Dual lattices such as honeycomb and hexagonal lattices typically obey Babinet's principle in optics, which states that the expected interference patterns of two complementary diffracting objects are identical and indistinguishable, except for their overall intensity. Here, we study Kapitza-Dirac diffraction of Bose-Einstein condensates in optical lattices and find that matter waves in dual lattices obey Babinet's principle only under the condition of weak-pulse Raman-Nath regime. In contrast, the Kapitza-Dirac matter-wave diffraction in the strong-pulse Raman-Nath regime, which generates subwavelength phase structures via phase wrapping, can break Babinet's principle and clearly resolve the distinct interference patterns of the dual honeycomb and hexagonal lattices. This method offers exceptional precision in characterizing lattice configurations and advance the study of symmetry-related phenomena, overcoming the limitations of real-space imaging.

We experimentally investigate four-wave mixing (FWM) of matter waves in two geometric configurations in ^39K Bose-Einstein condensates with the atomic interaction tuned via Feshbach resonances. For one configuration with the single-spin component, the FWM yield increases with a larger scattering length. For the two-spin component configuration, we specifically investigate FWM in both the droplet and gas parameter regimes. We find that the FWM yield reaches its maximum near the critical parameter region between the gas and droplet phases. Our research can help to optimize the FWM yield for matter-wave amplification and entangled atom pair generation, making it conducive to applications in quantum information processing and precision measurement.

Supersolids-exotic quantum states that combine superfluid flow with crystalline order-have recently been realized in quantum degenerate gases, yet a direct quantitative measurement of their superfluid fraction and understanding of their topological properties have remained elusive. In this work we show that the nonequilibrium dynamics of a spin-orbit coupled dipolar Bose-Einstein condensate under PT-symmetric driving and dissipation generates an oscillating current whose frequency exhibits a strong dependence on the superfluid fraction of the underlying supersolid. This dynamical response further reveals topological phase transitions between distinct supersolid phases characterized by their spin textures. Our findings establish a platform for exploring supersolids with topological properties and provide deep insight into their nonequilibrium behavior beyond conventional closed-system scenarios.

Precise control of optical intensity distributions is important for beam shaping, optical trapping, and optical potential engineering. We implement a digital micromirror device (DMD)-based programmable beam-shaping platform for generating high-fidelity optical intensity distributions with user-defined geometries. The approach combines precise system calibration, Fourier-plane spatial filtering via an optimized pinhole, and an iterative intensity feedback algorithm to transform imperfect Gaussian input beams into flat-top, lattice, and composite intensity distributions. The feedback loop typically converges within seven iterations, producing highly uniform flat-top profiles with 98.7% uniformity (corresponding to a root-mean-square error (RMSE) of 1.3%). Systematic studies identify the optimal Fourier-plane aperture that balances diffraction suppression with optical throughput. These results demonstrate a practical route to programmable beam shaping and optical intensity control.

Recent experimental progress on twisted bilayer optical lattices with ultracold atoms provides a highly controllable platform for flat-band physics beyond solid-state moir & eacute; materials. While previous studies established that interlayer coupling can generate flat bands near the Dirac points of the s-orbital bands in twisted bilayer honeycomb optical lattices-thereby enabling quantum simulation of magic-angle twisted bilayer graphene-an important open question is whether higher-orbital bands can host equally rich (and possibly distinct) flat-band structures, and how their topology and geometry differ from the s-orbital Dirac-point flat bands. Here we systematically investigate the single-particle band structures of ultracold atoms loaded into higher orbitals of a twisted bilayer honeycomb optical lattice under tunable interlayer coupling. Our results reveal that, with appropriate interlayer coupling, flat bands can also emerge i) near other band-degeneracy points in higher-orbital bands, and ii) near the band bottoms and band tops of the higher-orbital bands. Importantly, we identify two distinct flattening mechanisms with different coupling dependence. For degeneracy-induced flat bands, the bandwidth is minimized near a critical interlayer coupling, whereas stronger coupling restores dispersion and reduces the flatness. By contrast, flat bands forming near band bottoms or tops flatten monotonically as the interlayer coupling increases. In the deep-lattice regime, as the interlayer coupling is tuned, some higher-orbital flat bands can drift in energy across the spectrum. In particular, flat bands initially embedded in a continuum of dispersive bands may migrate toward (and eventually into) an energy gap, becoming increasingly isolated. We also analyze the topological and geometric properties of representative flat-band subspaces using non-Abelian Wilson loops. The flat bands induced by the s-orbital Dirac points exhibit a nontrivial Wilson-loop winding. By contrast, most higher-orbital flat bands show suppressed geometric-phase effects with vanishing Wilson-loop winding and Wilson-loop phases locked near zero. Notably, for flat bands induced by higher-orbital Dirac points, although a robust winding analogous to the s-orbital Dirac-point case is absent, the Wilson-loop phases display finite fluctuations around zero, signaling a residual non-Abelian geometric response. The demonstrated tunability of flatness, band isolation, and geometric response lays a foundation for future studies of interaction-driven strongly correlated phases and topological quantum phase transitions in ultracold-atom moir & eacute; systems.

