P. O. Schmidt

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 × 10–17. The ratio of aluminum and mercury single-ion optical clock frequencies νAl+/νHg+ is 1.052871833148990438(55), where the uncertainty comprises a statistical measurement uncertainty of 4.3 × 10–17, and systematic uncertainties of 1.9 × 10–17 and 2.3 × 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 α of batchmode documentclass[fleqn,10pt,legalpaper]{article} usepackage{amssymb} usepackage{amsfonts} usepackage{amsmath} pagestyle{empty} begin{document} ({dot{{alpha}}}{/}{alpha}=(-1.6{pm}2.3){times}10^{-17}{/}mathrm{year}) end{document}.

Long-lived qubit memory using atomic ions

We demonstrate experimentally a robust quantum memory using a magnetic-field-independent hyperfine transition in 9Be+ atomic ion qubits at a magnetic field B approximately = 0.01194 T. We observe that the single physical qubit memory coherence time is greater than 10 s, an improvement of approximately 5 orders of magnitude from previous experiments with 9Be+. We also observe long coherence times of decoherence-free subspace logical qubits comprising two entangled physical qubits and discuss the merits of each type of qubit.

Observation of theS01→P03Clock Transition inAl+27

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 aluminums electronic state to the berylliums 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.

Hyperfine Coherence in the Presence of Spontaneous Photon Scattering

The coherence of a hyperfine-state superposition of a trapped 9Be+ ion in the presence of off-resonant light is studied experimentally. It is shown that Rayleigh elastic scattering of photons that does not change state populations also does not affect coherence. We observe coherence times that exceed the average scattering time of 19 photons which is determined from measured Stark shifts. This result implies that, with sufficient control over its parameters, laser light can be used to manipulate hyperfine-state superpositions with very little decoherence.

Quantum control, quantum information processing, and quantum-limited metrology with trapped ions

We briefly discuss recent experiments on quantum information processing usingtrapped ions at NIST. A central theme of this work has been to increase our capa-bilities in terms of quantum computing protocols, but we have also applied the sameconcepts to improved metrology, particularly in the area of frequency standardsand atomic clocks. Such work may eventually shed light on more fundamentalissues, such as the quantum measurement problem.

Spectroscopy of atomic and molecular ions using quantum logic

Recently developed techniques for quantum computation using trapped ions allow precise coherent control of the internal and external states of single atoms. Here we report how these techniques can be employed to perform precision spectroscopy of atomic and molecular ions that lack accessible transitions for laser cooling and detection. Furthermore, we discuss how quantum logic can be used to laser‐cool molecules to near their rotational and vibrational ground state by avoiding detrimental spontaneous emission of photons from the molecule.

Ion optical clocks and quantum information processing

Techniques developed for quantum-information processing using trapped ions may be useful in future atomic clocks. Here, we summarize experiments at NIST that (1) use quantum gates to entangle ions and thereby improve the measurement signal-to-noise ratio in spectroscopy and (2) implement sympathetic cooling and quantum state transfer techniques, which might be used to increase the number of choices of ions used for clocks.

Trapped Atomic Ions and Quantum Information Processing

The basic requirements for quantum computing and quantum simulation (single‐ and multi‐qubit gates, long memory times, etc.) have been demonstrated in separate experiments on trapped ions. Construction of a large‐scale information processor will require synthesis of these elements and implementation of high‐fidelity operations on a very large number of qubits. This is still well in the future. NIST and other groups are addressing part of the scaling issue by trying to fabricate multi‐zone arrays of traps that would allow highly‐parallel and scalable processing. In the near term, some simple quantum processing protocols are being used to aid in quantum metrology, such as in atomic clocks. As the number of qubits increases, Schrodinger’s cat paradox and the measurement problem in quantum mechanics become more apparent; with luck, trapped ion systems might be able to shed light on these fundamental issues.

Frequency Comparison of Al+ and Hg+ Optical Standards

We compare the frequencies of two single ion frequency standards: Al and Hg . Systematic fractional frequency uncertainties of both standards are below 10, and the statistical measurement uncertainty is below 5× 10. Recent ratio measurements show a reproducibility that is better than 10. Although single-ion optical frequency standards promise a potential accuracy of 10 or better, this long-standing goal has not yet been realized due to various technical difficulties. Here we report progress for the NIST Hg and Al single-ion standards, as their systematic fractional frequency uncertainty approaches 10. In these measurements, the fourth harmonics of two clock lasers are locked to the mercury and aluminum clock transitions at 282 and 267 nm respectively. An octave-spanning self-referenced Ti:Sapphire femtosecond laser frequency comb (FLFC) is phase-locked to one clock laser, and the heterodyne beat-note of the other clock laser with the nearest comb-tooth is measured. The various beat-note and offset frequencies can be combined to yield a frequency ratio, which is independent of the Cs-based definition of the second, allowing this ratio to be measured even more accurately than the fundamental unit of time can be realized. In more recent comparisons of the frequencies of the two clock lasers, an octave-spanning self-referenced fiber comb laser has provided a second independent measure of the frequency ratio.

Observation of the {sup 1}S{sub 0}{yields}{sup 3}P{sub 0} Clock Transition in {sup 27}Al{sup +}

We report, for the first time, laser spectroscopy of the {sup 1}S{sub 0}{yields}{sup 3}P{sub 0} clock transition in {sup 27}Al{sup +}. 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 aluminums electronic state to the berylliums 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 {sup 1}S{sub 0} g factor g{sub S}=-0.000 792 48(14), and the excited state {sup 3}P{sub 0} g factor g{sub P}=-0.001 976 86(21), in units of the Bohr magneton.