Ran He

Hybrid quantum networks offer a promising architecture for scalable quantum information processing and a future quantum internet, as they can combine the complementary strengths of disparate physical platforms. While single-atom systems provide deterministic quantum logic gates, atomic ensembles enable large-capacity quantum storage. However, generating entanglement between such heterogeneous systems has remained an open challenge, primarily due to fundamental spectral mismatches and system complexity. Here, we demonstrate a hybrid quantum network that entangles a single trapped $\mathrm{^{171}Yb^{+}}$ ion and a quantum memory based on $\rm ^{153}Eu^{3+}\colon\!Y_2SiO_5$ crystal over a 75-m separation. Using polarization-maintaining quantum frequency conversion, we map spin-photon entanglement onto a hybrid entanglement between a single spin qubit and a collective excitation of the quantum memory. The resulting entangled state achieves a fidelity of $(89.21 \pm 2.23)\%$ and violates the CHSH-Bell inequality by 6 standard deviations ($S = 2.328 \pm 0.055$), confirming nonlocality between two heterogeneous nodes. This work establishes entanglement between a quantum processing module with a multiplexed quantum memory node, representing a key step toward a scalable, multifunctional quantum internet.

The construction of entangling gates with individual addressing capability represents a crucial approach for implementing quantum computation in trapped ion crystals. Conventional entangling gate schemes typically rely on laser beam wave vectors to couple the ions' spin and motional degrees of freedom. Here, we experimentally demonstrate an alternative method that employs a polarization gradient field generated by a tightly focused laser beam, previously proposed as a Magnus-type quantum logic gate. Using this technique, we perform Raman operations on nuclear spin qubits encoded in 171Yb+ ions, generating spin-dependent forces along axial motional modes in a linear trap. By utilizing an acousto-optic deflector to create arbitrary spot pairs for individual ion addressing in two-ion (four-ion) chains, we achieve MS gates with fidelities exceeding 98.5% (97.2%). Further improvements in numerical aperture and laser power could reduce gate durations while enhancing fidelity. This method is compatible with, and can significantly simplify, optical tweezer gate proposals, where motional mode engineering enables scalable trapped-ion quantum computation. The technique can be extended to two-dimensional ion crystals, representing a key step toward large-scale trapped-ion quantum processors.

Large-scale programmable trapped ion hardware, featuring high gate fidelity and long coherence times, is promising for realizing a practical fault-tolerant quantum computer (FTQC). However, individual addressing (IA) methods, which are important for implementing programmable gates in near-term quantum devices, can lead to undesired errors between the target ions and neighboring ions. In this work, we present a low-crosstalk optical addressing system based on multiple optical objectives and acousto-optic deflectors (AODs) with a symmetrical configuration. Two counter-propagating Raman operation beams are both tightly focused, generating an overlapping spot with a waist radius of approximately $1~\upmu\mathrm{m}$, to address the target ion. As a result, IA crosstalk, characterized by Rabi rate crosstalk on the spectator ion, is measured to be $1.19(5)\times10^{-3}$, with the two ions separated by approximately 5.5~$\upmu\mathrm{m}$. This low-crosstalk optical addressing system holds promise for high-fidelity entangling operations, and the symmetrically-configured AODs in our method can be readily extended to two dimensions to address a two-dimensional ion crystal.

In cold atomic systems, fast and high-resolution microscopy of individual atoms is crucial, since it can provide direct information on the dynamics and correlations of the system. Here, we demonstrate nanosecond-scale two-dimensional stroboscopic pictures of a single trapped ion beyond the optical diffraction limit, by combining the main idea of ground-state depletion microscopy with quantum state transition control in cold atoms. We achieve a spatial resolution up to 175~nm using an NA = 0.1 objective in the experiment, which represents a more than tenfold improvement compared with direct fluorescence imaging. To show the potential of this method, we apply it to observe the secular motion of the trapped ion, we demonstrate a temporal resolution up to 50~ns with a displacement detection sensitivity of 10~nm. Our method provides a powerful tool for probing particle positions, momenta, and correlations, as well as their dynamics in cold atomic systems.

The non-trivial zeros of the Riemann zeta function are central objects in number theory. In particular, they enable one to reproduce the prime numbers. They have also attracted the attention of physicists working in Random Matrix Theory and Quantum Chaos for decades. Here we present an experimental observation of the lowest non-trivial Riemann zeros by using a trapped ion qubit in a Paul trap, periodically driven with microwave fields. The waveform of the driving is engineered such that the dynamics of the ion is frozen when the driving parameters coincide with a zero of the real component of the zeta function. Scanning over the driving amplitude thus enables the locations of the Riemann zeros to be measured experimentally to a high degree of accuracy, providing a physical embodiment of these fascinating mathematical objects in the quantum realm.

For circuit-based quantum computation, experimental implementation of universal set of quantum logic gates with high-fidelity and strong robustness is essential and central. Quantum gates induced by geometric phases, which depend only on global properties of the evolution paths, have built-in noise-resilience features. Here, we propose and experimentally demonstrate nonadiabatic holonomic single-qubit quantum gates on two dark paths in a trapped $^{171}\mathrm{Yb}^{+}$ ion based on four-level systems with resonant drives. We confirm the implementation with measured gate fidelity through both quantum process tomography and randomized benchmarking methods. Meanwhile, we find that nontrivial holonomic two-qubit quantum gates can also be realized within current experimental technologies. Compared with previous implementations on three-level systems, our experiment share both the advantage of fast nonadiabatic evolution and the merit of robustness against systematic errors, and thus retains the main advantage of geometric phases. Therefore, our experiment confirms a promising method for fast and robust holonomic quantum computation.

Kibble-Zurek mechanism (KZM) is a universal framework which could in principle describe phase transition phenomenon in any system with required symmetry properties. However, a conflicting observation termed anti-KZ behavior has been reported in the study of ferroelectric phase transition, in which slower driving results in more topological defects [S. M. Griffin, et al. Phys. Rev. X. 2, 041022 (2012)]. Although this research is significant, its experimental simulations have been scarce until now. In this work, we experimentally demonstrate anti-KZ behavior under noisy control field in three kinds of quantum phase transition protocols using a single trapped Yb ion. The density of defects is studied as a function of the quench time and the noise intensity. We experimentally verify that the optimal quench time to minimize excitation scales as a universal power law of the noise intensity. Our research sets a stage for quantum simulation of such anti-KZ behavior in two-level systems and reveals the limitations of the adiabatic protocols such as quantum annealing.

Quantum computation with quantum gates induced by geometric phases is regarded as a promising strategy in fault tolerant quantum computation, due to its robustness against operational noises. However, because of the parametric restriction of previous schemes, the main robust advantage of holonomic quantum gates is smeared. Here, we experimentally demonstrate a solution scheme, demonstrating nonadiabatic holonomic single qubit quantum gates with optimal control in a trapped Yb ion based on three level systems with resonant drives, which also hold the advantages of fast evolution and convenient implementation. Compared with corresponding previous geometric gates and conventional dynamic gates, the superiority of our scheme is that it is more robust against control amplitude errors, which is confirmed by the measured gate infidelity through both quantum process tomography and random benchmarking methods. In addition, we also outline that nontrivial two qubit holonomic gates can also be realized within current experimental technologies. Therefore, our experiment validates the feasibility for this robust and fast holonomic quantum computation strategy.