We report measurements of the ac polarizabilities of ultracold ground-state $^{23}\rm{Na}^{87}\rm{Rb}$ molecules. While the polarizability of the ground rotational state $J = 0$ is isotropic, that of the first excited rotational state $J = 1$ is anisotropic and depends strongly on the light polarization angle. We obtain both polarizabilities precisely by combining trap oscillation frequency measurement and high resolution rotational spectroscopy driven by microwave. With the optimized light polarization angle and intensity combination, the nonuniformity of the differential ac Stark shift between the two rotational states is minimized and the rotational coherence time is observed to be the longest.
We study, both theoretically and experimentally, the dynamical polarizability $α(ω)$ of $\textrm{Rb}_2$ molecules in the rovibrational ground state of $\mathrm{a}^3Σ_u^+$. Taking all relevant excited molecular bound states into account, we compute the complex-valued polarizability $α(ω)$ for wave numbers up to $20000\:\textrm{cm}^{-1}$. Our calculations are compared to experimental results at $1064.5\:\textrm{nm}$ ($\sim9400\:\textrm{cm}^{-1}$) as well as at $830.4\:\textrm{nm}$ ($\sim12000\:\textrm{cm}^{-1}$). Here, we discuss the measurements at $1064.5\:\textrm{nm}$. The ultracold $\textrm{…
We report the measurement of the anisotropic AC polarizability of ultracold polar $^{40}$K$^{87}$Rb molecules in the ground and first rotationally excited states. Theoretical analysis of the polarizability agrees well with experimental findings. Although the polarizability can vary by more than 30%, a "magic" angle between the laser polarization and the quantization axis is found where the polarizability of the $|N=0,m_N=0>$ and the $|N=1,m_N=0>$ states match. At this angle, rotational decoherence due to the mismatch in trapping potentials is eliminated, and we observe a sharp increase in the …
We report on the determination of the dynamical polarizability of ultracold erbium atoms in the ground and in one excited state at three different wavelengths, which are particularly relevant for optical trapping. Our study combines experimental measurements of the light shift and theoretical calculations. In particular, our experimental approach allows us to isolate the different contributions to the polarizability, namely the isotropic scalar and anisotropic tensor part. For the latter contribution, we observe a clear dependence of the atomic polarizability on the angle between the laser-fie…
Selection of "magic" trapping conditions with ultracold atoms or molecules, where pairs of internal states experience identical trapping potentials, brings substantial benefits to precision measurements and quantum computing schemes. Working at such conditions could ensure that detrimental effects of inevitable inhomogeneities across an ultracold sample are significantly reduced. However, this aspect of confinement remains unexplored for ultracold polar molecules. Here, we present means to control the AC Stark shift of rotational states of ultracold polar molecules, when subjected to both trap…
Ultracold atoms confined in a dipole trap are submitted to a potential whose depth is proportional to the real part of their dynamic dipole polarizability. The atoms also experience photon scattering whose rate is proportional to the imaginary part of their dynamic dipole polarizability. In this article we calculate the complex dynamic dipole polarizability of ground-state erbium, a rare-earth atom that was recently Bose-condensed. The polarizability is calculated with the sum-over-state formula inherent to second-order perturbation theory. The summation is performed on transition energies and…
Ionic clocks exhibit as the most promising candidates for the frequency standards. Recent investigations show the profound advantages of interrogating two laser beams with different frequencies in developing the frequency standards. Here we present a scheme of a two-photon mechanism to calculate the dynamic polarizabilities for the clock states, 6$^2$S$_{\frac{1}{2}}$ and 5$^2$D$_{\frac{3}{2}, \frac{5}{2}}$, of Ba$^+$ by employing relativistic coupled-cluster method. We illustrate the Stark-shift cancellation between these clock states at the two-photon magic wavelengths. These magic wavelengt…
The efficiency of optical trapping of ultracold atoms depend on the atomic dynamic dipole polarizability governing the atom-field interaction. In this article, we have calculated the real and imaginary parts of the dynamic dipole polarizability of dysprosium in the ground and first excited level. Due to the high electronic angular momentum of those two states, the polarizabilities possess scalar, vector and tensor contributions that we have computed, on a wide range of trapping wavelengths, using the sum-over-state formula. Using the same formalism, we have also calculated the $C_6$ coefficien…
We investigate the effect of far-off-resonant trapping light on ultracold bosonic RbCs molecules. We use kHz-precision microwave spectroscopy to measure the differential AC Stark shifts between the ground and first excited rotational levels of the molecule with hyperfine-state resolution. We demonstrate through both experiment and theory that coupling between neighboring hyperfine states manifests in rich structure with many avoided crossings. This coupling may be tuned by rotating the polarization of the linearly polarized trapping light. A combination of spectroscopic and parametric heating …