Hyperfine constant A is a key parameter of the hyperfine structure and underpins precision spectroscopy and metrology. In this Letter, we develop a magnetic-field-calibration-free method for determining the ground-state hyperfine constant A in an ultracold ^40K Fermi gas by utilizing a pair of magnetically insensitive ("clock") transitions. This overcomes the stringent magnetic-field calibration requirements of conventional methods. We measure the transition frequency between these two magnetically insensitive transitions with Hz-level resolution over a range of magnetic fields, and obtain the ground-state hyperfine constant A = -h× 285.730536(2) MHz, corresponding to an absolute uncertainty of about 2 Hz. Our value reduces the uncertainty by nearly three orders of magnitude compared with previous determinations, providing a substantially improved reference for high-precision spectroscopy and metrology with ^40K.

This paper presents an experimental study of microwave single-photon transitions that are magnetic-fieldinsensitive in degenerate Fermi gases of 40K. This contrasts with microwave single-photon clock transitions for 0-0 magnetic-field-insensitive states and two-photon clock transitions for non-0-0 magnetic-field-insensitive states in bosonic alkali-metal atoms. We show that there are two sets of special transitions between two different hyperfine ground states (|F = 9/2, mF = 1/2) |7/2, -1/2) and |9/2, -1/2) |7/2, 1/2)), whose microwave single-photon transition frequency is insensitive to low magnetic fields, as the first-order Zeeman shift is almost completely canceled. By using the microwave spectrum and Ramsey interference fringes, we demonstrate the long-time stability of the coherent transition under magnetic field fluctuations. These magneticfield-insensitive microwave hyperfine transitions in ultracold 40K Fermi gases offer promising applications in quantum information and precision measurements.

Errors in observatory coordinates directly impact the precision of pulsar time-scale construction. Using the pulsar timing software TEMPO2, this study simulates various station position errors within the three-dimensional terrestrial reference frame for three different types of millisecond pulsars, over periods of 13 days and 5 years, and analyzes their effects on pulsar timing results.The findings demonstrate that,for both 13-day and 5-year observation spans, station coordinate errors substantially reduce the accuracy of pulsar timescale construction when the zenith angle exhibits long-term variations. This effect is independent of pulsar type and the daily observable time of the station antenna for the pulsar. A linear relationship is found between station coordinate errors and the Root-Mean-Square (RMS) of pulsar timing residuals, with fitted linear coefficients ranging from 1.36 × 10^-11 to 1.61 × 10^-9 for the three pulsars. The Roemer delay error caused by coordinate inaccuracies is notably larger than other delay and correction terms. Errors along the x- and y-axes have comparable influences on timing precision, whereas errors along the z-axis have a relatively smaller effect. Kendall correlation analysis between station error-induced Roemer delay and RMS yields a correlation coefficient r = 1.67% and p = 100% in all cases, indicating that, at current timing precision levels, coordinate errors primarily affect the Roemer delay term and thus the pulse arrival times, which is highly consistent with theoretical models.While these findings offer valuable insights into the key factors influencing pulsar timescale accuracy and related applications, they may not hold under conditions of a constant zenith angle or limited elevation angles, such as those at FAST.

