A spin-mechanical quantum chip for exploring exotic interactions.

How to illuminate dark matter has become the foremost open question in fundamental science nowadays, which is of great significance in understanding the laws of nature. Exploring exotic interactions beyond the standard model is one of the essential approaches to searching for dark matter particles. Although it has been explored in a variety of lab-scale and tabletop-scale setups over the past years, no such interactions have been observed, and improving the sensitivity significantly becomes of paramount importance, but challenging. Here, we formulate the conception of a spin-mechanical quantum chip compatible with scalable on-chip detectors. Utilizing the prototype chip realized by the integration of a mechanical resonator and a diamond with single nitrogen vacancy at the microscale, the constraints of spin-velocity-dependent interactions have been improved by two orders of magnitude, where there is no evidence for new bosons in the force range below 100 nm, i.e., in the rest-mass window of 2-10 electronvolts. Based on the proof-of-principle experiment, this promising chip can be scaled up to meet the requirements of searching for exotic interactions at preeminent sensitivity. Low-cost and high-yield chip-scale setups will accelerate the process of dark matter exploration, providing a path toward on-chip fundamental physics experiments.

New Constraints on Exotic Spin-Spin-Velocity-Dependent Interactions with Solid-State Quantum Sensors.

We report new experimental results on exotic spin-spin-velocity-dependent interactions between electron spins. We designed an elaborate setup that is equipped with two nitrogen-vacancy (NV) ensembles in diamonds. One of the NV ensembles serves as the spin source, while the other functions as the spin sensor. By coherently manipulating the quantum states of two NV ensembles and their relative velocity at the micrometer scale, we are able to scrutinize exotic spin-spin-velocity-dependent interactions at short force ranges. For a T-violating interaction, V_{6}, new limits on the corresponding coupling coefficient, f_{6}, have been established for the force range shorter than 1 cm. For a P,T-violating interaction, V_{14}, new constraints on the corresponding coupling coefficient, f_{14}, have been obtained for the force range shorter than 1 km.

Measurement of the Earth Tides with a Diamagnetic-Levitated Micro-Oscillator at Room Temperature.

The precise measurement of the gravity of Earth plays a pivotal role in various fundamental research and application fields. Although a few gravimeters have been reported to achieve this goal, miniaturization of high-precision gravimetry remains a challenge. In this work, we have proposed and demonstrated a miniaturized gravimetry operating at room temperature based on a diamagnetic levitated micro-oscillator with a proof mass of only 215 mg. Compared with the latest reported miniaturized gravimeters based on microelectromechanical systems, the performance of our gravimetry has substantial improvements in that an acceleration sensitivity of 15 µGal/sqrt[Hz] and a drift as low as 61 µGal per day have been reached. Based on this diamagnetic levitation gravimetry, we observed Earth tides, and the correlation coefficient between the experimental data and theoretical data reached 0.97. Some moderate foreseeable improvements can develop this diamagnetic levitation gravimetry into a chip size device, making it suitable for mobile platforms such as drones. Our advancement in gravimetry is expected to facilitate a multitude of applications, including underground density surveying and the forecasting of natural hazards.

Unraveling the Photoluminescent Properties of Sb-Doped Cd-Based Inorganic Halides: A First-Principles Study.

Sb-doped Cd-based inorganic halides, with varying connections of CdCl6 octahedra ranging from 0D to 3D, exhibit a variety of photoluminescent properties. Single-band emission is observed in Sb-doped Rb4CdCl6 (0D) and Cs2CdCl4 (2D), while dual-band emission is seen in Sb-doped RbCdCl3 (1D) and CsCdCl3 (3D). Density-functional-based first-principles calculations were conducted. The results reveal that cation vacancies, acting as charge compensators, influence the luminescence properties of dopant centers. In CsCdCl3, the local cation vacancy VCd″ for Sb3+ at the Cd2+ site ([Sb□Cl9]6-) significantly modifies the photoluminescence property, accounting for the observed dual-band emission alongside the nonlocal compensation case. This effect is insignificant in Sb-doped Rb4CdCl6, RbCdCl3, and Cs2CdCl4, due to the large distances or high formation energies of Cd vacancies in these hosts. However, in Sb-doped RbCdCl3, two different potential energy minima, one that involves typical structure relaxation and the other that is off-center, lead to the observed dual-band emission. Furthermore, the shift of the charge transition level illustrates the different temperature dependences of the dual-band emission caused by the charge-compensating point defects. These insights not only enhance our understanding of luminescent materials based on halides containing ns2 dopants but also provide valuable guidance for the design and optimization of luminescent materials.

