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arXiv2014

Photoassociation of ultracold LiRb* molecules: observation of high efficiency and unitarity-limited rate saturation

We report the production of ultracold heteronuclear 7Li85Rb molecules in excited electronic states by photoassociation (PA) of ultracold 7Li and 85Rb atoms. PA is performed in a dual-species 7Li-85Rb magneto-optical trap (MOT) and the PA resonances are detected using trap loss spectroscopy. We identify several strong PA resonances below the Li (2s 2S1/2) + Rb (5p 2P3/2) asymptote and experimentally determine the long range C6 dispersion coefficients. We find a molecule formation rate (P_LiRb) of 3.5x10^7 s^-1 and a PA rate coefficient (K_PA) of 1.3x10^-10 cm^3/s, the highest among heteronuclear bi-alkali molecules. At large PA laser intensity, we observe the saturation of the PA rate coefficient (K_PA) close to the theoretical value at the unitarity limit.

physics.atom-ph↗

arXiv2014

Generalized Pauli conditions on the spectra of one-electron reduced density matrices of atoms and molecules

The Pauli exclusion principle requires the spectrum of the occupation numbers of the one-electron reduced density matrix (1-RDM) to be bounded by one and zero. However, for a 1-RDM from a wave function, there exist additional conditions on the spectrum of occupation numbers, known as pure N-representability conditions or generalized Pauli conditions. For atoms and molecules, we measure through a Euclidean-distance metric the proximity of the 1-RDM spectrum to the facets of the convex set (polytope) generated by the generalized Pauli conditions. For the ground state of any spin symmetry, as long as time-reversal symmetry is considered in the definition of the polytope, we find that the 1-RDM's spectrum is pinned to the boundary of the polytope. In contrast, for excited states, we find that the 1-RDM spectrum is not pinned. Proximity of the 1-RDM to the boundary of the polytope provides a measurement and classification of electron correlation and entanglement within the quantum system. For comparison, this distance to the boundary of the generalized Pauli conditions is also compared to the distance to the polytope of the traditional Pauli conditions, and the distance to the nearest 1-RDM spectrum from a Slater determinant. We explain the difference in pinning in the ground- and excited-state 1-RDMs through a connection to the N-representability conditions of the two-electron reduced density matrix.

physics.chem-ph↗

arXiv2014

Slow and velocity-tunable beams of metastable He$_2$ by multistage Zeeman deceleration

Metastable helium molecules (He$_2^*$) have been generated by striking a discharge in a supersonic expansion of helium gas from a pulsed valve. When operating the pulsed valve at room temperature, 77K, and 10K, the mean velocity of the supersonic beam was measured to be 1900m/s, 980m/s, and 530m/s, respectively. A 55-stage Zeeman decelerator operated in a phase-stable manner was then used to further reduce the beam velocity and tune it in the range between 100 and 150m/s. The internal-state distribution of the decelerated sample was established by photoionization spectroscopy.

physics.chem-ph↗

arXiv2014

Strongly driven quantum pendulum of the OCS molecule

We demonstrate and analyze a strongly driven quantum pendulum in the angular motion of stateselected and laser aligned OCS molecules. Raman-couplings during the rising edge of a 50-picosecond laser pulse create a wave packet of pendular states, which propagates in the confining potential formed by the polarizability interaction between the molecule and the laser field. This wave-packet dynamics manifests itself as pronounced oscillations in the degree of alignment with a laser-intensity dependent period.

quant-ph↗

arXiv2014

Ground and excited state properties of the polar and paramagnetic RbSr molecule: a comparative study

This paper deals with the electronic structure of RbSr, a molecule possessing both a permanent magnetic and electric dipole moment in its own frame allowing its manipulation with external fields. Two complementary ab-initio approaches are used for the ground and lowest excited states: first, an approach relying on optimized effective core potentials with core polarization potentials based on a full configuration interaction involving three valence electrons, and second, an approach using a small-size effective core potential with 19 correlated electrons in the framework of coupled-cluster theory. We have found excellent agreement between these two approaches for the ground state properties including the permanent dipole moment. We have focused on studies of excited states correlated to the two lowest asymptotes Rb(5p)+Sr(5s) and Rb(5s)+Sr(5s5p) relevant for ongoing experiments on quantum degenerate gases. We present also the Hund c) case potential curves obtained using atomic spin-orbit constants. These potential curves are an excellent starting point for experimental studies of molecular structure of RbSr using high-resolution spectroscopy.

