Measuring a dynamical topological order parameter in quantum walks

Efficient learning of mixed-state tomography for photonic quantum walk

Noise-enhanced applications in open quantum walk (QW) has recently seen a surge due to their ability to improve performance. However, verifying the success of open QW is challenging, as mixed-state tomography is a resource-intensive process, and implementing all required measurements is almost impossible due to various physical constraints. To address this challenge, we present a neural-network-based method for reconstructing mixed states with a high fidelity (∼97.5%) while costing only 50% of the number of measurements typically required for open discrete-time QW in one dimension. Our method uses a neural density operator that models the system and environment, followed by a generalized natural gradient descent procedure that significantly speeds up the training process. Moreover, we introduce a compact interferometric measurement device, improving the scalability of our photonic QW setup that enables experimental learning of mixed states. Our results demonstrate that highly expressive neural networks can serve as powerful alternatives to traditional state tomography.

Aperiodic dynamical quantum phase transition in multi-band Bloch Hamiltonian and its origin

We investigate the dynamical quantum phase transition (DQPT) in the multi-band Bloch Hamiltonian of the one-dimensional periodic Kitaev model, focusing on quenches from a Bloch band. By analyzing the dynamical free energy and Pancharatnam geometric phase (PGP), we show that the critical times of DQPTs deviate from periodic spacing due to the multi-band effect, contrasting with results from two-band models. We propose a geometric interpretation to explain this non-uniform spacing. Additionally, we clarify the conditions needed for DQPT occurrence in the multi-band Bloch Hamiltonian, highlighting that a DQPT only arises when the quench from the Bloch states collapses the band gap at the critical point. Moreover, we establish that the dynamical topological order parameter, defined by the winding number of the PGP, is not quantized but still exhibits discontinuous jumps at DQPT critical times due to periodic modulation. Additionally, we extend our analysis to mixed-state DQPT and find its absence at non-zero temperatures.

Polar optical flow network: extracting overlapped holograms of dynamic particles

Digital holography with lensless in-line setup has been extensively used in particle field measurements. As particle concentration increases, the holograms of dynamic particles locating at different depths tend to superpose with each other with incoherent overlap, hampering effective measurement of individual particles with incomplete information. Drawing inspiration from suborbicular nature of the in-line holographic fringes, in this study, we propose an optical flow method in polar coordinates to mitigate the overlap issue. The approach employs a radial transformer-enhanced network that leverages both the radial and angular characteristics of the polar hologram. Through ablation tests and experimental results, we have demonstrated the effectiveness and superiority of our proposed method.

Real-time phase imaging with physics-enhanced network and equivariance

Learning-based phase imaging balances high fidelity and speed. However, supervised training requires unmistakable and large-scale datasets, which are often hard or impossible to obtain. Here, we propose an architecture for real-time phase imaging based on physics-enhanced network and equivariance (PEPI). The measurement consistency and equivariant consistency of physical diffraction images are used to optimize the network parameters and invert the process from a single diffraction pattern. In addition, we propose a regularization method based total variation kernel (TV-K) function constraint to output more texture details and high-frequency information. The results show that PEPI can produce the object phase quickly and accurately, and the proposed learning strategy performs closely to the fully supervised method in the evaluation function. Moreover, the PEPI solution can handle high-frequency details better than the fully supervised method. The reconstruction results validate the robustness and generalization ability of the proposed method. Specially, our results show that PEPI leads to considerable performance improvement on the imaging inverse problem, thereby paving the way for high-precision unsupervised phase imaging.

Phase customization in photonic integrated circuits with trimmed waveguides

Accurate photon phase control on a chip is essential to improve the expandability and stability of photonic integrated circuits (PICs). Here, we propose a novel, to the best of our knowledge, on-chip static phase control method in which a modified line is added close to the normal waveguide with a lower-energy laser. By controlling the laser energy and the position and length of the modified line, the optical phase can be precisely controlled with low loss and a three-dimensional (3D) path. Customizable phase modulation ranging from 0 to 2π is performed with a precision of λ/70 in a Mach-Zehnder interferometer. The proposed method can customize high-precision control phases without changing the waveguide's original spatial path, which is expected to control the phase and solve the phase error correction problem during processing of large-scale 3D-path PICs.

Diffraction-Net: a robust single-shot holography for multi-distance lensless imaging

Digital holography based on lensless imaging is a developing method adopted in microscopy and micro-scale measurement. To retrieve complex-amplitude on the sample surface, multiple images are required for common reconstruction methods. A promising single-shot approach points to deep learning, which has been used in lensless imaging but suffering from the unsatisfied generalization ability and stability. Here, we propose and construct a diffraction network (Diff-Net) to connect diffraction images at different distances, which breaks through the limitations of physical devices. The Diff-Net based single-shot holography is robust as there is no practical errors between the multiple images. An iterative complex-amplitude retrieval approach based on light transfer function through the Diff-Net generated multiple images is used for complex-amplitude recovery. This process indicates a hybrid-driven method including both physical model and deep learning, and the experimental results demonstrate that the Diff-Net possesses qualified generalization ability for samples with significantly different morphologies.

