Multi-mode heterodyne laser interferometry realized via software defined radio.

The agile generation and control of multiple optical frequency modes combined with the realtime processing of multi-mode data provides access to experimentation in domains such as optomechanical systems, optical information processing, and multi-mode spectroscopy. The latter, specifically spectroscopy of spectral-hole burning (SHB), has motivated our development of a multi-mode heterodyne laser interferometric scheme centered around a software-defined radio platform for signal generation and processing, with development in an entirely open-source environment. A challenge to SHB is the high level of shot noise due to the laser power constraint imposed by the spectroscopic sample. Here, we have demonstrated the production, detection, and separation of multiple optical frequency modes to the benefit of optical environment sensing for realtime phase noise subtraction as well as shot noise reduction through multi-mode averaging. This has allowed us to achieve improved noise performance in low-optical-power interferometry. Although our target application is laser stabilization via SHB in cryogenic temperature rare-earth doped crystals, these techniques may be employed in a variety of different contexts.

Double-heterodyne probing for an ultra-stable laser based on spectral hole burning in a rare-earth-doped crystal.

We present an experimental technique for realizing a specific absorption spectral pattern in a rare-earth-doped crystal at cryogenic temperatures. This pattern is subsequently probed on two spectral channels simultaneously, thereby producing an error signal allowing frequency locking of a laser on the said spectral pattern. Appropriate combination of the two channels leads to a substantial reduction in detection noise, paving the way to realizing an ultra-stable laser for which the detection noise can be made arbitrarily low when using multiple channels. We use this technique to realize a laser with a frequency instability of $ 1.7 \times 1{0^{{\bf - }15}} $1.7×10-15 at 1 s, not limited by the detection noise but by environmental perturbation of the crystal. This is comparable with the lowest instability demonstrated at 1 s to date for rare-earth-doped crystal stabilized lasers.

Dispersive heterodyne probing method for laser frequency stabilization based on spectral hole burning in rare-earth doped crystals.

Frequency-locking a laser to a spectral hole in rare-earth doped crystals at cryogenic temperature has been shown to be a promising alternative to the use of high finesse Fabry-Perot cavities when seeking a very high short term stability laser (M. J. Thorpe et al., Nature Photonics 5, 688 (2011)). We demonstrate here a novel technique for achieving such stabilization, based on generating a heterodyne beat-note between a master laser and a slave laser whose dephasing caused by propagation near a spectral hole generate the error signal of the frequency lock. The master laser is far detuned from the center of the inhomogeneous absorption profile, and therefore exhibits only limited interaction with the crystal despite a potentially high optical power. The demodulation and frequency corrections are generated digitally with a hardware and software implementation based on a field-programmable gate array and a Software Defined Radio platform, making it straightforward to address several frequency channels (spectral holes) in parallel.

A clock network for geodesy and fundamental science.

Leveraging the unrivalled performance of optical clocks as key tools for geo-science, for astronomy and for fundamental physics beyond the standard model requires comparing the frequency of distant optical clocks faithfully. Here, we report on the comparison and agreement of two strontium optical clocks at an uncertainty of 5 × 10(-17) via a newly established phase-coherent frequency link connecting Paris and Braunschweig using 1,415 km of telecom fibre. The remote comparison is limited only by the instability and uncertainty of the strontium lattice clocks themselves, with negligible contributions from the optical frequency transfer. A fractional precision of 3 × 10(-17) is reached after only 1,000 s averaging time, which is already 10 times better and more than four orders of magnitude faster than any previous long-distance clock comparison. The capability of performing high resolution international clock comparisons paves the way for a redefinition of the unit of time and an all-optical dissemination of the SI-second.

Experimental realization of an optical second with strontium lattice clocks.

Progress in realizing the SI second had multiple technological impacts and enabled further constraint of theoretical models in fundamental physics. Caesium microwave fountains, realizing best the second according to its current definition with a relative uncertainty of 2-4 × 10(-16), have already been overtaken by atomic clocks referenced to an optical transition, which are both more stable and more accurate. Here we present an important step in the direction of a possible new definition of the second. Our system of five clocks connects with an unprecedented consistency the optical and the microwave worlds. For the first time, two state-of-the-art strontium optical lattice clocks are proven to agree within their accuracy budget, with a total uncertainty of 1.5 × 10(-16). Their comparison with three independent caesium fountains shows a degree of accuracy now only limited by the best realizations of the microwave-defined second, at the level of 3.1 × 10(-16).

Laser locking to the 199Hg 1S0-3P0 clock transition with 5.4 × 10(-15)/✓τ fractional frequency instability.

With 199Hg atoms confined in an optical lattice trap in the Lamb-Dicke regime, we obtain a spectral line at 265.6 nm for which the FWHM is ~15 Hz. Here we lock an ultrastable laser to this ultranarrow 1S0-3P0 clock transition and achieve a fractional frequency instability of 5.4×10(-15)/✓τ for τ ≤ 400 s. The highly stable laser light used for the atom probing is derived from a 1062.6 nm fiber laser locked to an ultrastable optical cavity that exhibits a mean drift rate of -6.0×10(-17) s(-1) (-16.9 mHz s(-1) at 282 THz) over a six month period. A comparison between two such lasers locked to independent optical cavities shows a flicker noise limited fractional frequency instability of 4×10(-16) per cavity.

Neutral atom frequency reference in the deep ultraviolet with fractional uncertainty = 5.7×10(-15).

