Beyond-Ten-Hour Coherence in a Decoherence-Free Trapped-Ion Clock Qubit

Abstract

Quantum systems promise to revolutionize information processing science and technology [1-3]. The preservation of quantum coherence, the defining property of qubits, fundamentally constrains the performance of quantum information processing with quantum memories [4]. While trapped atomic ions theoretically support million-year coherence based on spontaneous emission [5-7], experimental demonstrations have reached far less, only about an hour [8-13]. Here we combine clock-state qubits with decoherence-free subspace (DFS) encoding to achieve coherence exceeding ten hours. Using correlation-based phase tracking in 171Yb+ ion pairs sympathetically cooled by 138Ba+ ion, we demonstrate this without magnetic shielding or enhanced microwave phase stabilization that previously limited coherence times. DFS encoding references the qubit phase to the inter-ion energy difference to reject microwave phase noise and common-mode magnetic fluctuations, while clock states provide environmental insensitivity. Throughout measurements extended to 1600 seconds, we observe minimal coherence decay, with exponential fits yielding a coherence time of (3.77 +/- 1.09) x 10^4 seconds. Our results establish DFS encoding as a form of passive error correction that eliminates technical noise constraints, unlocking the million-year coherence potential of atomic ions for scalable quantum information processing.

Figures (9)

• Figure 1: Extending Coherence Time of a $^{171}\text{Yb}^{+}$ DFS Qubit via $^{138}\text{Ba}^{+}$ Sympathetic Cooling. (a) Energy level diagrams for the $^{171}\text{Yb}^{+}$ qubit ion and the $^{138}\text{Ba}^{+}$ coolant ion. The $^{171}\text{Yb}^{+}$ qubit is encoded in the hyperfine clock transition of the ground state ($F=0 \leftrightarrow F=1$) with a splitting of $12.64\,\text{GHz}$. The $^{138}\text{Ba}^{+}$ ion is used for sympathetic cooling via the visible transitions shown (corresponding to $493\,\text{nm}$ and $650\,\text{nm}$). The central schematic depicts the linear Paul trap confining a mixed-species ion chain (Yb-Ba-Yb) subjected to a quantizing magnetic field of $B = 4.1\,\text{G}$. (b) Logical qubit encoding. The logical qubit $\{\ket{\textbf{0}}_{\rm L}, \ket{\textbf{1}}_{\rm L}\}$ is encoded in the decoherence-free subspace (DFS) spanned by the states $\{\ket{0}\ket{1}, \ket{1}\ket{0}\}$, providing robustness against collective magnetic noise. The general state $\Psi_{\varphi}$ is visualized on a logical Bloch sphere. (c) Pulse sequence for the coherence time measurement. After initialization and a rotation $R_{0}{\left(\frac{\pi}{2}\right)}$, a dynamical decoupling sequence with total duration of $\rm T$, composed of reverse style spin-echo blocks ($R_0(\pi), R_\pi(\pi)$) with waiting time $\tau$, is applied to the two $^{171}\text{Yb}^+$ qubits to measure the coherence of the logical state. After single ion decoherence, $\rho_{p}$ (Eq. \ref{['eq:DFS']}) is prepared. Throughout the whole sequence, continuous Doppler cooling is applied to the $^{138}\text{Ba}^{+}$ ion (sympathetic cooling) to suppress thermal motion.
• Figure 2: Coherence time of DFS qubit.(Top) Long-term evolution of the Ramsey parity contrast extended up to $1600\,\text{s}$. The parity contrast (blue circles) representing the DFS qubit coherence, remains stable near its maximum value of 0.5(dashed blue line). A fit(solid blue line) to the full dataset yields a coherence time of $\rm (3.77 \pm 1.09)\times 10^{4}~\mathrm{s}$. The Ramsey contrasts of individual ions (red and green circles)vanish effectively to zero, indicating complete decoherence of the physical qubits (mean values of $-0.029 \pm 0.032$ and $-0.019 \pm 0.032$). (Bottom) Zoomed-in view of the first 12s, indicated by the purple shaded region of top figure. The panel shows the rapid decoherence of physical qubits, with coherence times of $\rm T_{Ion1} = 8.10 \pm 0.27$ s and $\rm T_{Ion2} = 8.09 \pm 0.27$ s by gaussian decay fit(solid red and green lines). Beyond this decoherence timescale, the state $\rho_p$(Eq. \ref{['eq:DFS']}) is effectively prepared.
• Figure 3: Lifetime measurement of the computational basis states. The average parity contrast of the $\ket{0}\ket{0}$ state and $\ket{1}\ket{1}$ state are monitored over time up to 1600s(blue circles). The data show no statistically significant decay, where exponential fits(solid blue line) yield lower bounds on the lifetimes of $\rm T_1 = (1.01 \pm 0.71)\times 10^5$ s. Contrast of individual qubits $\sigma_z$ are shown in red and green circles.
• Figure 4: Investigation of coherence limiting mechanisms.(a) Simulated coherence limits under varying ion hopping rates and magnetic field gradients, where the gradient intensity is parameterized by the DFS clock qubit phase evolution period $T_{\varphi}$. The black circles represents unoptimized conditions ($T_{\varphi}=1.8s,\gamma_{\rm hop}=6\times 10^{-4}$ Hz). While direct hopping rate suppression ($10^{-5}$ Hz, blue squares) yields optimal stability, suppressing the magnetic field gradient (increasing $T_{\varphi}$ to 1250s, green triangles) also substantially extends coherence, offering an effective alternative. Conversely, increasing spin-echo pulse density ($\tau=2s$, orange; $\tau=0.4s$, red) proves inefficient. (b) Experimental DFS Zeeman qubit decay. With an acquisition time far shorter than the hopping timescale, this measurement representing the coherence limit where hopping is negligible. The fitting result $\rm T_{\text{Zeeman}} = 145 \pm 14$ s (blue line) allows projection of the magnetic-field-limited Clock coherence. Individual qubit means: $\braket{\sigma_{z1}} = -0.010\pm0.022$, $\braket{\sigma_{z2}} = -0.006\pm0.022$.
• Figure 5: Characterization of the suppressed magnetic field gradient via Zeeman DFS oscillations. While an ideal zero-gradient environment would yield no oscillation, the long periods observed here demonstrate a highly homogeneous field achieved via active compensation. (a) A representative lower bound for the oscillation period ($T_{\varphi}^{Zeeman} = 1.68 \pm 0.05$ s) observed under typical compensated conditions. (b) An attained upper bound showing a period of $T_{\varphi}^{Zeeman} = 13 \pm 1$ s. Compared to the uncompensated period of $\approx 3$ ms, these results represent an improvement of over three orders of magnitude.