State selective production of molecules in optical lattices

Non-Relativistic Electronic-Structure Computation of Neutral and Cationic Systems [Fr2, Fr-AEM+ (AEM= Ca, Sr, Ba)]

The experimental field of ultracold ion-atom mixtures including an alkali-metal atom and an alkaline-earth-metal ion as well as of homonuclear alkali dimers has paved the way for creating and manipulating the ultracold molecules. The present paper is focused on a study of molecules such us francium dimer and a comparative spectroscopic investigation of the cationic systems Fr-(Ca⁺, Sr⁺, Ba⁺). We adopt a computational scheme without spin-orbit coupling reposed on the full configuration interaction and semi-empirical pseudo-potential theory of the atomic cores Fr⁺, Ca²⁺, Sr²⁺, and Ba²⁺ with extended and optimized basis sets. We have determined the adiabatic potentials with their relative spectroscopic constants, the electric dipole moments and the vibrational levels spacings for the ^1,3Σ_u,g⁺ and ^1,3Σ⁺ electronic states for Fr₂ and Fr-AEM⁺, respectively, correlated toward {Fr(7s) + Fr(7s, 7p, 6d, 8s, 8p)}, {Ca(4s², 4s4p, 4s3d), Sr(5s², 5s5p, 5s4d), Ba(6s², 6s6p, 6s5d) + Fr⁺}, and {Ca⁺(4s, 3d), Sr⁺(5s, 4d), Ba⁺(6s, 5d) + Fr(7s, 7p)}. The accuracy and reliability of the current results are discussed by comparing with theoretical data available in the literature. The occurrence of some avoided crossings between the neighboring electronic states is leading to a charge or excitation transfer for atom-ion collisions in the diverse charge or excited states. The Σ⁺-Σ⁺ transitions are determined in order to evaluate the future radiative lifetimes of vibrational states serving the direct laser cooling.

Quantum register of fermion pairs

Quantum control of motion is central for modern atomic clocks¹ and interferometers². It enables protocols to process and distribute quantum information^3,4, and allows the probing of entanglement in correlated states of matter⁵. However, the motional coherence of individual particles can be fragile to maintain, as external degrees of freedom couple strongly to the environment. Systems in nature with robust motional coherence instead often involve pairs of particles, from the electrons in helium, to atom pairs⁶, molecules⁷ and Cooper pairs. Here we demonstrate long-lived motional coherence and entanglement of pairs of fermionic atoms in an optical lattice array. The common and relative motion of each pair realize a robust qubit, protected by exchange symmetry. The energy difference between the two motional states is set by the atomic recoil energy, is dependent on only the mass and the lattice wavelength, and is insensitive to the noise of the confining potential. We observe quantum coherence beyond ten seconds. Modulation of the interactions between the atoms provides universal control of the motional qubit. The methods presented here will enable coherently programmable quantum simulators of many-fermion systems⁸, precision metrology based on atom pairs and molecules^9,10 and, by implementing further advances^11-13, digital quantum computation using fermion pairs¹⁴.

Collective Dissipative Molecule Formation in a Cavity

We propose a mechanism to realize high-yield molecular formation from ultracold atoms. Atom pairs are continuously excited by a laser, and a collective decay into the molecular ground state is induced by a coupling to a lossy cavity mode. Using a combination of analytical and numerical techniques, we demonstrate that the molecular yield can be improved by simply increasing the number of atoms, and can overcome efficiencies of state-of-the-art association schemes. We discuss realistic experimental setups for diatomic polar and nonpolar molecules, opening up collective light matter interactions as a tool for quantum state engineering, enhanced molecule formation, collective dynamics, and cavity mediated chemistry.