Modeling the Zigzag Curves of Transition Metal Ions' Charge Transition Levels in Crystals.

Predicting the defect levels of transition metal (TM) dopants in the band gap of crystals is critical in determining the charge states of TM dopants and explaining their electronic and optical properties. By analyzing the calculated charge transition levels and the crystal-field strengths of all the 3d-TM ions in several insulators, we demonstrate that the variation trend of the 3d-TM dopants in a crystal is a scaling of the variation of 3d-electron binding energies (ionization potential) of the free TM ions corrected by adding the contribution of the 3d-orbital's crystal-field splitting. We therefore develop a model to predict the relative location of TM ions' defect levels in the band gap from the defect level and crystal-field splitting of a reference TM ion in the host of concern. The model is applied to predict the defect levels of the series of TM ions in ß-Ga2O3 and ZnO, which have moderate to small band gaps, making some of the levels fall into the conduction or valence bands. These results show that the model may serve as a quick reference for related material design and optimization.

Improved Limits on an Exotic Spin- and Velocity-Dependent Interaction at the Micrometer Scale with an Ensemble-NV-Diamond Magnetometer.

Searching for exotic interactions provides a path for exploring new particles beyond the standard model. Here, we used an ensemble-NV-diamond magnetometer to search for an exotic spin- and velocity-dependent interaction between polarized electron spins and unpolarized nucleons at the micrometer scale. A thin layer of nitrogen-vacancy electronic spin ensemble in diamond is utilized as both the solid-state spin quantum sensor and the polarized electron source, and a vibrating lead sphere serves as the moving unpolarized nucleon source. The exotic interaction is searched by detecting the possible effective magnetic field induced by the moving unpolarized nucleon source using the ensemble-NV-diamond magnetometer. Our result establishes new bounds for the coupling parameter f_{⊥} within the force range from 5 to 400 µm. The upper limit of the coupling parameter at 100 µm is |f_{⊥}|≤1.1×10^{-11}, which is 3 orders of magnitude more stringent than the previous constraint. This result shows that NV ensemble can be a promising platform to search for hypothetical particles beyond the standard model.

Experimental Test of the Jarzynski Equality in a Single Spin-1 System Using High-Fidelity Single-Shot Readouts.

The Jarzynski equality (JE), which connects the equilibrium free energy with nonequilibrium work statistics, plays a crucial role in quantum thermodynamics. Although practical quantum systems are usually multilevel systems, most tests of the JE were executed in two-level systems. A rigorous test of the JE by directly measuring the work distribution of a physical process in a high-dimensional quantum system remains elusive. Here, we report an experimental test of the JE in a single spin-1 system. We realized nondemolition projective measurement of this three-level system via cascading high-fidelity single-shot readouts and directly measured the work distribution utilizing the two-point measurement protocol. The validity of the JE was verified from the nonadiabatic to adiabatic zone and under different effective temperatures. Our work puts the JE on a solid experimental foundation and makes the nitrogen-vacancy (NV) center system a mature toolbox to perform advanced experiments of stochastic quantum thermodynamics.

Mechanistic insights for regulating the site occupancy, valence states and optical transitions of Mn ions in yttrium-aluminum garnets via codoping.

