Quantum-logic spectroscopy of forbidden vibrational transitions in single nitrogen molecular ions

Electric-dipole forbidden spectroscopic transitions in atoms form the basis of many advanced implementations of quantum computers, atomic clocks and quantum sensors. Coherently addressing such transitions in molecules which are among the most ubiquitous and versatile quantum objects has remained a long-standing challenge owing to their complex energy-level structure. Here, we report the search, observation and coherent manipulation of electric-quadrupole rotational-vibrational transitions in single trapped molecules using a quantum-logic-spectroscopy protocol. We identified individual hyperfine-Zeeman-rotational components of the fundamental vibrational transition of the nitrogen molecular ion, N$_2^+$, and performed coherent population transfer between energy levels. Our work opens up new perspectives for precision molecular spectroscopy, for high-fidelity qubits encoded in the rotational-vibrational motion of molecules, for precise infrared molecular clocks and for searches for new physics

💡 Research Summary

The authors present the first demonstration of quantum‑logic spectroscopy (QLS) applied to electric‑quadrupole (E2) rotational‑vibrational transitions in a single trapped nitrogen molecular ion (N₂⁺). Forbidden electric‑dipole transitions are intrinsically weak (line strengths up to ten orders of magnitude smaller than typical infrared dipole‑allowed lines), making them extremely difficult to detect with conventional spectroscopic techniques. By co‑trapping a single N₂⁺ ion with a calcium atomic “logic” ion in a linear radio‑frequency trap, the authors exploit the shared center‑of‑mass motional mode as a quantum bus. The logic ion is laser‑cooled to the motional ground state and serves as a highly sensitive, non‑destructive probe of the molecular internal state via a state‑dependent optical dipole force (ODF) generated by a one‑dimensional traveling optical lattice. When N₂⁺ resides in its rovibrational ground state |↓⟩ (v = 0, N = 0), the ODF excites the shared motion; this excitation is read out by Rabi flopping on the Ca⁺ 729 nm clock transition’s blue sideband, achieving >99 % detection fidelity.

The molecular transition of interest is the fundamental vibrational band S(0): |v″ = 0, N″ = 0⟩ → |v′ = 1, N′ = 2⟩ in the X²Σ⁺_g electronic ground state. This transition splits into 12 hyperfine‑Zeeman components due to nuclear spin (I = 0 and I = 2) and the external magnetic field (4.7 G). Precise frequencies of these components were previously unknown because electric‑quadrupole line strengths are extremely small. To locate them, the authors employ rapid adiabatic passage (RAP) with a quantum‑cascade laser (QCL) operating at 4.57 µm (65.54 THz). The QCL is phase‑locked to an optical frequency comb (OFC) that is in turn disciplined to an ultralow‑expansion (ULE) cavity and referenced to the Swiss primary frequency standard via a stabilized fiber link, ensuring sub‑kilohertz laser linewidth and SI traceability.

RAP consists of a linear frequency sweep (Δf = 2 MHz) over a controlled duration (t_chirp = 500 ms for strong Zeeman components, 1500 ms for weaker ones). This technique does not require prior knowledge of the exact resonance frequency; any transition lying within the sweep interval is driven with high probability (theoretical transfer ≈ 80 %). After each RAP pulse, a QND measurement determines whether the molecule has changed its internal state. The full QLS sequence comprises four steps: (1) background measurement without ODF, (2) verification that the molecule is initially in |↓⟩, (3) RAP excitation attempt, (4) verification of excitation, followed by a second RAP pulse to return the molecule to |↓⟩ for the next cycle. Positive outcomes (both RAP pulses cause a state change) indicate that a transition lies within the scanned interval; negative outcomes (no change) indicate its absence.

Scanning across the S(0) band, the authors record over 1000 individual RAP attempts on several hundred single molecules, each initially prepared in a random hyperfine‑Zeeman sublevel. The resulting histogram of normalized population‑transfer probabilities reveals distinct peaks corresponding to the twelve hyperfine‑Zeeman components. Gaussian fits to the peaks yield central frequencies with uncertainties of ~0.5 MHz, improving the previously reported fundamental vibrational frequency by an order of magnitude. The measured transfer probabilities (≈ 70 % ± 10 % for the strongest component) agree with the theoretical RAP model (≈ 79 %). The observed Zeeman splitting matches the applied magnetic field, confirming the ability to resolve magnetic substructure despite the modest field strength.

The significance of this work is multifold. First, it demonstrates a non‑destructive, single‑ion method for detecting ultra‑weak forbidden transitions, eliminating the need for chemical detection schemes that destroy the molecule each cycle. This enables duty cycles limited only by the trap and laser stability, dramatically enhancing signal‑to‑noise ratios. Second, the achieved spectral resolution and accuracy open the path toward infrared molecular clocks based on quadrupole transitions, which promise quality factors (Q) exceeding 10¹⁵ and reduced systematic sensitivities compared with atomic clocks. Third, the rotational‑vibrational degree of freedom can serve as a high‑coherence qubit, potentially offering longer coherence times than electronic spin qubits and new avenues for quantum information processing. Finally, precise molecular spectroscopy provides stringent tests of fundamental physics, such as variations of fundamental constants, searches for dark photons, and improved determinations of molecular constants.

In conclusion, the paper establishes quantum‑logic spectroscopy combined with rapid adiabatic passage as a powerful tool for probing forbidden molecular transitions at the single‑particle level. The methodology is readily extensible to other homonuclear diatomic ions (e.g., H₂⁺, O₂⁺, I₂⁺) and to more complex polyatomic species, paving the way for a new generation of precision molecular metrology, quantum technologies, and fundamental‑physics experiments.