses

Precision spectroscopy at ultraviolet and shorter wavelengths has been hindered by the poor access of narrow-band lasers to that spectral region. We demonstrate high-accuracy quantum interference metrology on atomic transitions with the use of an amplified train of phase-controlled pulses from a femtosecond frequency comb laser. The peak power of these pulses allows for efficient harmonic upconversion, paving the way for extension of frequency comb metrology in atoms and ions to the extreme ultraviolet and soft x-ray spectral regions. A proof-of-principle experiment was performed on a deep-ultraviolet (2 x 212.55 nanometers) two-photon transition in krypton; relative to measurement with single nanosecond laser pulses, the accuracy of the absolute transition frequency and isotope shifts was improved by more than an order of magnitude.

Optical frequency measurements of6sS1∕22–6pP3∕22transition in aCs133atomic beam using a femtosecond laser frequency comb

Optical frequencies of the hyperfine components of the ${D}_{2}$ line in $^{133}\mathrm{Cs}$ are determined using high-resolution spectroscopy and a femtosecond laser frequency comb. A narrow-linewidth probe laser excites the $6s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}(F=3,4)\ensuremath{\rightarrow}6p\phantom{\rule{0.2em}{0ex}}^{2}P_{3∕2}(F=2,3,4,5)$ transition in a highly collimated atomic beam. Fluorescence spectra are taken by scanning the laser frequency over the excited-state hyperfine structure. The laser optical frequency is referenced to a Cs fountain clock via a reference laser and a femtosecond laser frequency comb. A retroreflected laser beam is used to estimate and minimize the Doppler shift due to misalignment between the probe laser and the atomic beam. We achieve an angular resolution on the order of $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\phantom{\rule{0.3em}{0ex}}\mathrm{rad}$. The final uncertainties $(\ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}5\phantom{\rule{0.3em}{0ex}}\mathrm{kHz})$ in the frequencies of the optical transitions are a factor of 20 better than previous results [T. Udem et al., Phys. Rev. A 62, 031801 (2000).]. We find the centroid of the $6s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}\ensuremath{\rightarrow}6p\phantom{\rule{0.2em}{0ex}}^{2}P_{3∕2}$ transition to be ${f}_{D2}=351\phantom{\rule{0.2em}{0ex}}725\phantom{\rule{0.2em}{0ex}}718.4744(51)\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$.

Accumulative effects in the coherence of three-level atoms excited by femtosecond-laser frequency combs

We investigate coherent accumulation processes in three-level atoms excited by a train of ultrashort pulses in the case where the atomic relaxation times are greater than the laser repetition period. In this situation the resonances of the laser field with the atomic system are determined by the laser frequency comb rather than by the spectrum of a single pulse. Using the density matrix formalism, we develop a perturbative theory that is valid for arbitrary pulse shapes. The excitation of a Doppler-broadened atomic vapor by hyperbolic-secant pulses and $0\ensuremath{\pi}$ pulses is analyzed. It is shown that pulse shape has a great influence on the accumulation process and can change the spectral periodicity of the pattern impressed on the Doppler profile of the medium due to the two-photon absorption process. The effect of interpulse phases is also investigated, and we show that the atomic populations can vary by more than one order of magnitude with small variations of the laser repetition rate, while being insensitive to variations of the laser offset. Finally, the theory is adapted for the temporal-coherent-control technique, and its results are compared with previously reported experimental data.

Absolute frequency measurement of 12C 16O 2 laser lines with a femtosecond laser comb and new determination of the 12C 16O 2 molecular constants and frequency grid

Absolute frequency measurements of a CO 2 laser stabilized on saturated absorption resonances of CO 2 laser lines are reported. They were performed using a femtosecond-laser frequency comb generator and two laser diodes at 852 and 782 nm as intermediate oscillators, with their frequency difference phase-locked to the CO 2 laser. Twenty 12C 16O 2 laser lines in the P and R bands at 9 μm were measured with a relative uncertainty of a few 10 −12 limited by the CO 2 frequency reproducibility. A new determination of the CO 2 molecular constants was obtained from these data and previous measurements in the 10 μm band. The CO 2 frequency grid was also calculated, with an improvement of two orders of magnitude compared to the previous grid of Maki et al. [J. Mol. Spectrosc. 167 (1994) 211].

Two-photon Ramsey fringes at 30 THz referenced to an H maser/Cs fountain via an optical-frequency comb at the 1-Hz level

Aspects of two-photon Ramsey fringes in SF/sub 6/ at 30 THz obtained with a 1-m separation between the two absorption zones are presented. The experiment is referenced to a primary standard, the Hydrogen maser/Cs fountain located at BNM-SYRTE, via a femtosecond laser frequency comb generator. This results in a stability below 1 Hz for 1000 s of averaging, and absolute frequency measurements to /spl plusmn/2 Hz which corresponds to 6/spl times/10/sup -14/ in relative frequency. Resolution of the hyperfine structure now approaches 10 Hz, while the fringe period of 200 Hz provides a frequency discriminator 100 times narrower than any other currently in use in the spectral region.

Stabilization of femtosecond laser frequency combs with subhertz residual linewidths.

We demonstrate that femtosecond laser frequency combs (FLFCs) can have a subhertz linewidth across their entire emission spectra when they are phase locked to a reference laser with a similarly narrow linewidth. Correspondingly, the coherence time of the comb components relative to the reference laser can be of the order of a few seconds. Thus we are able to detect high-contrast spectral interferograms at up to 10-s integration time between two FLFCs locked to a common optical reference.

