A coherent control scheme for the population distribution in the vibrational states of nonpolar molecules is proposed. Our theoretical analysis and results of numerical simulations for the interaction of the hydrogen molecular ion in its electronic ground state with an infrared laser pulse reveal a selective two-photon transition between the vibrational states via a coupling with the first excited dissociative state. We demonstrate that for a given temporal intensity profile the population transfer between vibrational states, or a superposition of vibrational states, can be made complete for a single chirped pulse or a train of chirped pulses, which accounts for the accumulated phase difference due to the AC Stark effect. Effects of a spatial intensity (or, focal) averaging are discussed.
We propose a quantum computer architecture which is robust against decoherence and scalable. As a qubit, we adopt rotational states of a nonpolar ionic molecule trapped in an ion-trap. It is revealed that the rotational-state qubits are much more immune to decoherence than the conventional electronic-state qubits of atomic ions. A complete method set for state preparation, single-qubit gate, controlled-NOT gate, and qubit-readout suitable for the rotational-state qubits is provided. Since the ionic molecules can be transported in an array of ion traps, the rotational-state qubits are expected …
Addressing intramolecular vibrational redistribution in a single molecule through pump and probe surface-enhanced vibrational spectroscopy
Centro de Física de Materiales (CFM-MPC), CSIC-EHU（材料物理中心）；Donostia International Physics Center (DIPC)（多诺西亚国际物理中心）；Department of Electricity and Electronics, FCT-ZTF, UPV-EHU（巴斯克国立大学电气与电子工程系）；Department of Polymers and Advanced Materials, Faculty of Chemistry, The University of the Basque Country, UPV/EHU（巴斯克国立大学化学学院高分子与先进材料系）；IKERBASQUE, Basque Foundation for Science（伊克尔巴斯基克科学基金会）
A pair of coherent femtosecond pulse excitations applied to a molecule with strong electron-phonon coupling creates a coherent superposition of a low momentum and a high momentum wavepacket in the vibrational states of both the excited state and the ground state of the coherent transition. As the excited state is accelerated further, interference between the high momentum ground state contribution and the low momentum excited state contribution causes a photon echo. This photon echo is a direct consequence of quantum interference between separate vibrational trajectories and can therefore prov…
We present a rigorous study of vibrational relaxation in p-H2 + p-H2 collisions at cold and ultracold temperatures and identify an efficient mechanism of ro-vibrational energy transfer. If the colliding molecules are in different rotational and vibrational levels, the internal energy may be transferred between the molecules through an extremely state-selective process involving simultaneous conservation of internal energy and total rotational angular momentum. The same transition in collisions of distinguishable molecules corresponds to the rotational energy transfer from one vibrational state…
This article covers few selected aspects of quantum theory of molecular rotations and vibrations. Triatomic molecules are the simplest systems, which show qualitative characteristics of larger polyatomic molecules. On the minimal example of triatomic molecules we demonstrate several theoretical methods used to calculate highly accurate rotational-vibrational-electronic energies, wavefunctions and transition intensities. The reader can view this article as a tutorial, by no means comprehensive, which still touches some of the unsolved problems in modern theoretical molecular spectroscopy.
We {\it analytically} investigate the population and coherence dynamics and relaxations in the vibrational energy transport in molecules. The corresponding two time scales $t_1$ and $t_2$ are explored. Coherence-population entanglement is found to considerably promote the time scale $t_2$ for dephasing and the amplitude of coherence. This is attributed to the suppression of the environment-induced drift force by coherence. Moreover the population imbalance (magnetization) is shown to be significantly amplified with the coherence-population entanglement. Contrary to the previous studies, we exa…
Accurate solution of the Schrödinger equation with Deng-Fan potential is presented by means of Nikiforov-Uvarov method. A modified Pekeris-type approximation is proposed for the centrifugal term, from a linear combination of the $r \to 0$ and $r \to r_e$ limits. It can potentially offer a series of approximations (depending on an adjustable parameter $λ$). The existing approximations in the literature can then be recovered in certain special cases. Its efficiency and feasibility is demonstrated by a critical comparison of eigenvalues produced at various $λ$'s for four molecules, \emph{viz.}, H…
Strong coupling of molecular vibrations to an infrared cavity mode affects their nature by creating dressed polariton states. We show how the single and double vibrational polariton manifolds may be controlled by varying the cavity coupling strength, and probed by a time domain 2DIR technique, Double Quantum Coherence (DQC). Applications are made to the amide-I ($CO$) and amide-II ($CN$) bond vibrations of $N-methylacetamide$ (NMA).