Reconstructing the dynamical quantum phase transitions via dimensional expansion in a generalized Su-Schrieffer-Heeger model

We know that a one-dimensional (1D) modulated system can simulate 2D topological states by expanding the dimension. This scenario provides a justifiable avenue to test the dilatation of the dynamical quantum phase transition (DQPT). Through a generalized Su-Schrieffer-Heeger model, we have shown how the Loschmidt echo, Fisher zero, and Dynamical topological order parameter (DTOP) transit from one to two dimensions. Owing to the introduced pseudomomentum, the derivative of the return rate does not always capture the DQPT well, but the Fisher zero and the DTOP can be treated as faithful indicators. A topology-independent parameter will also affect the occurrence of the DQPTs for quenches inside a given phase. Moreover, a comparison with the Haldane model owning the same phase diagram implies that a pair of fixed points will lead to different critical momentum distributions, thus different robustness, further reminding us that the correspondences between the equilibrium and dynamical phases transitions are multifarious.

Experimental verification of generalized eigenstate thermalization hypothesis in an integrable system

Identifying the general mechanics behind the equilibration of a complex isolated quantum system towards a state described by only a few parameters has been the focus of attention in non-equilibrium thermodynamics. And several experimentally unproven conjectures are proposed for the statistical description of quantum (non-)integrable models. The plausible eigenstate thermalization hypothesis (ETH), which suggests that each energy eigenstate itself is thermal, plays a crucial role in understanding the quantum thermalization in non-integrable systems; it is commonly believed that it does not exist in integrable systems. Nevertheless, integrable systems can still relax to the generalized Gibbs ensemble. From a microscopic perspective, understanding the origin of this generalized thermalization that occurs in an isolated integrable system is a fundamental open question lacking experimental investigations. Herein, we experimentally investigated the spin subsystem relaxation in an isolated spin-orbit coupling quantum system. By applying the quantum state engineering technique, we initialized the system with various distribution widths in the mutual eigenbasis of the conserved quantities. Then, we compared the steady state of the spin subsystem reached in a long-time coherent dynamics to the prediction of a generalized version of ETH and the underlying mechanism of the generalized thermalization is experimentally verified for the first time. Our results facilitate understanding the origin of quantum statistical mechanics.

Detecting Non-Bloch Topological Invariants in Quantum Dynamics

Non-Bloch topological invariants preserve the bulk-boundary correspondence in non-Hermitian topological systems, and are a key concept in the contemporary study of non-Hermitian topology. Here we report the dynamic detection of non-Bloch topological invariants in single-photon quantum walks, revealed through the biorthogonal chiral displacement, and crosschecked with the dynamic spin textures in the generalized quasimomentum-time domain following a quantum quench. Both detection schemes are robust against symmetry-preserving disorders, and yield consistent results with theoretical predictions. Our experiments are performed far away from any boundaries, and therefore underline non-Bloch topological invariants as intrinsic properties of the system that persist in the thermodynamic limit. Our work sheds new light on the experimental investigation of non-Hermitian topology.

Floquet dynamical quantum phase transitions in periodically quenched systems

Dynamical quantum phase transitions (DQPTs) are characterized by nonanalytic behaviors of physical observables as functions of time. When a system is subject to time-periodic modulations, the nonanalytic signatures of its observables could recur periodically in time, leading to the phenomena of Floquet DQPTs. In this work, we systematically explore Floquet DQPTs in a class of periodically quenched one-dimensional system with chiral symmetry. By tuning the strength of quench, we find multiple Floquet DQPTs within a single driving period, with more DQPTs being observed when the system is initialized in Floquet states with larger topological invariants. Each Floquet DQPT is further accompanied by the quantized jump of a dynamical topological order parameter, whose values remain quantized in time if the underlying Floquet system is prepared in a gapped topological phase. The theory is demonstrated in a piecewise quenched lattice model, which possesses rich Floquet topological phases and is readily realizable in quantum simulators like the nitrogen-vacancy center in diamonds. Our discoveries thus open a new perspective for the Floquet engineering of DQPTs and the dynamical detection of topological phase transitions in Floquet systems.

Enhanced directional quantum emission by tunable topological doubly resonant cavities

How to utilize topological microcavities to control quantum emission is one of the ongoing research topics in the optical community. In this work, we investigate the emission of quantum emitters in a doubly-resonant topological Tamm microcavity, which can simultaneously achieve dual resonances at two arbitrary wavelengths according to the needs of practical application. To achieve the enhancement of quantum emission in such cavities, we have exploited the tunable doubly-resonant modes, in which one of resonant modes corresponds to the pump laser wavelength and the other one is located at the emission wavelength of quantum emitters. Both theoretical and experimental results demonstrate that the pump excitation and emission efficiencies of quantum emitters are greatly enhanced. The main physical mechanism can be explained by the doubly-resonant cavity temporal coupled-mode theory. Furthermore, we observe the faster emission rate and the higher efficiency of unidirectional quantum emission, which have promising applications in optical detection, sensing, filtering, and light-emitting devices.