physics.chem-ph↗

arXiv2014

Gate count estimates for performing quantum chemistry on small quantum computers

As quantum computing technology improves and quantum computers with a small but non-trivial number of N > 100 qubits appear feasible in the near future the question of possible applications of small quantum computers gains importance. One frequently mentioned application is Feynman's original proposal of simulating quantum systems, and in particular the electronic structure of molecules and materials. In this paper, we analyze the computational requirements for one of the standard algorithms to perform quantum chemistry on a quantum computer. We focus on the quantum resources required to find the ground state of a molecule twice as large as what current classical computers can solve exactly. We find that while such a problem requires about a ten-fold increase in the number of qubits over current technology, the required increase in the number of gates that can be coherently executed is many orders of magnitude larger. This suggests that for quantum computation to become useful for quantum chemistry problems, drastic algorithmic improvements will be needed.

quant-ph↗

arXiv2014

Ab initio properties of the ground-state polar and paramagnetic europium-alkali-metal-atom and europium-alkaline-earth-metal-atom molecules

The properties of the electronic ground state of the polar and paramagnetic europium-$S$-state-atom molecules have been investigated. Ab initio techniques have been applied to compute the potential energy curves for the europium-alkali-metal-atom, Eu$X$ ($X$=Li, Na, K, Rb, Cs), europium-alkaline-earth-metal-atom, Eu$Y$ ($Y$=Be, Mg, Ca, Sr, Ba), and europium-ytterbium, EuYb, molecules in the Born-Oppenheimer approximation for the high-spin electronic ground state. The spin restricted open-shell coupled cluster method restricted to single, double, and noniterative triple excitations, RCCSD(T), was employed and the scalar relativistic effects within the small-core energy-consistent pseudopotentials were included. The permanent electric dipole moments and static electric dipole polarizabilities were computed. The leading long-range coefficients describing the dispersion interaction between atoms at large internuclear distances $C_6$ are also reported. The EuK, EuRb, and EuCs molecules are examples of species possessing both large electric and magnetic dipole moments making them potentially interesting candidates for ultracold many-body quantum simulations when confined in an optical lattice in combined electric and magnetic fields.

physics.atom-ph↗

arXiv2014

Cold molecular ions on a chip

We report the sympathetic cooling and Coulomb crystallization of molecular ions above the surface of an ion-trap chip. N$_2^+$ and CaH$^+$ ions were confined in a surface-electrode radiofrequency ion trap and cooled by the interaction with laser-cooled Ca$^{+}$ ions to secular translational temperatures in the millikelvin range. The configuration of trapping potentials generated by the surface electrodes enabled the formation of planar bicomponent Coulomb crystals and the spatial separation of the molecular from the atomic ions on the chip. The structural and thermal properties of the Coulomb crystals were characterized using molecular dynamics simulations. The present study extends chip-based trapping techniques to Coulomb-crystallized molecular ions with potential applications in mass spectrometry, cold chemistry, quantum information science and spectroscopy.

physics.atom-ph↗

arXiv2014

Nonlinear transmission spectroscopy with dual frequency combs

We show how two frequency combs $\mathcal{E}_1$, $\mathcal{E}_2$ can be used to measure single-photon, two-photon absorption (TPA), and Raman resonances in a molecule with three electronic bands, by detecting the radio frequency modulation of the nonlinear transmission signal. Some peaks are independent of the carrier frequency of the comb and others shift with that frequency and have a width close to the comb width. TPA and Raman resonances independent of the carrier frequency are selected by measuring the transmission signal $\sim\mathcal{E}_1^2 \mathcal{E}_2^2$ and the single-photon resonances are selected by measuring the transmission signal $\sim\mathcal{E}_1^3\mathcal{E}_2$. Sinusoidal spectral phase shaping strongly affects the TPA, but not the Raman resonances.

physics.chem-ph↗

arXiv2014

Exact and approximate Kohn-Sham potentials in ensemble density-functional theory

We construct exact Kohn-Sham potentials for the ensemble density-functional theory (EDFT) from the ground and excited states of helium. The exchange-correlation (XC) potential is compared with the quasi-local-density approximation and both single determinant and symmetry eigenstate ghost-corrected exact exchange approximations. Symmetry eigenstate Hartree-exchange recovers distinctive features of the exact XC potential and is used to calculate the correlation potential. Unlike the exact case, excitation energies calculated from these approximations depend on ensemble weight, and it is shown that only the symmetry eigenstate method produces an ensemble derivative discontinuity. Differences in asymptotic and near-ground-state behavior of exact and approximate XC potentials are discussed in the context of producing accurate optical gaps.