Coherently forming a single molecule in an optical trap

Ultracold single molecules have wide-ranging potential applications, such as ultracold chemistry, precision measurements, quantum simulation, and quantum computation. However, given the difficulty of achieving full control of a complex atom-molecule system, the coherent formation of single molecules remains a challenge. Here, we report an alternative route to coherently bind two atoms into a weakly bound molecule at megahertz levels by coupling atomic spins to their two-body relative motion in a strongly focused laser with inherent polarization gradients. The coherent nature is demonstrated by long-lived atom-molecule Rabi oscillations. We further manipulate the motional levels of the molecules and measure the binding energy precisely. This work opens the door to full control of all degrees of freedom in atom-molecule systems.

Antiferromagnetic Spin Correlation of SU(N) Fermi Gas in an Optical Superlattice

Large-spin cold atomic systems can exhibit unique phenomena that do not appear in spin-1/2 systems. We report the observation of nearest-neighbor antiferromagnetic spin correlations of a Fermi gas with SU(N) symmetry trapped in an optical lattice. The precise control of the spin degrees of freedom provided by an optical pumping technique enables us a straightforward comparison between the cases of SU(2) and SU(4). Our important finding is that the antiferromagnetic correlation is enhanced for the SU(4)-spin system compared with SU(2) as a consequence of a Pomeranchuk cooling effect. This work is an important step towards the realization of novel SU(N>2) quantum magnetism.

Theoretical study of the CsNa molecule: adiabatic and diabatic potential energy and dipole moment

The adiabatic and diabatic potential energy curves of the low-lying electronic states of the NaCs molecule dissociating into Na (3s, 3p) + Cs (6s, 6p, 5d, 7s, 7p, 6d, 8s, 4f) have been investigated. The molecular calculations are performed using an ab initio approach based on nonempirical pseudopotential, parametrized l-dependent polarization potentials and full configuration interaction calculations through the CIPCI quantum chemistry package. The derived spectroscopic constants (Re, De, Te, ωe, ωexe, and Be) of the ground state and lower excited states are compared with the available theoretical and experimental works. Moreover, accurate permanent and transition dipole moment have been determined as a function of the internuclear distance. The adiabatic permanent dipole moment for the first nine (1)Σ(+) electronic states have shown both ionic characters associated with electron transfer related to Cs(+)Na(-) and Cs(-)Na(+) arrangements. By a simple rotation, the diabatic permanent dipole moment is determined and has revealed a linear behavior, particularly at intermediate and large distances. Many peaks around the avoided crossing locations have been observed for the transition dipole moment between neighbor electronic states.

High-fidelity cluster state generation for ultracold atoms in an optical lattice

We propose a method for generating high-fidelity multipartite spin entanglement of ultracold atoms in an optical lattice in a short operation time with a scalable manner, which is suitable for measurement-based quantum computation. To perform the desired operations based on the perturbative spin-spin interactions, we propose to actively utilize the extra degrees of freedom (DOFs) usually neglected in the perturbative treatment but included in the Hubbard Hamiltonian of atoms, such as, (pseudo-)charge and orbital DOFs. Our method simultaneously achieves high fidelity, short operation time, and scalability by overcoming the following fundamental problem: enhancing the interaction strength for shortening the operation time breaks the perturbative condition of the interaction and inevitably induces unwanted correlations among the spin and extra DOFs.

Calculating and modeling the exchange energies of homonuclear and heteronuclear alkali dimers based on the surface integral method

The exchange energies of all homonuclear and heteronuclear alkali dimers are calculated based on the surface integral method. These results are generally in good agreement with both ab initio calculations and experimental results where available. It is also shown that the exchange energies could be fitted by an analytical expression of AR(b) exp(-cR). b and c can be calculated by two simple formulas that are only related to the ionization energies of the constituent atoms. A is the only parameter in this expression. More interestingly, it is found that the parameter A for the heteronuclear dimers could be approximated by a combining rule.

Rabi oscillations between atomic and molecular condensates driven with coherent one-color photoassociation

We demonstrate coherent one-color photoassociation of a Bose-Einstein condensate, which results in Rabi oscillations between atomic and molecular condensates. We attain atom-molecule Rabi frequencies that are comparable to decoherence rates by driving photoassociation of atoms in an ^{88}Sr condensate to a weakly bound level of the metastable 1S0+3P1 molecular potential, which has a long lifetime and a large Franck-Condon overlap integral with the ground scattering state. Transient shifts and broadenings of the excitation spectrum are clearly seen at short times, and they create an asymmetric excitation profile that only displays Rabi oscillations for blue detuning from resonance.

