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The use of nanophotonics for optical manipulation has continuously attracted interest in both fundamental research and practical applications, due to its significantly enhanced capabilities at the nanoscale. In this work, we showed that plasmonic particles can be trapped at off-axis location in Gaussian beams assisted by surface plasmon resonance. The off-axis displacement can be tuned at the sub-wavelength scale by the incident light beams. Based on these, we propose that a superfast orbital rotation of particles in continuous-wave laser beam can be realized in tightly focused circularly polarized Gaussian beams. The rotation has a tunable orbital radius at the sub-wavelength scale and a superfast rotation speed (more than 10^4 r/s in water under common laboratory conditions). Our work will aid in the development of optically driven nanomachines, and find applications in micro/nano-rheology, micro-fluid mechanics, and biological research at the nanoscale., 5 pages, 5 figures

Optical microscopy image plays an important role in scientific research through the direct visualization of the nanoworld, where the imaging mechanism is described as the convolution of the point spread function (PSF) and emitters. Based on a priori knowledge of the PSF or equivalent PSF, it is possible to achieve more precise exploration of the nanoworld. However, it is an outstanding challenge to directly extract the PSF from microscopy images. Here, with the help of self-supervised learning, we propose a physics-informed masked autoencoder (PiMAE) that enables a learnable estimation of the PSF and emitters directly from the raw microscopy images. We demonstrate our method in synthetic data and real-world experiments with significant accuracy and noise robustness. PiMAE outperforms DeepSTORM and the Richardson-Lucy algorithm in synthetic data tasks with an average improvement of 19.6\% and 50.7\% (35 tasks), respectively, as measured by the normalized root mean square error (NRMSE) metric. This is achieved without prior knowledge of the PSF, in contrast to the supervised approach used by DeepSTORM and the known PSF assumption in the Richardson-Lucy algorithm. Our method, PiMAE, provides a feasible scheme for achieving the hidden imaging mechanism in optical microscopy and has the potential to learn hidden mechanisms in many more systems.

Non-equilibrium thermodynamics provides a general framework for understanding non-equilibrium processes, particularly in small systems that are typically far from equilibrium and dominated by fluctuations. However, the experimental investigation of non-equilibrium thermodynamics remains challenging due to the lack of approaches to precisely manipulate non-equilibrium states and dynamics. Here, by shaping the effective potential of energy, we propose a general method to construct a non-equilibrium steady state (NESS) with arbitrary energy distribution. Using a well-designed energy-dependent feedback damping, the dynamics of an optically levitated nanoparticle in vacuum is manipulated and driven into a NESS with the desired energy distribution. Based on this approach, a phonon laser state is constructed with an ultra-narrow linewidth of 6.40 uHz. Such an arbitrary NESS construction method provides a new approach to manipulating the dynamics processes of micromechanical systems and paves the way for the systematic study of non-equilibrium dynamics in interdisciplinary research fields.

Nitrogen-vacancy quantum defects in diamond offer a promising platform for magnetometry because of their remarkable optical and spin properties. In this Letter, we present a high-sensitivity and wide-bandwidth fiber-based quantum magnetometer for practical applications. By coating the diamond surface with silver reflective film, both the fluorescence collection and excitation efficiency are enhanced. Additionally, tracking pulsed optically detected magnetic resonance spectrum allowed a magnetic field sensitivity of $35$ pT$/\sqrt{\rm{Hz}}$ and a bandwidth of $4.1$ KHz. Finally, this magnetometer was successfully applied to map the magnetic field induced by the current-carrying copper-wire mesh. Such a stable and compact magnetometry can provide a powerful tool in many areas of physical, chemical, and biological researches., 5 pages, 5 figures

The newly established Heisenberg limit in arbitrary waveform estimation is quite different with parameter estimation and shows a unique characteristic of a future quantum version of oscilloscope. However, it is still a non-trivial challenge to generate a large number of exotic quantum entangled states to achieve this quantum limit. Here, by employing the time-domain quantum difference detection method, we demonstrate Heisenberg-limited waveform quantum estimation with diamond spins under ambient condition in the experiment. Periodic dynamical decoupling is applied to enhance both the dynamic range and sensitivity by one order of magnitude. Using this quantum-enhanced estimation scheme, the estimation error of an unknown waveform is reduced by more than $5$ dB below the standard quantum limit with $N\sim{\text{2}} \times {\text{1}}{{\text{0}}^3}$ resources, where more than ${1 \times {\text{1}}{{\text{0}}^5}}$ resources would be required to achieve a similar error level using classical detection. This work provides an essential step towards realizing quantum-enhanced structure recognition in a continuous space and time., Comment: 15 pages, 8 figures

