Laser spectroscopy of trapped atomic ions

Recent developments in laser spectroscopy of atomic ions stored in electromagnetic traps are reviewed with emphasis on techniques that appear to hold the greatest promise of attaining extremely high resolution. Among these techniques are laser cooling and the use of single, isolated ions as experimental samples. Doppler shifts and other perturbing influences can be largely eliminated. Atomic resonances with line widths of a few parts in 10(11) have been observed at frequencies ranging from the radio frequency to the ultraviolet. Experimental accuracies of one part in 10(18) appear to be attainable.

Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place

Time has always had a special status in physics because of its fundamental role in specifying the regularities of nature and because of the extraordinary precision with which it can be measured. This precision enables tests of fundamental physics and cosmology, as well as practical applications such as satellite navigation. Recently, a regime of operation for atomic clocks based on optical transitions has become possible, promising even higher performance. We report the frequency ratio of two optical atomic clocks with a fractional uncertainty of 5.2 x 10(-17). The ratio of aluminum and mercury single-ion optical clock frequencies nuAl+/nuHg+ is 1.052871833148990438(55), where the uncertainty comprises a statistical measurement uncertainty of 4.3 x 10(-17), and systematic uncertainties of 1.9 x 10(-17) and 2.3 x 10(-17) in the mercury and aluminum frequency standards, respectively. Repeated measurements during the past year yield a preliminary constraint on the temporal variation of the fine-structure constant alpha of alpha/alpha = (-1.6+/-2.3) x 10(-17)/year.

Observation of the 1S0-->3P0 clock transition in 27Al+

We report, for the first time, laser spectroscopy of the 1S0-->3P0 clock transition in 27Al+. A single aluminum ion and a single beryllium ion are simultaneously confined in a linear Paul trap, coupled by their mutual Coulomb repulsion. This coupling allows the beryllium ion to sympathetically cool the aluminum ion and also enables transfer of the aluminum's electronic state to the beryllium's hyperfine state, which can be measured with high fidelity. These techniques are applied to measure the clock transition frequency nu=1,121,015,393,207,851(6) Hz. They are also used to measure the lifetime of the metastable clock state tau=20.6+/-1.4 s, the ground state 1S0 g factor gS=-0.000,792,48(14), and the excited state 3P0 g factor gP=-0.001,976,86(21), in units of the Bohr magneton.

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)<alpha/alpha<0.4x10(-15) yr-1 and -2.7x10(-15)<d/dtlnmicroCs/microB<8.6x10(-15) yr-1.

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.

Spectroscopy Using Quantum Logic

We present a general technique for precision spectroscopy of atoms that lack suitable transitions for efficient laser cooling, internal state preparation, and detection. In our implementation with trapped atomic ions, an auxiliary "logic" ion provides sympathetic laser cooling, state initialization, and detection for a simultaneously trapped "spectroscopy" ion. Detection is achieved by applying a mapping operation to each ion, which results in a coherent transfer of the spectroscopy ion's internal state onto the logic ion, where it is then measured with high efficiency. Experimental realization, by using 9Be+ as the logic ion and 27Al+ as the spectroscopy ion, indicates the feasibility of applying this technique to make accurate optical clocks based on single ions.

Measurement of the (199)Hg+ 5d9 6s2 (2)D(5/2) electric quadrupole moment and a constraint on the quadrupole shift

The electric-quadrupole moment of the (199)Hg+ 5d9 6s2 (2)D(5/2) state is measured to be theta(D,5/2) = -2.29(8) x 10(-40) C m2. This value was determined by measuring the frequency of the (199)Hg+ 5d10 6s (2)S(1/2) --> 5d9 6s2 (2)D(5/2) optical clock transition for different applied electric-field gradients. An isolated, mechanically stable optical cavity provides a frequency reference for the measurement. We compare the results with theoretical calculations and discuss the implications for the accuracy of an atomic clock based upon this transition. We now expect that the frequency shift caused by the interaction of the quadrupole moment with stray electric-field gradients will not limit the accuracy of the Hg+ optical clock at the 10(-18) level.

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.