We present an assessment of the (6s2) (1)S0 ↔ (6s6p)(3)P0 clock transition frequency in 199Hg with an uncertainty reduction of nearly 3 orders of magnitude and demonstrate an atomic quality factor Q of ∼10(14). The 199Hg atoms are confined in a vertical lattice trap with light at the newly determined magic wavelength of 362.5697±0.0011 nm and at a lattice depth of 20E(R). The atoms are loaded from a single-stage magneto-optical trap with cooling light at 253.7 nm. The high Q factor is obtained with an 80 ms Rabi pulse at 265.6 nm. We find the frequency of the clock transition to be 1,128,575,290,808,162.0±6.4(syst)±0.3(stat) Hz (i.e., with fractional uncertainty=5.7×10(-15)). Neither an atom number nor second order Zeeman dependence has yet been detected. Only three laser wavelengths are used for the cooling, lattice trapping, probing, and detection.

Optical-fiber pulse rate multiplier for ultralow phase-noise signal generation.

In this Letter we report on an all optical-fiber approach to the synthesis of ultralow-noise microwave signals by photodetection of femtosecond laser pulses. We use a cascade of Mach-Zehnder fiber interferometers to realize stable and efficient repetition rate multiplication. This technique increases the signal level of the photodetected microwave signal by close to 18 dB. That in turn allows us to demonstrate a residual phase-noise level of -118 dBc/Hz at 1 Hz and -160 dBc/Hz at 10 MHz from a 12 GHz signal. The residual noise floor of the fiber multiplier and photodetection system alone is around -164 dBc/Hz at the same offset frequency, which is very close to the fundamental shot-noise floor.

Optical lattice trapping of 199Hg and determination of the magic wavelength for the ultraviolet 1S(0)↔3P(0) clock transition.

We report on the Lamb-Dicke spectroscopy of the doubly forbidden (6s(2))(1)S(0)↔(6s6p)(3)P(0) transition in (199)Hg atoms confined to a vertical 1D optical lattice. With lattice trapping of ≲10(3) atoms and a 265.6 nm probe laser linked to the LNE-SYRTE primary frequency reference we have determined the center frequency of the transition for a range of lattice wavelengths and at two lattice trap depths. We find the Stark-free (magic) wavelength to be 362.53(0.21) nm-essential knowledge for future use of this line in a clock with anticipated 10(-18) range accuracy. We also present evidence of the laser excitation of a Wannier-Stark ladder of states in a lattice of well depth 10E(R).

Ultra-low-noise microwave extraction from fiber-based optical frequency comb.

In this Letter we report on an all-optical-fiber approach to the generation of ultra-low-noise microwave signals. We make use of two erbium fiber mode-locked lasers phase locked to a common ultrastable laser source to generate an 11.55 GHz signal with an unprecedented relative phase noise of -111 dBc/Hz at 1 Hz from the carrier. The residual frequency instability of the microwave signals derived from the two optical frequency combs is below 2.3x10(-16) at 1 s and about 4x10(-19) at 6.5x10(4) s (in 5 Hz bandwidth, three days of continuous operation).

Doppler-free spectroscopy of the 1S0-3P0 optical clock transition in laser-cooled fermionic isotopes of neutral mercury.

We report direct laser spectroscopy of the 1S0-3P0 transition at 265.6 nm in fermionic isotopes of neutral mercury in a magneto-optical trap. Measurements of the frequency against the LNE-SYRTE primary reference using an optical frequency comb yield 1 128 575 290 808.4+/-5.6 kHz in 199Hg and 1 128 569 561 139.6+/-5.3 kHz in 201Hg. The uncertainty, allowed by the observation of the Doppler-free recoil doublet, is 4 orders of magnitude lower than previous indirect determinations. Mercury is a promising candidate for future optical lattice clocks due to its low sensitivity to blackbody radiation.

Sr lattice clock at 1 x 10(-16) fractional uncertainty by remote optical evaluation with a Ca clock.

Optical atomic clocks promise timekeeping at the highest precision and accuracy, owing to their high operating frequencies. Rigorous evaluations of these clocks require direct comparisons between them. We have realized a high-performance remote comparison of optical clocks over kilometer-scale urban distances, a key step for development, dissemination, and application of these optical standards. Through this remote comparison and a proper design of lattice-confined neutral atoms for clock operation, we evaluate the uncertainty of a strontium (Sr) optical lattice clock at the 1 x 10(-16) fractional level, surpassing the current best evaluations of cesium (Cs) primary standards. We also report on the observation of density-dependent effects in the spin-polarized fermionic sample and discuss the current limiting effect of blackbody radiation-induced frequency shifts.

Beam quality of a nonideal atom laser.

We study the propagation of a noninteracting atom laser distorted by the strong lensing effect of the Bose-Einstein condensate (BEC) from which it is outcoupled. We observe a transverse structure containing caustics that vary with the density within the residing BEC. Using the WKB approximation, Fresnel-Kirchhoff integral formalism, and ABCD matrices, we are able to describe analytically the atom-laser propagation. This allows us to characterize the quality of the nonideal atom-laser beam by a generalized M2 factor defined in analogy to photon lasers. Finally we measure this quality factor for different lensing effects.

Atom laser divergence.

We measure the angular divergence of a quasicontinuous, rf-outcoupled, free-falling atom laser as a function of the outcoupling frequency. The data are compared to a Gaussian-beam model of laser propagation that generalizes the standard formalism of photonic lasers. Our treatment includes diffraction, magnetic lensing, and interaction between the atom laser and the condensate. We find that the dominant source of divergence is the condensate-laser interaction.