In this work, the RF-dressed potentials generated using a static magnetic field of a quadrupole trap and various radio frequency (RF) fields, have been theoretically investigated for trapping and manipulations of cold atoms in a two-dimensional (2D) geometry. It is shown that, in this scheme, the RF fields of some particular polarizations and phases can give rise to some novel static and time-dependent anisotropic two-dimensional potentials which are useful to trap and manipulate the cold atoms in the 2D geometry. The generated time-dependent 2D potentials, rotating on the circular ring, can b…
We report on measurements of the anisotropic dynamical polarizability of Dy near the 626-nm intercombination line, employing modulation spectroscopy in a one-dimensional optical lattice. To eliminate large systematic uncertainties resulting from the limited knowledge of the spatial intensity distribution, we use K as a reference species with accurately known polarizability. This method can be applied independently of the sign of the polarizability, i.e., for both attractive and repulsive optical fields on both sides of a resonance. By variation of the laser polarization we extract the scalar a…
In Heisenberg models with exchange anisotropy, transverse spin components are not conserved and can decay not only by transport, but also by dephasing. Here we utilize ultracold atoms to simulate the dynamics of 1D Heisenberg spin chains, and observe fast, local spin decay controlled by the anisotropy. Additionally, we directly observe an effective magnetic field created by superexchange which causes an inhomogeneous decay mechanism due to variations of lattice depth between chains, as well as dephasing within each chain due to the twofold reduction of the effective magnetic field at the edges…
We characterize the anisotropic differential ac-Stark shift for the Dy $626$ nm intercombination transition, induced in a far-detuned $1070$ nm optical dipole trap, and observe the existence of a "magic polarization" for which the polarizabilities of the ground and excited states are equal. From our measurements we extract both the scalar and tensorial components of the dynamic dipole polarizability for the excited state, $α_E^\text{s} = 188 (12)\,α_\text{0}$ and $α_E^\text{t} = 34 (12)\,α_\text{0}$, respectively, where $α_\text{0}$ is the atomic unit for the electric polarizability. We also p…
We have developed the general grid method for multi-channel scattering of bosonic atoms inside a harmonic waveguide with transverse anisotropy. This approach is employed to analyze elastic as well as inelastic multi-channel confined scattering. For the elastic scattering, the effects of the range and form of interatomic potential and the waveguide anisotropy on the confinement induced resonance are studied. We have also investigated quantitatively the reactive rate constant in confined atom-atom collisions. It is found that a slight anisotropy to the confining trap considerably enhances the re…
We study the effects of a static electric field on the photoassociation of a heteronuclear atom-pair into a polar molecule. The interaction of permanent dipole moment with a static electric field largely affects the ground state continuum wave function of the atom-pair at short separations where photoassociation transitions occur according to Franck-Condon principle. Electric field induced anisotropic interaction between two heteronuclear ground state atoms leads to scattering resonances at some specific electric fields. Near such resonances the amplitude of scattering wave function at short s…
We study the system of two ultracold atoms in a three-dimensional (3D) or two-dimensional (2D) completely anisotropic harmonic trap. We derive the algebraic equation J_{3D}(E) = 1/a_{3D} (J_{2D}(E) = ln a_{2D}) for the eigen-energy E of this system in the 3D (2D) case, with a_{3D} and a_{2D} being the corresponding s-wave scattering lengths, and provide the analytical expressions of the functions J_{3D}(E) and J_{2D}(E). In previous researches this type of equation was obtained for spherically or axially symmetric harmonic traps (T. Busch, et. al., Found. Phys. 28, 549 (1998); Z. Idziaszek and…
We analytically derive the transport tensor of thermal conductivity in an ultracold, but not yet quantum degenerate, gas of Bosonic lanthanide atoms using the Chapman-Enskog procedure. The tensor coefficients inherit an anisotropy from the anisotropic collision cross section for these dipolar species, manifest in their dependence on the dipole moment, dipole orientation, and $s$-wave scattering length. These functional dependencies open up a pathway for control of macroscopic gas phenomena via tuning of the microscopic atomic interactions. As an illustrative example, we analyze the time evolut…
Synthetic quantum systems with interacting constituents play an important role in quantum information processing and in elucidating fundamental phenomena in many-body physics. Following impressive advances in cooling and trapping techniques, ensembles of ultracold polar molecules have emerged as a promising synthetic system that combines several advantageous properties. These include a large set of internal states for encoding quantum information, long nuclear and rotational coherence times and long-range, anisotropic interactions. The latter are expected to allow the exploration of intriguing…
