Frequency-comb spectroscopy on pure quantum states of a single molecular ion

Abstract

Spectroscopy is a powerful tool for studying molecules and is commonly performed on large thermal molecular ensembles that are perturbed by motional shifts and interactions with the environment and one another, resulting in convoluted spectra and limited resolution. Here, we use generally applicable quantum-logic techniques to prepare a trapped molecular ion in a single quantum state, drive terahertz rotational transitions with an optical frequency comb, and read out the final state non-destructively, leaving the molecule ready for further manipulation. We resolve rotational transitions to 11 significant digits and derive the rotational constant of 40 CaH + to be B R = 142 501 777.9(1.7) kHz. Our approach suits a wide range of molecular ions, including polyatomics and species relevant for tests of fundamental physics, chemistry, and astrophysics.Precision molecular spectroscopy produces information that is essential to understand molecular properties and functions, which underpin chemistry and biology. In particular, microwave rotational spectroscopy can precisely determine various aspects of molecular structure, such as bond lengths and angles, and help identify molecules. However, even in a dilute gas, where the interaction with surrounding molecules is reduced, spectroscopic experiments often fall short of the ultimate resolution set by the natural linewidth of the transitions. This is due to effects that crowd and blur molecular spectra, such as uncontrolled nuclear, rotational, vibrational, and electronic states, line shifts and broadening from external fields, reduced interaction time from time-of-flight, and the Doppler effect. These limitations have motivated efforts toward trapping molecules and cooling them close to absolute zero temperature. Laser cooling and trapping [1-3], which revolutionized atomic physics, have enabled formation of molecules from cold atoms [4] and precision molecular spectroscopy [5]. Direct laser cooling of molecules shows promise for species with advantageous level structures that only require a few laser wavelengths [6-8], but is infeasible for the vast majority of molecules.Furthermore, even with trapped and cooled molecules [9], commonly used detection methods, such as state-dependent photo-dissociation or ionization [10,11], destroy the molecules under study, making them unavailable for further manipulation.In this work, we perform high resolution spectroscopy on rotational states of a molecular ion using methods that are generally applicable to a broad range of molecular ions, which are readily trapped in electromagnetic potentials [12] and cooled by coupling to co-trapped atomic ions amenable to laser cooling [13,14]. The long interrogation times and low translational temperature enabled by trapping and sympathetic cooling lead to high resolution [15], which has, among other advances, enabled the most stringent test of fundamental theory carried out by molecular ions [16]. We prepare a trapped 40 CaH + molecular ion at rest in a single, known quantum state and coherently ...

From megahertz to terahertz qubits encoded in molecular ions: theoretical analysis of dipole-forbidden spectroscopic transitions in N2+

“…These include molecular-beam slowing and trapping, [1][2][3] direct laser cooling, [4][5][6] assembly from ultracold atoms, 7 and sympathetic cooling. 8,9 In this context, experiments in which single molecular ions are co-trapped with single atomic ions [10][11][12][13][14][15] show excellent prospects for achieving the long-standing goal of gaining full control over the quantum state and dynamics of single isolated molecules. In these experiments, a quantum-logic approach 16 is pursued in which the co-trapped atomic ion is used to cool the external motion of the molecular ion to the quantum ground state and to nondestructively detect its internal quantum state.…”

“…In these experiments, a quantum-logic approach 16 is pursued in which the co-trapped atomic ion is used to cool the external motion of the molecular ion to the quantum ground state and to nondestructively detect its internal quantum state. Coherent Rabi and Ramsey spectroscopy, 11,13 quantum-non demolition state detection 10,12,15 and atom-molecule entanglement 14 have recently been demonstrated.…”

“…A full control over the quantum states of cold and trapped molecules will enable improved experiments in the realm of precision spectroscopy. Applications range from precisely validating existing physical theories such as quantum electrodynamics, [17][18][19] testing fundamental concepts 20,21 such as a possible time variation of physical constants 22,23 and the putative existence of new forces of nature, 24 benchmarking molecularstructure theory, 13,25 performing controlled chemical reactions, 26,27 to implementing new time standards based on narrow rovibrational molecular transitions in the mid-infrared spectral domain. [28][29][30] In many sensitive approaches to the spectroscopy of molecular ions, the molecule is destroyed in the process of detection.…”

Bichromatic Photoassociation Spectroscopy for the Determination of Rotational Constants of Cs2 0 u + Long-Range State below the 6S1/2 + 6P1/2 Asymptote

“…Ideal (high-phase-space-density, low-temperature below 1 mK) gases of ultracold molecules can be produced from ultracold alkali atomic gases with indirect approaches such as photoassociation (PA) [4] or the magnetoassociation over a Feshbach resonance [5] followed by a Stimulated Raman Adiabatic Passage (STIRAP) [6] to deeply bound ground states [7]. Various robust and exquisite control techniques have enabled the ultracold molecules as promising candidates in extensive applications, such as precision measurement [8], cold-reaction chemistry [9], high-resolution spectroscopy [10], quantum information processing [11], and quantum simulation [12]. Due to its relatively low requirements for the initial temperature and density parameters of atomic samples, the PA has been proven to be a versatile and simple method to prepare weakly bound ultracold molecules at the micro-Kelvin range, both for homonuclear and heteronuclear molecules [4,13,14], which demonstrate van der Waals potentials proportional to 1/R 3 or 1/R 6 (where R is the inter-nuclear distance) in their excited molecular states at large internuclear separations.…”

Identification of molecular quantum states using phase-sensitive forces

“…Recent progress in the quantum control of single trapped molecules [13][14][15][16][17] has enabled the detection 13,15 , coherent manipulation 14,16 and entanglement 17 of molecular quantum states on the singleparticle level. These advances aim at encoding qubits in rotational and vibrational molecular energy states 18,19 and at performing precise spectroscopic measurements 20 with applications including the development of mid-infra-red frequency standards 21 and testing a possible variation of fundamental constants such as the proton-toelectron-mass ratio [22][23][24][25][26] .…”