Dynamic dipole polarizabilities of heteronuclear alkali dimers: optical response, trapping and control of ultracold molecules

Abstract

In this article we address the general approach for calculating dynamical dipole polarizabilities of small quantum systems, based on a sum-over-states formula involving in principle the entire energy spectrum of the system. We complement this method by a few-parameter model involving a limited number of effective transitions, allowing for a compact and accurate representation of both the isotropic and anisotropic components of the polarizability. We apply the method to the series of ten heteronuclear molecules composed of two of ( 7 Li, 23 Na, 39 K, 87 Rb, 133 Cs) alkali-metal atoms. We rely on both up-to-date spectroscopically-determined potential energy curves for the lowest electronic states, and on our systematic studies of these systems performed during the last decade for higher excited states and for permanent and transition dipole moments. Such a compilation is timely for the continuously growing researches on ultracold polar molecules. Indeed the knowledge of the dynamic dipole polarizabilities is crucial to model the optical response of molecules when trapped in optical lattices, and to determine optimal lattice frequencies ensuring optimal transfer to the absolute ground state of initially weakly-bound molecules. When they exist, we determine the so-called "magic frequencies" where the ac-Stark shift and thus the viewed trap depth, is the same for both weakly-bound and ground-state molecules.

Dipolar exchange quantum logic gate with polar molecules

“…However, ground-state cooling is imperfect and the molecules gain kinetic energy due to photon recoil. Given the imaginary polarizability of NaCs Im[ α ] ≈ 10 –4 (atomic units), 49 the total scattering rate for a 600 kHz deep trap is approximately 0.8 Hz with a heating rate of 0.44 quanta per second axially and 0.023 quanta per second for each radial direction. Therefore, it is desirable for the gate fidelity to exceed the ground-state occupation fidelity.…”

C6 coefficients for interacting Rydberg atoms and alkali-metal dimers

“…It was shown in Ref. [31], that for frequencies up to ∼ 10 3 THz, the isotropic electronic molecular polarizability can be accurately approximated by…”

“…For the alkali-metal dimers used in this work, we take the parameters listed in Ref. [31] to estimate the electronic contribution to the molecular polarizability in over the frequencies of interest. Finally, we compute directly the downward transition terms that contribute to C 6 in Eq.…”

Anisotropic polarizability of erbium atoms

“…the energy of the transition hω JJ and the natural linewidth of the excited state γ J . In constant-sign convention [27], α (K) J (ω) is indeed given by a sum-over-state formula over all dipole-allowed transitions (∆J = 0, ±1), the term in the squared brackets is connected to the off-resonant photon scattering rate. As will be discussed in the next section, a precise knowledge of the atomic spectrum is highly non-trivial for multi-electron atomic species with submerged-shell structure and requires advanced spectroscopic calculations.…”

“…This term gives rise to a light shift, which is quadratic in the angular-momentum projection quantum number, m J , and provides an additional tool for optical spin manipulation, as recently studied in ultracold Dy experiments [21]. The anisotropy in the polarizability has been observed not only in atoms with large orbital-momentum quantum number but also in large-spin atomic system, such as cromium (Cr), [22,23] and molecular systems [24][25][26][27]. This paper reports on the measurement of the dynamical polarizability in ultracold Er atoms in both the ground state and one excited state for trapping-relevant wavelengths.…”