Standards of Time and Frequency at the Outset of the 21st Century

After 50 years of development, microwave atomic clocks based on cesium have achieved fractional uncertainties below 1 part in 10(15), a level unequaled in all of metrology. The past 5 years have seen the accelerated development of optical atomic clocks, which may enable even greater improvements in timekeeping. Time and frequency standards with various levels of performance are ubiquitous in our society, with applications in many technological fields as well as in the continued exploration of the frontiers of basic science. We review state-of-the-art atomic time and frequency standards and discuss some of their uses in science and technology.

Testing the stability of fundamental constants with the 199Hg+ single-ion optical clock

Over a two-year duration, we have compared the frequency of the 199Hg+ 5d(10)6s (2)S(1/2)(F=0)<-->5d(9)6s(2) (2)D(5/2)(F=2) electric-quadrupole transition at 282 nm with the frequency of the ground-state hyperfine splitting in neutral 133Cs. These measurements show that any fractional time variation of the ratio nu(Cs)/nu(Hg) between the two frequencies is smaller than +/-7 x 10(-15) yr(-1) (1sigma uncertainty). According to recent atomic structure calculations, this sets an upper limit to a possible fractional time variation of g(Cs)(m(e)/m(p))alpha(6.0) at the same level.

An optical clock based on a single trapped 199Hg+ ion

Microwave atomic clocks have been the de facto standards for precision time and frequency metrology over the past 50 years, finding widespread use in basic scientific studies, communications, and navigation. However, with its higher operating frequency, an atomic clock based on an optical transition can be much more stable. We demonstrate an all-optical atomic clock referenced to the 1.064-petahertz transition of a single trapped 199Hg+ ion. A clockwork based on a mode-locked femtosecond laser provides output pulses at a 1-gigahertz rate that are phase-coherently locked to the optical frequency. By comparison to a laser-cooled calcium optical standard, an upper limit for the fractional frequency instability of 7 x 10(-15) is measured in 1 second of averaging-a value substantially better than that of the world's best microwave atomic clocks.

Absolute frequency measurements of the Hg+ and Ca optical clock transitions with a femtosecond laser

The frequency comb created by a femtosecond mode-locked laser and a microstructured fiber is used to phase coherently measure the frequencies of both the Hg+ and Ca optical standards with respect to the SI second. We find the transition frequencies to be f(Hg) = 1 064 721 609 899 143(10) Hz and f(Ca) = 455 986 240 494 158(26) Hz, respectively. In addition to the unprecedented precision demonstrated here, this work is the precursor to all-optical atomic clocks based on the Hg+ and Ca standards. Furthermore, when combined with previous measurements, we find no time variations of these atomic frequencies within the uncertainties of the absolute value of( partial differential f(Ca)/ partial differential t)/f(Ca) < or =8 x 10(-14) yr(-1) and the absolute value of(partial differential f(Hg)/ partial differential t)/f(Hg) < or =30 x 10(-14) yr(-1).

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.

Primary Atomic Frequency Standards at NIST

The development of atomic frequency standards at NIST is discussed and three of the key frequency-standard technologies of the current era are described. For each of these technologies, the most recent NIST implementation of the particular type of standard is described in greater detail. The best relative standard uncertainty achieved to date for a NIST frequency standard is 1.5×10(-15). The uncertainties of the most recent NIST standards are displayed relative to the uncertainties of atomic frequency standards of several other countries.

Sub-dekahertz ultraviolet spectroscopy of 199Hg+

Using a laser that is frequency locked to a Fabry-Perot etalon of high finesse and stability, we probe the 5d(10)6s (2)S(1/2)(F = 0)<-->5d(9)6s(2) (2)D(5/2)(F = 2) Deltam(F) = 0 electric-quadrupole transition of a single laser-cooled 199Hg+ ion stored in a cryogenic radio-frequency ion trap. We observe Fourier-transform limited linewidths as narrow as 6.7 Hz at 282 nm ( 1.06x10(15) Hz), yielding a line Q approximately 1.6x10(14). We perform a preliminary measurement of the 5d(9)6s(2) (2)D(5/2) electric-quadrupole shift due to interaction with the static fields of the trap, and discuss the implications for future trapped-ion optical frequency standards.

