Trapping Ions in Pairs Extends the Reach of Ultraprecise Optical Spectroscopy

In standards labs around the world, physicists are building and testing the next generation of atomic clocks. Like their cesium-based forebears, the new clocks keep time by locking onto atomic resonances. To deliver high accuracy, a resonance must be sharp, but it must also be stable.

Because high frequency brings high stability, clockmakers seek optical transitions. And because the environment undermines stability, they work with single atoms or ions isolated in traps.

Spectrally speaking, the singly charged aluminum cation looks ideal for making an atomic clock. One of its hyperfine transitions (¹ S ₀→³ P ₀), has a Q of 2 × 10¹⁷ and barely wavers under the influence of stray electric and magnetic fields that leak from lab equipment.

But aluminum has an unfortunate drawback. Unlike the current favorite ions of atomic clockmakers—strontium, ytterbium, and mercury—aluminum lacks a convenient transition for removing kinetic energy. If the ion remains too restless after being isolated in its trap, its motion shifts and smears the clock transition’s superlative sharpness.

Now, David Wineland and his collaborators at NIST’s campus in Boulder, Colorado, have demonstrated an ultraprecise method of frequency determination that doesn’t require a fortuitous coincidence of clock and cooling transitions in the same species. Instead, the NIST group picks two different ion species. ¹ One ion provides the clock transition, while the other provides the cooling transition. Thanks to the ions’ Coulomb coupling, the cooling ion not only removes excess energy from both ions, but also acquires then divulges the probability amplitudes of the clock ion’s quantum state. From those amplitudes, the clock transition’s frequency is derived.

The NIST team is already running an atomic clock based on aluminum and beryllium ion pairs, but the method works for other combinations and has other applications. With an anticipated precision of 1 part in 10¹⁸, the method can potentially validate the most exacting calculations of quantum electrodynamics, measure the nuclear charge radius of short-lived isotopes, and test if nature’s fundamental constants vary in time.

Motional modes

Piet Schmidt, who is now at the University of Innsbruck in Austria, Till Rosenband of NIST, and Christopher Langer, a graduate student at the University of Colorado, set up and ran the first demonstration of the pairedion method. For the experiment, which took place early this year, they paired ²⁷ Al ⁺ with ⁹Be⁺. The aluminum ion’s prime clock transition ¹ S ₀→³ P ₀ is somewhat difficult to work with. To test their method, the NIST group chose instead a different transition, ¹ S ₀→³ P ₁.

When trapped together, the two positively charged ions repel each other while the trap’s potential pushes them together. That coupling puts the ions in shared motional modes whose quantized levels (labeled n = 0, 1, and so on) split the ions’ ground and excited states (see Figure 1(a)).

In a typical trapped-ion spectroscopy experiment, an ion is irradiated with a series of pulses from a laser whose frequency is stabilized by a high-finesse cavity. The laser’s frequency is stepped up in value from below the expected resonance to above it. At each frequency, the probability of absorption—and the corresponding point on the resonance curve—is determined through the ion’s fluorescence.

Because an ion either fluoresces or doesn’t, several hundred measurements are taken at each frequency to evaluate the probability. Once the resonance curve has been sampled, the laser frequency is electronically steered to the ion’s resonance and a device called a frequency comb deter-mines its value (see the article by James Bergquist, Steven Jefferts, and Wineland, Physics Today, March 2001, page 37 ). What makes the NIST approach different is that a second ion, not the clock ion itself, manifests the resonance.

The procedure begins with the ions in their ground states (figure 1(a)). Next, the ions are irradiated with a laser pulse tuned close to the ²⁷ Al ⁺ target transition. The outcome (Figure 1(b)), is a two-state superposition between the ²⁷ Al ⁺ ground and excited states with probability amplitudes α and β, respectively. Transferring those amplitudes intact from the clock ion to the cooling ion is the key to the NIST method. Here’s how it works.

After the ²⁷ Al ⁺ ion has been excited, the ions are irradiated again—this time with what’s called a red sideband pulse. As Figure 1(c) shows, the RSB pulse is tuned to stimulate the transition of ²⁷ Al ⁺ from its first excited state to the ground state’s n = 1 sublevel. Now the ions’ motional coupling comes into play. A second RSB pulse (Figure 1(d)) hits the ions—this time tuned to excite ⁹Be⁺ from the n = 1 sublevel of its ground state to the n = 0 sublevel its first excited state.

The final pulse, not shown in Figure 1, stimulates the emission of fluorescence photons from the ⁹Be⁺ whenever the ⁹Be⁺ is in the ground state. The fluorescence rate forms the resonance curve.

The motional modes faithfully transfer α and β not just because they link the two ions. Because the n = −1 mode doesn’t exist, the first RSB pulse can’t excite ²⁷ Al ⁺ from its n = 0 ground state, nor can the second RSB pulse excite ⁹Be⁺ from its n = 0 ground state. As a result, the probability amplitudes engendered by the first pulse remain intact, despite two subsequent pulses.

During the experiment, the ²⁷ Al ⁺ ion acquires kinetic energy from ambient electric fields. To avoid blurring the clock transition line—and, indeed, to put the ion into its ground state at the beginning of the procedure—the excess kinetic energy is removed by ⁹Be⁺ through the ions’ coupled motion.

Applications

With just one electron, the helium ion is simple enough that its energy levels can be calculated with extreme precision. Like aluminum, it’s also hard to cool on its own. Two experiments performed last year exemplify how the NIST paired-ion method could bring the calculations into closer, possibly decisive, confrontation with data.

In the short-lived neutron-rich isotope ⁶He, the extra neutrons occupy an extended halo that shifts the isotopes’ atomic spectra. Almost all the shift comes from the halo’s mass, but the halo’s charge volume also contributes.

Last year, a team from Argonne National Laboratory in Illinois trapped ⁶He atoms and ⁴He atoms, compared the frequency of their ³ S ₁→³ P ₂ transition, and deduced the nuclear charge radius of ⁶He to be 2.054 ± 0.014 fm. ² That value was accurate enough to rule out some models of nuclear structure, but not all them.

Helium also provides a route to measure the Rydberg constant and its possible variation in time. Earlier this year, Stephan Schiller, Bernhard Roth, and Ulf Fröhlich of the University of Düsseldorf in Germany succeeded in cooling ensembles of several thousand helium ions in a trap by coupling them to an ensemble of several thousand beryllium ions. ³ Schiller hopes to apply the NIST paired-ion approach to single pairs of helium and beryllium ions. Using helium to measure the Rydberg constant would complement values obtained from hydrogen.

The course of basic research is hard to predict and sometimes surprising. The paired-ion method exploits techniques the NIST researchers had developed to manipulate ions for quantum computation. Those techniques, in turn, grew out of their work on atomic clocks.