Jaume Carbonell, Rimantas Lazauskas, Dominique Delande, Laurent Hilico, Senem Kılıç
A new state of the H$_2^+$ molecular ion with binding energy of 1.09$\times10^{-9}$ a.u. below the first dissociation limit is predicted, using highly accurate numerical nonrelativistic quantum calculations. It is the first L=0 excited state, antisymmetric with respect to the exchange of the two protons. It manifests itself as a huge p-H scattering length of $a=750\pm 5$ Bohr radii.
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In order to use a collection of trapped ions for experiments where a well defined preparation of vibrational states is necessary, all vibrational modes have to be cooled to ensure precise and repeatable manipulation of the ions' quantum states. A method for simultaneous sideband cooling of all axial vibrational modes is proposed. By application of a magnetic field gradient the absorption spectrum of each ion is modified such that sideband resonances of different vibrational modes coincide. The ion string is then irradiated with monochromatic electromagnetic radiation, in the optical or microwa…
The ion trap quantum computer proposed by Cirac and Zoller is analyzed for decoherence due to vibrations of the ions. An adiabatic approximation exploiting the vast difference between the frequencies of the optical intraionic transition and the vibrational modes is used to find the decoherence time at any temperature T. The scaling of this decoherence time with the number of ions is discussed, and compared to that due to spontaneous emission.
The non-relativistic three-body Schrödinger equation of the heteronuclear molecular ion HD$^+$ is solved in perimetric coordinates using the Lagrange-mesh method. Energies and wave functions of the four lowest vibrational bound or quasibound states $v=0-3$ are calculated for total orbital momenta from 0 to 47. Energies are given with an accuracy from about 12 digits for the lowest vibrational level to at least 9 digits for the third vibrational excited level. With a simple calculation using the corresponding wave functions, accurate dipole transition probabilities per time unit between those l…
After the study of the three body molecular system H$_2^+$ ({\it J. Phys. B: At. Mol. Opt. Phys.} {\bf 45} 065101), its isotopomer, the deuterium molecular ion D$_2^+$ is studied. The three-body Schrödinger equation is solved using the Lagrange-mesh method in perimetric coordinates. Energies and wave functions for four vibrational states $v=0-3$ and bound or quasibound states for total orbital momenta from 0 to 56 are calculated. The 1986 fundamental constant $m_d=3670.483014\,m_e$ is used. The obtained energies have an accuracy from about 13 digits for the lowest vibrational state to at least…
Quantum-logic spectroscopy of forbidden vibrational transitions in single nitrogen molecular ions
该研究利用量子逻辑光谱学技术，实现了单个氮分子离子中被禁止的旋转-振动跃迁的相干操控，为高精度分子光谱和量子计算提供了新方法。
Vibrational degrees of freedom in trapped-ion systems have recently been gaining attention as a quantum resource, beyond the role as a mediator for entangling quantum operations on internal degrees of freedom, because of the large available Hilbert space. The vibrational modes can be represented as quantum harmonic oscillators and thus offer a Hilbert space with infinite dimension. Here we review recent theoretical and experimental progress in the coherent manipulation of the vibrational modes, including bosonic encoding schemes in quantum information, reliable and efficient measurement techni…
A model based on the strong-field and Born-Oppenheimer approximations qualitatively describes the distribution over vibrational states formed in a diatomic molecular ion following ionization of the neutral molecule by intense laser pulses. Good agreement is found with a recent experiment [X. Urbain et al., Phys. Rev. Lett. 92, 163004 (2004)]. In particular, the observed deviation from a Franck-Condon-like distribution is reproduced. Additionally, we demonstrate control of the vibrational distribution by a variation of the peak intensity or a change of frequency of the laser pulse.
