🔬 atomic physics

Hybrid qubit-oscillator module from motional states of two interacting atoms

This paper proposes a high-fidelity hybrid qubit-oscillator platform using the motional states of two interacting atoms in an optical tweezer, which enables versatile bosonic operations and achieves sub-Hz resolution for detecting magnetic dipolar interactions within a tweezer array.

Original authors: Jaeyong Hwang, Tianrui Xu, Sean R. Muleady, Steven K. Pampel, Gur Lubin, Dawson P. Hewatt, Cindy A. Regal, Ana Maria Rey

Published 2026-07-21

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CC BY 4.0

Original authors: Jaeyong Hwang, Tianrui Xu, Sean R. Muleady, Steven K. Pampel, Gur Lubin, Dawson P. Hewatt, Cindy A. Regal, Ana Maria Rey

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a world where the tiniest building blocks of matter, atoms, don't just sit still like marbles on a table. Instead, they are like dancers on a stage, capable of vibrating, spinning, and jumping between different energy levels. For decades, scientists have been trying to control these atomic dancers to build powerful quantum computers and ultra-sensitive sensors. Usually, they focus on the atoms' "internal" states—like their spin or magnetic orientation—treating their physical movement as a nuisance that causes errors. However, a new idea is taking hold: what if we stop fighting the movement and start using it? What if the way atoms jiggle and bounce could actually be the key to storing information and measuring the universe with incredible precision? This is the frontier of "motional quantum control," where the physical dance of atoms becomes the language of computation and sensing.

In this spirit, a team of researchers has proposed a clever new way to turn two interacting atoms into a hybrid machine that acts like both a digital bit and a mechanical oscillator. Think of two atoms trapped inside a tiny, invisible bottle made of laser light, known as an optical tweezer. Usually, scientists try to keep these atoms perfectly still. But here, the researchers suggest shaking the bottle in a very specific, rhythmic pattern. By doing this, they can turn the atoms' physical motion into a versatile tool. One part of the motion acts like a standard computer bit (a "qubit") that can be in a state of 0 or 1, while the other part acts like a mechanical spring (an "oscillator") that can vibrate with different amplitudes. The magic happens because the atoms bump into each other; this tiny contact creates a non-linear effect that locks the qubit states in place, preventing them from leaking out of control.

The paper suggests that by modulating the laser trap, they can perform a full set of operations on this system. They can "displace" the oscillator (push it), "squeeze" it (change its shape), and even make the qubit control the oscillator's movement. In their simulations, these operations work with extremely high accuracy, often exceeding 99% fidelity. The researchers show that this setup isn't just a toy for quantum computing; it's a super-sensitive detector. They demonstrate that this hybrid system could measure incredibly weak magnetic interactions between the atoms with a sensitivity of about 10 Hz in just one second, and potentially reach sub-Hz resolution (less than one cycle per second) after a few minutes of averaging. This is achieved even when accounting for realistic experimental imperfections, like tiny fluctuations in the laser intensity.

The core of their proposal relies on a technique called "potential painting." Imagine a single laser beam that moves so fast between different positions that the atoms can't keep up; to the atoms, it looks like a single, smooth, custom-shaped trap. By rapidly flashing the laser between up to five different spots, the team can "paint" a potential landscape that is highly controllable. They use this to generate the necessary forces to manipulate the atoms' motion. The results, derived from detailed numerical simulations of the Schrödinger equation, indicate that this approach allows for the creation of a universal set of quantum gates. These gates can be used to transduce tiny interaction-induced phase shifts into measurable movements of the atoms' center of mass, effectively turning a microscopic quantum phase into a macroscopic signal that can be read out with high precision.

The implications of this work are broad. By establishing a platform where motional states are fully controlled, the researchers open the door to new types of quantum simulations and precision sensing. They specifically highlight the ability to detect weak magnetic dipole-dipole interactions, which are notoriously difficult to measure in individual atom pairs. This method could work for a wide variety of atoms, from weakly magnetic ones to strongly dipolar species, without needing complex spin dynamics. While the current work is a theoretical proposal supported by simulations, it outlines a clear path for experimental realization. If built, such a system could serve as a versatile module for quantum information processing and a powerful tool for exploring the fundamental forces between individual particles, all while keeping the atoms dancing in perfect step.

Technical Summary: Hybrid Qubit-Oscillator Module from Motional States of Two Interacting Atoms

Problem Statement
Trapped neutral-atom systems have traditionally utilized internal atomic levels as qubits, with motional degrees of freedom (d.o.f.) often treated as a source of decoherence limiting gate fidelity. While recent advances have enabled control over motional states for single atoms and specific multi-atom states (e.g., Laughlin states), achieving full, universal control over both internal and motional d.o.f. for a single neutral atom remains challenging due to competing decoherence mechanisms like differential light shifts and sideband heating. Furthermore, detecting weak magnetic dipolar interactions in ultracold atoms is difficult, as traditional methods (dipolar relaxation, spin dynamics) are often insufficient for weakly magnetic species, and bulk magnetic resonance techniques lack single-pair resolution.

