Rydberg Molecules Research Articles

A protocol to realize triatomic ultralong range Rydberg molecules in an ultracold KRb gas

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.

Radio Emission of Rydberg Atoms in the Upper Atmosphere Modified by High-Power HF Radio Waves

We report on the results of studying the radio emission of the Rydberg states of atoms and molecules in the Earth’s upper atmosphere at ionospheric altitudes when the ionosphere is modified by high-power HF radio waves radiated by the Sura heating facility. Radio emission from the upper atmosphere, caused by the emission of highly excited Rydberg atoms and molecules with the principal quantum number n = 163–169 and n = 225 (decimeter wavelength range) and two spectral features that coincide with the frequencies of transitions between Rydberg states m = 169 → n = 168 with the transition frequency νn = 1375.35 MHz and m = 166 → n = 165 with νn = 1451.5 MHz were detected. Characteristic altitudes of the Rydberg radiation generation region were 150–250 km. The radio emission intensity corresponds to 10–45 K, which is comparable with the intensity of the radio emission generated during solar flares.

Formation of ultracold ion pairs through long-range Rydberg molecules

We propose a new approach to excite ion-pair states of ultracold dimers. The central idea is a two-step process where first long-range Rydberg molecules are formed by photoassociation, which are then driven by stimulated emission towards the ion-pair state, a process bearing features of a photo-induced harpooning reaction. We assess the feasibility of this approach through a detailed experimental and theoretical study on a specific system, p-wave-scattering dominated long-range Rydberg molecules in caesium, and discuss potential applications for the study of strongly correlated plasmas consisting of oppositely charged particles of equal or similar mass.

Observation of spin-orbit-dependent electron scattering using long-range Rydberg molecules

We present experimental evidence for spin-orbit interaction of an electron as it scatters from a neutral atom. The scattering process takes place within a Rb$_2$ ultralong-range Rydberg molecule, consisting of a Rydberg atomic core, a Rydberg electron, and a ground state atom. The spin-orbit interaction leads to characteristic level splittings of vibrational molecular lines which we directly observe via photoassociation spectroscopy. We benefit from the fact that molecular states dominated by resonant $p$-wave interaction are particularly sensitive to the spin-orbit interaction. Our work paves the way for studying novel spin dynamics in ultralong-range Rydberg molecules. Furthermore, it shows that the molecular setup can serve as a microlaboratory to perform precise scattering experiments in the low-energy regime of a few meV.

Rydberg polyatomic molecules: Electronic structure and experimental proposal for their creation

SynopsisWe describe the electronic structure and main features of ultralong range Rydberg molecules formed by a Rydberg atom, either Rb or K, and the heteronuclear diatomic molecule KRb. By analyzing their electronic structure, we propose a protocol to create these molecules experimentally from a mixture of ultracold atoms and ultracold molecules.

Excitation of vibrationally-excited ultralong-range strontium Rydberg molecules in quantum gases

SynopsisThe photoexcitation rate for ultralong-range Rydberg molecules is sensitive to the initial spatial sepa-ration of the atoms from which they are formed. Here we explore the photoexcitation of different molecular vibrational states as a probe of spatial correlations in a cold atomic gas.

Measurements of spatial correlations in quantum gases using ultralong-range strontium Rydberg molecules

SynopsisThe photoexcitation of ultralong-range Rydberg molecules is demonstrated as a probe of spatial cor-relations in a quantum gas on previously inaccessible length scales of 1400-3200 a 0. Measurements using cold (∼1 μK) (fermionic) 87Sr and (bosonic) 84Sr reveal the effects of quantum statistics on the pair correlation function g (2)(R).

Creation of vibrationally-excited ultralong-range Rydberg molecules in polarized and unpolarized cold gases of 87Sr

Photoexcitation rates for creation of ultralong-range Rydberg molecules with 31 ≲ n ≲ 41 in both ground and excited vibrational levels in cold (T ∼ 900 nK) gases of polarized and unpolarized 87Sr are presented. The measured production rates of the ν = 0, 1 and 2 vibrational levels reveal rather different n dependences which are analyzed by evaluating the Franck–Condon factors associated with excitation of the different vibrational levels and molecular rotational states. In particular, for gases of spin-polarized fermions, only Rydberg dimers with odd rotational quantum numbers are excited due to the requirement that their wave functions be anti-symmetric with respect to exchange. The data also demonstrate that measurements of the formation of vibrationally-excited ν = 1 molecules can furnish a probe of pair correlations over intermediate length scales.