The site-dependent photoluminescence of activators can be regulated by the sintering atmosphere, coexistence conditions, and especially cation codoping, which have been intensively studied for design and optimization of optical functional materials. Here, first-principles calculations are performed to determine the regulation of the site occupancy, valence states and optical transitions of Mn activators via codoping in yttrium aluminum garnets (YAGs), which contain three different cation sites. Without any codopants, Mnoct3+ dominates in defect concentration and photoluminescence, which can hardly be tuned by the sintering atmosphere or coexistence conditions of YAGs with other competing compounds. With the low formation energy of Ca2+, Be2+, Mg2+, and Sr2+ codopants and in an oxidation sintering atmosphere, the Fermi energy is lowered and the concentration and luminescence of Mnoct4+ are enhanced. Na+ and Li+ codopants with relatively high formation energy have little influence on tuning the Fermi energy. Then with the low formation energy of Ti4+, Si4+ codopants and in a reducing sintering atmosphere, the Fermi energy is lifted and the luminescence of Mndod2+ and Mnoct2+ is enhanced as a result of increased concentrations. The proposed first-principles scheme, with general applicability and encouraging predictive power, provides an effective approach for elucidating the effects of codoping impurities on the design and optimization of optical materials.

Experimental Investigation of Quantum Correlations in a Two-Qutrit Spin System.

We report an experimental investigation of quantum correlations in a two-qutrit spin system in a single nitrogen-vacancy center in diamond at room temperatures. Quantum entanglement between two qutrits was observed at room temperature, and the existence of nonclassical correlations beyond entanglement in the qutrit case has been revealed. Our work demonstrates the potential of the NV centers as the multiqutrit system to execute quantum information tasks and provides a powerful experimental platform for studying the fundamental physics of high-dimensional quantum systems in the future.

Experimental Realization of Nonreciprocal Adiabatic Transfer of Phonons in a Dynamically Modulated Nanomechanical Topological Insulator.

High quality nanomechanical oscillators are promising platforms for quantum entanglement and quantum technology with phonons. Realizing coherent transfer of phonons between distant oscillators is a key challenge in phononic quantum information processing. Here, we report on the realization of robust unidirectional adiabatic pumping of phonons in a parametrically coupled nanomechanical system engineered as a one-dimensional phononic topological insulator. By exploiting three nearly degenerate local modes-two edge states and an interface state between them-and the dynamic modulation of their mutual couplings, we achieve nonreciprocal adiabatic transfer of phononic excitations from one edge to the other with near unit fidelity. We further demonstrate the robustness of such adiabatic transfer of phonons in the presence of various noises in the control signals. Our experiment paves the way toward nonreciprocal phonon dynamics via adiabatic pumping and is valuable for phononic quantum information processing.

Elucidating the Multisite and Multivalence Nature of Mn Ions in Solids and Predicting Their Optical Transition Properties: A Case Study on a Series of Garnet Hosts.

The abundant site occupancy and optical transitions of multivalence Mn dopants in luminescent materials have attracted much attention. Here, detailed first-principles calculations based on density functional theory have been carried out to clarify the multisite and multivalence nature of Mn ions in solids and predict their optical transition properties by using garnets as prototype systems. The formation energies of dodecahedral, octahedral, and tetrahedral coordinated Mn dopants are evaluated with chemical potential environments, and the preferable site occupancy and valence state of Mn ions in three garnet systems are clarified. The results show that even in a fixed atmosphere, taking Ca3Al2Ge3O12 in air as an example, not only can the preference of Mn ions switch between dodecahedral and octahedral sites, but also can the valence state change from Mn2+ to Mn3+ and Mn4+. Furthermore, for all of the three garnet systems, the calculation results of the energy-level structure and photoluminescence of Mn ions at different sites in the different valence states provide a reliable interpretation of the available spectroscopic data. The proposed first-principles scheme, with general applicability and encouraging predictive power, provides an effective approach for elucidating and characterizing the site occupancy, valence state, and optical transition of Mn activators in insulators, and will greatly benefit the design and optimization of related materials.

Angular Jahn-Teller Effect and Photoluminescence of the Tetrahedral Coordinated Mn2+ Activators in Solids-A First-Principles Study.