We demonstrate a sideband Pound-Drever-Hall (SPDH) locking scheme that enables the simultaneous narrow-linewidth stabilization and continuous broadband frequency tuning of a laser referenced to an ultra-stable cavity. The method employs dual-frequency modulation applied to a fiber electro-optic modulator, where high-frequency modulation generates tunable sidebands and low-frequency modulation provides the error signal. We experimentally stabilize a 922 nm seed laser to the cavity and achieve a laser linewidth of 85(1) kHz with frequency noise suppression of up to 25 dB. The residual amplitude modulation (RAM) remains below 0.08% across the full tuning range. In addition, we demonstrate a continuous frequency tuning range of 1.4 GHz for a frequency-doubled 461 nm laser, with scan rates up to 317 MHz/s, while preserving stable locking to the cavity. This approach avoids complex waveform generation and provides a simple and robust solution for broadband laser frequency control.

A chiral supersolid is a quantum phase that simultaneously exhibits crystalline order, superfluidity, and topological spin texture, with spontaneously broken translational, U(1) gauge, and chiral symmetries. Here, we demonstrate a chiral supersolid with tunable non-equilibrium dynamics in a spin-orbit coupled dipolar Bose-Einstein condensate. By adjusting dipolar interaction and spin-orbit coupling, we uncover two distinct quantum phase transitions: (i) a first-order transition from a single skyrmion superfluid to a triangular meron supersolid, and (ii) a second-order transition from this superfluid to a square skyrmion supersolid. These phases are characterized by their lattice symmetries, nonclassical rotational inertia, and spin textures. Under parity-time symmetric dissipation, we predict phase-dependent damping of the current oscillations, directly linked to the superfluid fraction. The predicted chiral supersolid phase can be experimentally observed in ultracold magnetic atoms with spin-orbit coupling. Our results establish dipolar quantum gases as a platform for designing topological matter with spintronic functionality.

Neutral atom arrays have emerged as one of the most promising physical platforms for quantum computing and quantum information processing due to their precise single-atom control and tunable strong interactions. The acousto-optic deflector (AOD) is a key device for constructing and manipulating neutral atom arrays, enabling rapid and high-precision atom trapping and arrangement. However, TeO2-based anomalous Bragg AODs still face challenges in practical applications, such as unclear broadband diffraction conditions, polarization sensitivity, and low efficiency, which limit their performance in multi-degree-of-freedom control.This study investigates the acousto-optic effects in AOD and acousto-optic modulator (AOM), and reveals their differences in diffraction efficiency, polarization characteristics, and applications. By adjusting the azimuthal angle of the AOD, we measure the efficiency and RF bandwidth of the ±1st-order diffracted beams under horizontal and vertical polarization incident light, and propose an experimental method to determine the broadband diffraction center frequency and diffraction order. Additionally, we systematically characterize the operational parameters of AOM, clarifying their performance mechanisms and application-specific differences compared with those of AOD. The main conclusions are as follows:1) The beam deflection performance of an AOD is closely related to the ultrasonic mode or acoustic velocity: a lower sound velocity results in a larger deflection angles. For TeO2 crystals, when a shear wave propagates along the [110] axis (sound velocity: 0.617 km/s), the diffraction angle reaches 0.842 mrad/MHz (laser wavelength: 532 nm). In contrast, when TeO2 is used in AOM with a longitudinal wave along the [001] axis (sound velocity: 4.26 km/s), the diffraction angle decreases to 0.133 mrad/MHz under the same wavelength.2) To achieve high diffraction efficiency and a broad operational frequency range, the AOD must satisfy the phase-matching condition for anomalous Bragg diffraction. Taking the AOD (model: AA DTSX-250) for example, it operates in a unidirectional incident mode: when horizontally polarized light (extro-ordinary light) is incident, only the –1st-order diffracted beam satisfies the anomalous Bragg condition. The beam undergoes polarization conversion to vertically polarized light (ordinary light), enabling high-efficiency broadband deflection (center frequency: 82 MHz, bandwidth: 45 MHz). To support future two-dimensional deflection implementations, the input and output surfaces of the TeO2 crystal are fabricated with slight bevel angles, ensuring collinearity between the –1st-order diffracted beam and the incident beam at the center frequency. In other cases—(i) +1st-order diffraction of horizontally polarized light and (ii) ±1st-order diffraction of vertically polarized light—the anomalous Bragg condition is not met. These beams retain their original polarization and allow only narrowband deflection.These results demonstrate that AODs, leveraging anomalous acousto-optic effects, can achieve high diffraction efficiency, wide frequency tuning ranges, and large deflection angles, making them suitable for high-speed, high-precision beam steering applications. In contrast, AOMs utilize normal acousto-optic effects to perform rapid modulation of beam intensity, frequency, and phase, and are widely used in laser communication and optical fiber transmission. This study provides a detailed technical reference for understanding the operational principles of AODs and their applications in programmable neutral atom arrays.

