Optical atomic phase reference and timing.

Atomic clocks based on laser-cooled atoms have made tremendous advances in both accuracy and stability. However, advanced clocks have not found their way into widespread use because there has been little need for such high performance in real-world/commercial applications. The drive in the commercial world favours smaller, lower-power, more robust compact atomic clocks that function well in real-world non-laboratory environments. Although the high-performance atomic frequency references are useful to test Einstein's special relativity more precisely, there are not compelling scientific arguments to expect a breakdown in special relativity. On the other hand, the dynamics of gravity, evidenced by the recent spectacular results in experimental detection of gravity waves by the LIGO Scientific Collaboration, shows dramatically that there is new physics to be seen and understood in space-time science. Those systems require strain measurements at less than or equal to 10-20 As we discuss here, cold atom optical frequency references are still many orders of magnitude away from the frequency stability that should be achievable with narrow-linewidth quantum transitions and large numbers of very cold atoms, and they may be able to achieve levels of phase stability, ΔΦ/Φtotal ≤ 10-20, that could make an important impact in gravity wave science.This article is part of the themed issue 'Quantum technology for the 21st century'.

Generation of 20 GHz, sub-40 fs pulses at 960 nm via repetition-rate multiplication.

Optical filtering of a stabilized 1 GHz optical frequency comb produces a 20 GHz comb with approximately 40 nm bandwidth (FWHM) at 960 nm. Use of a low-finesse Fabry-Pérot cavity in a double-pass configuration provides a broad cavity coupling bandwidth (Deltalambda/lambda approximately 10%) and large suppression (50 dB) of unwanted modes. Pulse durations shorter than 40 fs with less than 2% residual amplitude modulation are achieved.

Improved signal-to-noise ratio of 10 GHz microwave signals generated with a mode-filtered femtosecond laser frequency comb.

We use a Fabry-Perot cavity to optically filter the output of a Ti:sapphire frequency comb to integer multiples of the original 1 GHz mode spacing. This effectively increases the pulse repetition rate, which is useful for several applications. In the case of low-noise microwave signal generation, such filtering leads to improved linearity of the high-speed photodiodes that detect the mode-locked laser pulse train. The result is significantly improved signal-to-noise ratio at the 10 GHz harmonic with the potential for a shot-noise limited single sideband phase noise floor near -168 dBc/Hz.

Optical lattice induced light shifts in an yb atomic clock.

We present an experimental study of the lattice-induced light shifts on the (1)S(0) --> (3)P(0) optical clock transition (nu(clock) approximately 518 THz) in neutral ytterbium. The "magic" frequency nu(magic) for the 174Yb isotope was determined to be 394 799 475(35) MHz, which leads to a first order light shift uncertainty of 0.38 Hz. We also investigated the hyperpolarizability shifts due to the nearby 6s6p(3)P(0) --> 6s8p(3)P(0), 6s8p(3)P(2), and 6s5f(3)F(2) two-photon resonances at 759.708, 754.23, and 764.95 nm, respectively. By measuring the corresponding clock transition shifts near these two-photon resonances, the hyperpolarizability shift was estimated to be 170(33) mHz for a linear polarized, 50 microK deep, lattice at the magic wavelength. These results indicate that the differential polarizability and hyperpolarizability frequency shift uncertainties in a Yb lattice clock could be held to well below 10(-17).

Demonstration of high-performance compact magnetic shields for chip-scale atomic devices.

We have designed and tested a set of five miniature nested magnetic shields constructed of high-permeability material, with external volumes for the individual shielding layers ranging from 0.01 to 2.5 cm(3). We present measurements of the longitudinal and transverse shielding factors (the ratio of external to internal magnetic field) of both individual shields and combinations of up to three layers. The largest shielding factor measured was 6 x 10(6) for a nested set of three shields, and from our results we predict a shielding factor of up to 1 x 10(13) when all five shields are used. Two different techniques were used to measure the internal field: a chip-scale atomic magnetometer and a commercially available magnetoresistive sensor. Measurements with the two methods were in good agreement.

High-contrast coherent population trapping resonances using four-wave mixing in 87Rb.

We demonstrate very high-contrast coherent population trapping(1) (CPT) resonances by using four-wave mixing in (87)Rb atoms. In the experiment, we take advantage of the spectral overlap between F=2-->F(?) and F=3-->F(?) optical resonances on the D1 line of (87)Rb and (85)Rb atoms, respectively, to eliminate the DC-light background from the CPT resonance signal. We observe a CPT resonance with a contrast in the range of 90%, compared with a few percent achieved by alternative methods.

Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance.

We report tests of local position invariance and the variation of fundamental constants from measurements of the frequency ratio of the 282-nm 199Hg+ optical clock transition to the ground state hyperfine splitting in 133Cs. Analysis of the frequency ratio of the two clocks, extending over 6 yr at NIST, is used to place a limit on its fractional variation of <5.8x10(-6) per change in normalized solar gravitational potential. The same frequency ratio is also used to obtain 20-fold improvement over previous limits on the fractional variation of the fine structure constant of |alpha/alpha|<1.3x10(-16) yr-1, assuming invariance of other fundamental constants. Comparisons of our results with those previously reported for the absolute optical frequency measurements in H and 171Yb+ vs other 133Cs standards yield a coupled constraint of -1.5x10(-15)

Kilohertz-resolution spectroscopy of cold atoms with an optical frequency comb.

We have performed sub-Doppler spectroscopy on the narrow intercombination line of cold calcium atoms using the amplified output of a femtosecond laser frequency comb. Injection locking of a 657-nm diode laser with a femtosecond comb allows for two regimes of amplification, one in which many lines of the comb are amplified, and one where a single line is predominantly amplified. The output of the laser in both regimes was used to perform kilohertz-level spectroscopy. This experiment demonstrates the potential for high-resolution absolute-frequency spectroscopy over the entire spectrum of the frequency comb output using a single high-finesse optical reference cavity.

Single-atom optical clock with high accuracy.

For the past 50 years, atomic standards based on the frequency of the cesium ground-state hyperfine transition have been the most accurate time pieces in the world. We now report a comparison between the cesium fountain standard NIST-F1, which has been evaluated with an inaccuracy of about 4 x 10(-16), and an optical frequency standard based on an ultraviolet transition in a single, laser-cooled mercury ion for which the fractional systematic frequency uncertainty was below 7.2 x 10(-17). The absolute frequency of the transition was measured versus cesium to be 1,064,721,609,899,144.94 (97) Hz, with a statistically limited total fractional uncertainty of 9.1 x 10(-16) the most accurate absolute measurement of an optical frequency to date.

Atomic-based stabilization for laser-pumped atomic clocks.

We describe a novel technique for stabilizing frequency shifts in laser-interrogated vapor-cell atomic clocks. The method suppresses frequency shifts due to changes in the laser frequency, intensity, and modulation index as well as atomic vapor density. The clock operating parameters are monitored by using the atoms themselves, rather than by using conventional schemes for laser frequency and cell temperature control. The experiment is realized using a chip-scale atomic clock. The novel atomic-based stabilization approach results in a simpler setup and improved long-term performance.

Magnetic field-induced spectroscopy of forbidden optical transitions with application to lattice-based optical atomic clocks.

We develop a method of spectroscopy that uses a weak static magnetic field to enable direct optical excitation of forbidden electric-dipole transitions that are otherwise prohibitively weak. The power of this scheme is demonstrated using the important application of optical atomic clocks based on neutral atoms confined to an optical lattice. The simple experimental implementation of this method--a single clock laser combined with a dc magnetic field--relaxes stringent requirements in current lattice-based clocks (e.g., magnetic field shielding and light polarization), and could therefore expedite the realization of the extraordinary performance level predicted for these clocks. We estimate that a clock using alkaline-earth-like atoms such as Yb could achieve a fractional frequency uncertainty of well below 10(-17) for the metrologically preferred even isotopes.

Direct excitation of the forbidden clock transition in neutral 174Yb atoms confined to an optical lattice.

We report direct single-laser excitation of the strictly forbidden (6s2)1S0 <--> (6s6p)3P0 clock transition in 174Yb atoms confined to a 1D optical lattice. A small (approximately 1.2 mT) static magnetic field was used to induce a nonzero electric dipole transition probability between the clock states at 578.42 nm. Narrow resonance linewidths of 20 Hz (FWHM) with high contrast were observed, demonstrating a resonance quality factor of 2.6 x 10(13). The previously unknown ac Stark shift-canceling (magic) wavelength was determined to be 759.35 +/- 0.02 nm. This method for using the metrologically superior even isotope can be easily implemented in current Yb and Sr lattice clocks and can create new clock possibilities in other alkaline-earth-like atoms such as Mg and Ca.

Atomic vapor cells for chip-scale atomic clocks with improved long-term frequency stability.