We report on the observation of a large anisotropy in the rethermalization dynamics of an ultracold dipolar Fermi gas driven out of equilibrium. Our system consists of an ultracold sample of strongly magnetic $^{167}$Er fermions, spin-polarized in the lowest Zeeman sublevel. In this system, elastic collisions arise purely from universal dipolar scattering. Based on cross-dimensional rethermalization experiments, we observe a strong anisotropy of the scattering, which manifests itself in a large angular dependence of the thermal relaxation dynamics. Our result is in very good agreement with rec…
We calculate pair potential curves for interacting Rydberg atoms in a constant electric field and use them to determine the effective $C_3$ dipole-dipole and $C_6$ van der Waals coefficients. We compare the $C_3$ and $C_6$ with experiments where the angle of a polarizing electric field is varied with respect to the axis of a quasi-1-dimensional trap at ultracold temperatures. The dipoles produced via polarization of the atoms have an angular dependent dipole-dipole interaction. We focus on the interaction potential of two rubidium Rydberg atoms in $50S_{1/2}$ states in the blockade regime. For…
The dipolar collision between ultracold polar molecules is an important topic both by its own right from the fundamental point of view and for the successful exploration of many-body physics with strong and long-range dipolar interactions. Here, we report the investigation of collisions between ultracold ground-state sodium-rubidium molecules in electric fields with induced electric dipole moments as large as 0.7$\;$D. We observe a step-wise enhancement of losses due to the coupling between different partial waves induced by the increasingly stronger anisotropic dipolar interactions. Varying t…
This paper reviews recent advances in the study of strongly interacting systems of dipolar molecules. Heteronuclear molecules feature large and tunable electric dipole moments, which give rise to long-range and anisotropic dipole-dipole interactions. Ultracold samples of dipolar molecules with long-range interactions offer a unique platform for quantum simulations and the study of correlated many-body physics. We provide an introduction to the physics of dipolar quantum gases, both electric and magnetic, and summarize the multipronged efforts to bring dipolar molecules into the quantum regime.…
We propose an experimentally realizable scheme to produce triatomic ultralong-range Rydberg molecules (TURM), formed in ultracold KRb traps. A near resonant coupling of the non-zero quantum defect Rydberg levels with the KRb molecule in N=0 and N=2 rotational levels, is engineered which exploits the unique Rydberg electron-molecule anisotropic dipole interaction. This near resonant coupling enhances the TURM binding and produces favorable Franck-Condon factors. Schemes for both postassium and rubidium excitations are demonstrated.
The prospects of sympathetic cooling of polar molecules with magnetically co-trapped alkali-metal atoms are generally considered poor due to strongly anisotropic atom-molecule interactions leading to large spin relaxation rates. Using rigorous quantum scattering calculations based on ab initio interaction potentials, we show that inelastic spin relaxation in low-temperature collisions of CaH(2Sigma) molecules with Li and Mg atoms occurs at a slow rate despite the strongly anisotropic interactions. This unexpected result, which we rationalize using multichannel quantum defect theory, opens up t…
We show theoretically that ultracold hydrogen atoms have very favorable properties for sympathetic cooling of molecules to microkelvin temperatures. We calculate the potential energy surfaces for spin-polarized interactions of H atoms with the prototype molecules NH(triplet-Sigma-) and OH(doublet-Pi) and show that they are shallow (50 to 80 cm-1) and only weakly anisotropic. We carry out quantum collision calculations on H+NH and H+OH and show that the ratio of elastic to inelastic cross sections is high enough to allow sympathetic cooling from temperatures well over 1 K for NH and around 250 …
Interactions in a spin-polarized ultracold Fermi gas are governed by $p$-wave collisions and can be characterized by the $p$-wave scattering volume. Control of these collisions by Feshbach resonances is hampered by huge inelastic losses. Here, we suggest non-resonant light control of $p$-wave collisions, exploiting the anisotropic coupling of non-resonant light to the polarizability of the atoms. The $p$-wave scattering volume can be controlled by strong non-resonant light, in close analogy to the $s$-wave scattering length. For collision partners that are tightly trapped, the non-resonant lig…