Ultracold diatomic molecules have achieved significant breakthroughs in recent years, enabling the exploration of quantum chemistry, precision measurements, and strongly correlated many-body physics. Extending ultracold molecular complexity to polyatomic molecules, such as triatomic and tetratomic molecules, has attracted considerable interest. However, the realization of ultracold polyatomic molecules remains technically challenging due to their complex energy-level structures. While only a few experiments have successfully demonstrated the formation of polyatomic molecules by magnetoassociation or electroassociation, here we present the first step toward producing tetratomic molecules through the development of a microwave association technique combined with microwave dressing. When the two lowest rotational states of the molecules are dressed by a microwave field, weakly bound tetramer states emerge in the entrance channel with free dark excited states |0⟩ and a dressed state |+⟩. The spectroscopy of these weakly bound tetramers is probed by another microwave field that drives transitions from the populated dressed states |+⟩. By precisely discriminating the complex hyperfine structure of the dark excited level |0⟩ from the dressed-state spectroscopy, the binding energy of the tetratomic molecules is measured and characterized. Our work contributes to the understanding of complex few-body physics within a system of microwave-dressed molecules and may open an avenue toward the creation and control of ultracold polyatomic molecules.

When two or more energy bands become degenerate at a singular point in the momentum space, such singularity, or “Dirac points", gives rise to intriguing quantum phenomena as well as unusual material properties. Systems at the Dirac points can possess topological charges and their unique properties can be probed by various methods, such as transport measurement, interferometry and momentum spectroscopy. While the topology of Dirac point in the momentum space is well studied theoretically, observation of topological defects in a many-body quantum systems at Dirac point remain an elusive goal. Based on atomic Bose-Einstein condensate in a graphene-like optical honeycomb lattice, we directly observe emergence of quantized vortices at the Dirac point. The phase diagram of lattice bosons at the Dirac point is revealed. Our work provides a new way of generating vortices in a quantum gas, and the method is generic and can be applied to different types of optical lattices with topological singularity, especially twisted bilayer optical lattices.

In recent years, flat electronic bands in twisted bilayer graphene (TBG) have attracted significant attention due to their intriguing topological properties, extremely slow electron velocities, and enhanced density of states. Extending twisted bilayer systems to new configurations is highly desirable, as it offers promising opportunities to explore flat bands beyond TBG. Here, we study both topological and trivial flat bands in a twisted bilayer honeycomb lattice for ultracold atoms and present the evolution of the flat bands with different interlayer coupling strength (ICS). Our results demonstrate that an isolated topological flat band can emerge at the Dirac-point energy for a specific value of weak ICS, referred to as the "critical coupling." This occurs over a wide range of twist angles, surpassing the limits of the magic angle in TBG systems. When the ICS is slightly increased beyond the critical coupling value, the topological flat band exhibits degenerate band crossings with both the upper and lower adjacent bands at the high-symmetry Pspoint. As the ICS is further increased into the strong coupling regime, trivial flat bands arise around Dirac-point energy. Meanwhile, more trivial flat bands appear, extending from the lowest to higher energy bands, and remain flat as the ICS increases. The topological properties of the flat bands are studied through the winding pattern of the Wilson loop spectrum. Our research provides deeper insights into the formation of flat bands in ultracold atoms with highly controllable twisted bilayer optical lattices, and may contribute to the discovery of new strongly correlated states of matter.