A novel technique for microfabricating alkali atom vapor cells is described in which alkali atoms are evaporated into a micromachined cell cavity through a glass nozzle. A cell of interior volume 1 mm3, containing 87Rb and a buffer gas, was made in this way and integrated into an atomic clock based on coherent population trapping. A fractional frequency instability of 6 x 10(-12) at 1000 s of integration was measured. The long-term drift of the F=1, mF=0-->F=2, mF=0 hyperfine frequency of atoms in these cells is below 5 x 10(-11)/day.

Observation and absolute frequency measurements of the 1S0-3P0 optical clock transition in neutral ytterbium.

We report the direct excitation of the highly forbidden (6s2) 1S0 <--> (6s6p) 3P0 optical transition in two odd isotopes of neutral ytterbium. As the excitation laser frequency is scanned, absorption is detected by monitoring the depletion from an atomic cloud at approximately 70 microK in a magneto-optical trap. The measured frequency in 171Yb (F=1/2) is 518,295,836,591.6 +/- 4.4 kHz. The measured frequency in 173Yb (F=5/2) is 518,294,576,847.6 +/- 4.4 kHz. Measurements are made with a femtosecond-laser frequency comb calibrated by the National Institute of Standards and Technology cesium fountain clock and represent nearly a 10(6)-fold reduction in uncertainty. The natural linewidth of these J=0 to J=0 transitions is calculated to be approximately 10 mHz, making them well suited to support a new generation of optical atomic clocks based on confinement in an optical lattice.

High-resolution spectroscopy with a femtosecond laser frequency comb.

The output of a mode-locked femtosecond laser is used for precision single-photon spectroscopy of 133Cs in an atomic beam. By changing the laser's repetition rate, the cesium D1 (6s 2S(1/2)-->6p 2P(1/2)) and D2 (6s 2S(1/2)-->6p 2P(3/2)) transitions are detected and the optical frequencies are measured with accuracy similar to that obtained with a cw laser. Control of the femtosecond laser repetition rate by use of the atomic fluorescence is also implemented, thus realizing a simple cesium optical clock.

Stabilized frequency comb with a self-referenced femtosecond Cr:forsterite laser.

A frequency comb is generated with a Cr:forsterite femtosecond laser, spectrally broadened through a highly nonlinear optical fiber to span from 1.0 to 2.2 ,m, and stabilized using the f-to-2f self-referencing technique. The repetition rate and the carrier-envelope offset frequency are stabilized to a hydrogen maser, calibrated by a cesium atomic fountain clock. Simultaneous frequency measurement of a 657-nm cw laser by use of the stabilized frequency combs from this Cr:forsterite system and a Ti:sapphire laser agree at the 10(-13) level. The frequency noise of the comb components is observed at 1064, 1314, and 1550 nm by comparing the measured beat frequencies between cw lasers and the supercontinuum frequency combs.

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.

A chip-scale atomic clock based on 87Rb with improved frequency stability.

We demonstrate a microfabricated atomic clock physics package based on coherent population trapping (CPT) on the D1 line of 87Rb atoms. The package occupies a volume of 12 mm3 and requires 195 mW of power to operate at an ambient temperature of 200 degrees C. Compared to a previous microfabricated clock exciting the D2 transition in Cs [1], this 87Rb clock shows significantly improved short- and long-term stability. The instability at short times is 4 x?10-11 / tau?/2 and the improvement over the Cs device is due mainly to an increase in resonance amplitude. At longer times (tau?> 50 s), the improvement results from the reduction of a slow drift to ?5 x 10-9 / day. The drift is most likely caused by a chemical reaction of nitrogen and barium inside the cell. When probing the atoms on the D1 line, spin-exchange collisions between Rb atoms and optical pumping appear to have increased importance compared to the D2 line.

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.

Absolute-frequency measurements with a stabilized near-infrared optical frequency comb from a Cr:forsterite laser.

A frequency comb is generated with a chromium-doped forsterite femtosecond laser, spectrally broadened in a dispersion-shifted highly nonlinear fiber, and stabilized. The resultant evenly spaced comb of frequencies ranges from 1.1 to beyond 1.8 microm. The frequency comb was referenced simultaneously to the National Institute of Standards and Technology's optical frequency standard based on neutral calcium and to a hydrogen maser that is calibrated by a cesium atomic fountain clock. With this comb we measured two frequency references in the telecommunications band: one half of the frequency of the d/f crossover transition in 87Rb at 780 nm, and the methane v2 + 2v3 R(8) line at 1315 nm.