The efficiency of optical trapping is determined by the atomic dynamic dipole polarizability, whose real and imaginary parts are associated with the potential energy and photon-scattering rate respectively. In this article we develop a formalism to calculate analytically the real and imaginary parts of the scalar, vector and tensor polarizabilities of lanthanide atoms. We assume that the sum-over-state formula only comprises transitions involving electrons in the valence orbitals like $6s$, $5d$, $6p$ or $7s$, while transitions involving $4f$ core electrons are neglected. Applying this formali…
We report the creation and characterization of a near quantum-degenerate gas of polar $^{40}$K-$^{87}$Rb molecules in their absolute rovibrational ground state. Starting from weakly bound heteronuclear KRb Feshbach molecules, we implement precise control of the molecular electronic, vibrational, and rotational degrees of freedom with phase-coherent laser fields. In particular, we coherently transfer these weakly bound molecules across a 125 THz frequency gap in a single step into the absolute rovibrational ground state of the electronic ground potential. Phase coherence between lasers involved…
We predict the existence of a class of ultracold giant molecules formed from trapped ultracold Rydberg atoms and polar molecules. The interaction which leads to the formation of such molecules is the anisotropic charge-dipole interaction ($a/R^2$). We show that prominent candidate molecules such as KRb and deuterated hydroxyl (OD) should bind to Rydberg rubidium atoms, with energies $E_b\simeq 5-25$ GHz at distances $R\simeq 0.1-1 \ μ$m. These molecules form in double wells, mimicking chiral molecules, with each well containing a particular dipole orientation. We prepare a set of correlated dr…
The rapid development of experimental techniques to produce ultracold alkali molecules opens the ways to manipulate them and to control their dynamics using external electric fields. A prerequisite quantity for such studies is the knowledge of their static dipole polarizabilities. In this paper, we computed the variations with internuclear distance and with vibrational index of the static dipole polarizability components of all homonuclear alkali dimers including Fr$_2$, and of all heteronuclear alkali dimers involving Li to Cs, in their electronic ground state and in their lowest triplet stat…
Progress in ultracold experiments with polar molecules requires a clear understanding of their interactions and reactivity at ultra-low collisional energies. Two important theoretical steps in this process are the characterization of interaction potentials between molecules and the modeling of reactive scattering mechanism. Here, we report on the {\it abinitio} calculation of isotropic and anisotropic van der Waals interaction potentials for polar KRb and RbCs colliding with each other or with ultracold atoms. Based on these potentials and two short-range scattering parameters we then develop …
We propose an experiment to demonstrate a novel blockade mechanism caused by long-range anisotropic interactions in an ultracold dipolar gas composed of the recently observed "butterfly" Rydberg molecules. At the blockade radius, the strong intermolecular interaction between two adjacent molecules shifts their molecular states out of resonance with the photoassociation laser, preventing their simultaneous excitation. When the molecules are prepared in a quasi-one-dimensional (Q1D) trap, the interaction's strength can be tuned via a weak external field. The molecular density thus depends strong…
Rigorous quantum scattering calculations on ultracold molecular collisions in external fields present an outstanding computational problem due to strongly anisotropic atom-molecule interactions that depend on the relative orientation of the collision partners, as well as on their vibrational degrees of freedom. Here, we present the first numerically exact three-dimensional quantum scattering calculations on strongly anisotropic atom-molecule (Li+CaH) collisions in an external magnetic field based on the parity-adapted total angular momentum representation and a new three-dimensional potential …
We investigate the properties of two interacting ultracold polar molecules described as distinguishable quantum rigid rotors, trapped in a one-dimensional harmonic potential. The molecules interact via a multichannel two-body contact potential, incorporating the short-range anisotropy of intermolecular interactions including dipole-dipole interaction. The impact of external electric and magnetic fields resulting in Stark and Zeeman shifts of molecular rovibrational states is also investigated. Energy spectra and eigenstates are calculated by means of the exact diagonalization. The importance a…
We explore the character of a novel set of ``field-linked'' states that were predicted in [A. V. Avdeenkov and J. L. Bohn, Phys. Rev. Lett. 90, 043006 (2003)]. These states exist at ultralow temperatures in the presence of an electrostatic field, and their properties are strongly dependent on the field's strength. We clarify the nature of these quasi-bound states by constructing their wave functions and determining their approximate quantum numbers. As the properties of field-linked states are strongly defined by anisotropic dipolar and Stark interactions, we construct adiabatic surfaces as fu…
Ultracold molecular collisions in magnetic fields: Efficient incorporation of hyperfine structure in the total rotational angular momentum representation