The three-body Schrödinger equation of the H$_2^+$ hydrogen molecular ion with Coulomb potentials is solved in perimetric coordinates using the Lagrange-mesh method. The Lagrange-mesh method is an approximate variational calculation with variational accuracy and the simplicity of a calculation on a mesh. Energies and wave functions of up to four of the lowest vibrational bound or quasibound states for total orbital momenta from 0 to 40 are calculated. The obtained energies have an accuracy varying from about 13 digits for the lowest vibrational state to at least 9 digits for the third vibratio…
Electron-impact cross sections for the dissociation process of vibrationally excited He2+ molecular ion, as a function of the incident electron energy are calculated for the dissociative transition X2Σ+u \to A2Σ+g by using the R-matrix method in the adiabatic-nuclei approximation. The potential energy curves for the involved electronic states and target properties, also calculated with the R-matrix method, were found to be in good agreement with the results reported in literature.
We present a study of vibrational quenching and chemical processes of molecular ions immersed in an ultracold atomic gas by means of the quasi-classical trajectory (QCT) method. In particular, BaRb$^+(v)$ + Rb collisions are studied at cold temperatures revealing a highly efficient energy transfer between the translational degrees of freedom and internal degrees of the molecular ion. Thus leading to a large vibrational quenching cross section which follows the Langevin capture model prediction. These results play a key role on the understanding of relaxation phenomena of cold molecular ions in…
High-precision variational calculations of the operators for the relativistic corrections in the leading $mα^4$ order are presented. The ro-vibrational states in the range of the total orbital angular momentum $L\!=\!0\!-\!4$ and vibrational quantum number $v\!=\!0\!-\!10$ for the $\mbox{H}_2^+$ and $\mbox{HD}^+$ molecular ions are considered. We estimate that about ten significant digits are obtained. This high precision is required for making theoretical predictions for transition frequencies at the level of $10^{-12}$ relative uncertainty.
The major goal of the high-precision studies of ro-vibrational states in the hydrogen molecular ions is to provide an alternative way for improving the electron-to-proton mass ratio, or the atomic mass of electron. By now the complete set of relativistic and radiative corrections have been obtained for a wide range of ro-vibrational states of H_2^+ and HD^+ up to order R_\inftyα^4. In this work we complete calculations of various contributions to the R_\inftyα^4 order by computing the relativistic corrections to the binding energy of electron.
We present theoretical thermally-averaged rate constants for vibrational and rotational (de-)excitation of the H3+ ion by electron impact. The constants are calculated using the multi-channel quantum-defect approach. The calculation includes processes that involve a change Delta J<=2 in the rotational angular momentum J of H3+. The rate constants are calculated for states with J<=5 for rotational transitions of the H3+ ground vibrational level. The thermal rates for transitions among the lowest eight vibrational levels are also presented, averaged over the rotational structure of the vibration…
Hybrid ion-atom systems provide an excellent platform for studies of state-resolved quantum chemistry at low temperatures, where quantum effects may be prevalent. Here we study theoretically the process of vibrational relaxation of an initially weakly bound molecular ion due to collisions with the background gas atoms. We show that this inelastic process is governed by the universal long-range part of the interaction potential, which allows for using simplified model potentials applicable to multiple atomic species. The product distribution after the collision can be estimated by making use of…
Theoretical study of dissociative recombination and vibrational excitation of the BF$_2^+$ ion by an electron impact
本文结合正则模式近似与UK R-matrix方法，计算了BF$_2^+$离子的解离复合和电子碰撞振动激发截面，并给出了10-3000 K范围内的热平均速率系数。
A linear rotor trapped and coupled to the vibrational modes of an ion crystal
该研究针对共囚禁于保罗阱的分子离子与原子离子，确定了考虑分子超精细结构的共振偶极-声子耦合条件，提出用边带分辨激光光谱和退相干测量探测该耦合的方案，为量子控制提供了可行路径。
Relativistic and QED corrections to the recently discovered first vibrational $2pσ_u$ state are presented. This state has an extremely small nonrelativistic binding energy $E_B=1.085045252(1)\times10^{-9}$ a.u. Its wave functions has a maximum at $R\approx100$ a.u. and extends up to several hundreds. It is shown that this state does not disappear if higher order relativistic and QED corrections, including the Casimir--Polder effect, are taken into account.