Methodology
The authors propose a hybrid qubit-oscillator platform encoded entirely in the motional states of two bosonic atoms confined within a single, stroboscopically engineered optical tweezer.

System Encoding:
- Oscillator: Encoded in the center-of-mass (COM) mode ( $R_x$ ), behaving as a harmonic oscillator.
- Qubit: Encoded in the two lowest relative motional states ( $r_x$ ). The nonlinearity required to isolate these states arises from the intrinsic contact interaction between the atoms. This interaction shifts the energy spectrum, creating an anharmonicity that separates the $|0\rangle$ and $|2\rangle$ relative states (denoted as $|\uparrow\rangle$ and $|\downarrow\rangle$ ) from higher excitations.
- Hamiltonian: The system is described by a qubit-oscillator Hamiltonian where the qubit transition energy is determined by the contact interaction strength $u$ .
Control Mechanism (Potential Painting):
- The authors utilize a "painted" potential technique, where a laser beam is rapidly flashed between $j_{max}$ different positions with tunable trap depths. This stroboscopic modulation creates a time-averaged, highly harmonic 1D effective potential with tunable anharmonicity.
- By modulating the trap depths at specific frequencies, the authors engineer time-dependent terms in the Hamiltonian.
- Gate Generation:
  - Native Gates: Displacement ( $D$ ), Rotation ( $R$ ), Qubit Rotation ($QR$), and Squeezing ( $S$ ) are generated by modulating specific orders of the potential (e.g., linear terms for displacement, quadratic terms for rotation/squeezing).
  - Hybrid Gates: Controlled-Displacement ($CD$), Controlled-Rotation ($CR$), and Controlled-Squeezing ($CS$) are realized by simultaneously modulating higher-order potential terms (e.g., cubic or quartic) with frequencies that couple the COM and relative modes. For instance, modulating the $x^3$ term with frequencies $\tilde{\omega} \pm \omega_x$ generates a $CD$ gate.
Simulation and Fidelity:
- The performance of these gates is evaluated via full numerical evolution of the time-dependent Schrödinger equation, including 3D effects and higher-order potential terms.
- Simulations use parameters relevant to $^{87}\text{Rb}$ atoms (trap depth $V_0 \sim 1$ mK, beam waist $W=700$ nm).
- Gate infidelities are optimized by tuning the modulation strength $\lambda$ to minimize leakage and higher-order contributions.

Key Results

Universal Gate Set: The proposed platform supports a complete set of native bosonic gates and their qubit-controlled counterparts.
- In noiseless simulations, native gates ($D, S, R, QR$) achieve fidelities $>99\%$ over a wide parameter range.
- Hybrid gates ($CD, CR, CS$) also achieve high fidelities ( $>99\%$ for $CD$ with moderate displacement, $>99\%$ for $CS$), though $CD$ fidelity decreases for large displacements ( $|\alpha| > 2$ ) in the minimal setting ( $j_{max}=5$ ).
- Gate times range from $\sim 1\text{--}10$ $\mu$ s for displacement to $\sim 1\text{--}10$ ms for controlled operations.
Sensing Application: The authors demonstrate a protocol for detecting weak magnetic dipole-dipole interactions.
- Protocol: The interaction induces a frequency shift $\nu$ between qubit states. This phase is accumulated during a dark time $t_d$ and then coherently mapped to the COM oscillator displacement using a $CD$ gate.
- Enhancement: The signal is amplified by placing the $CD$ gate between squeezing and unsqueezing operations, utilizing the squeezed state as a metrological resource.
- Performance: Under realistic experimental imperfections (modeled as 0.2% intensity noise in trap parameters), the protocol achieves a sensitivity of $\sim 10$ Hz in one second. With averaging over a few minutes in a $20 \times 20$ tweezer array, sub-Hz resolution is projected.
- The interaction strength $\nu$ depends on the magnetic field orientation, varying from 0 to $\sim 2\pi \times 119$ Hz for $^{87}\text{Rb}$ in a 1 mK trap.

Significance and Claims
The paper claims to establish a versatile platform for the motional quantum control of two atoms, leveraging intrinsic contact interactions to encode a hybrid qubit-oscillator system without relying on internal atomic states.

Versatility: The approach is species-independent regarding spin dynamics, relying instead on motional control and interaction-induced frequency shifts, making it applicable from weakly magnetic alkali atoms to strongly dipolar species.
Precision Sensing: It enables interaction-resolved spectroscopy of weak dipolar couplings with single-atom-pair resolution, overcoming the limitations of ensemble-averaged measurements.
Scalability: The architecture is compatible with reconfigurable optical tweezer arrays, allowing for parallel high-precision measurements.
Future Directions: The authors suggest that extending this framework to multiple motional modes or richer relative-coordinate manifolds could enhance sensitivity to anisotropic interactions and enable quantum simulation of molecular systems. They also note that non-classical encodings (e.g., cat states) could further improve robustness against decoherence.

The work is presented as a proposal and theoretical demonstration, with simulations validating the feasibility of high-fidelity gate operations and sensing protocols under realistic experimental constraints.

Technical Summary: Hybrid Qubit-Oscillator Module from Motional States of Two Interacting Atoms

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