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Non-destructive state detection for quantum logic spectroscopy of molecular ions


Precision laser spectroscopy1 of cold and trapped molecular ions is a powerful tool in fundamental physics—used, for example, in determining fundamental constants2, testing for their possible variation in the laboratory3,4, and searching for a possible electric dipole moment of the electron5. However, the absence of cycling transitions in molecules poses a challenge for direct laser cooling of the ions6, and for controlling7,8,9,10,11 and detecting their quantum states. Previously used state-detection techniques based on photodissociation12 or chemical reactions13 are destructive and therefore inefficient, restricting the achievable resolution in laser spectroscopy. Here, we experimentally demonstrate non-destructive detection of the quantum state of a single trapped molecular ion through its strong Coulomb coupling to a well controlled, co-trapped atomic ion. An algorithm based on a state-dependent optical dipole force14 changes the internal state of the atom according to the internal state of the molecule. We show that individual quantum states in the molecular ion can be distinguished by the strength of their coupling to the optical dipole force. We also observe quantum jumps (induced by black-body radiation) between rotational states of a single molecular ion. Using the detuning dependence of the state-detection signal, we implement a variant of quantum logic spectroscopy15,16 of a molecular resonance. Our state-detection technique is relevant to a wide range of molecular ions, and could be applied to state-controlled quantum chemistry17 and to spectroscopic investigations of molecules that serve as probes for interstellar clouds18,19.

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Figure 1: Coupling strength of an optical dipole force to the atomic and molecular ions.
Figure 2: Mapping of the molecular state to the motional qubit.
Figure 3: Non-destructive state detection.
Figure 4: Quantum logic spectroscopy.


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We acknowledge the support of the Deutsche Forschungsgemeinschaft through QUEST and grant SCHM2678/3-1. This work was financially supported by the State of Lower-Saxony, Hannover, Germany. Y.W. acknowledges support from the Braunschweig International Graduate School of Metrology. We thank E. Tiemann, H. Knöckel, O. Dulieu and I.D. Leroux for discussions; M. Drewsen and O. Dulieu for the transition-matrix elements for 24MgH+; and E. Tiemann, B. Hemmerling, and I.D. Leroux for reading the manuscript.

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Authors and Affiliations



P.O.S. conceived and supervised the experiment. F.W. developed the read-out algorithm. F.W., J.C.H. and C.S. carried out the measurements. Y.W. performed the simulations and calculated the lattice coupling strength. F.W. and P.O.S. wrote the main part of the manuscript. Y.W. and F.G. built essential parts of the experiment. All authors discussed the results and contributed to the manuscript.

Corresponding author

Correspondence to Piet O. Schmidt.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Single trajectory from a Monte Carlo simulation of molecular dynamics.

a, The ion initially prepared in the rotational ground state is transferred to higher rotational states because of coupling to black-body radiation at 300 K. b, The probability of finding the ion in a certain rotational state in the simulation (red bars) follows a thermal distribution. The blue bars are calculated values from a master equation approach. The deviation between the red and blue bars results from the finite time interval of the Monte Carlo wavefunction simulation. c, The dwell time decreases for higher rotational states.

Extended Data Figure 2 Rabi flopping between motional states.

Implementation of the sequence shown in Fig. 2 for ΩMgH = 0. The duration of the applied optical lattice is varied to induce Rabi flopping between the motional qubit states |↓〉m and |↑〉m. The error bars show the 95% confidence interval of the photon-distribution fit35. The red dashed line shows a fit to a damped oscillation.

Extended Data Figure 3 Full experimental sequence.

a, Circuit description of the sequence. i, A BSB π-pulse initializes the atom in the state |↑〉Mg and the motional state in the qubit state |↓〉m. ii, The ODF rotates the motional qubit controlled by the internal state of the molecule (see Fig. 2). iii, A second BSB π-pulse maps the motional state (which contains the information about the molecule’s internal state) to the atomic qubit. iv, The atomic qubit’s state is read out by state-dependent fluorescence. b, Pictorial representation of the laser couplings in a simplified level scheme.

Extended Data Figure 4 Raw data for δφ ≈ 0.

a, Theoretically predicted signal for δφ ≈ 0, corresponding to ωIP ≈ 2.21 MHz. b, Expansion of the region shown in a with the seven measured data points that are shown as red diamonds in Fig. 4. The error bars indicate the 68% confidence interval of the photon-distribution fit35.

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Wolf, F., Wan, Y., Heip, J. et al. Non-destructive state detection for quantum logic spectroscopy of molecular ions. Nature 530, 457–460 (2016).

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