First-principles calculations based on density functional theory have been performed to investigate the electronic structure, excited-state Jahn-Teller distortion, and photoluminescence of the multielectron d5 system of the strongly covalent tetrahedral coordinated Mn2+ activator in solids. The electronic structure of the 4T1 and 4A1/4E excited states is analyzed, and Slater's transition-state method and occupation matrix control methodology are applied to deal with the spin contamination in the lower-spin excited states, which is due to the mixing of the ground state of the same spin projection number. In a series of covalent tetrahedral coordinations, the 6A1 → 4T1 and 4A1/4E excitations and the 4T1 → 6A1 emission energies are obtained and compared to the reported experimental results. The nephelauxetic effect follows O2- < S2- ≈ Se2- < N3-, and the larger nephelauxetic effect and crystal field strength lead to the red-shifted emission of nitride phosphors. The Jahn-Teller distortion of the 4T1 states is dominated by the e-type angular distortion of the [MnL4] moiety (L being the ligand), which accounts for the small Stokes shift of tetrahedral coordinated Mn2+. The results show that the ground- and excited-state electronic and geometric structures and the luminescent property of tetrahedral coordinated Mn2+ can be reliably predicted. The method can be further explored to interpret and discriminate the luminescent properties of materials containing a variety of different Mn2+ sites and complexes and even other transition metals.

Experimental and Theoretical Studies of the Site Occupancy and Luminescence of Ce3+ in LiSr4(BO3)3 for Potential X-ray Detecting Applications.

Ce3+-doped LiSr4(BO3)3 phosphors have been prepared by a high-temperature solid-state reaction method, and structural refinement of the host compound has been performed. The excitation and emission spectra in the vacuum ultraviolet-ultraviolet-visible range at cryogenic temperatures reveal that Ce3+ ions preferentially occupy eight-coordinated Sr2+ sites in LiSr4(BO3)3. Such experimental attribution is well corroborated by the calculated 4f-5d transition energies and defect formation energies of Ce3+ ions at two distinct Sr2+ sites in the first-principles framework. In addition, the doping concentration-dependent luminescence and the temperature-dependent luminescence are systematically investigated by luminescence intensity and lifetime measurements, respectively. This shows that concentration quenching does not occur in the investigated doping range, but inhomogeneous broadening exists in the concentrated samples. With the estimated thermal quenching activation energy, the discussions on the thermal quenching mechanisms suggest that the thermal-ionization process of the 5d electron is a dominant channel for thermal quenching of Ce3+ luminescence, despite the fact that thermally activated concentration quenching cannot be excluded for the highly doped samples. Finally, the X-ray excited luminescence measurement demonstrates the promising applications of the phosphors in X-ray detection.

The photoluminescence of isolated and paired Bi3+ ions in layered LnOCl crystals: a first-principles study.

Luminescent ns2 centers have shown great potential for applications as phosphors and scintillators. First-principles calculations based on density functional theory are performed to systematically analyze the luminescent centers of isolated and paired Bi3+(6s2) ions in layered LnOCl (Ln = Y, Gd, La) crystals. The spin-orbit coupling and orbital hybridization both show important effects on the luminescence properties. The luminescence of the isolated Bi ion is confirmed as the interconfigurational transition of 3P0,1 → 1S0. For the Bi pair, the adiabatic potential energy surfaces are calculated and the charge transfer excited state is the most stable, which accounts for the visible emission of a large Stokes shift. Furthermore, the electron-hole pair separation, absorption, excitonic state and emission of the material with fully-concentrated Bi3+, BiOCl, are discussed. This study shows that the first-principles calculations can serve as an effective tool for the photoluminescence analysis and engineering of materials activated with isolated, paired and even fully-concentrated ns2 ions.

Dynamic Observation of Topological Soliton States in a Programmable Nanomechanical Lattice.