Resonant Rydberg-atom–microwave-field interactions in the ultrastrong-driving regime: Beyond the rotating-wave approximation

The coherent interaction of Rydberg atoms with microwave fields in the ultrastrong-driving regime, in which the Rabi frequency is of the same order of magnitude as the transition frequency, has been studied for states with principal quantum number $n=105$ in helium. Experiments were performed in pulsed supersonic beams, and the effects of the ultrastrong 1.280 GHz microwave driving field, tuned to near resonance with the $1s105s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}\ensuremath{\rightarrow}1s105p\phantom{\rule{0.16em}{0ex}}^{3}P$ transition, were identified from Autler-Townes splittings of the $1s3p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}\ensuremath{\rightarrow}1s105s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}$ transition by cw laser spectroscopy. The microwave field strength was calibrated in situ in the apparatus from Autler-Townes splittings measured in the weak-driving regime in which the rotating-wave approximation holds. The results of the experiments were compared to the energy-level structure of the atoms in the presence of the microwave field calculated using Floquet methods. From this comparison, the microwave-field strengths for which the rotating-wave approximation and the two-level approximation break down have been identified. The feasibility of implementing microwave traps for Rydberg atoms and molecules, which operate in the ultrastrong-driving regime, has been evaluated.

Control of molecular ultracold plasma relaxation dynamics by mm-wave Rydberg–Rydberg transitions

Resonant mm-wave fields drive transitions in a state-selected Rydberg gas of NO. This transformation produces a clear signature in the selected field ionisation spectrum and dramatically increases the intensity of corresponding features in the spectrum of the Rydberg series observed in UV–UV double resonant transitions via the state. Here, refers to the principal quantum number of an f Rydberg state converging to the rotational state of NO. Enhancement owing to transitions from (f) to (g) appears both in the electron signal detected at early time by the field ionisation of Rydberg molecules and, later, as the late-peak signal of plasma in a state of arrested relaxation. Similar stabilisation and enhanced intensity also occurs for shorter-lived interloping complex resonances, and . We conclude from these observations that avalanche alone does not guarantee a plasma state of arrested relaxation. But rather, the formation of an arrested phase requires both avalanche-produced NO ions and a persistent population of long-lived Rydberg molecules.

Precision Spectroscopy of Negative-Ion Resonances in Ultralong-Range Rydberg Molecules.

The level structure of negative ions near the electron detachment limit dictates the low-energy scattering of an electron with the parent neutral atom. We demonstrate that a single ultracold atom bound inside a Rydberg orbit forming an ultralong-range Rydberg molecule provides an atomic-scale system that is highly sensitive to electron-neutral scattering and thus allows for detailed insights into the underlying near-threshold anion states. Our measurements reveal the so-far unobserved fine structure of the ^{3}P_{J} triplet of Rb^{-} and allows us to extract parameters of the associated p-wave scattering resonances that deviate from previous theoretical estimates. Moreover, we observe a novel alignment mechanism for Rydberg molecules mediated by spin-orbit coupling in the negative ion.

Probing nonlocal spatial correlations in quantum gases with ultra-long-range Rydberg molecules

We present photo-excitation of ultra-long-range Rydberg molecules as a probe of spatial correlations in quantum gases. Rydberg molecules can be created with well-defined internuclear spacing, set by the radius of the outer lobe of the Rydberg electron wavefunction $R_n$. By varying the principal quantum number $n$ of the target Rydberg state, the molecular excitation rate can be used to map the pair-correlation function of the trapped gas $g^{(2)}(R_n)$. We demonstrate this with ultracold Sr gases and probe pair-separation length scales ranging from $R_n = 1400 - 3200$ $a_0$, which are on the order of the thermal de Broglie wavelength for temperatures around 1 $\mu$K. We observe bunching for a single-component Bose gas of $^{84}$Sr and anti-bunching due to Pauli exclusion at short distances for a polarized Fermi gas of $^{87}$Sr, revealing the effects of quantum statistics.

Spectroscopic constants and potential-energy curves for the Rydberg states of NaHe

Thirty eight doublet electronic states of the Rydberg molecule NaHe are studied by means of numerical solution of the Schrödinger equation using the finite element method. Twelve of these 38 electronic states are studied for the first time. It is confirmed that potential-energy curves (PECs) of high Rydberg Σ–states have several wells and barriers at large internuclear distances due to radial oscillations of the electron density in the Rydberg states of the sodium atom.

Local frame transformation theory for two classes of diatomic molecules

ABSTRACTThis study develops an alternative, analytical approach for computing the electronic spectra of long-range diatomic Rydberg molecules with charged atomic cores in which either each core is identical, or else one core is a bare ion with no screening. This approach involves a frame transformation between locally separable regions of the configuration space, and an analytic expression for the frame transformation matrix is derived for Σ states. Results for states of Li and LiH are compared with available theoretical calculations.