Focusing electromagnetic field to enhance the interaction with matter has been promoting researches and applications of nano electronics and photonics. Usually, the evanescent-wave coupling is adopted in various nano structures and materials to confine the electromagnetic field into a subwavelength space. Here, based on the direct coupling with confined electron oscillations in a nanowire, we demonstrate an extreme localization of microwave field down to 10$^{-6}��$. A hybrid nanowire-bowtie antenna is further designed to focus the free-space microwave to this deep-subwavelength space. Detected by the nitrogen vacancy center in diamond, the field intensity and microwave-spin interaction strength are enhanced by 2.0$\times$10$^{8}$ and 1.4$\times$10$^{4}$ times, respectively. Such an extreme concentration of microwave field will further promote integrated quantum information processing, sensing and microwave photonics in a nanoscale system., 16 pages, 10 figures

The sensitivity of a practical quantum magnetometer is challenged by both inhomogeneous coupling between sensors and environment and errors in quantum control. Based on the physical criteria of modern quantum sensing, we present a robust and effective composite-pulse for high fidelity operation against inhomogeneous broadening of sensor and control errors via optimized modulation of control field. Such a technique is verified on nitrogen-vacancy (NV) center in diamond to keep almost perfect operation up to a detuning as larger as $110\%$. The sensitivity of the magnetometer with NV center ensemble is experimentally improved by a factor of $4$, comparing to dynamical decoupling with normal rectangular pulse. Our work marks an important step towards high trustworthy ultra-sensitive quantum sensing with imperfect quantum control in realistic systems. The used principle however, is universal and not restricted to NV center ensemble magnetometer., 16 pages, 6 figures

The atom-light interaction in a three-level system has shown significant physical phenomena, such as electromagnetically induced transparency and Autler{Townes splitting (ATS), for broad applications in classical and quantum information techniques. Here, we optimally demonstrated the ATS with a quantum state manipulation method. The ATS in the dephasing-dominated diamond NV center system was successfully recovered by coherent microwave control, which cannot be observed with traditional method. The dynamical process of ATS was investigated in detail, revealing a nontrivial quantum interference with geometric phase modulations. Based on the quantum interference, the signal of the optimal ATS is twice as intense as those with traditional observation method., 10 pages and 9 figures

The nitrogen vacancy (NV) center in diamond has been widely applied for quantum information and sensing in last decade. Based on the laser polarization dependent excitation of fluorescence emission, we propose a super-resolution microscopy of NV center. A series of wide field images of NV centers are taken with different polarizations of the linear polarized excitation laser. The fluorescence intensity of NV center is changed with the relative angle between excitation laser polarization and the orientation of NV center dipole. The images pumped by different excitation laser polarizations are analyzed with Monte Carlo method. Then the symmetry axis and position of NV center are obtained with sub-diffraction resolution.

Quantum metrology with entangled states in realistic noisy environments always suffers from decoherence. Therefore, the measurement precision is greatly reduced. Here we applied the dynamical decoupling method to protect the $N$-qubit quantum metrology protocol and successfully revived the scaling of the measurement precision as ${N^{-k}}$ with $k\in \left[{5/6,11/12}\right]$. The degree of the precision revival, as determined by the noise spectrum distribution, indicates that the performance of the protected protocol can be further improved by controlling the noise spectrum. Such a protected protocol is proved to be universal for entanglement-based quantum metrology in the pure dephasing and relaxation noise, which should stimulate the development of practical quantum metrology for weak signal detection of microscopic physics., 8 pages, 4 figures, to appear in PRA

Solid-state electronic spin system of the nitrogen-vacancy (NV) center in diamond is attractive as a nanoscale quantum sensor under room-temperature dueto its unique characteristics such as stable fluorescence, long coherent time, and near-atomic size under ambient conditions. Nowadays, the NV center plays a significant role in super-resolution microscopies. Different super-resolution microscopies have been used on NV center to archievenanoscale spatial resolution. Moreover, the spin state in NV center can be regraded as a solid-state qubit, which can be optically polarized and read out. The spin state can couple with electromagnetic fields and strain, which enables the NV center to be an excellent quantum sensor with high spatial resolution and high sensitivity. Such an NV-center based quantum sensing technique is being developed for applications in newmateriales, single protein nuclear spin dynamic field, life science, etc. This review will introduce the basic principle of such a nanoscale quantum sensor, the experimental realization, methods of enhancing the sensitivity, and some applications in high-spatial-resolution and high-sensitivity sensing.