Topological soliton states, existing in the topological structures with edge defect or interface defect, are usually studied under steady state. Here, we experimentally observe the dynamic processes of the generation and the extinction of such soliton states in the Su-Schrieffer-Heeger model. The different topological structures are implemented on a programmable nanomechanical lattice, consisting of eight adjacent string resonators which are parametrically coupled by manipulation voltages. Moreover, the beating and localization behaviors at different topological interfaces are also observed in the same device. These results explicitly exhibit the dynamic processes of topological soliton states, which reveal real potential toward integrated multifunctional topological materials.

Dynamically Encircling an Exceptional Point in a Real Quantum System.

The exceptional point, known as the non-Hermitian degeneracy, has special topological structure, leading to various counterintuitive phenomena and novel applications, which are refreshing our cognition of quantum physics. One particularly intriguing behavior is the mode switch phenomenon induced by dynamically encircling an exceptional point in the parameter space. While these mode switches have been explored in classical systems, the experimental investigation in the quantum regime remains elusive due to the difficulty of constructing time-dependent non-Hermitian Hamiltonians in a real quantum system. Here we experimentally demonstrate dynamically encircling the exceptional point with a single nitrogen-vacancy center in diamond. The time-dependent non-Hermitian Hamiltonians are realized utilizing a dilation method. Both the asymmetric and symmetric mode switches have been observed. Our Letter reveals the topological structure of the exceptional point and paves the way to comprehensively explore the exotic properties of non-Hermitian Hamiltonians in the quantum regime.

Self-Activated and Bismuth-Related Photoluminescence in Rare-Earth Vanadate, Niobate, and Tantalate Series-A First-Principles Study.

Rare-earth vanadates, niobates, and tantalates have shown self-activated and Bi3+-activated emissions. Their intrinsic emission has been attributed to self-trapped excitons (STEs), but the detailed information concerning the geometric and electronic structures of the excited states has remained unknown. Regarding the Bi3+ dopants in these hosts, the luminescence has been attributed to two different mechanisms, i.e., Bi3+↔ (V/Nb/Ta)5+ metal-to-metal charge transfer and interconfigurational (3P0,1 → 1S0) transition. Here, first-principles calculations using hybrid functionals are employed to resolve these issues. The STEs are shown to be composed of an electron localized on an individual vanadium, niobium, or tantalum ion and a hole localized on a single nearest-neighbor oxygen ion that is not shared by covalent complexes, and the bond length of the (V/Nb/Ta)-O bond with oxygen accommodating the hole is significantly elongated. The Bi3+-related emission is identified as the recombination of an exciton with a hole and an electron localized correspondingly at Bi3+ and (V/Nb/Ta)5+ ions, while the excitation is dominated by the 6s → 6p transition of Bi3+. Furthermore, Bi3+ has a hole trap level in all of the hosts considered with the trap levels in the vacuum-referred binding energy diagram being nearly flat but has an electron trap level only in rare-earth tantalates. Furthermore, the long-wavelength emission observed in niobates and tantalates is interpreted based on our calculations to be excitons bound to intrinsic defects. The insights gained in this work deepen our understanding of the STEs and form the basis for interpreting similar luminescence phenomena in other ternary closed-shell d0 transition-metal oxides. The clarification of Bi3+-related transitions and the analyses with the vacuum-referred binding energy diagram may find applications for the design and optimization of Bi3+-activated phosphors.

First-Principles Study of Bi3+-Related Luminescence and Electron and Hole Traps in (Y/Lu/La)PO4.