We describe the theoretical advances that influenced the experimental creation of vibrationally and translationally cold polar $^{40}$K$^{87}$Rb molecules \cite{nphys08,science08}. Cold molecules were created from very-weakly bound molecules formed by magnetic field sweeps near a Feshbach resonance in collisions of ultra-cold $^{40}$K and $^{87}$Rb atoms. Our analysis include the multi-channel bound-state calculations of the hyperfine and Zeeman mixed X$^1Σ^+$ and a$^3Σ^+$ vibrational levels. We find excellent agreement with the hyperfine structure observed in experimental data. In addition, w…
We report here on the production of an ultracold gas of tightly bound Rb2 molecules in the ro-vibrational triplet ground state, close to quantum degeneracy. This is achieved by optically transferring weakly bound Rb2 molecules to the absolute lowest level of the ground triplet potential with a transfer efficiency of about 90%. The transfer takes place in a 3D optical lattice which traps a sizeable fraction of the tightly bound molecules with a lifetime exceeding 200 ms.
A new physical implementation for quantum computation is proposed. The vibrational modes of molecules are used to encode qubit systems. Global quantum logic gates are realized using shaped femtosecond laser pulses which are calculated applying optimal control theory. The scaling of the system is favourable, sources for decoherence can be eliminated. A complete set of one and two quantum gates is presented for a specific molecule. Detailed analysis regarding experimental realization shows that the structural resolution of today's pulse shapers is easiliy sufficient for pulse formation.
Recent experiments of chemical reactions in optical cavities have shown great promise to alter and steer chemical reactions but still remain poorly understood theoretically. In particular the origin of resonant effects between the cavity and certain vibrational modes in the collective limit is still subject to active research. In this paper, we study unimolecular dissociation reactions of many molecules collectively interacting with an infrared cavity mode through their vibrational dipole moment. We find that the reaction rate can slow down by increasing the number of aligned molecules if the …
We study the collective behavior of molecules placed in an infrared (IR) microcavity, incorporating the local fluctuations, i.e., dynamical disorder. The cooperative feature in vibrational polaritons is shown to be dynamically eroded, due to intermolecule coherence. To further resolve such process, we develop a two-dimensional infrared spectroscopy (2D-IR) for molecules interacting with cavity modes. The cooperative feature in correspondence to the spectroscopic signal is specified. The results reveal the dark states by the cross peaks apart from the ones for polaritons, as a result of the bre…
The vibrational motion equations of both homo and hetero-nuclei diatomic molecules are here derived for the first time. A diatomic molecule is first considered as a one dimensional quantum mechanics oscillator. The second and third-order Hamiltonian operators are then formed by substituting the number operator for the quantum number in the corresponding vibrational energy eigenvalues. The expectation values of relative position and linear momentum operators of two oscillating atoms are calculated by solving Heisenbergs equations of motion. Subsequently, the expectation values of potential and …
We propose a method for achieving highly efficient transfer between the vibrational states in a diatomic molecule. The process is mediated by strong laser pulses and can be understood in terms of light-induced potentials. In addition to describing a specific molecular system, our results show how, in general, one can manipulate the populations of the different quantum states in double well systems.
We investigate cooperative phenomena and superradiance for vibrational transitions in polar molecule spectroscopy when a high optical-depth (OD) sample is studied. Such cooperativity comes from the build-up of inter-particle coherence through dipole-dipole interactions and leads to the speed-up of decay process. We compare our calculation to recent work [Deiglmayr et al., Eur. Phys. J. D 65, 99 (2011)] and find very good agreement, suggesting that superradiant effects need to be included in a wide variety of ultracold molecule setups including vibrational and rotational states.