Engineering novel optical lattices

Optical lattices have developed into a widely used and highly recognized tool to study many-body quantum physics with special relevance for solid state type systems. One of the most prominent reasons for this success is the high degree of tunability in the experimental setups. While at the beginning quasi-static, cubic geometries were mainly explored, the focus of the field has now shifted toward new lattice topologies and the dynamical control of lattice structures. In this review we intend to give an overview of the progress recently achieved in this field on the experimental side. In addition, we discuss theoretical proposals exploiting specifically these novel lattice geometries.

Optical production of stable ultracold (88)Sr(2) molecules

We have produced large samples of stable ultracold (88)Sr(2) molecules in the electronic ground state in an optical lattice. The fast, all-optical method of molecule creation involves a near-intercombination-line photoassociation pulse followed by spontaneous emission with a near-unity Franck-Condon factor. The detection uses excitation to a weakly bound electronically excited vibrational level corresponding to a very large dimer and yields a high-Q molecular vibronic resonance. This is the first of two steps needed to create deeply bound (88)Sr(2) for frequency metrology and ultracold chemistry.

Ultracold triplet molecules in the rovibrational ground state

We report here on the production of an ultracold gas of tightly bound Rb2 triplet molecules in the rovibrational 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.

Prospects for making polar molecules with microwave fields

We propose a mechanism to produce ultracold polar molecules with microwave fields. It converts trapped ultracold atoms into vibrationally excited molecules by a single microwave transition and entirely depends on the existence of a permanent dipole moment in the molecules. As opposed to production of molecules by photoassociation or magnetic-field Feshbach resonances, our method does not rely on properties of excited states or existence of Feshbach resonances. We determine conditions for optimal creation of polar molecules in vibrationally excited states of the ground-state potential by changing frequency and intensity of the microwave field. We also explore the possibility to produce vibrationally cold molecules by combining the microwave field with an optical Raman transition or by applying a microwave field to Feshbach molecules. The production mechanism is illustrated for KRb and RbCs.

Exact removal of the center-of-mass spurious states from level densities

We give recursive formulae for the exact removal of the contribution of the center-of-mass spurious states from the fixed-spin and parity nuclear level density found in shell-model calculations, provided the total level density for restricted configurations is known. The method is valid for a large class of problems using a harmonic oscillator basis. Using our earlier methods based on statistical spectroscopy that utilize the centroids and widths for a restricted class of fixed-spin configurations, such as Nvariant Planck's over 2piomega excitations, one can calculate very accurately level densities free of spurious states. The approach is applicable to other fermion and boson systems trapped by an oscillator potential.

Confinement effects on the stimulated dissociation of molecular Bose-Einstein condensates

We show that a molecular Bose-Einstein condensate in a trap is stabilized against stimulated dissociation if the trap size is smaller than the resonance healing length (Planck's 2/2mgsqrt[n]);1/2. The condensate shape determines the critical atom-molecule coupling frequency. We discuss an experiment for triggering dissociation by a sudden change of coupling or trap parameters. This effect demonstrates one of the unique collective features of "superchemistry" in that the yield of a chemical reaction depends critically on the size and shape of the reaction vessel.

Coherent optical transfer of Feshbach molecules to a lower vibrational state

Using the technique of stimulated Raman adiabatic passage (STIRAP) we have coherently transferred ultracold (87)Rb(2) Feshbach molecules into a more deeply bound vibrational quantum level. Our measurements indicate a high transfer efficiency of up to 87%. Because the molecules are held in an optical lattice with not more than a single molecule per lattice site, inelastic collisions between the molecules are suppressed and we observe long molecular lifetimes of about 1 s. Using STIRAP we have created quantum superpositions of the two molecular states and tested their coherence interferometrically. These results represent an important step towards Bose-Einstein condensation of molecules in the vibrational ground state.