Bismuth ion-doped phosphate crystals have shown rich luminescence phenomena. However, the complexity and variety of Bi3+-related transitions bring great challenges to the understanding of the underlying mechanisms, rendering it hard to rationally design new phosphors and optimize their performance. In this work, we perform first-principles calculations based on the generalized gradient approximation of density functional to obtain the excited state equilibrium geometric structures and then calculate the electronic structures for various Bi3+-related excited states in phosphates RPO4:Bi3+ (R = Y, Lu, La) by utilizing the hybrid density functional method. The experimentally measured excitation and emission features are well interpreted by our theoretical calculations. Specifically, we reveal that the emission in LaPO4:Bi3+ is of charge transfer nature, whereas the dominant emission in YPO4:Bi3+ or LuPO4:Bi3+ is the characteristic A band emission. Trapped holes above the valence band maximum due to intrinsic defects are deemed to play a role in the charge-transfer emission of LaPO4. Our calculations show that the excited state of the Bi3+ pair in YPO4 or LuPO4 is (Bi3+-Bi3+)*, rather than Bi2+-Bi4+. Such a Bi3+ pair contributes to the longer wavelength emission. Furthermore, our calculations on charge transition levels show that Bi3+ ions can act as electron and hole traps in RPO4 (R = Y, Lu, La). Our work indicates that first-principles calculations can be useful in exploring the diverse luminescence processes in Bi3+-doped inorganic insulators.

Mechanisms of bismuth-activated near-infrared photoluminescence - a first-principles study on the MXCl3 series.

Bismuth dopants have attracted intensive studies experimentally for their extremely broad near-infrared luminescence. Here we performed first-principles calculations to investigate the site occupancy and valence state by taking the condition of synthesis into consideration, and then calculated the excited states and various transitions of the bismuth ions by focusing on the targeted valent state Bi+ in a variety of ternary chloride MXCl3 (M = K, Rb, Cs; X = Mg, Cd) hosts. The results on formation energies and charge transition levels show that vacant defects play an important role in the charge compensation for the bismuth dopants, and a lower chemical potential of chlorine benefits the stabilization of Bi+ at monovalent M sites. The multi-configurational quantum-chemical method and the constrained occupancy approach together confirm the near-infrared photoluminescence of Bi+, and the spontaneous emission rates due to electric-dipole and magnetic-dipole contributions are evaluated and analyzed in terms of transition selection rules, to affirm the Bi+ nature of the long lifetime luminescence. Our results show that the mechanisms revealed in this study, and the combination of density-functional calculations for defect formation energies with the wave-function based calculations for optical transitions, are effective in exploring the luminescence of bismuth dopants in solids.

First-Principles Study on Self-Activated Luminescence and 4f → 5d Transitions of Ce3+ in M5(PO4)3X (M = Sr, Ba; X = Cl, Br).

The origin of the self-activated luminescence in the apatite-type M5(PO4)3X (MPOX; M = Sr or Ba; X = Cl or Br) samples and the spectral assignment for cerium-doped Sr5(PO4)3Cl (SPOC) phosphors are determined from first-principles methods combined with hybrid density functional theory (DFT) calculations, using the standard PBE0 hybrid functional, with wave function-based embedded-cluster ab initio calculations (at the CASSCF/CASPT2/RASSI-SO level). Electronic structure calculations are performed in order to accurately derive the band gaps of the hosts, the locations of impurity states in the energy bands that are caused by native defects and doped Ce3+ ions, and the charge-compensation mechanisms of aliovalent doping. The calculations of defect formation energies under O-poor conditions demonstrate that the native defects are easily generated in the undoped MPOX samples prepared under reducing atmospheres, from which thermodynamic and optical transition energy levels, as well as the corresponding energies, are derived in order to interpret the luminescence mechanisms of the undoped MPOX as previously reported. Our calculations reveal that the self-activated luminescence is mainly attributed to the optical transitions of the excitons bound to the oxygen vacancies (VO), along with their transformation of the charge states 0 ↔ 1+. Furthermore, the eight excitation bands observed in the synchrotron radiation excitation spectra of SPOC: Ce3+, Na+ phosphors are successfully assigned according to the ab initio calculated energies and relative oscillator strengths of the 4f1 → 5d1-5 transitions for the Ce3+ ions at both the Sr(1) and Sr(2) sites in the host. It is hoped that the feasible first-principles approaches in this work are applied in order to explore the origins of the luminescence in undoped and lanthanide-doped phosphors, complementing the experiments from the perspective of chemical compositions and the microstructures of materials.