An ancient and counterintuitive phenomenon known as the Mpemba effect (water can cool faster when initially heated up) showcases the critical role of initial conditions in relaxation processes. How to realize and utilize this effect for speeding up relaxation is an important but challenging task in purely quantum system till now. Here, we experimentally study the strong Mpemba effect in a single trapped ion system in which an exponentially accelerated relaxation in time is observed by preparing an optimal quantum initial state with no excitation of the slowest decaying mode. Also, we demonstrate that the condition of realizing such effect coincides with the Liouvillian exceptional point, featuring the coalescence of both the eigenvalues and the eigenmodes of the systems. Our work provides an efficient strategy to engineer the dynamics of open quantum system, and suggests a link unexplored yet between the Mpemba effect and the non-Hermitian physics.

Parity-time ($\mathcal{PT}$)-symmetric systems, featuring real eigenvalues despite their non-Hermitian nature, undergo spontaneous $\mathcal{PT}$ symmetry breaking at the exceptional point (EP). The phase transition from $\mathcal{PT}$ symmetry to $\mathcal{PT}$ symmetry breaking has shown exotic functionalities in the classical realm, such as loss-induced transparency or lasing revival. This transition is also expected to produce a more unconventional effect in pure quantum $\mathcal{PT}$ devices. Here, we report experimental evidences of spontaneous $\mathcal{PT}$ symmetry breaking in a single cold ${}^{40}\mathrm{Ca}^{+}$ ion and, more importantly, a counterintuitive effect of perfect quantum coherence occurring at the EP. Excellent agreement between experimental results and theoretical predictions is identified. In view of the versatile role of cold ions in building a quantum memory or processor, our experiment provides an alternative platform to explore $\mathcal{PT}$-symmetric physics and utilize pure quantum EP effects.

We theoretically propose and experimentally demonstrate a parallel electromagnetically induced transparency (parallel EIT) cooling technique for ion crystals in the Paul trap. It breaks the stringent cooling requirements of the standard EIT cooling, thus allowing, in principle, to simultaneously cool the motional mode spectrum with an arbitrary range. Experimentally a large cooling range over 5 MHz is proved by using a single trapped ${}^{40}{\mathrm{Ca}}^{+}$ ion. We also observe simultaneous near-ground-state cooling for all motional modes of a 4-ion chain with the best average phonon number of about 0.2. For cooling a large number of modes, we only need to modulate the probe beam of the standard EIT cooling with several rf frequencies. This cooling scheme has no selectivity for the types of ions (e.g., ${}^{171}{\mathrm{Yb}}^{+}$, ${}^{40}{\mathrm{Ca}}^{+}$), therefore it would be a powerful tool for initialization of all kinds of operational trapped-ion quantum computers or simulators.

Self-testing allows one to characterise quantum systems under minimal assumptions. However, existing schemes rely on quantum nonlocality and cannot be applied to systems that are not entangled. Here, we introduce a robust method that achieves self-testing of individual systems by taking advantage of contextuality. The scheme is based on the simplest contextuality witness for the simplest contextual quantum system—the Klyachko-Can-Binicioğlu-Shumovsky inequality for the qutrit. We establish a lower bound on the fidelity of the state and the measurements as a function of the value of the witness under a pragmatic assumption on the measurements. We apply the method in an experiment on a single trapped⁴⁰Ca⁺using randomly chosen measurements and perfect detection efficiency. Using the observed statistics, we obtain an experimental demonstration of self-testing of a single quantum system.

Leggett-Garg inequality (LGI) is used to detect whether the macroscopic superposition state exists. Classical systems obey the LGI, but quantum systems may violate it. In the multilevel system, different state update rules determine different upper bounds of LGI. In this work, we experimentally test the LGI in a three-level trapped-ion system under the Lüders and the von Neumann state update rules, respectively. The maximum observed value of the Leggett-Garg correlator under the von Neumann state update rule is $K_3=1.739\pm 0.014$, which demonstrates a violation of the Lüders bound by 17 standard deviations and is by far the most significant violation under the specific model. The method used in our experiment could also be used in other multilevel experiments in the trapped-ion system.