Sub-systems for optical frequency measurements: application to the 282-nm (199)Hg(+) transition and the 657-nm Ca line

We are developing laser frequency measurement technologies that should allow us to construct an optical frequency synthesis system capable of measuring optical frequencies with a precision limited by the atomic frequency standards. The system will be used to interconnect and compare new advanced optical-frequency references (such as Ca, Hg(+ ), and others) and eventually to connect these references to the Cs primary frequency standard. The approach we are taking is to subdivide optical frequency intervals into smaller and smaller pieces until we are able to use standard electronic-frequency-measurement technology to measure the smallest interval.

Diode-Pumped Nd:FAP Laser at 1.126 microm: A Possible Local Oscillator for a Hg+ Optical Frequency Standard

We report the efficient operation of a continuous-wave, single-frequency, diode-pumped Nd:FAP laser at 1.126 mum. When frequency quadrupled, such a laser might be used as a local oscillator for an optical frequency standard based on the single-photon (2)S(1/2)-(2)D(5/2) electric quadrupole transition of a trapped and laser-cooled (199)Hg(+) ion. Since the frequencies of the atomic transition and the laser are harmonically related, this scheme helps to simplify the measurement of the S-D clock transition frequency by a phase-coherent chain to the cesium primary frequency standard.

Sum-frequency generation of continuous-wave light at 194 nm

Over 2 mW of continuous-wave tunable 194-nm light is produced by sum-frequency mixing approximately 500 mW of 792-nm and 500 mW of 257-nm radiation in beta-barium borate (BBO). The powers in both fundamental beams are enhanced in separate ring cavities whose optical paths overlap in the Brewster-cut BBO crystal. Due to the higher circulating fundamental powers, the sum-frequency-generated power is nearly 2 orders of magnitude greater than previously reported values.

Progress at NIST toward absolute frequency standards using stored ions

Experiments directed toward the realization of frequency standards of high accuracy using stored ions are briefly summarized. In one experiment, an RF oscillator is locked to a nuclear spin-flip hyperfine transition (frequency approximately 3.03x10(8) Hz) in (9 )Be(+) ions that are stored in a Penning trap and sympathetically laser-cooled. Stability is better than 3x10(-12)tau(-(1/2)) and uncertainty in Doppler shifts is estimated to be less than 5x10(-15). In a second experiment, a stable laser is used to probe an electric quadrupole transition (frequency approximately 1.07x10(15) Hz) in a single laser-cooled (199)Hg(+) ion stored in a Paul trap. The measured Q value of this transition is approximately 10(13). Future possible experiments are discussed.

Absorption spectroscopy at the limit: detection of a single atom

We investigate the sensitivity limit of absorption spectroscopy. An experiment is described in which the decrease in transmitted light intensity that is due to absorption by a single, electromagnetically confined atomic ion is observed.

Generation of continuous-wave 194-nm radiation by sum-frequency mixing in an external ring cavity

Several microwatts of tunable cw radiation near 194 nm in a linewidth of less than 2 MHz have been generated by sum-frequency mixing the radiation from a frequency-doubled argon-ion laser with the radiation from a ring dye laser in a crystal of potassium pentaborate. An external ring cavity resonant with the dye laser gives an enhancement factor of about 14 in the sum-frequency-generated radiation power. The Doppler-limited absorption spectrum of the 6s(2)S((1/2))-6p(2)P((1/2)) first resonance line of natural Hg II has been resolved, and the vacuum wave number for the mass-202 isotope has been measured to be 51485.904(20) cm(-1).

Double-resonance and optical-pumping experiments on electromagnetically confined, laser-cooled ions

Experiments illustrating advantages and unique features of double-resonance and optical pumping on electromagnetically confined, laser-cooled ions are discussed. In certain cases, scattered light from the cooling transition can be used as a monitor in double-resonance experiments to give nearly 100% detection efficiency. Nonradiative relaxation rates are extremely small for stored ions, permitting nearly complete optical pumping, even in extremely weak pumping schemes.