Experimental optimal generation of hybrid entangled states in photonic quantum walks

While the existence of disorders is commonly believed to weaken the unique properties of quantum systems, recent progress has predicted that it can exhibit a counterintuitive enhanced effect on the behavior of entanglement generation, which is even independent of the chosen initial conditions and physical platforms. However, to achieve a maximally entangled state in such disordered quantum systems, the key limitation of this is the scarcity of an infinite coherence time, which makes its experimental realization challenging. Here, we experimentally investigate the entanglement entropy dynamics in a photonic quantum walk with disorders in time. Through the incorporation of a classic optimization algorithm, we experimentally demonstrate that such disordered systems can relax to a high-entanglement hybrid state at any given time step. Moreover, this prominent entangling ability is universal for a wide variety of initial conditions. Our results may inspire achieving a well-controlled entanglement generator for quantum computation and information tasks.

Entanglement View of Dynamical Quantum Phase Transitions

The analogy between an equilibrium partition function and the return probability in many-body unitary dynamics has led to the concept of dynamical quantum phase transition (DQPT). DQPTs are defined by nonanalyticities in the return amplitude and are present in many models. In some cases, DQPTs can be related to equilibrium concepts, such as order parameters, yet their universal description is an open question. In this Letter, we provide first steps toward a classification of DQPTs by using a matrix product state description of unitary dynamics in the thermodynamic limit. This allows us to distinguish the two limiting cases of "precession" and "entanglement" DQPTs, which are illustrated using an analytical description in the quantum Ising model. While precession DQPTs are characterized by a large entanglement gap and are semiclassical in their nature, entanglement DQPTs occur near avoided crossings in the entanglement spectrum and can be distinguished by a complex pattern of nonlocal correlations. We demonstrate the existence of precession and entanglement DQPTs beyond Ising models, discuss observables that can distinguish them, and relate their interplay to complex DQPT phenomenology.

Microstructure and domain engineering of lithium niobate crystal films for integrated photonic applications

Recently, integrated photonics has attracted considerable interest owing to its wide application in optical communication and quantum technologies. Among the numerous photonic materials, lithium niobate film on insulator (LNOI) has become a promising photonic platform owing to its electro-optic and nonlinear optical properties along with ultralow-loss and high-confinement nanophotonic lithium niobate waveguides fabricated by the complementary metal-oxide-semiconductor (CMOS)-compatible microstructure engineering of LNOI. Furthermore, ferroelectric domain engineering in combination with nanophotonic waveguides on LNOI is gradually accelerating the development of integrated nonlinear photonics, which will play an important role in quantum technologies because of its ability to be integrated with the generation, processing, and auxiliary detection of the quantum states of light. Herein, we review the recent progress in CMOS-compatible microstructure engineering and domain engineering of LNOI for integrated lithium niobate photonics involving photonic modulation and nonlinear photonics. We believe that the great progress in integrated photonics on LNOI will lead to a new generation of techniques. Thus, there remains an urgent need for efficient methods for the preparation of LNOI that are suitable for large-scale and low-cost manufacturing of integrated photonic devices and systems.

Topological Quantum Walks in Momentum Space with a Bose-Einstein Condensate

We report the experimental implementation of discrete-time topological quantum walks of a Bose-Einstein condensate in momentum space. Introducing stroboscopic driving sequences to the generation of a momentum lattice, we show that the dynamics of atoms along the lattice is effectively governed by a periodically driven Su-Schrieffer-Heeger model, which is equivalent to a discrete-time topological quantum walk. We directly measure the underlying topological invariants through time-averaged mean chiral displacements, which are consistent with our experimental observation of topological phase transitions. We then observe interaction-induced localization in the quantum-walk dynamics, where atoms tend to populate a single momentum-lattice site under interactions that are nonlocal in momentum space. Our experiment opens up the avenue of investigating discrete-time topological quantum walks using cold atoms, where the many-body environment and tunable interactions offer exciting new possibilities.

Micro-Raman spectroscopy study of the effect of Mid-Ultraviolet radiation on erythrocyte membrane

Mid-Ultraviolet (UVB) has a significant influence on human health. In this study, human erythrocytes were exposed to UVB to investigate the effects of UVB radiation on erythrocytes membrane. And Micro-Raman spectroscopy was employed to detect the damage. Principal component analysis (PCA) was used to classify the control erythrocytes and the irradiated erythrocytes. Results showed that the erythrocytes membrane was damaged by Mid-Ultraviolet (UVB) radiation. The intensity of the Raman peaks at 1126 cm(-1) and 1082 cm(-1) were used to calculate the Longitudinal Order-Parameters in Chains (S(trans)) which can present the liquidity and ionic permeability of erythrocyte membrane. After UVB radiation for 30 min, both the liquidity and ionic permeability decreased. At the same time, the intensity of the peaks at 1302 cm(-1) (α-helix), 1254 cm(-1) (random coil), 1452 cm(-1) and 1430 cm(-1) (CH(2)/CH(3) stretch) have also changed which indicated the membrane protein also been damaged by UVB. In the whole process of radiation, the more UVB radiation dose the more damage on the erythrocyte membrane.