A transition described as “forbidden” sounds like something physics should prevent. In spectroscopy, the word means something more specific: an energy change that cannot occur through the usual, strongest interaction with light. Weaker interactions can still produce it, making the signal exceptionally difficult to locate and measure.

Researchers at the University of Basel have now found and reversibly controlled such transitions in individual nitrogen molecular ions. The study, published in Nature Communications, uses a second trapped particle to reveal the molecule’s state. Crucially, the measurement does not require destroying and replacing the molecule each time.

The work opens a practical route to investigating forbidden molecular vibrations, which could become useful references for timekeeping and quantum information. Related advances in atomic clocks show why controlling narrow transitions matters. Molecules offer additional internal motions that could provide different sensitivities and applications.

Stefan Willitsch led the team, with Aleksandr Shlykov and Meissa L. Diouf as co-first authors. Richard Karl, Mikolaj Roguski and Umesh C. Joshi also contributed. Their experiment establishes a spectroscopy and control method, adding to research on qubit control without yet delivering a molecular quantum computer.

The strongest common interaction between light and matter is called electric-dipole coupling. Some transitions fail its selection rules, which specify the energy-state changes that interaction permits. Other, weaker couplings remain possible. Here, the researchers addressed electric-quadrupole transitions involving changes in both the molecule’s vibration and rotation.

The paper describes line strengths around ten orders of magnitude weaker than typical dipole-allowed infrared transitions. That is roughly a factor of ten billion. The challenge is therefore not simply building a sensitive detector. Researchers must also search for a very faint resonance whose position theory cannot predict precisely enough.

Weak coupling can bring an advantage: a very narrow natural spectral line. That means the transition has a sharply defined frequency, potentially useful for a clock reference. Work on nuclear clocks explores a different physical transition, but similarly depends on finding, controlling and measuring a precise resonance.

Molecules complicate that search because they can rotate and vibrate as well as change electronic states. Additional spin and magnetic effects split their energy levels further. Such structure makes precision spectroscopy demanding, while also providing a wider choice of transitions with potentially useful properties.

The team trapped one positively charged nitrogen molecule, N₂⁺, alongside one positively charged calcium atom, Ca⁺. Electric fields held the pair, and laser cooling reduced their shared motion. Electrical repulsion couples the particles’ movement, allowing information about the molecule to pass through a motion they share.

This is quantum-logic spectroscopy: the molecule is the object being studied, while calcium supplies an accessible readout. Calcium responds readily to laser-based detection. The experiment therefore avoids relying on a convenient fluorescence signal from nitrogen itself, which lacks the simple optical behavior needed for that approach.

Carefully chosen laser beams generate a force that strongly excites the shared motion when nitrogen occupies its lowest rotational and vibrational state. The researchers then probe calcium to determine whether that motion occurred. Experiments with trapped ions likewise exploit collective motion as a sensitive carrier of information.

The state readout leaves the molecule chemically intact and preserves the internal state being tested. That is a major difference from the group’s 2014 chemical-detection experiment. “To achieve the highest precision, it is much better to perform experiments on single molecules, and not lose them in the process,” Willitsch said. Such paired-ion methods also underpin other quantum operations.

A separate infrared laser addressed the forbidden transition near a wavelength of 4.574 micrometers. Rather than requiring an exactly known starting frequency, the researchers swept the pulse frequency across a small interval. This technique, called rapid adiabatic passage, transfers population between energy states when a resonance lies within the sweep.

Each cycle checked the initial state, applied a pulse and checked again. A second pulse could return an excited molecule to its starting state. Seeing both changes supplied evidence that the laser had encountered a transition. Resetting the molecule also made it available for the next measurement.

“Using the same molecule again and again was crucial. It made the search for such faint lines feasible”, Shlykov said. This repeatability distinguishes the method from destructive detection. It connects controlled laser pulses with a readout that can verify whether the intended state change occurred.

The transfer was not perfect. One representative experiment produced 22 state changes from 38 infrared pulses, with a transfer probability of 70% ± 10% in the strongest frequency interval. Those results demonstrate reversible manipulation, rather than a finished, exceptionally reliable qubit. Broader research into quantum vibrations addresses other ways to control and detect weak molecular signals.

Although each experiment studied one molecule, the complete spectrum combined results from several hundred independently prepared molecules. Their initial populations occupied different spin-related sublevels. Combining the measurements allowed the team to identify multiple components of the transition, rather than expecting one molecule to supply every spectral feature.

The researchers extracted an improved fundamental vibrational frequency after accounting for rotational and other contributions to the measured line. Their result was about 65.1973562 terahertz, with a reported uncertainty of 2.1 megahertz. That uncertainty is approximately ten times smaller than the most precise previous determination discussed in the paper.

This is progress in measuring a molecular frequency, not evidence that a new clock now outperforms established atomic timekeepers. The experiment’s survey resolution depended on its laser-frequency sweep. A narrow theoretical natural linewidth does not automatically become the linewidth or uncertainty achieved by a laboratory measurement.

That distinction is important across molecular sensing and quantum measurement. The team stabilized its laser with an optical frequency comb and referenced it to Switzerland’s primary frequency standard through an optical-fiber link. Those external references helped make the measured frequencies traceable to the SI second.

Several identified transitions are predicted to respond only weakly to certain disturbances. At particular magnetic fields, selected components may become insensitive to magnetic-field changes to first order. Those theoretical properties make them candidates for further precision work, but their best projected performance was not demonstrated in this experiment.

A future molecular clock would need sustained interrogation, control of systematic shifts and a complete uncertainty assessment. Encoding useful quantum information would likewise require testing coherence and operational reliability. Advances in ion clocks provide context for the demanding work between controlling a transition and operating a precision device.

Forbidden molecular vibrations could also help test whether the proton-to-electron mass ratio changes over time. Comparing suitable references repeatedly could search for a relative drift, complementing other tests of fundamental constants. The Basel study did not detect such a change. It supplied a more repeatable way to reach transitions that might eventually make that search possible.

These resources explain the methods and earlier findings behind the experiment. They exclude the featured paper and appear newest first.

Spectroscopy Using Quantum Logic
The foundational demonstration uses an auxiliary ion to cool and read another ion, providing the general strategy behind quantum-logic spectroscopy. (Science, July 2005)