High-fidelity quantum state control of a polar molecular ion in a cryogenic environment

TL;DR

This work demonstrates high-fidelity quantum state control of a polar molecular ion CaH+ using quantum-logic spectroscopy in a cryogenic environment, where reduced thermal radiation extends rotational lifetimes by about an order of magnitude. By adaptively probing the molecule and reading out through a co-trapped Ca+ logic ion, the authors achieve SPAM infidelity below $6\times10^{-3}$ and observe Rabi flopping with over $99\%$ contrast between states, all without molecule-specific lasers and with non-destructive detection. The rotational lifetimes for $J=1$ and $J=2$ reach $18\pm2$ s and $10\pm1$ s, enabling longer coherence and more reliable state preparation, while the technique remains broadly applicable to other molecular ions. This cryogenic, molecule-agnostic QLS protocol paves the way for high-precision measurements, molecular quantum information processing, and controlled chemistry in a pristine quantum regime, with plans to extend to additional species and deterministic state control.

Abstract

We use a quantum-logic spectroscopy (QLS) protocol to control the quantum state of a CaH+ ion in a cryogenic environment, in which reduced thermal radiation extends rotational state lifetimes by an order of magnitude over those at room temperature. By repeatedly and adaptively probing the molecule, detecting the outcome of each probe via an atomic ion, and using a Bayesian update scheme to quantify confidence in the molecular state, we demonstrate state preparation and measurement (SPAM) in a single quantum state with infidelity less than 6x10^-3 and measure Rabi flopping between two states with greater than 99% contrast. The protocol does not require any molecule-specific lasers and the detection scheme is non-destructive.

Figures (7)

• Figure 1: (a) Schematic of the two-ion crystal, static magnetic field (quantization axis, 0.4 mT), and laser beam geometry. Molecular Raman transitions are driven by two 1064 nm beams. Doppler and sideband laser cooling of the two-ion crystal is performed on the atomic ion. (b) CaH+ level structure. The molecule primarily occupies the $J=0-2$ rotational manifolds and, in equilibrium, is spread over all associated spin-rotational Zeeman sublevels. While the molecular state is unknown, Raman and microwave transitions are used to pump the molecule to $|\textsl{i}_J\rangle$, $J\in\{1,2,3\}$. High-fidelity preparation (in $|\textsl{i}_J\rangle$) and measurement is accomplished by probing back and forth with motion-adding sidebands on the signature transition, $|\textsl{i}_J\rangle\leftrightarrow|\textsl{ii}_J\rangle$, and evaluating the result of each probe via a QLS protocol. A Raman shelving pulse that drives transitions between the prepared state ($|\textsl{i}_1\rangle$) and an auxiliary level ($\ket{1, -1/2, +}$) may be introduced between preparation and measurement.
• Figure 2: Results of SPAM infidelity characterization vs confidence threshold $C_T$ for the $J=1$ (blue triangles) and $J=2$ (red squares) signature manifolds. Infidelities are calculated by observing the fraction of measurement sequences that determine the molecule to be out of the prepared manifold immediately after preparation. Post-selected infidelity omits measurements that are followed by preparation in a different rotational level. Error bars denote one Wilson interval. For $C_T \lesssim 0.997$, infidelity tracks $1-C_T$ (black dashed line). Lifetime-limited infidelity (blue (red) dashed curves for $J=1(2)$) is calculated by dividing the observed average measurement sequence duration by the observed average lifetime for each data point; the uncertainties, indicated by the shaded backgrounds, are chiefly due to uncertainties in the experimentally-determined lifetimes. As $C_T$ approaches 1, more and more probes are needed for measurement, increasing the likelihood of population loss during measurement. For comparison, we also provide the expected limit in a room-temperature environment (dot-dashed lines) based on theoretical lifetimes.
• Figure 3: Rabi flopping on $\ket{\textsl{i}_1} \leftrightarrow\ket{1,-1/2,+}$ by a pulse of variable duration that is resonant with the transition and applied between preparation and measurement. The fit is to an exponentially-decaying sinusoidal function.After a $\pi$-pulse (620 $\mu$s duration), the molecule is measured in manifold with probability $(5.6\pm1.2)\times10^{-3}$. Error bars denote one Wilson interval.
• Figure 4: Full experimental sequence, including Bayesian state preparation and detection. Here, $J_g$ and $\ket{m_g}$ are the system's current determined molecular rotational and signature manifold state, respectively: they are initialized to $J_g=1$ and $\ket{m_g}=\ket{\textsl{i}_J}$. Grey boxes represent sub-protocols expanded elsewhere in the flowchart, dark blue boxes indicate physical actions performed on the ions, green boxes indicate software logic updates, and light blue ovals indicate the endpoint of a subprotocol. The experimental sequence is performed (with occasional breaks for ion order check and servo experiments) until the desired amount of data has been collected.
• Figure 5: Comparison of infidelity mechanism contributions vs $C_T$. At low $C_T$, most errors are attributable to the sub-unity threshold, while at high $C_T$, TR-induced loss dominates.