Spin-orbit coupling (SOC) in ultracold atoms is engineered by light-atom interaction, such as two-photon Raman transitions between two Zeeman spin states. In this paper, we propose and experimentally realize chiral Raman coupling to generate SOC in ultracold atomic gases, which exhibits high quantization axis direction dependence. Chiral Raman coupling for SOC is created by chiral light-atom interaction, in which a circularly polarized electromagnetic field generated by two Raman lasers interacts with two Zeeman spin states delta mF = +/- 1 (chiral transition). We present a simple scheme of chiral one-dimensional (1D) Raman coupling by employing two Raman lasers at an intersecting angle 90 degrees with the proper polarization configuration. In this case, Raman coupling for SOC exists in one direction of the magnetic quantization axis and disappears in the opposite direction. Then we extend this scheme into a chiral two-dimensional (2D) optical square Raman lattice configuration to generate the 1D SOC. There are two orthogonal 1D SOCs, which exist in the positive and negative directions of the magnetic quantization axis respectively. This case is compared with 2D SOC based on the nonchiral 2D optical Raman lattice scheme for studying the topological energy band. This paper broadens the horizon for understanding chiral physics and simulating topological quantum systems.

Objective Optically trapped ultracold atoms in optical lattices are important physical systems for conducting quantum computing,quantum simulation,and quantum precision measurement.The study of ultracold atoms in optical lattices serves as a bridge connecting the microscopic world and macroscopic condensed matter.It can be used to simulate strongly correlated quantum many-body systems,gauge fields,and novel topological quantum states.In these experiments,the depth of the optical lattice is a key parameter for regulating interaction strength and energy level structure.It directly affects the dynamical properties of atoms in the optical lattice,including Bloch oscillations,tunneling effects,and quantum phase transitions.Therefore,high-precision calibration of the optical lattice trap depth is crucial for achieving precise quantum control of ultracold atom systems. Methods We propose a high-precision methodology for calibrating the trap depth of optical lattices based on the principle of multiple-pulse Kapitza-Dirac(KD)diffraction.Accurate calibration of the optical lattice depth is achieved by measuring the high diffraction efficiency of the first-order momentum state of atoms within the optical lattice.To validate the effectiveness of this method,a comprehensive comparison is made with single-pulse KD diffraction,Raman-Nath(RN)diffraction,and parametric oscillation heating.In the experimental process,Bose-Einstein condensation(BEC)of 87Rb atoms is initially realized using a crossed optical dipole trap.The atoms are then loaded into a one-dimensional optical lattice under various experimental conditions.Finally,the diffraction distribution of the atoms is observed in momentum space using time-of-flight expansion imaging.By carefully analyzing their dynamic behaviors,the depth of the optical lattice is precisely determined. Results and Discussions The multiple-pulse KD diffraction method proposed in this paper utilizes the interference effect produced by a multiple-pulse optical lattice sequence to enhance the diffraction resolution of atoms,thereby improving the accuracy of calibrating the depth of the optical lattice.A comprehensive and systematic measurement of the experimental process is performed for lattice depth calibration,and the practicality and limitations of the four methods—multiple-pulse KD diffraction,single-pulse KD diffraction,RN diffraction,and parametric oscillation heating—are analyzed.The optical lattice depths obtained using the single-pulse and multiple-pulse KD diffraction methods maintain a high degree of linearity with the detection voltage over the entire range,and these two methods are applicable to a wide range of depths and time intervals.However,the single-pulse KD diffraction method determines the depth of the optical lattice through the fitting of experimental data,which requires collecting a large amount of data.This fitting process introduces potential errors and increases the complexity of the measurement.In the multiple-pulse KD diffraction method,the transmission fidelity of diffraction orders is highly sensitive to the lattice depth,and no data fitting is required during the measurement process,which ensures highly accurate calibration of the optical lattice depth.When the laser interaction time is long,the optical lattice depth measured by the RN diffraction method is consistent with the first two methods.However,as the interaction time between the optical lattice and the atoms increases,the diffraction process must account for changes in atomic momentum,and thus the optical lattice depth obtained by this method may have deviations from the true value.The parametric oscillation heating method can be used for optical lattices of different depths and is effective within a wide parameter range.However,at low depths,the wide energy band of the optical lattice increases the frequency range of atomic loss due to resonant heating,which affects the determination of the resonant frequency and further increases measurement error. Conclusions Through the analysis of the experimental results,we assess the practicality and limitations of the four trap depth measurement methods.RN diffraction is suitable for cases with short interaction time between the optical lattice and the atoms,and its core mechanism is phase modulation based on the momentum state.When the optical lattice interaction time becomes longer,the momentum change becomes significant,which leads to the breakdown of the diffraction mode approximation.The KD diffraction method has the advantage of a broad range of applicability in both time and depth.It can accurately describe multi-stage diffraction phenomena and remains effective even at high depths.Compared to the single-pulse method,the multiple-pulse KD diffraction method is based on the interference effect.By applying a series of pre-set optical lattice pulses,all atoms are transferred to the first-order diffraction momentum state.Compared to RN diffraction and the single-pulse KD diffraction method,this approach improves the intensity and resolution of the diffraction signal,thereby enhancing the accuracy of depth measurements.Furthermore,it has a broad range of applicability in both time and depth.The advantage of the parametric oscillation heating method is its direct detection of the lattice band structure and calibration through the relationship between band transition frequency and depth.However,at low depths,the frequency range of atomic loss caused by resonance heating increases,which can affect the determination of the resonance frequency.The multiple-pulse KD diffraction method enhances lattice depth measurement accuracy.Therefore,this method is expected to provide a technical reference for optical lattice quantum precision measurements and quantum regulation.

