Rotational spectroscopy of cold, trapped molecular ions in the Lamb-Dicke regime

Abstract

Sympathetic cooling of trapped ions has been established as a powerful technique for manipulation of non-laser-coolable ions (Raizen1992,Waki1992,Bowe1999,Barrett2003). For molecular ions, it promises vastly enhanced spectroscopic resolution and accuracy. However, this potential remains untapped so far, with the best resolution achieved being not better than $5\times 10^{-8}$ fractionally, due to residual Doppler broadening being present in ion clusters even at the lowest achievable translational temperatures (Bressel2012). Here we introduce a general and accessible approach that enables Doppler-free rotational spectroscopy. It makes use of the strong radial spatial confinement of molecular ions when trapped and crystallized in a linear quadrupole trap, providing the Lamb-Dicke regime for rotational transitions. We achieve a line width of $1\times 10^{-9}$ fractionally and $1.3\text{kHz}$ absolute, an improvement by $50$ and nearly $3\times 10^3$, respectively, over other methods. The systematic uncertainty is $2.5\times 10^{-10}$. As an application, we demonstrate the most precise test of $\text{ab initio}$ molecular theory and the most precise ($1.3\text{PPB}$) spectroscopic determination of the proton mass. The results represent the long overdue extension of Doppler-free microwave spectroscopy of laser-cooled atomic ion clusters (Berkeland1998) to higher spectroscopy frequencies and to molecules. This approach enables a vast range of high-precision measurements on molecules, both on rotational and, as we project, vibrational transitions.

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Cited by in corpus (28)

• Quantum control of molecular rotation
• Proton-Electron Mass Ratio from Laser Spectroscopy of HD${}^{+}$ at the Part-Per-Trillion Level
• Quantum entanglement between an atom and a molecule
• Proton-electron mass ratio by high-resolution optical spectroscopy of ion ensembles in the resolved-carrier regime
• Quantum non-demolition state detection and spectroscopy of single trapped molecules
• Precision frequency-comb terahertz spectroscopy on pure quantum states of a single molecular ion
• Quantum control of molecules for fundamental physics
• High-precision mass spectrometer for light ions
• Cold trapped molecular ions and hybrid platforms for ions and neutral particles
• Non-adiabatic, Relativistic, and Leading-order QED Corrections for Rovibrational Intervals of ${}^4$He${}_2^{+}$ ($X{}^2{\Sigma }_{\mathrm{u}}^{+}$)
• Trapping, cooling, and photodissociation analysis of state-selected H$\_2^{+}$ ions produced by (3+1) multiphoton ionization
• NRQED approach to the fine and hyperfine structure corrections of order $m{\alpha }^6$ and $m{\alpha }^6(m/M)$ -- Application to the hydrogen atom
• Precision Measurements in Few-Electron Molecules: The Ionization Energy of Metastable ${}^4$He${}_2$ and the First Rotational Interval of ${}^4$He${{}_2}^{+}$
• All-order relativistic computations for atoms and molecules using an explicitly correlated Gaussian basis
• Higher-order corrections to spin-spin scalar interactions in HD${}^{+}$ and H${}_2^{+}$
• Mass-selective removal of ions from Paul traps using parametric excitation
• From megahertz to terahertz qubits encoded in molecular ions: theoretical analysis of dipole-forbidden spectroscopic transitions in N${}_2^{+}$
• Leading order relativistic corrections to the ro-vibrational spectrum of $\mbox{H}^+_2$ and $\mbox{HD}^+$ molecular ions
• H${}_3^{+}$ as a five-body problem described with explicitly correlated Gaussian basis sets
• Laser-stimulated electric quadrupole transitions in the molecular hydrogen ion H2+
• Canceling spin-dependent contributions and systematic shifts in precision spectroscopy of the molecular hydrogen ions
• Stark quenching of rovibrational states of H2+ due to motion in a magnetic field
• Experimental Demonstration of a Terahertz Frequency Reference based on Coherent Population Trapping
• Tank-Circuit Assisted Coupling Method for Sympathetic Laser Cooling
• Hyperfine structure and electric quadrupole transitions in the deuterium molecular ion
• Adiabatically controlled motional states of a ground-state cooled CaO${}^{+}$ and Ca${}^{+}$ trapped ion chain
• Thermal bistability in laser-cooled trapped ions
• QED corrections of orders $m{\alpha }^6$ and $m{\alpha }^6(m/M)$ for HD${}^{+}$ rovibrational transitions beyond Born-Oppenheimer approximation