physics.chem-ph↗

arXiv2014

Kohn-Sham potentials in exact density-functional theory at non-integer electron numbers

Within exact electron density-functional theory, we investigate Kohn-Sham (KS) potentials, orbital energies, and non-interacting kinetic energies of the fractional ions of Li, C and F. We use quantum Monte Carlo densities as input, which are then fitted, interpolated at non-integer electron numbers $N$, and inverted to produce accurate KS potentials $v_s^N(r)$. We study the dependence of the KS potential on $N$, and in particular we numerically reproduce the theoretically predicted spatially constant discontinuity of $v_s^N(r)$ as $N$ passes through an integer. We further show that, for all the cases considered, the inner orbital energies and the non-interacting kinetic energy are nearly piecewise linear functions of $N$. This leads us to propose a simple approximation of the KS potential $v_s^N(r)$ at any fractional electron number $N$ which uses only quantities of the systems with the adjacent integer electron numbers.

physics.chem-ph↗

arXiv2014

Universality in Efimov associated tetramers in 4He

We calculated, using seven realistic 4He-4He potentials in the literature, the Efimov spectra of the 4He trimer and tetramer and analyzed the universality of the systems. The three-(four-)body Schroedinger equations were solved fully nonadiabatically with the high-precision calculation method employed in our previous work on the 4He trimer and tetramer [Phys. Rev. A 85, 022502 (2012); 85, 062505 (2012)]. We found the following universality in the four-boson system: i) The critical scattering lengths at which the tetramer ground and excited states couple to the four-body threshold are independent of the choice of the two-body realistic potentials in spite of the difference in the short-range details and do not contradict the corresponding values observed in the experiments in ultracold alkali atoms when scaled with the van der Waals length r_vdW, and ii) the four-body hyperradial potential has a repulsive barrier at the four-body hyperradius R_4 \approx 3 r_vdW, which prevents the four particles from getting close together to explore nonuniversal features of the interactions at short distances. This result is an extension of the universality in Efimov trimers that the appearance of the repulsive barrier at the three-body hyperradius R_3 \approx 2 r_vdW makes the critical scattering lengths independent of the short-range details of the interactions as reported in the literature and also in the present work for the 4He trimer with the realistic potentials.

cond-mat.quant-gas↗

arXiv2014

Concept of effective states of atoms in compounds to describe properties determined by the densities of valence electrons in atomic cores

A new approach for describing the effective electronic states of "atoms in compounds" to study the properties of molecules and condensed matter which are circumscribed by the operators heavily concentrated in atomic cores is proposed. Among the properties are hyperfine structure, space parity (P) and time reversal invariance (T) nonconservation effects, chemical shifts of x-ray emission lines (XES), Mössbauer effect, etc. Advantage of the approach is that a good quantitative agreement of predicted and experimental data can be attained even for such difficult cases as XES chemical shifts providing correct quantum-mechanical interpretation of the experimental data. From computational point of view the method can be quite efficient being implemented in the framework of the relativistic pseudopotential theory [Int.J. Quantum Chem. 71, 359 (1999)] and procedures of recovering the wave functions in heavy-atom cores [Int.J. Quantum Chem. 104, 223 (2005)] after a molecular, cluster or periodic structure calculation performed on the basis of pseudoorbitals smoothed near the nuclei within the pseudopotential approximation. We report results of our studies of a number of atomic and molecular systems to demonstrate the capabilities of the approach.

physics.chem-ph↗

arXiv2014

Statistical product distributions for ultracold reactions in external fields

The main limitation of most ultracold chemistry studies to date is the lack of an analysis of reaction products. Here, we discuss the first generally tractable, rigorous theoretical framework for computing statistical product-state distributions for ultracold reactions in external fields. We show that fields have two main effects on the products of a statistical reaction, by: (1) modifying the product energy levels thus potentially reshaping the product distributions; and/or (2) adding or removing product states by changing the reaction exothermicity. By analyzing these effects and the strength of the formalism to distinguish between different reaction mechanisms in benchmark reactions involving $^{40}$K and $^{87}$Rb species, we argue that statistical predictions will help understanding product formation and control, and lead developments to realize the full potential of ultracold chemistry.

physics.chem-ph↗

arXiv2014

Nonsequential double ionization with time-dependent renormalized-natural-orbital theory