Let f be a g-starlike mapping of complex order λ such that x = 0 is a zero of order k + 1 of f(x) − x. By utilizing the geometric properties of f, we characterize its growth theorems and coefficient bounds. The established results yield a unified representation for the growth theorems and coefficient bounds of the subfamilies of normalized biholomorphic mappings with distinct geometric interpretations, respectively. In particular, the estimates are sharp when λ ≤ 0.

Neutral atom arrays have emerged as one of the most promising physical platforms for quantum computing and quantum information processing due to their precise single-atom control and tunable strong interactions. The acousto-optic deflector (AOD) is a key device for constructing and manipulating neutral atom arrays, enabling rapid and high-precision atom trapping and arrangement. However, TeO2-based anomalous Bragg AODs still face challenges in practical applications, such as unclear broadband diffraction conditions, polarization sensitivity, and low efficiency, which limit their performance in multi-degree-of-freedom control. This study investigates the acousto-optic effects in AOD and acousto-optic modulator (AOM), and reveals their differences in diffraction efficiency, polarization characteristics, and applications. By adjusting the azimuthal angle of the AOD, we measure the efficiency and RF bandwidth of the +/- 1st-order diffracted beams under horizontal and vertical polarization incident light, and propose an experimental method to determine the broadband diffraction center frequency and diffraction order. Additionally, we systematically characterize the operational parameters of AOM, clarifying their performance mechanisms and application-specific differences compared with those of AOD. The main conclusions are as follows: 1) The beam deflection performance of an AOD is closely related to the ultrasonic mode or acoustic velocity: a lower sound velocity results in a larger deflection angles. For TeO2 crystals, when a shear wave propagates along the [110] axis (sound velocity: 0.617 km/s), the diffraction angle reaches 0.842 mrad/MHz (laser wavelength: 532 nm). In contrast, when TeO2 is used in AOM with a longitudinal wave along the [001] axis (sound velocity: 4.26 km/s), the diffraction angle decreases to 0.133 mrad/MHz under the same wavelength. 2) To achieve high diffraction efficiency and a broad operational frequency range, the AOD must satisfy the phase-matching condition for anomalous Bragg diffraction. Taking the AOD (model: AA DTSX-250) for example, it operates in a unidirectional incident mode: when horizontally polarized light (extro-ordinary light) is incident, only the -1st-order diffracted beam satisfies the anomalous Bragg condition. The beam undergoes polarization conversion to vertically polarized light (ordinary light), enabling high-efficiency broadband deflection (center frequency: 82 MHz, bandwidth: 45 MHz). To support future two-dimensional deflection implementations, the input and output surfaces of the TeO2 crystal are fabricated with slight bevel angles, ensuring collinearity between the -1st-order diffracted beam and the incident beam at the center frequency. In other cases-(i) +1st-order diffraction of horizontally polarized light and (ii) +/- 1st-order diffraction of vertically polarized light-the anomalous Bragg condition is not met. These beams retain their original polarization and allow only narrowband deflection. These results demonstrate that AODs, leveraging anomalous acousto-optic effects, can achieve high diffraction efficiency, wide frequency tuning ranges, and large deflection angles, making them suitable for high-speed, high-precision beam steering applications. In contrast, AOMs utilize normal acousto-optic effects to perform rapid modulation of beam intensity, frequency, and phase, and are widely used in laser communication and optical fiber transmission. This study provides a detailed technical reference for understanding the operational principles of AODs and their applications in programmable neutral atom arrays.