Ultracold Rydberg molecules

Abstract

Ultracold molecules formed from association of a single Rydberg atom with surrounding atoms or molecules and those from double Rydberg excitations are discussed in this review. Ultralong-range Rydberg molecules possess a novel molecular bond resulting from scattering of the Rydberg electron from the perturber atoms or molecules. The strong interactions between Rydberg atoms in ultracold gases may lead to formation of macroscopic Rydberg macrodimers. The exquisite control over the properties of the Rydberg electron means that interesting and unusual few-body and quantum many-body features can be realized in such systems.

Fig. 1

Ultracold Rydberg molecules and macrodimers. Schematics of Rydberg molecular electronic density and potential energy curves; a depicts an ultralong-range Rydberg molecule while b shows a Rydberg macrodimer. The ultralong-range Rydberg molecule consists of a ground state atom or a polar molecule embedded in the electronic orbital of the Rydberg atom. The potential energy curves exhibit oscillations. A Rydberg macrodimer consists of two Rydberg atoms interacting via macroscopic electrostatic multipolar interactions. The Rydberg electron orbitals (~ 0.1 μm) in this schematic are not shown in proportion to the separation distances

Fig. 2

Trilobite Rydberg molecules in an ultracold Cs gas. a Calculated electron density distributions for the ³Σ⁺ states of Cs correlating to 37s + 6s, 39s + 6s, and 40s + 6s. b The corresponding potential energy curves for the states shown in a with calculated vibrational levels. c The broadening of the vibrational levels indicated by an arrow in b as a function of applied electric field. The changes in the lineshape as a function of electric field are used to determine the dipole moments indicated in the figure. Figure from ref. . Reprinted with permission from AAAS

Fig. 3

Singlet/triplet mixing in Cs Rydberg molecule BO potential energy curves. The interaction potentials including spin-dependent relativistic interactions (see Box 3 for details). The lowest potential is mainly a S = 1 (triplet) BO potential for a Cs(6s_1/2) - Cs(32p_3/2) Rydberg molecule in the ground hyperfine state, F = 3. The excited BO potential curve is predominantly a spin-mixed S = 0 and S = 1 (singlet and triplet) state. Unphysical cusps can be seen in both potentials at R ~ 1629 a.u. The cusps are the result of the semi-classical description of the energy-dependent scattering length at the transition from the classically allowed to the classically forbidden region. The cusps cannot be removed at the level of approximation discussed in this review, but they have little influence on the nature of molecular states of interest here. These potentials were recently employed in ref. for interpretation of the observation of spin-mixed states in ref.

Fig. 4

Cs Rydberg macrodimer BO potential energy curves. The Cs Rydberg macrodimer potentials in the region of the 89d + 89d asymptote in the presence of an electric field, ε. The total electronic angular momentum projection quantum number is m = 3. The electric field lies along the internuclear axis. Some potential energy curve crossings that support bound states are labeled, C1, C2, C1′, and C2′. The labels along the vertical axes give the angular momentum j for each atom of the pair. The potential energy curves are shown for 0 mV cm⁻¹ (a), 30 mV cm⁻¹ (b), 60 mV cm⁻¹ (c) and 120 mV cm⁻¹ (d). Figure from ref. , reprinted with permission from Taylor & Francis Ltd

Fig. 5

Kinetic energy spectra from the fragmentation of macrodimers. The kinetic energy as a function of the delay, τ, between when a particular molecular complex was excited and when it was probed via field ionization. In the leftmost panel a state correlating to 88d + 90d is first excited. The other figures correspond to states correlating with 63d + 65d, 64d + 66d, 65d + 67d, and 66d + 68d. The dashed line in the leftmost panel shows the kinetic energy expected for a pair of Cs atoms photoassociated at R = 2.8 μm and moving uniformly apart at a velocity of 17 cm s⁻¹. The other four panels show the same quantity for macrodimer states for an electric field of 224 mV cm⁻¹ for 63d + 65d, 205 mV cm⁻¹ for 64d + 66d, 190 mV cm⁻¹ for 65d + 67d and 158 mV cm⁻¹ for 66d + 68d. The red points are the data while the dashed line is what is expected for a laser induced collision of the pair of Cs atoms with a recoil energy equal to the thermal energy of the atoms in the ultracold atom trap. Figure from ref. . Reprinted with permission from Nature Publishing Group

Fig. 6

Polyatomic Rb molecules and many-body spectra. a The observation of polyatomic s-wave Rydberg molecules (dimers, trimers, and tetramers) in photoassociation of Rydberg molecules; figure reprinted from ref. , b density averaged absorption spectra for Rb(71s) excitations. In a, the gas is thermal at T = 0.5 μK and the MOT center density is ρ = 1.7 × 10¹² cm⁻³. The laser profile illuminates the cloud over the full cylindrical radius (black) and in a small waist (dashed, blue); data is reported in Gaj et al.. In b, the density averaged absorption spectrum at T/T_c = 0.47 for a partially condensed gas of (zero temperature) at peak density ρ = 2.3 × 10¹⁴ cm⁻³. Reprinted figure with permission from ref. Copyright (2016) by the American Physical Society