A beam of diatomic molecules scattered off a standing wave laser mode splits according to the rovibrational quantum state of the molecules. Our numerical calculation shows that single state resolution can be achieved by properly tuned, monochromatic light. The proposed scheme allows for selecting non-vibrating and non-rotating molecules from a thermal beam, implementing a laser Maxwell's demon to prepare a rovibrationally cold molecular ensemble.
Vibrational spectra of long-range molecules are determined accurately and to arbitrary accuracy with the Canonical Function Method. The energy levels of the $0^-_g$ and $1_u$ electronic states of the $^{23}{\rm Na}_2$ molecule are determined from the Ground state up to the continuum limit. The method is validated by comparison with previous results obtained by Stwalley et al. using the same potential and Trost et al. whose work is based on the Lennard-Jones potential adapted to long-range molecules.
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…
The optomechanical character of molecules was discovered by Raman about one century ago. Today, molecules are promising contenders for high-performance quantum optomechanical platforms because their small size and large energy-level separations make them intrinsically robust against thermal agitations. Moreover, the precision and throughput of chemical synthesis can ensure a viable route to quantum technological applications. The challenge, however, is that the coupling of molecular vibrations to environmental phonons limits their coherence to picosecond time scales. Here, we improve the optom…
We present an approximate analytic solution of the Klein-Gordon equation in the presence of equal scalar and vector generalized deformed hyperbolic potential functions by means of parameteric generalization of the Nikiforov-Uvarov method. We obtain the approximate bound state rotational-vibrational (ro-vibrational) energy levels and the corresponding normalized wave functions expressed in terms of the Jacobi polynomial for a spin-zero particle in a closed form. Special cases are studied including the non-relativistic solutions obtained by appropriate choice of parameters and also the s-wave so…
An algebraic model taking into account the influence of the molecular rotation on the wave functions of vibrational-rotational states of the diatomic molecule using the formalism of the ladder operators and an expansion in a small parameter characterizing the vibrational-rotational interaction have been proposed for the potentials whose the creation and annihilation operators can be constructed. Expressions for the expansion of the wave function of the vibrational-rotational states in a set of wave functions of the rotationless vibrational states have been obtained of the second order in the p…
Explicit algebraic expressions for the expansion of the vibrational matrix elements in series of matrix elements on the wave functions of the ground vibrational state have been obtained for arbitrary sufficiently differentiable functions of the internuclear distance, arbitrary values v and v', and the potential curves whose ladder operators can be constructed. A diagram technique have been developed for it that consists in: 1) the numeration of the matrix elements by points of the 2D diagram with coordinates (l, k), 2) the drawing arrows between points of this diagram corresponding to the acti…
We present detailed calculations at the basis of our recent proposal for simultaneous cooling the rotational, vibrational and external molecular degrees of freedom. In this method, the molecular rovibronic states are coupled by an intense laser and an optical cavity via coherent Raman processes enhanced by the strong coupling with the cavity modes. For a prototype system, OH, we showed that the translational motion is cooled to few micro Kelvin and the molecule is brought to the internal ground state in about a second. Here, we investigate numerically the dependence of the cooling scheme on th…
This work presents the bound-state spectra of Morse oscillator, which remains one of the oldest important model potentials for molecules. Accurate ro-vibrational energies are obtained by means of a generalized pseudospectral method that offers an optimal, non-uniform discretization of the radial grid. Both s-wave ($\ell=0$) and rotational ($\ell \neq 0$) states for low and high quantum numbers are calculated for four representative diatomic molecules, namely H$_2$, LiH, HCl and CO. First nine states belonging to a maximum of $n, \ell =2$ are computed with good accuracy, along with nine other h…
Rotational excitation of molecules in the regime of strong ro-vibrational coupling: Comparison between an optical centrifuge and a transform-limited pulse
Universidad de Granada（格拉纳达大学）；The University of British Columbia（不列颠哥伦比亚大学）；Freie Universität Berlin（柏林自由大学）；Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada（格拉纳达大学卡洛斯一世理论与计算物理研究所）
Exact solutions for vibrational levels of diatomic molecules via the Morse potential are obtained by means of the asymptotic iteration method. It is shown that, the numerical results for the energy eigenvalues of $^{7}Li_{2}$ are all in excellent agreement with the ones obtained before. Without any loss of generality, other states and molecules could be treated in a similar way.
