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arXiv:2211.07319

Simulating conical intersections with trapped ions

Jacob Whitlow, Zhubing Jia, Ye Wang, Fang, Chao, Jungsang Kim, Kenneth R. Brown

Published Nov 14, 2022• 7 citations
arXivHTMLPDF

Abstract

Conical intersections are common in molecular physics and photochemistry, and are often invoked to explain observed reaction products. A conical intersection can occur when an excited electronic potential energy surface intersects with the ground electronic potential energy surface in the coordinate space of the nuclear positions. Theory predicts that the conical intersection will result in a geometric phase for a wavepacket on the ground potential energy surface. Although conical intersections have been observed experimentally, the geometric phase has not been observed in a molecular system. Here we use a trapped atomic ion system to perform a quantum simulation of a conical intersection. The internal state of a trapped atomic ion serves as the electronic state and the motion of the atomic nuclei are encoded into the normal modes of motion of the ions. The simulated electronic potential is constructed by applying state-dependent forces to the ion with a near-resonant laser. We experimentally observe the geometric phase on the ground-state surface using adiabatic state preparation followed by motional state measurement. Our experiment shows the advantage of combining spin and motion degrees of freedom in a quantum simulator.

DOI
10.48550/arxiv.2211.07319

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Conical intersections are common in molecular physics and photochemistry, and are often invoked to explain observed reaction products. A conical intersection can occur when an excited electronic potential energy surface intersects with the ground electronic potential energy surface in the coordinate space of the nuclear positions. Theory predicts that the conical intersection will result in a geometric phase for a wavepacket on the ground potential energy surface. Although conical intersections have been observed experimentally, the geometric phase has not been observed in a molecular system. Here we use a trapped atomic ion system to perform a quantum simulation of a conical intersection. The internal state of a trapped atomic ion serves as the electronic state and the motion of the atomic nuclei are encoded into the normal modes of motion of the ions. The simulated electronic potential is constructed by applying state-dependent forces to the ion with a near-resonant laser. We experimentally observe the geometric phase on the ground-state surface using adiabatic state preparation followed by motional state measurement. Our experiment shows the advantage of combining spin and motion degrees of freedom in a quantum simulator.
Conical intersections between electronic potential energy surfaces are paradigmatic for the study of nonadiabatic processes in the excited states of large molecules. However, since the corresponding dynamics occurs on a femtosecond timescale, their investigation remains challenging and requires ultrafast spectroscopy techniques. We demonstrate that trapped Rydberg ions are a platform to engineer conical intersections and to simulate their ensuing dynamics on larger length scales and timescales of the order of nanometers and microseconds, respectively; all this in a highly controllable system. Here, the shape of the potential energy surfaces and the position of the conical intersection can be tuned thanks to the interplay between the high polarizability and the strong dipolar exchange interactions of Rydberg ions. We study how the presence of a conical intersection affects both the nuclear and electronic dynamics demonstrating, in particular, how it results in the inhibition of the nuclear motion. These effects can be monitored in real time via a direct spectroscopic measurement of the electronic populations in a state-of-the-art experimental setup.
We study spin-phonon coupled dynamics in the vicinity of a sloped conical intersection created by laser coupling the electronic (spin) and vibrational degrees of freedom of a pair of trapped Rydberg ions. We show that the shape of the potential energy surfaces can be engineered and controlled by exploiting the sideband transitions of the crystal vibration and dipole-dipole interactions between Rydberg ions in the Lamb-Dicke regime. Using the sideband transition, we realize a sloped conical intersection whose cone axis is only tilted along one spatial axis. When the phonon wavepacket is located in the potential minimum of the lower potential surface, the spin and phonon dynamics are largely frozen owing to the geometric phase effect. When starting from the upper potential surface, the electronic and phonon states tunnel to the lower potential surface, leading to a partial revival of the initial state. In contrast, the dynamics drastically change when the initial wavepackets are away from the conical intersection. The initial state is revived, and is almost entirely irrelevant to whether it is from the lower or upper potential surface. Complete Rabi oscillations of the adiabatic states are found when the wavepacket is initialized on the upper potential surface. The dynamics occur on the microsecond and nanometer scales, implying that Rydberg ions provide a platform for simulating nonadiabatic processes in the vicinity of a sloped conical intersection.
Conical intersections of potential energy surfaces widely appear in molecules which consist of more than two atoms. No conical intersections exist in the case of free diatomic molecules. We show here that diatomic molecules interacting with standing laser waves produce periodic arrays of conical intersections. At these laser-induced intersections the non-adiabatic effects are infinitely strong. The translational and rovibrational molecular motions become strongly coupled to each other and energy exchange between the various degrees of freedom influences the dynamics of the system. As an illustrative example, an effect of the laser-induced conical intersections on trapping of ultracold diatomic molecules by light is discussed.
High Resolution Image Download MS PowerPoint Slide Conical intersections are crossing points or lines between two or more adiabatic electronic potential energy surfaces in the multidimensional coordinate space of colliding atoms and molecules. Conical intersections and corresponding nonadiabatic coupling can greatly affect molecular dynamics and chemical properties. In this paper, we predict significant or measurable nonadiabatic effects in an ultracold atom–ion charge-exchange reaction in the presence of laser-induced conical intersections (LICIs). We investigate the fundamental physics of these LICIs on molecular reactivity under unique conditions: those of relatively low laser intensity of 10 8 W/cm 2 and ultracold temperatures below 1 mK. We predict irregular interference effects in the charge-exchange rate coefficients between K and Ca + as functions of the laser frequency. These irregularities occur in our system due to the presence of two LICIs. To further elucidate the role of the LICIs on the reaction dynamics, we compare these rate coefficients with those computed for a system where the CIs have been “removed”. In the laser frequency window, where conical interactions are present, the difference in rate coefficients can be as large as 1 × 10 –9 cm 3 /s.
We theoretically show that when two largely separated trapped atoms interact with a trapped ion via Rydberg excitation of the atoms, the ion-mediated interaction between the atoms exceeds the direct atom-atom interaction by several orders of magnitude. Since the motion of the atoms is much slower than the motion of the ion, we resort to Born-Oppenheimer approximation to calculate the ion-mediated adiabatic potential. We also calculate the ion-mediated phonon modes of the atoms that are separated by more than 10 micron. For cylindrical geometry of the system and both the atoms being excited to the same Rydberg state, the stretched and center-of-mass (COM) axial or transverse phonon modes are found to be almost degenerate, while the phonon modes are non-degenerate when one atom is in a Rydberg state and the other in the ground state. We discuss the non-adiabatic effects in the system that give rise to a Gauge structure and associated geometric phase in the system. This study may open a new perspective in quantum computing and exploring molecular physics associated with a conical intersection using an ion-atom hybrid architecture.
Non-adiabatic processes near conical intersections are rooted in the stronger coupling between electronic and nuclear degrees of freedom. Using a system of two trapped Rydberg ions, their high polarizability and strong dipolar interactions allow to form a conical intersection, where dynamics takes place on a microsecond time scale. Rydberg lifetimes are typically from a few to tens of microseconds, which could affect the conical dynamics. We study the effect of the finite lifetime of the Rydberg state on the vibronic dynamics around the conical intersection via analyzing the master equation. Through mean field and numerical calculations, damping dynamics are found in both the phonon populations and electronic states depending on the initial states. It is found that oscillatory vibronic dynamics can be seen clearly within the Rydberg lifetime, permitting to observe the conical effect in the trapped Rydberg ion system.