Unresolved sideband photon recoil spectroscopy of molecular ions

Abstract

We reflect on the prospect of exploiting the recoil associated with absorption and emission of photons to perform spectroscopy of a single molecular ion. For this recoil to be detectable, the molecular ion is sympathetically cooled by a laser-cooled atomic ion to near their common quantum mechanical ground state within a trapping potential. More specifically, we present a general framework for simulating the expected photon recoil spectra in regimes where either the natural transition linewidth ${\Gamma }_t$ of the molecular ion or the spectral width ${\Gamma }_L$ of the exciting light source exceeds the motional frequencies of the two-ion system. To exemplify the framework, we present two complementary cases: spectroscopy of the broad 3s ${}^2$S${}_{1/2}$ - 3p ${}^2$P${}_{3/2}$ electronic transition (${\Gamma }_t/2\pi =41.8$ MHz) of a single ${}^{24}$Mg${}^{+}$ ion at $\lambda =279.6$ nm by a narrow laser source (${\Gamma }_L/2\pi \lesssim 1$ MHz) and mid-infrared vibrational spectroscopy of the very narrow $|v=0,J=1⟩$ - $|v^{\prime }=1,J^{\prime }=0⟩$ transition (${\Gamma }_t/2\pi =2.50$ Hz) at $\lambda =6.17$ $\mu$m in the ${}^1{\Sigma }^{+}$ electronic ground state of ${}^{24}$MgH${}^{+}$ by a broadband laser source (${\Gamma }_L/2\pi \gtrsim$ 50 MHz). The atomic ion ${}^{24}$Mg${}^{+}$ has been picked to introduce a simple system to make comparisons with experimental results while still capturing most of the physics involved in electronic excitations of molecular ions.

20 pages, 19 figures

References in corpus (7)

• Quantum entanglement between an atom and a molecule
• 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
• Frequency Metrology on single trapped ions in the weak binding limit: The 3s1/2-3p3/2 transition in 24-Mg+
• Efficient sympathetic motional ground-state cooling of a molecular ion
• Sympathetic cooling of molecular ion motion to the ground state
• Identification of molecular quantum states using phase-sensitive forces

Cited by in corpus (3)

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• A scheme for quantum-logic based transfer of accuracy in polarizability measurement for trapped ions using a moving optical lattice
• Line search by quantum logic spectroscopy enhanced with squeezing and statistical tests