Hybrid qubit-oscillator module with motional states of two trapped interacting atoms

TL;DR

This work proposes a hybrid qubit–oscillator module built from the motional degrees of two interacting neutral atoms trapped in a stroboscopically engineered optical tweezer. The center‑of‑mass motion provides a bosonic oscillator while the relative motion encodes a two‑level qubit via anharmonicity induced by contact interactions, avoiding internal states to gain robustness against spin noise. A universal bosonic gate set is realized by temporally modulating the trap: displacement, rotation, and squeezing gates, along with their qubit‑conditioned counterparts CD, CR, CS; full simulations show gate fidelities above 99% for most operations across realistic parameters, with D/CD requiring up to five flashing positions. The scheme scales to arrays through dipolar or Rydberg‑dressed couplings, offering a platform for quantum computing with bosonic modes, quantum metrology, and spin–boson simulations while leveraging purely motional degrees of freedom.

Abstract

We propose the use of motional states of two interacting atoms trapped in a potential stroboscopically engineered by an optical tweezer as a means to implement a qubit-oscillator system, in analogy to those implemented in circuit quantum electrodynamics and trapped ions. In our setting, the center of mass degree of freedom of the atoms plays the role of a photon or phonon mode, while the interacting, relative mode acts as a qubit. No internal state is involved in our system, which makes this motional qubit robust to spin-dependent noise. We show that a universal set of bosonic operations, including displacement, rotation, squeezing, and the corresponding set of gates controlled by the qubit, can be implemented through precise temporal modulation of the optical tweezers. We numerically check that these gates can be generated with high fidelity, and discuss possible schemes for initial state preparation and final state readout. While we restrict the discussion to a single qubit-oscillator module, scalability can be achieved by coupling arrays of atoms via dipolar or Rydberg-dressed interactions.

Figures (4)

• Figure 1: Hybrid qubit--oscillator module from the motion of two atoms in a stroboscopically engineered optical tweezer. Rapid switching among $j_{\max}$ dimensionless beam positions $\{\zeta_j\}$ with depths $\{U_j(t)\}$ produces a highly harmonic time-averaged trap. The qubit $\{\ket{\uparrow},\ket{\downarrow}\}$ resides in the two lowest relative-motional states, energetically isolated by the nonlinearity generated via the contact interaction $\propto u$, while a bosonic mode $\{\ket{0},\ket{1},\cdots\}$ is encoded in the center-of-mass coordinate $R_x$.
• Figure 2: Implementing controlled displacement (CD) and controlled squeezing (CS) gates. (a) Starting from $\ket{\uparrow}\ket{0}$, a controlled-displacement operation $\mathrm{CD}=\exp[(\alpha \hat{a}^\dagger - \alpha^*\hat{a})\hat{\sigma}_x]$ generates the superposition $\tfrac{1}{\sqrt{2}}(\ket{+}\ket{\alpha}+\ket{-}\ket{-\alpha})$, equivalent to a Schrödinger-cat state in the oscillator conditioned on the qubit. This gate is implemented by modulating the $x^3$ term at frequencies $\tilde{\omega}\pm\omega_x$. (b) A controlled-squeezing operation $\mathrm{CS}=\exp[\tfrac{1}{2}(\xi^*\hat{a}^2-\xi\hat{a}^{\dagger 2})\hat{\sigma}_x]$, producing superpositions of squeezed states, is realized by modulating the $x^4$ term at $2\omega_x\pm\tilde{\omega}$.
• Figure 3: A list of native gates: displacement (D), rotation (R), spin rotation (SR), squeezing (S), controlled displacement (CD), controlled rotation (CR), and controlled squeezing (CS). Left: Gate infidelities for {D, S, CD, CS} evaluated from the initial ground state $\ket{\uparrow}\ket{0}$ using representative parameters ($|\alpha|=3$, $|\xi|=1$), and for {R, SR, CR} from the displaced state $\ket{\uparrow}\ket{\alpha{=}1}$ with rotation angle $\gamma=\pi/2$; see supp for details. Right: Numerical gate fidelities for {D, S, CD, CS}. Gates {D, CD} use $j_{\max}=5$, while {S, CS} use $j_{\max}=3$. Each point corresponds to the maximal fidelity optimized over modulation strengths $\lambda$. Inset: optimum values of $\lambda$ used. The dotted lines mark the upper limits for {D, CD}, beyond which a trap depth becomes negative and thus nonphysical.
• Figure S1: Infidelities of (a) Rotation, (b) Spin Rotation, and (c) Controlled Rotation gates with higher-order corrections (solid lines). We use the initial state $\ket{\uparrow}\ket{\alpha}$, where $\ket{\alpha}$ is a displaced coherent state in the COM coordinate. From dark to bright (or bottom to top) lines, we use (a) $\alpha=3,6,9,12$, (b) $\alpha=0,3,6,9,12$, and (c) $\alpha=1.5,3,4.5,6$. The dashed line in panel (b) is the infidelity for $\alpha=6$, without accounting for higher-order corrections.