Inserting two atoms into a single optical micropotential

We recently demonstrated that strings of trapped atoms inside a standing wave optical dipole trap can be rearranged using optical tweezers [Y. Miroshnychenko, Nature 442, 151 (2006)]. This technique allows us to actively set the interatomic separations on the scale of the individual trapping potential wells. Here, we use such a distance-control operation to insert two atoms into the same potential well. The detected success rate of this manipulation is 16(-3)(+4)%, in agreement with the predictions of a theoretical model based on our experimental parameters.

d-Wave resonating valence bond states of fermionic atoms in optical lattices

We study controlled generation and measurement of superfluid d-wave resonating valence bond (RVB) states of fermionic atoms in 2D optical lattices. Starting from loading spatial and spin patterns of atoms in optical superlattices as pure quantum states from a Fermi gas, we adiabatically transform this state to an RVB state by a change of the lattice parameters. Results of exact time-dependent numerical studies for ladders systems are presented, suggesting generation of RVB states on a time scale smaller than typical experimental decoherence times.

Probing number squeezing of ultracold atoms across the superfluid-Mott insulator transition

The evolution of on-site number fluctuations of ultracold atoms in optical lattices is experimentally investigated by monitoring the suppression of spin-changing collisions across the superfluid-Mott insulator transition. For low atom numbers, corresponding to an average filling factor close to unity, large on-site number fluctuations are necessary for spin-changing collisions to occur. The continuous suppression of spin-changing collisions is thus direct evidence for the emergence of number-squeezed states. In the Mott insulator regime, we find that spin-changing collisions are suppressed until a threshold atom number, consistent with the number where a Mott plateau with doubly occupied sites is expected to form.

Long-lived Feshbach molecules in a three-dimensional optical lattice

We have created and trapped a pure sample of Feshbach molecules in a three-dimensional optical lattice. Compared to previous experiments without a lattice, we find dramatic improvements such as long lifetimes of up to 700 ms and a near unit efficiency for converting tightly confined atom pairs into molecules. The lattice shields the trapped molecules from collisions and, thus, overcomes the problem of inelastic decay by vibrational quenching. Furthermore, we have developed an advanced purification scheme that removes residual atoms, resulting in a lattice in which individual sites are either empty or filled with a single molecule in the vibrational ground state of the lattice.

Molecules of fermionic atoms in an optical lattice

We create molecules from fermionic atoms in a three-dimensional optical lattice using a Feshbach resonance. In the limit of low tunneling, the individual wells can be regarded as independent three-dimensional harmonic oscillators. The measured binding energies for varying scattering length agree excellently with the theoretical prediction for two interacting atoms in a harmonic oscillator. We demonstrate that the formation of molecules can be used to measure the occupancy of the lattice and perform thermometry.

Quantum phases in a resonantly interacting boson-fermion mixture

We consider a resonantly interacting boson-fermion mixture of 40K and 87Rb atoms in an optical lattice. We show that by using a red-detuned optical lattice the mixture can be accurately described by a generalized Hubbard model for 40K and 87Rb atoms, and 40K-87Rb molecules. The microscopic parameters of this model are fully determined by the details of the optical lattice and the interspecies Feshbach resonance in the absence of the lattice. We predict a quantum phase transition to occur in this system already at low atomic filling fraction, and present the phase diagram as a function of the temperature and the applied magnetic field.

Creating ground state molecules with optical feshbach resonances in tight traps

We propose to create ultracold ground state molecules in an atomic Bose-Einstein condensate by adiabatic crossing of an optical Feshbach resonance. We envision a scheme where the laser intensity and possibly also frequency are linearly ramped over the resonance. Our calculations for (87)Rb show that for sufficiently tight traps it is possible to avoid spontaneous emission while retaining adiabaticity, and conversion efficiencies of up to 50% can be expected.