Recently introduced time-dependent renormalized natural orbital theory (TDRNOT) is tested on non-sequential double ionization (NSDI) of a numerically exactly solvable one-dimensional model He atom subject to few-cycle, 800-nm laser pulses. NSDI of atoms in strong laser fields is a prime example of non-perturbative, highly correlated electron dynamics. As such, NSDI is an important "worst-case" benchmark for any time-dependent few and many-body technique beyond linear response. It is found that TDRNOT reproduces the celebrated NSDI "knee," i.e., a many-order-of-magnitude enhancement of the double ionization yield (as compared to purely sequential ionization) with only the ten most significant natural orbitals (NOs) per spin. Correlated photoelectron spectra - as "more differential" observables - require more NOs.

physics.atom-ph↗

arXiv2014

Time-dependent generalized-active-space configuration-interaction approach to photoionization dynamics of atoms and molecules

We present a wave-function based method to solve the time-dependent many-electron Schrödinger equation (TDSE) with special emphasis on strong-field ionization phenomena. The theory builds on the configuration-interaction (CI) approach supplemented by the generalized-active-space (GAS) concept from quantum chemistry. The latter allows for a controllable reduction in the number of configurations in the CI expansion by imposing restrictions on the active orbital space. The method is similar to the recently formulated time-dependent restricted-active-space (TD-RAS) CI method [D. Hochstuhl, and M. Bonitz, Phys. Rev. A 86, 053424 (2012)]. We present details of our implementation and address convergence properties with respect to the active spaces and the associated account of electron correlation in both ground state and excitation scenarios. We apply the TD-GASCI theory to strong-field ionization of polar diatomic molecules and illustrate how the method allows us to uncover a strong correlation-induced shift of the preferred direction of emission of photoelectrons.

quant-ph↗

arXiv2014

Formation of deeply bound ultracold LiRb molecules via photoassociation near the Li 2S$_{1/2}$ + Rb 5P$_{3/2}$ asymptote

We present spectra of ultracold $^7$Li$^{85}$Rb molecules in their electronic ground state formed by spontaneous decay of weakly bound photoassociated molecules. Beginning with atoms in a dual species magneto-optical trap (MOT), weakly bound molecules are formed in the 4(1) electronic state, which corresponds to the B$^1Π$ state at short range. These molecules spontaneously decay to the electronic ground state and we use resonantly enhanced multiphoton ionization (REMPI) to determine the vibrational population distribution in the electronic ground states after spontaneous emission. Many of the observed lines from the spectra are consistent with transitions from the X$^1Σ^+$ ground electronic state to either the B$^1Π$ or D$^1Π$ electronic states that have been previously observed, with levels possibly as low as X$^1Σ^+$ $(v'' = 2)$ being populated. We do not observe decay to weakly bound vibrational levels of the X$^1Σ^+$ or a$^3Σ^+$ electronic states in the spectra. We also deduce a lower bound of 3900 cm$^{-1}$ for the dissociation energy of the LiRb$^+$ molecular ion.

physics.atom-ph↗

arXiv2014

Collisional trap losses of cold, magnetically-trapped Br atoms

Near-threshold photodissociation of Br$_2$ from a supersonic beam produces slow bromine atoms that are trapped in the magnetic field minimum formed between two opposing permanent magnets. Here, we quantify the dominant trap loss rate due to collisions with two sources of residual gas: the background limited by the vacuum chamber base pressure, and the carrier gas during the supersonic gas pulse. The loss rate due to collisions with residual Ar in the background follows pseudo first-order kinetics, and the bimolecular rate coefficient for collisional loss from the trap is determined by measurement of this rate as a function of the background Ar pressure. This rate coefficient is smaller than the total elastic collision rate coefficient, as it only samples those collisions that lead to trap loss, and is determined to be $\langleνσ\rangle = (1.12\pm0.09)\times10^{-9}\,\text{cm}^3\, \text{s}^{-1}$. The calculated differential cross section can be used with this value to estimate a trap depth of $293\pm24\,\text{mK}$. Carrier gas collisions occur only during the tail of the supersonic beam pulse. Using the differential cross section verified by the background-gas collision measurements provides an estimate of the peak molecular beam density of $(3.0\pm0.3)\times10^{13}\,\text{cm}^{-3}$ in good agreement with the prediction of a simple supersonic expansion model. Finally, we estimate the trap loss rate due to Majorana transitions to be negligible, owing to the relatively large trapped-atom phase-space volume.

physics.atom-ph↗