Simultaneous nondestructive measurement of many polar molecules using Rydberg atoms

Abstract

Tweezer arrays of polar molecules present new opportunities for quantum science and quantum information. However, a major challenge, especially in bialkali molecule platforms, is the fact that current measurement schemes for the internal states are destructive. In this work, we present a method to use Rydberg atoms to nondestructively measure the internal state of a molecular qubit. We achieve this via microwave dressing of both molecules and Rydberg atoms, allowing us to tune the interactions so that there are minimal Rydberg-Rydberg interactions and many measurements can take place simultaneously. We consider two experimentally-motivated examples of detecting $^{23}$Na$^{133}$Cs and $^{87}$Rb$^{133}$Cs with $^{133}$Cs atoms. Finally, we discuss several strategies for mitigating various sources of crosstalk.

Figures (5)

• Figure 1: (a) Each molecule (left) is paired with a nearby atom (right) with interaction $V_{\text{am}}$, entangling each pair. The internal molecular state $\alpha |+\rangle + \beta |-\rangle$ is then measured by measuring the internal state of the entangled atom. (b) Example of dressing scheme. The molecules are dressed resonantly with circular polarization, producing eigenstates $|\pm\rangle \equiv (|N,m_N\rangle \pm |N',m_N'\rangle)/\sqrt{2}$, where $N,m_N$ are the quantum numbers for the molecules rotational angular momentum and its $z$-projection and $m_N' = m_N+1$ in this example. The molecular drive also couples the Rydberg states $|r\rangle, |r_\sigma\rangle$ of the atom, which is subject to an additional drive with linear polarization that couples $|r\rangle$ and $|r_\pi\rangle$. With proper choice of the drives, the $|a\rangle$ eigenstate does not interact with itself but interacts with the molecule.
• Figure 2: Schematic of nondestructive measurement scheme. (a) Atomic pulse sequence used to entangle atom-molecule pairs via atom-molecule interaction $V_{\text{am}} \hat{Z}_\text{m} |a \rangle \langle a|$ for Rydberg state $|a\rangle$ and long-lived states $|g\rangle, |g'\rangle$, where the atoms are initialized in $|g\rangle$. (b) Effective quantum circuit for molecular ($|\psi_{\text{m}_i} \rangle$) and atomic ($|\psi_{\text{a}_i}\rangle$) wavefunction pairs realized via pulse sequence which is composed of Hadamard gates $\textsc{H}_{X/Y}$, controlled-Z gates CZ enabled by the interaction, and measurements. See text for additional details on steps (i)-(iv).
• Figure 3: Nullified vdW interactions for (a) NaCs and (b) RbCs Young2021Weber2017. We plot the overlap of the corresponding two-atom eigenstate $|\psi(r_{\text{aa}})\rangle$ with $|aa\rangle$ for (c) NaCs and (d) RbCs. The lines denote fits using the perturbative values of $C_6 = 0, P_6$ (see End Matter) with $C_9, C_{12}, P_{12}$ as fitting parameters. For NaCs, $(C_9,C_{12})/2\pi = (163GHz.µm^9,-105THz.µm^{12})$ and $(P_6,P_{12}) = ([2.06µm]^6$$,[3.49µm]^{12})$. For RbCs, $(C_9,C_{12})/2\pi$$~=~$$(4.8THz.µm^9,-12PHz.µm^{12})$ and $(P_6,P_{12}) = ([3µm]^6,[5.42µm]^{12})$.
• Figure 4: Spin-echo pulse sequence for reducing cross-talk. Only atom/molecules in same pulse class (A, B, C, ...) interact with one another, reducing unwanted crosstalk. In the above example, there are three classes.
• Figure 5: Perturbative vdW nullification for NaCs (left) and RbCs (right). Stars denote the parameters used in the main text. For NaCs (RbCs), the Hilbert space is truncated to $L\leq 3$, $60 (73) \leq n \leq 67 (80)$, and pair-state energies up to $2 \pi \times 16GHz$ ($2 \pi \times 9GHz$) away from the dressed-state energies.