Long-term absolute frequency measurements of 633 nm iodine-stabilized laser standards at NRC and demonstration of high reproducibility of such devices in international frequency measurements

The absolute optical frequency of a 633 nm, I2-stabilized He–Ne laser system is measured with a femtosecond laser frequency comb. Results over a three-year period using chain- and comb-based measurements yield an operating frequency of ff = (473 612 353 602 850 ± 570) Hz for the INMS 3 laser stabilized to the f or a16 component of the 11-5 R(127) transition in 127I2 at the operating conditions specified for the realization of the recommended value of this radiation. The frequency of the NRC INMS 2 laser system has recently been measured with combs at NRC and BIPM and was shown to be reproducible to better than 600 Hz (1 × 10−12) after transport. These results indicate the high level of reproducibility attainable by such widely used optical frequency standards.

Absolute frequency measurement of the iodine-stabilized Ar+ laser at 514.6 nm using a femtosecond optical frequency comb

The frequency of 127I2 hyperfine component a3 of the P(13) 43-0 transition at 514.6 nm has been measured with an optical clockwork based on a femtosecond laser frequency comb generator. The measured frequency at an iodine pressure of 0.12 Pa is 67.3(0.75) kHz higher than the value of 582490603.38(15) MHz, adopted by the CIPM in 2003 [9] but is in a good agreement with the value measured by [29]. In our experiment we used H-maser reference frequency located at BNM-SYRTE Observatoire de Paris and transported to our laboratory by a 43 km optical fibre link.

Absolute frequency measurement in the 28-THz spectral region with a femtosecond laser comb and a long-distance optical link to a primary standard

A new frequency chain was demonstrated to measure an optical frequency standard based on a rovibrational molecular transition in the 28-THz spectral region accessible to a CO2 laser. It uses a femtosecond-laser frequency comb generator and two laser diodes at 852 nm and 788 nm as intermediate oscillators, with their frequency difference phase locked to the CO2 laser. The rf repetition rate of the femtosecond laser was compared with a 100-MHz signal from a hydrogen maser, located at BNM-SYRTE. The 100-MHz signal is transmitted by amplitude modulation of a 1.55-μm laser diode through a 43-km telecommunication optical fibre. As a first example, the absolute measurement of a saturation line of OsO4 in the vicinity of the P(16) laser line of CO2 is reported with a relative uncertainty of 10-12, limited by the CO2/OsO4 frequency day-to-day reproducibility. The current limit on the stability of the frequency measurement is 4×10-13 at 1 s.

Systematic frequency shifts of the 467 nm electric octupole transition in 171Yb+

The 2S1/2 (F = 0) →2F7/2 (F = 3, mF = 0)transition at 467 nm in a single trapped, laser-cooled ion of 171Yb+has the potential to be an extremely accurate optical frequency reference. Thesystematic shifts of the transition frequency currently make a significantcontribution to the uncertainty on absolute frequency measurements of thetransition. Here the systematic shifts of a recent absolute frequency measurementusing a femtosecond laser frequency comb generator are evaluated, andrealistic limits for the ultimate performance of the standard are estimated.

Subkilohertz absolute-frequency measurement of the 467-nm electric octupole transition in171Yb+

The {sup 2}S{sub 1/2}(F=0){yields}{sup 2}F{sub 7/2}(F=3,m{sub F}=0) transition at 467 nm in a single trapped, laser-cooled ion of {sup 171}Yb{sup +} has been measured to be f{sub Yb{sup +}}=642 121 496 771.26(23) kHz using a femtosecond laser frequency comb generator. The measurement is limited by measurement statistics and by the ac Stark shift, both related to the 4.5 kHz linewidth of the probe laser at the time. The systematic shifts of the transition, including ac Stark, second-order Zeeman, quadrupole, and blackbody shifts, have been evaluated.

Optical frequency metrology.

Extremely narrow optical resonances in cold atoms or single trapped ions can be measured with high resolution. A laser locked to such a narrow optical resonance could serve as a highly stable oscillator for an all-optical atomic clock. However, until recently there was no reliable clockwork mechanism that could count optical frequencies of hundreds of terahertz. Techniques using femtosecond-laser frequency combs, developed within the past few years, have solved this problem. The ability to count optical oscillations of more than 1015 cycles per second facilitates high-precision optical spectroscopy, and has led to the construction of an all-optical atomic clock that is expected eventually to outperform today's state-of-the-art caesium clocks.

Direct RF to optical frequency measurements with a femtosecond laser comb

By spanning an optical octave (>300 THz) with a broadened femtosecond laser frequency comb, we directly measure the frequencies of optical standards at 1064/532 nm, 633 nm and 778 nm in terms of the microwave frequency that controls the comb spacing. This microwave frequency can be linked directly to the cesium standard.

Direct comparison of two cold-atom-based optical frequency standards by using a femtosecond-laser comb

With a fiber-broadened, femtosecond-laser frequency comb, the 76-THz interval between two laser-cooled optical frequency standards was measured with a statistical uncertainty of 2x10(-13) in 5 s , to our knowledge the best short-term instability thus far reported for an optical frequency measurement. One standard is based on the calcium intercombination line at 657 nm, and the other, on the mercury ion electric-quadrupole transition at 282 nm. By linking this measurement to the known Ca frequency, we report a new frequency value for the Hg(+) clock transition with an improvement in accuracy of ~10(5) compared with its best previous measurement.

Optical frequency measurement across a 104-THz gap with a femtosecond laser frequency comb

The frequency-domain mode comb of a Ti:sapphire femtosecond laser centered at 350 THz is broadened to 150 THz (full width at -30 dBc) by self-phase modulation in a single-mode optical fiber. By phase locking continuous-wave lasers to elements of the comb near 1064 and 778 nm, we measure the 104-THz frequency gap between these two lasers with a relative uncertainty of 2.7 x 10(-11) in 1 s.