Ion-atom two-qubit quantum gate based on phonon blockade

Abstract

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. In this paper, we demonstrate the universal two-qubit CNOT gate with high fidelity 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. 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.

Figures (4)

• Figure 1: A schematic of control-NOT gate using phonon blockade: A single atomic qubit (the left level diagram) is placed at a small separation from an ionic qubit (the right level diagram). The atom is assumed to be trapped in an optical tweezer which is positioned near the ion in a Paul trap. Two hyperfine levels in the ground state manifold constitute the two atomic qubit states $|0\rangle$ and $|1\rangle$. The ionic qubit may be composed of two ground-state hyperfine levels or one ground-state hyperfine level and one metastable excited level. The tweezer is considered to be collinear with the $x$-axis of the Paul trap. Here controlled NOT gate is realized via phonon blockade through controllable ion-atom interaction. When the atomic qubit state $|0\rangle$ is coupled to the Rydberg state $|r\rangle$ by a two-photon process via the intermediate state $\mid e \rangle$, the ion-atom interaction is enhanced by many orders of magnitude. Ion's qubit states are coupled to its phonon states by a two-photon laser coupling, with $\omega_{L_1}$ and $\omega_{L_2}$ being the frequencies of the two lasers. First, a two-photon $\pi$ pulse acts on the control (atom), then a $\pi$ rotation is given to the target (ion), lastly another $\pi$ pulse is applied on the control. By this pulse sequence, a controlled NOT gate is realized (see text).
• Figure 2: The shifted phonon frequency (in MHz) (a) and the shifted equilibrium position (in $\mu$m)(b) are plotted as a function of ion-atom distance $x_0$ (in $\mu$m) for $^{87}$Rb+$^{9}$Be$^{+}$ system, when the atom is excited to the Rydberg state with principal quantum number $n=90$. The ion's unperturbed trapping frequency (dashed line) is $2\pi \times 11.2$ MHz.
• Figure 3: The real and imaginary parts of the amplitude of different states $|\rm{a}, \rm{i ph}\rangle$ are plotted as a function of dimensionless time.
• Figure 4: Fidelity is plotted as a function of the atomic Rabi frequency $\Omega_{a}$ in GHz.