Motional frequency shifts of trapped ions in the Lamb-Dicke regime

First order Doppler effects are usually ignored in laser driven trapped ions when the recoil frequency is much smaller than the trapping frequency (Lamb-Dicke regime). This means that the central, carrier excitation band is supposed to be unaffected by vibronic transitions in which the vibrational number changes. While this is strictly true in the Lamb-Dicke limit (infinitely tight confinement), the vibronic transitions do play a role in the Lamb-Dicke regime. In this paper we quantify the asymptotic behaviour of their effect with respect to the Lamb-Dicke parameter. In particular, we give analytical expressions for the frequency shift, ``pulling'' or ``pushing'', produced in the carrier absorption band by the vibronic transitions both for Rabi and Ramsey schemes. This shift is shown to be independent of the initial vibrational state.Comment: 9 pages, 6 figure

Vibronic "Rabi resonances" in harmonic and hard-wall ion-traps for arbitrary laser intensity and detuning

We investigate laser-driven vibronic transitions of a single two-level atomic ion in harmonic and hard wall traps. In the Lamb-Dicke regime, for tuned or detuned lasers with respect to the internal frequency of the ion, and weak or strong laser intensities, the vibronic transitions occur at well isolated "Rabi Resonances", where the detuning-adapted Rabi frequency coincides with the level spacing of the vibrational modes. These vibronic resonances are characterized as avoided crossings of the dressed levels (eigenvalues of the full Hamiltonian). Their peculiarities due to symmetry constraints and trapping potential are also examined.Comment: 7 pages, 4 figure

Vibronic spectroscopy of an artificial molecule

With advanced fabrication techniques it is possible to make nanoscale electronic structures that have discrete energy levels. Such structures are called artificial atoms because of analogy with true atoms. Examples of such atoms are quantum dots in semiconductor heterostructures and Josephson-junction qubits. It is also possible to have artificial atoms interacting with each other. This is an artificial molecule in the sense that the electronic states are analogous to the ones in a molecule. In this letter we present a different type of artificial molecule that, in addition to electronic states, also includes the analog of nuclear vibrations in a diatomic molecule. Some of the earlier experiments could be interpreted using this analogy, including qubits coupled to oscillators and qubits driven by an intense field. In our case the electronic states of the molecule are represented by a Josephson-junction qubit, and the nuclear separation corresponds to the magnetic flux in a loop containing the qubit and an LC oscillator. We probe the vibronic transitions, where both the electronic and vibrational states change simultaneously, and find that they are analogous to true molecules. The vibronic transitions could be used for sideband cooling of the oscillator, and we see damping up to sidebands of order 10.Comment: 5 pages, 4 figure

Vibronic interactions in the visible and near-infrared spectra of C60− anions

Electron-phonon coupling is an important factor in understanding many properties of the C60 fullerides. However, there has been little success in quantifying the strength of the vibronic coupling in C60 ions, with considerable disagreement between experimental and theoretical results. We will show that neglect of quadratic coupling in previous models for C60- ions results in a significant overestimate of the linear coupling constants. Including quadratic coupling allows a coherent interpretation to be made of earlier experimental and theoretical results which at first sight are incompatible

Control of Vibronic Transition Rates by Resonant Single-Molecule-Nanoantenna Coupling

Plasmonic nanostructures dramatically alter the radiative and nonradiative properties of single molecules in their vicinity. This coupling-induced change in decay channels selectively enhances specific vibronic transitions, which can enable plasmonic control of molecular reactivity. Here, we report coupling-dependent spectral emission shaping of single Rhodamine 800 molecules in the vicinity of plasmonic gold nanorods. We show that the relative vibronic transition rates of the first two vibronic transitions of the spontaneous emission spectrum can be tuned in the weak coupling regime, by approximately 25-fold, on the single molecule level.Peer ReviewedPostprint (author's final draft

High accuracy theoretical investigations of CaF, SrF, and BaF and implications for laser-cooling

The NL-eEDM collaboration is building an experimental setup to search for the permanent electric dipole moment of the electron in a slow beam of cold barium fluoride molecules [Eur. Phys. J. D, 72, 197 (2018)]. Knowledge of molecular properties of BaF is thus needed to plan the measurements and in particular to determine an optimal laser-cooling scheme. Accurate and reliable theoretical predictions of these properties require incorporation of both high-order correlation and relativistic effects in the calculations. In this work theoretical investigations of the ground and the lowest excited states of BaF and its lighter homologues, CaF and SrF, are carried out in the framework of the relativistic Fock-space coupled cluster (FSCC) and multireference configuration interaction (MRCI) methods. Using the calculated molecular properties, we determine the Franck-Condon factors (FCFs) for the $A^2\Pi_{1/2} \rightarrow X^2\Sigma^{+}_{1/2}$ transition, which was successfully used for cooling CaF and SrF and is now considered for BaF. For all three species, the FCFs are found to be highly diagonal. Calculations are also performed for the $B^2\Sigma^{+}_{1/2} \rightarrow X^2\Sigma^{+}_{1/2}$ transition recently exploited for laser-cooling of CaF; it is shown that this transition is not suitable for laser-cooling of BaF, due to the non-diagonal nature of the FCFs in this system. Special attention is given to the properties of the $A'^2\Delta$ state, which in the case of BaF causes a leak channel, in contrast to CaF and SrF species where this state is energetically above the excited states used in laser-cooling. We also present the dipole moments of the ground and the excited states of the three molecules and the transition dipole moments (TDMs) between the different states.Comment: Minor changes; The following article has been submitted to the Journal of Chemical Physics. After it is published, it will be found at https://publishing.aip.org/resources/librarians/products/journals

Pressure-induced transition from the dynamic to static Jahn-Teller effect in (Ph4_{4}P)2_{2}IC60_{60}

High-pressure infrared transmission measurements on \PhC60 were performed up to 9 GPa over a broad frequency range (200 - 20000 cm$^{-1}$) to monitor the vibrational and electronic/vibronic excitations under pressure. The four fundamental T$_{1u}$ modes of \C60a\ are split into doublets already at the lowest applied pressure and harden with increasing pressure. Several cation modes and fullerene-related modes split into doublets at around 2 GPa, the most prominent one being the G$_{1u}$ mode. The splitting of the vibrational modes can be attributed to the transition from the dynamic to static Jahn-Teller effect, caused by steric crowding at high pressure. Four absorption bands are observed in the NIR-VIS frequency range. They are discussed in terms of transitions between LUMO electronic states in \C60a, which are split because of the Jahn-Teller distortion and can be coupled with vibrational modes. Various distortions and the corresponding symmetry lowering are discussed. The observed redshift of the absorption bands indicates that the splitting of the LUMO electronic states is reduced upon pressure application.Comment: 10 pages, 17 figure