We propose an experimental scheme to realize the four-dimensional projective measurements for a single photon. The photon polarization and time—energy provide the four-dimensional Hilbert space. Based on this scheme, we suggest an experiment to test the violation of Bell inequalities of four-dimensional systems. In addition, by virtue of a maximally entangled biphoton state, we also show that it is possible to construct a quantum key distribution channel that can provide two-bit key with one pair of entangled photons.

It is well known that the indistinguishability of particles causes interference. We give a ``which way'' experiment of two-photon interference marked with polarization. The result shows that the greater the distinguishability of the path by which two-photon passes, the lower the fringe visibility will be, and this phenomenon will disappear when the path becomes completely distinguishable.

The ultralong distance coupling between two Asymmetric Resonant Microcavities (ARCs) is studied. Different from traditional short distance tunneling coupling between microcavities, the high efficient free space directional emission and excitation allow ultralong distance energy transfer between ARCs. In this paper, a novel unidirectional emission ARC, which shows directionality I40 = 0.54, is designed for materials of refractive index n = 2.0. Compared with regular whispering gallery microresonators, the coupled unidirectional emission ARCs show modulations of resonance frequency and linewidth even when the distance between cavities is much longer than wavelength. The performances and properties of the ultralong distance interaction between ARCs are analyzed and studied by coupling mode theory in details. The ultralong distance interaction between ARCs provides a new way to free-space based optical interconnects between components in integrated photonic circuits., 9 pages, 6 figures

The photonic bound state in the continuum (BIC) is discovered in a hybrid photonic circuit with low refractive index waveguide on a high refractive index thin membrane, where the optical dissipation is forbidden because of the destructive interference of different leakage channels. Based on the photonic BIC, the low mode area in a hybrid waveguide and high quality factor in a microresonator can be applied to enhance the light-matter interaction. Taking the fabrication-friendly polymer structure on diamond membrane as an example, those excellent optical performances can exist in a wide range of structure parameters with large fabrication tolerance and induce the strong coupling between photon and nitrogen-vacancy center in the diamond for scalable quantum information processors and networks. Such a fabrication-friendly structure with photonic BIC is also very promising in laser, nonlinear optical and quantum optical applications., Comment: 5 pages,4 figures

The coupled negatively charged nitrogen-vacancy (NV−) center system is a promising candidate for scalable quantum information techniques. In this work, ionized nitrogen molecules are implanted into bulk diamond to generate coupled NV− center pairs. The two-photon autocorrelation measurement and optically detected magnetic resonance measurement are carried out to confirm the production of the NV− center pair. Also, both 1.3 μs decoherence time and 4.9 kHz magnetic coupling strength of the NV− center pair are measured by controlling and detecting the spin states. Along with nanoscale manipulation and detection methods, such coupled NV− centers through short distance dipole-dipole interaction would show high potential in scalable quantum information processes.

Collimated directional emission is essentially required an asymmetric resonant cavity. In this paper, we theoretically investigate a type of peanut-shaped microcavity which can support highly directional emission with the emission divergence as small as 2.5o. The mechanism of the collimated emission is explained with the short-term ray trajectory and the intuitive lens model in detail. Wave simulation also confirms these results. This extremely narrow divergence of the emission holds a great potential in highly collimated lasing from on-chip microcavities.

The maximum entangled number state (NOON state) can improve the sensitivity of physical quantity measurement to the Heisenberg limit 1/N. In this work, the magnetic field measurement based on the individual solid spin NOON state is investigated. Based on the tunable effective coupling coefficient, we propose a generation scheme of the three-spin NOON state, i.e, the Greenberger—Horne—Zeilinger (GHZ) state, and discussed the measurement resolution reduction due to decoherence. It is unnecessary to entangle spins as many as possible when decoherence exists. In practice, defect spins in diamond and 31P donors with long coherence time can be applied with current techniques in the nano-scaled high resolution magnetic measurement.

We proposed a protocol of measuring the duration of ultra-short single-photon pulse with two-photon interference. The pulse duration can be obtained from the width of the visibility of two-photon Hong-Ou-Mandel interference or the indistinguishability of the two photons. Moreover, the shape of a single-photon pulse can be measured with ultra-short single-photon pulses through the two-photon interference.