Electric-field-induced wave-packet dynamics and geometrical rearrangement of trilobite Rydberg molecules

Frederic Hummel, Kevin Keiler, and Peter Schmelcher

Phys. Rev. A 103, 022827 – Published 19 February 2021

Abstract

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.

Received 14 December 2020
Accepted 5 February 2021

DOI:https://doi.org/10.1103/PhysRevA.103.022827

Physics Subject Headings (PhySH)

Atomic & molecular processes in external fields Cold and ultracold molecules Electronic structure of atoms & molecules Long-range interactions Potential energy surfaces

Exotic atoms & molecules Rydberg atoms & molecules

Adiabatic approximation Molecular dynamics Perturbative methods Quantum chemistry methods

Atomic, Molecular & Optical

Authors & Affiliations

Frederic Hummel ^1,*, Kevin Keiler¹, and Peter Schmelcher ^1,2

¹Zentrum für Optische Quantentechnologien, Fachbereich Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
²The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany

^*frederic.hummel@physnet.uni-hamburg.de

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 103, Iss. 2 — February 2021

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Illustration of a trilobite molecule in an electric field. The Rydberg electronic density (gray) ties the ionic core (blue) and the ground-state atom (red) together along $R$ . $θ$ is the angle relative to the electric field axis $F$ . (b) The field-free adiabatic potential $ε_{0} (R)$ (black) along with the dipole moment $d (R)$ (brown), a classical dipole $r - n^{2} / 2$ for comparison (gray), and selected vibrational levels (colored). (c) The two-dimensional adiabatic potential $ε (R, θ)$ for the field strength $F = 200 V / m$ .
Reuse & Permissions
Figure 2
Molecular wave-packet dynamics after a sudden quench of the electric field, initialized from the isotropic, field-free ground state. (a) Dynamically relevant section of the radial potential before (solid) and after the quench to different field strengths $F$ . [(b)–(d)] Temporal evolution of the radial density $ρ_{1} (R)$ corresponding to the fields. (e) The angular potential before (solid) and after (dashed) the quench. [(f)–(h)] Temporal evolution of the corresponding angular density $ρ_{2} (θ)$ . Two timescales of radial oscillations are apparent, the slower of which is correlated to the angular oscillations and depends on the field strength $F$ .
Reuse & Permissions
Figure 3
Mean value (a) and variance (b) of the radial one-body density after a quench of the electric field to $F = 100 V / m$ initialized from the isotropic, field-free ground state. This corresponds to the density shown in Fig. 2 and highlights the presence of two dipole-oscillation modes accompanied by breathing oscillations.
Reuse & Permissions
Figure 4
Molecular wave-packet dynamics after a sudden inversion of the electric field direction initialized from the localized, vibrational ground state at $F_{0} = - 400 V / m$ . (a) Dynamically relevant section of the radial potential before (solid) and after the quench (dashed) in the case of $F = 50 V / m$ . [(b)–(d)] Temporal evolution of the radial radial density $ρ_{1} (R)$ for different field strengths $F$ . (e) The angular potential before (solid) and after (dashed) the quench. [(f)–(h)] Temporal evolution of the corresponding angular density $ρ_{2} (θ)$ . The angular dynamics correspond to a rotation.
Reuse & Permissions
Figure 5
Molecular wave-packet dynamics after a sudden inversion of the electric field direction initialized from the localized, vibrational ground state at $F_{0} = - 400 V / m$ . (a) The dynamically relevant cuts of the radial potential at $θ = 0$ before (solid) and after (dashed) the quench (or vice versa at $θ = π$ ). (b) Temporal evolution of the radial and (c) angular densities. (d) The angular potential before (solid) and after (dashed) the quench. For this field strength, radial, large-amplitude, interwell oscillations occur and correspondingly, the angular rotation blurs out after approximately half its period.
Reuse & Permissions
Figure 6
Analysis of the radial components of the initial wave function. (a) The field-free trilobite potential (solid) with its vibrational eigenstates (symbol and color). [(b) and (c)] Fidelities $F_{i}$ of the radial components with these eigenstates (same symbol and color) for a waiting time between quenches of (b) $T = 3$ and (c) $5 ns$ . The waiting time strongly influences the number of contributing states. In (c), the quenches are discontinued after $t = 50 ns$ and coherent oscillations follow.
Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information