We report the first measurement of a tune-out wavelength for ground-state bosonic Dy and linearly polarized light. The tune-out wavelength measured is near the narrow-line 741-nm transition in $^{162}$Dy, and is the wavelength at which the total Stark shift of the ground state vanishes. We find that it strongly depends on the relative angle between the optical field and quantization axis due to Dy's large tensor polarizability. This anisotropy provides a wide, 22-GHz tunability of the tune-out frequency for linearly polarized light, in contrast to Rb and Cs whose near-infrared tune-out wavelen…
We study collisional rethermalization in ultracold dipolar thermal gases, made intricate by their anisotropic differential cross sections. Theoretical methods are provided to derive the number of collisions per rethermalization, which for dipolar gases, is highly dependent on the dipole alignment axis. These methods are formulated to be easily applied in experimental contexts, even reducing to analytic expressions if the route to thermal equilibrium is governed by short-time dynamics. In the analytic case, collisional rethermalization is fully characterized by the dipole magnitude and orientat…
Recently, the quest for an ultracold and dense ensemble of polar molecules has attracted strong interest. Polar molecules have bright prospects for novel quantum gases with long-range and anisotropic interactions, for quantum information science, and for precision measurements. However, high-density clouds of ultracold polar molecules have so far not been produced. Here, we report a key step towards this goal. Starting from an ultracold dense gas of heteronuclear 40K-87Rb Feshbach molecules with typical binding energies of a few hundred kHz and a negligible dipole moment, we coherently transfe…
Ultracold polar molecules offer the possibility of exploring quantum gases with interparticle interactions that are strong, long-range, and spatially anisotropic. This is in stark contrast to the dilute gases of ultracold atoms, which have isotropic and extremely short-range, or "contact", interactions. The large electric dipole moment of polar molecules can be tuned with an external electric field; this provides unique opportunities such as control of ultracold chemical reactions, quantum information processing, and the realization of novel quantum many-body systems. In spite of intense exper…
We consider collisional properties of polyatomic aromatic hydrocarbon molecules immersed into ultracold atomic gases and investigate intermolecular interactions of exemplary benzene, naphthalene, and azulene with alkali-metal (Li, Na, K, Rb, Cs) and alkaline-earth-metal (Mg, Ca, Sr, Ba) atoms. We apply the state-of-the-art \textit{ab initio} techniques to compute the potential energy surfaces (PESs). We use the coupled cluster method restricted to single, double, and noniterative triple excitations to reproduce the correlation energy and the small-core energy-consistent pseudopotentials to mod…
It has been roughly three decades since laser cooling techniques produced ultracold atoms, leading to rapid advances in a vast array of fields. Unfortunately laser cooling has not yet been extended to molecules because of their complex internal structure. However, this complexity makes molecules potentially useful for many applications. For example, heteronuclear molecules possess permanent electric dipole moments which lead to long-range, tunable, anisotropic dipole-dipole interactions. The combination of the dipole-dipole interaction and the precise control over molecular degrees of freedom …
Loosely bound van der Waals dimers of lanthanide atoms, as might be obtained in ultracold atom experiments, are investigated. These molecules are known to exhibit a degree of quantum chaos, due to the strong anisotropic mixing of their angular spin and rotation degrees of freedom. Within a model of these molecules, we identify different realms of this anisotropic mixing, depending on whether the spin, the rotation, or both, are significantly mixed by the anisotropy. These realms are in turn generally correlated with the resulting magnetic moments of the states.
We explore the suitability of ultracold collisions between spin-polarized SrF($^2Σ^+$) molecules and Rb($^2$S) atoms as elementary steps for the sympathetic cooling of SrF($^2Σ^+$) molecules in a magnetic trap. To this end, we carry out quantum mechanical scattering calculations on ultracold Rb+SrF collisions in a magnetic field based on an accurate potential energy surface for the triplet electronic state of Rb-SrF developed ab initio using a spin-restricted coupler cluster method with single, double and noniterative triple excitations [RCCSD(T)]. The Rb-SrF interaction has a global minimum w…
Using the multipolar expansion of electrostatic and magnetostatic potential energies, we characterize the long-range interactions between two weakly-bound diatomic molecules, taking as an example the paramagnetic Er$_2$ Feshbach molecules which were produced recently. Since inside each molecule, individual atoms conserve their identity, the intermolecular potential energy can be expanded as the sum of pairwise atomic potential energies. In the case of Er$_2$ Feshbach molecules, we show that the interaction between atomic magnetic dipoles gives rise to the usual $R^{-3}$ term of the multipolar …