In this paper we present a closed-form expression of the vibrational partition function for the one-dimensional q-deformed Morse potential energy model. Through this function the related thermodynamic functions are derived and studied in terms of the parameters of the model. Specially, we plotted the q-deformed vibrational partition function, and vibrational specific heat for some diatomic molecule systems such as H2, HCl, LiH and CO. The idea of a critical temperature T_{C} is introduced in relation to the specific heat.
Nonadiabatic phenomena are investigated in the rovibrational motion of molecules confined in an infrared cavity. Conical intersections (CIs) between vibrational polaritons, similar to CIs between electronic polaritonic surfaces, are found. The spectral, topological, and dynamic properties of the vibrational polaritons show clear fingerprints of nonadiabatic couplings between molecular vibration, rotation and the cavity photonic mode. Furthermore, it is found that for the investigated system, composed of two rovibrating HCl molecules and the cavity mode, breaking the molecular permutational sym…
We have calculated the isotropic $C\_6$ coefficients characterizing the long-range van der Waals interaction between two identical heteronuclear alkali-metal diatomic molecules in the same arbitrary vibrational level of their ground electronic state $X^1Σ^+$. We consider the ten species made up of $^7$Li, $^{23}$Na, $^{39}$K, $^{87}$Rb and $^{133}$Cs. Following our previous work [M.~Lepers \textit{et.~al.}, Phys.~Rev.~A \textbf{88}, 032709 (2013)] we use the sum-over-state formula inherent to the second-order perturbation theory, composed of the contributions from the transitions within the gr…
We consider two-color heteronuclear photoassociation of atoms into dipolar molecules in the J=1 electro-vibrational ground state, where a free-ground laser couples atoms directly to the ground state and a free-bound laser couples the atoms to an electronically-excited state. This problem raises an interest because heteronuclear photoassociation from atoms to near-ground state molecules is limited by the small size of the target state. Nevertheless, the addition of the excited state creates a second pathway for creating ground state molecules, leading to quantum interference between direct phot…
Since their first experimental observation, ultralong-range Rydberg molecules consisting of a highly excited Rydberg atom and a ground state atom have attracted the interest in the field of ultracold chemistry. Especially the intriguing properties like size, polarizability and type of binding they inherit from the Rydberg atom are of interest. An open question in the field is the reduced lifetime of the molecules compared to the corresponding atomic Rydberg states. In this letter we present an experimental study on the lifetimes of the ^3Σ(5s-35s) molecule in its vibrational ground state and i…
With a specific choice of laser parameters resulting into a so-called exceptional point in the wavelength-intensity plane, it is possible to produce the coalescence of two Floquet resonances describing the photodissociation of the molecule Na$_2$, which is one of the candidates for molecular cooling. Appropriately tuning laser parameters, following a contour around the exceptional point, the resonances exchange their labels. This represents a laser control of the vibrational transfer from one field-free state to another, through an adiabatic transport involving these resonances. The proportion…
We propose a process to convert ultracold metastable Cs$_2$ molecules in their lowest triplet state into (singlet) ground state molecules in their lowest vibrational levels. Molecules are first pumped into an excited triplet state, and the triplet-singlet conversion is facilitated by a two-step spontaneous decay through the coupled $A^{1}Σ_{u}^{+} \sim b ^{3}Π_{u}$ states. Using spectroscopic data and accurate quantum chemistry calculations for Cs$_2$ potential curves and transition dipole moments, we show that this process has a high rate and competes favorably with the single-photon decay ba…
