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

Abstract

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

Figures (8)

• Figure 1: Details of the experiment.(A) Energy levels and spectroscopic transitions of N$_2^+$ relevant for the current study. Coloured arrows indicate (hyper)fine components of the S(0) rovibrational band observed in this work. $v, N, J, I$ and $F$ stand for the vibrational, rotational, spin-rotational, nuclear-spin and total-angular-momentum quantum numbers. (B) Schematic of the experiment, see text for details. Abbreviations: QCL - quantum cascade laser; OFC - optical frequency comb; ECDL - external-cavity diode laser; ULE - ultralow expansion; SFG - sum-frequency generation; AOM - acousto-optic modulator; METAS - Swiss Federal Institute of Metrology.
• Figure 2: Quantum-logic spectroscopy protocol.(A) Population $P_{\left| \uparrow \right\rangle_{\text{Ca}^+}}$ of the excited state of Ca$^+$ as a function of 729 nm laser-pulse duration $t_{729}$ during Rabi flops on a blue motional sideband of the clock transition $\left| \uparrow \right\rangle_{\text{Ca}^+}\rightarrow\left| \downarrow \right\rangle_{\text{Ca}^+}$ in Ca$^+$ following coherent motional excitation of a Ca$^+$-N$_2^+$ two-ion string by a state-dependent optical dipole force on N$_2^+$. The red and green traces show experiments with N$_2^+$ in its rovibrational ground ($\left| \downarrow \right\rangle_{\text{N}_2^+}$) and an excited state ($\left| \uparrow \right\rangle_{\text{N}_2^+}$), respectively. The black trace represents the signal obtained without the application of an ODF. The blue-shaded area indicates the interval of 729 nm laser pulse lengths for which maximum detection contrast was achieved. Error bars represent the standard error of the mean of the binomial distribution of 150, 75 and 150 measurements for the red, green and black traces. (B) 'Negative' and (C) 'positive' outcomes of the quantum-logic protocol for the excitation of a dipole-forbidden infrared transition. State-detection results after every step of the sequence are indicated by the colored dots, and represent an average of 50 state-detection measurements. The colors of the dots match the steps in panel (D) which illustrates the quantum-logic protocol used for the spectroscopy of N$_2^+$ ion. See text for details.
• Figure 3: Probability of population transfer. Probability for coherent population transfer using rapid adiabatic passage as a function of the Rabi frequencies $\Omega$ of the transition for two different sets of RAP parameters (chirp bandwidth and duration) used in the experiment (dashed and solid lines). Coloured dots and circles represent the calculated probability of population transfer for the strongest Zeeman components of the relevant (hyper)fine transitions (color coded as in Fig. \ref{['fig:schemes']}). Inset: Results of an experiment on a single N$_2^+$ ion indicating the experimental probability of population transfer on the $\left| J"=1/2, m_F=\pm1/2 \right\rangle \rightarrow \left| J'=5/2,m_F=\pm5/2 \right\rangle~(L4)$ transition (green dots in main figure). Values inside the bins denote experimental state-changing probabilities in the relevant frequency interval. Error bars indicate the standard errors of a binomial distribution.
• Figure 4: Experimental spectrum and simulation.(Top) Rapid-adiabatic-passage quantum-logic spectrum of the S(0) rovibrational band of N$_2^+$. The red histogram bars indicate successful population transfer by RAP normalized to the number of attempts (grey bars) within each frequency bin. The dashed lines represent Gaussian fits to the data. (Bottom) Simulated line strengths $S$ and Rabi frequencies $\Omega$ of individual Zeeman-(hyper)fine components of the S(0) rovibrational line (labels are color-coded as in Fig. \ref{['fig:schemes']}). See text for details.
• Figure 5: Fundamental vibrational frequency $\Delta G_{10}$ of N$_2^+$. Values reported in the literature (colored dots) compared to the present result (red diamond). For the numerical values, see tab. \ref{['tab:vib_constants']}. The width of the red line represents the $1\sigma$ uncertainty of the present result, error bars indicate the uncertainties quoted in the literature.