Molecular ions can be held in a chain of laser-cooled atomic ions by sympathetic cooling. This system is ideal for performing high-precision molecular spectroscopy with applications in astrochemistry and fundamental physics. Here we show that this same system can be coupled with a broadband laser to discover new molecular transitions. We use three-ion chains of Ca$^{+}$ and CaH$^{+}$ to observe vibrational transitions via resonance enhanced multiphoton dissociation detected by Ca$^{+}$ fluorescence. Based on theoretical calculations, we assign the observed peaks to the transition from the grou…
Vibrational dynamics in conventional molecules usually takes place on a timescale of picoseconds or shorter. A striking exception are ultralong-range Rydberg molecules, for which dynamics is dramatically slowed down as a consequence of the huge bond length of up to several micrometers. Here, we report on the direct observation of vibrational dynamics of a recently observed Rydberg-atom-ion molecule. By applying a weak external electric field of a few mV/cm, we are able to control the orientation of the photoassociated ultralong-range Rydberg molecules and induce vibrational dynamics by quenchi…
We reconsider the calculation of rovibrational transition frequencies in hydrogen molecular ions. Some previously neglected contributions, such as the deuteron polarizability, are included into consideration in comparison with our previous work. In particular, one-loop and two-loop QED corrections at $mα^7$ and $mα^8$ orders are recalculated in the framework of the adiabatic approximation, with systematic inclusion of corrections associated with vibrational motion. Improved theoretical transitions frequencies are obtained and found to be in very good agreement with recent high-precision spectr…
Some of us have recently reported in Science 321 232 (2008) vibrational cooling of translationally cold Cs_2 molecules into the lowest vibrational level v=0 of the singlet X 1Sigma_g ground electronic state. Starting from a sample of cold molecules produced in a collection of vibrational levels of the ground state, our method was based on repeated optical pumping by laser light with a spectrum broad enough to excite all populated vibrational levels but frequency-limited in such a way to eliminate transitions from v=0 level, in which molecules accumulate. In this paper this method is generalize…
Accurate $EF{}^1Σ^+_g-X{}^1Σ^+_g$ transition energies in molecular hydrogen were determined for transitions originating from levels with highly-excited vibrational quantum number, $v=11$, in the ground electronic state. Doppler-free two-photon spectroscopy was applied on vibrationally excited H$_2^*$, produced via the photodissociation of H$_2$S, yielding transition frequencies with accuracies of $45$ MHz or $0.0015$ cm$^{-1}$. An important improvement is the enhanced detection efficiency by resonant excitation to autoionizing $7pπ$ electronic Rydberg states, resulting in narrow transitions du…
The charge transfer reaction Ar+ + N2 --> Ar + N2+ has been investigated in a crossed beam experiment in combination with three-dimensional velocity map imaging. Angular differential state-to-state cross sections were determined as a function of the collision energy. We found that scattering into the first excited vibrational level dominates as expected, but only for scattering in the forward direction. Higher vibrational excitations up to v'=6 have been observed for larger scattering angles. For decreasing collision energy, scattering into higher scattering angles becomes increasingly importa…
Coherent vibrational dynamics in molecular bond breaking: methyl radical umbrella mode probed by femtosecond x-ray spectroscopy
通过飞秒X射线光谱探测甲基自由基伞形振动模式的相干振动动力学，揭示了高能级振动与量子拍动现象。
State-selective molecular orientation by vibrational Autler-Townes adiabatic passage
提出全光Autler-Townes态选择性绝热通道，将分子制备到单一$|J,M\ angle$子能级，在$^{13}$CO$_2$中验证分裂并预测转移效率接近90%，可扩展至多种分子。
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