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arXiv:2310.05101

Trapped ion-mediated interactions between two distant trapped atoms

Subhra Mudli, Subhanka Mal, Anushree Dey, Bimalendu Deb

Published Oct 8, 2023• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2310.05101

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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.
We propose a toy model of ion-atom hybrid quantum system for quantum computing. We show that when two atomic qubits in two largely separated optical tweezers interact with a single trapped ion through Rydberg excitation of the atoms, there exists an ion-mediated atom-atom interaction which exceeds the direct interatomic interaction at large separation. We employ this mediated interaction to demonstrate a two-qubit control phase-gate operation with 97% fidelity by addressing the individual atomic qubits with lasers.
We theoretically demonstrate the universal two-qubit CNOT gate between an ionic and an atomic qubit relying on Rydberg excitation of the atom and the resulting phonon blockade in the motional states of the harmonically trapped ion. The phonon blockade arises due to strong ion-atom interaction when the atom is excited to a Rydberg state. For realistic parameters, the gate fidelity is found to be about 90%90\%90%. In a previous paper [S. Mudli {\it et al.} Phys. Rev. A 110, 062618 (2024)], it was shown that a trapped ion can mediate interaction between two largely separated Rydberg atoms, and this mediated interaction can be leveraged to perform a universal two-qubit gate operation between neutral atom qubits in optical tweezers. These demonstrations suggest that an ion-atom hybrid system can serve as a resourceful platform or module for quantum computing and quantum networking as it can utilize the best features of charged as well as neutral atom qubits. Finally, we discuss how to achieve higher gate fidelity by extending our proposed protocol and operating in a different parameter regime.
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.
We theoretically investigate the possibility of creating phonon-mediated spin-spin interactions between neutral atoms trapped in optical tweezers. By laser coupling the atoms to Rydberg states, collective modes of motion appear. We show that these can be used to mediate effective spin-spin interactions or quantum logic gates between the atoms in analogy to schemes employed in trapped ions. In particular, we employ Rydberg dressing in a novel scheme to induce the needed interaction, and we show that it is possible to replicate the working of the Mølmer-Sørensen entanglement scheme. The Mølmer-Sørensen gate is widely used in emerging quantum computers using trapped ion qubits and currently features some of the highest fidelities of any quantum gate under consideration. We find arbitrarily high fidelity for the coherent time evolution of the two-atom state even at non-zero temperature.
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.
Hybrid quantum systems combining neutral atoms and trapped ions offer the prospect of integrating the scalability of atom arrays with the high-fidelity control available in trapped-ion platforms. Here we propose and analyze a quantum interface between individually trapped neutral atoms and a trapped-ion crystal. In our scheme, a neutral 88Sr atom trapped in optical tweezers interacts with a small 88Sr+ ion crystal, and by exciting the atom to a Rydberg state, the atom-ion polarization interaction is strongly enhanced, resulting in a state-dependent modification of the ions' collective motional modes. We show that this shift enables conditional control of a MS gate, allowing the neutral atom to act as a control qubit for an entangling operation between two ions. We investigate the feasibility of the scheme by analyzing Rydberg trapping in the combined optical tweezers and Paul trap potentials, identifying negative-polarizability Rydberg states as particularly favorable for stable confinement. We further evaluate the relevant trapping conditions, Rydberg lifetimes, and coherence requirements, and show that the proposed interface is compatible with realistic experimental parameters. These results establish a practical route toward deterministic atom-ion hybrid quantum gates and quantum interfaces.