Excitation of Rydberg Molecules in Ultracold Quantum Gases

Recent experiments in our group on the excitation of Rydberg molecules in ultracold quantum gases have been reviewed. Quantum gases are a well‐suited environment to excite Rydberg molecules, due to the high atomic density and the perfect control of the internal spin degrees of freedom and the center of mass motion of the atoms. In parallel, the coupling to Rydberg molecules can be used to probe and manipulate the interaction in ultracold quantum gases. In this Feature Article, a comprehensive introduction to the field of Rydberg molecules, including ultralong‐range molecules and butterfly molecules is given. The Rydberg molecules have been characterized spectroscopically and their internal spin structure is discussed. Then, it is shown how these Rydberg molecules work as a tool to monitor the double occupancy in optical lattice experiments and to change the inter‐particle interaction with the help of a so‐called optical Feshbach resonance.

Deeply bound ( 24DJ+5S1/2 ) Rb87 and Rb85 molecules for eight spin couplings

We observe long-range $^{85}$Rb and $^{87}$Rb (24$D$+5$S_{1/2}$) Rydberg molecules for eight different spin couplings, with binding energies up to 440~MHz and sub-percent relative uncertainty. Isotopic effects of the molecular binding energies arise from the different masses and nuclear spins. Because the vibrational states involve different spin configurations and cover a wide range of internuclear separations, the states have different dependencies on the $s$-wave and $p$-wave scattering phase shifts for singlet and triplet scattering. Fitting the spectroscopic data, we comprehensively determine all four scattering length functions over the relevant energy range as well as the zero-energy scattering lengths of the two $s$-wave channels. Our unusually high temperature and low density (180 $\mu$K, 1 $\times$ 10$^{11}$ cm$^{-3}$) suggest that the molecule excitation occurs through photoassisted collisions.

Building principle of triatomic trilobite Rydberg molecules

We investigate triatomic molecules that consist of two ground state atoms and a highly excited Rydberg atom, bound at large internuclear distances of thousands of \AA ngstroms. In the molecular state the Rydberg electron is in a superposition of high angular momentum states whose probability densities resemble the form of trilobite fossils. The associated potential energy landscape has an oscillatory shape and supports a rich variety of stable geometries with different bond angles and bond lengths. Based on an electronic structure investigation we analyze the molecular geometry systematically and develop a simple building principle that predicts the triatomic equilibrium configurations. %based on the properties of diatomic trilobite molecules. As a representative example we focus on $^{87}$Rb trimers correlated to the $n=30$ Rydberg state. Using an exact diagonalization scheme we determine and characterize localized vibrational states in these potential minima with energy spacings on the order of 100 MHz$\times h$.

Formation of ultralong-range fermionic Rydberg molecules in 87Sr: role of quantum statistics

ABSTRACTMeasurements of ultralong-range Rydberg molecule formation in cold gases of fermionic 87Sr atoms are presented. Measurements undertaken using polarised and unpolarised cold atom samples demonstrate that studies of Rydberg molecule formation can provide a window into the important role played by quantum statistics in determining the pair-correlation function, , and, more generally, can furnish a sensitive probe of spatial correlations in quantum gases that is suitable for use in a number of different applications.

Alignment of s -state Rydberg molecules in magnetic fields

We unravel some peculiar properties of ultralong-range Rydberg molecules formed by an $s$-state $^{87}$Rb Rydberg atom and a corresponding ground-state atom whose electronic orbitals are spherically symmetric and therefore should not be influenced by the presence of weak magnetic fields. However, the electron-atom interaction, which establishes the molecular bond, is under certain conditions subject to a sizeable spin-orbit coupling and, hence, sensitive to the magnetic field. This mechanism can be harnessed to counterintuitively align the $s$-state molecules with respect to the field axis. We demonstrate this by analyzing the angular-dependent Born-Oppenheimer potential energy surfaces and the supported vibrational molecular states. Our predictions open novel possibilities to access the physics of relativistic electron-atom scattering experimentally.

Formation of long-range Rydberg molecules in two-component ultracold gases

We present a comprehensive study of the diverse properties of heteronuclear Rydberg molecules, placing a special emphasis on those composed of the light alkali atoms, Li, Na, and K. Electron-atom scattering phase shifts, which determine the strength of the molecular bond, are calculated at very low energy and then used in a spin-dependent theoretical model to calculate accurate Rydberg molecule potential energy curves. The wide parameter range accessible by combining the various properties of different alkali atoms often leads to hybridized electronic states accessible via one or two photon excitation schemes. This analysis of heteronuclear molecules leads to a prediction that the relative densities and spatial distributions of atoms in an ultracold mixture can be probed at controllable length scales via spectroscopic detection of these molecules.