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arXiv:2408.02134 · Physical Review A

Internal diffraction dynamics of trilobite molecules

Rohan Srikumar, Seth T. Rittenhouse, Peter Schmelcher

Published Dec 10, 2024• 3 citations
arXivHTMLPDF

Abstract

Trilobite molecules are ultralong-range Rydberg molecules formed when a high angular momentum Rydberg electron scatters off of a ground-state atom. Their unique electronic structure and highly oscillatory potential energy curves support a rich variety of dynamical effects yet to be explored. We analyze the vibrational motion of these molecules using a framework of adiabatic wave-packet propagation dynamics and observe that for appropriate initial states, the trilobite potential acts as molecular diffraction grating. The quantum dynamic effects observed are explained using a Fourier analysis of the scattering potential and the associated scattered wave packet. Furthermore, vibrational ground states of the low angular momentum ultralong-range Rydberg molecules are found to be particularly suitable to prepare the relevant wave packets. Hence, we propose a time-resolved pump-probe scheme designed for the realization of the effect in question, and advertise the utilization of a single diatomic Rydberg molecule as a test bed for the study of exaggerated quantum dynamical phenomena.

DOI
10.1103/physreva.110.062808

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Trilobite molecules are ultralong-range Rydberg molecules formed when a high angular momentum Rydberg electron scatters off of a ground-state atom. Their unique electronic structure and highly oscillatory potential energy curves support a rich variety of dynamical effects yet to be explored. We analyze the vibrational motion of these molecules using a framework of adiabatic wave-packet propagation dynamics and observe that for appropriate initial states, the trilobite potential acts as molecular diffraction grating. The quantum dynamic effects observed are explained using a Fourier analysis of the scattering potential and the associated scattered wave packet. Furthermore, vibrational ground states of the low angular momentum ultralong-range Rydberg molecules are found to be particularly suitable to prepare the relevant wave packets. Hence, we propose a time-resolved pump-probe scheme designed for the realization of the effect in question, and advertise the utilization of a single diatomic Rydberg molecule as a test bed for the study of exaggerated quantum dynamical phenomena.
We investigate the non-adiabatic quantum dynamics of ultralong-range Rydberg molecules using a vibronically coupled two-channel treatment. The two-channels are composed of coupled trilobite and butterfly electronic states, formed as a result of SSS-wave and PPP-wave scattering of high angular momentum Rydberg electrons with perturbing ground state atoms. Within the Born-Oppenheimer treatment, the PPP-wave scattering channel introduces an adiabatic decay pathway that affects the stability and lifetimes of trilobite states. Our numerical results show that the vibronic coupling is dependent on the principal quantum number nnn, and for certain nnn there is non-adiabatic stabilization against internal molecular decay, facilitating previously studied dynamical effects in pure trilobite molecules. Apart from the internal diffraction effect caused by the backscattering of vibrational wavepackets from the trilobite potential, we also observe interesting multi-well tunneling effects during low-energy oscillations for a range of nnn-values. Our work serves to highlight that the unique vibrational coordinate dependent electronic structure of these polar molecules, along with high level densities, promise many exciting dynamical effects.
In trilobite Rydberg molecules, an atom in the ground state is bound by electron-atom scattering to a Rydberg electron that is in a superposition of high angular momentum states. This results in a homonuclear molecule with a permanent electric dipole moment in the kilo-debye range. Trilobite molecules have previously been observed only with admixtures of low-l states. Here we report on the observation of two vibrational series of pure trilobite Rubidium-Rydberg molecules that are nearly equidistant. They are produced by three-photon photoassociation and lie energetically more than 15 GHz below the atomic 22F state of rubidium. We show that these states can be used to measure the electron-atom scattering length at low energies in order to benchmark current theoretical calculations. In addition to measuring their kilo-Debye dipole moments, we also show that the molecular lifetime is increased compared to the 22F state due to the high-l character. The observation of an equidistant series of vibrational states opens the way to observe coherent molecular wave packet dynamics.
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 angstroms. 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. As a representative example we focus on 87Rb^{87}\mathrm{Rb}87Rb trimers correlated to the n=30n=30n=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 $\mathrm{MHz}\ifmmode\times\else\texttimes\fi{}h$.
We investigate the quantum dynamics of ultra-long-range trilobite molecules exposed to homogeneous electric fields. A trilobite molecule consists of a Rydberg atom and a ground-state atom, which is trapped at large internuclear distances in an oscillatory potential due to scattering of the Rydberg electron off the ground-state atom. Within the Born-Oppenheimer approximation, we derive an analytic expression for the two-dimensional adiabatic electronic potential energy surface in weak electric fields valid up to 500 V/m. This is used to unravel the molecular quantum dynamics employing the multiconfigurational time-dependent Hartree method. Quenches of the electric field are performed to trigger the wave-packet dynamics including the case of field inversion. Depending on the initial wave packet, we observe radial intrawell and interwell oscillations as well as angular oscillations and rotations of the respective one-body probability densities. Opportunities to control the molecular configuration are identified, a specific example being the possibility to superimpose different molecular bond lengths by a series of periodic quenches of the electric field.
We report on the observation of highly excited ( ν ∼ 100 ) vibrational states of a trilobite ultralong-range Rydberg molecule in Rb 87 . These states manifest spectroscopically in a regularly spaced series of peaks red-detuned from the 25 f 7 / 2 dissociation threshold. The existence and observed stability of these states require the almost complete suppression of the adiabatic decay pathway induced by the P -wave shape resonance of Rb. This stabilization is predicted to occur only for certain Rydberg levels where the avoided crossing between trilobite and P -wave-dominated butterfly potential energy curves nearly vanishes, allowing the vibrational states to diabatically traverse the crossing with almost unit probability. This is the first direct measurement of beyond-Born-Oppenheimer physics in long-range Rydberg molecules, and paves the way for future experiments to access and manipulate wave packets formed from high-lying vibrational states.
Ultralong-range Rydberg molecules provide an exciting testbed for molecular physics at exaggerated scales. In the so-called trilobite and butterfly Rydberg molecules, the Born-Oppenheimer approximation can fail due to strong nonadiabatic couplings arising from the combination of radial oscillations and rapid energy variations in the adiabatic potential energy curves. We utilize an accurate coupled-channel treatment of the vibronic system to observe the breakdown of Born-Oppenheimer physics, such as nonadiabatic trapping and decay of molecular states found near pronounced avoided crossings in the adiabatic potential curves. Even for vibrational states localized far away from avoided crossings, a single-channel model is quantitatively sufficient only after including the diagonal nonadiabatic corrections to the Born-Oppenheimer potentials. Our results indicate the importance of including nonadiabatic physics in the description of ultralong-range Rydberg molecules and in the interpretation of measured vibronic spectra.