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.

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.

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.

We report on the optimal production of the Bose and Fermi mixtures with Rb-87 and K-40 in a crossed optical dipole trap (ODT). We measure the atomic number and lifetime of the mixtures in combination of the spin state |F = 9/2, m(F) = 9/2 > of K-40 and |1, 1 > of Rb-87 in the ODT, which is larger and longer compared with the combination of the spin state |9/2, 9/2 > of K-40 and |2, 2 > of Rb-87 in the ODT. We observe the atomic numbers of Rb-87 and K-40 shown in each stage of the sympathetic cooling process while gradually reducing the depth of the optical trap. By optimizing the relative loading time of atomic mixtures in the MOT, we obtain the large atomic number of K-40 (similar to 6 x 10(6)) or the mixtures of atoms with an equal number (similar to 1.6 x 10(6)) at the end of evaporative cooling in the ODT. We experimentally investigate the evaporative cooling in an enlarged volume of the ODT via adding a third laser beam to the crossed ODT and found that more atoms (8 x 10(6)) and higher degeneracy (T/T-F = 0.25) of Fermi gases are obtained. The ultracold atomic gas mixtures pave the way to explore phenomena such as few-body collisions and the Bose-Fermi Hubbard model, as well as for creating ground-state molecules of (RbK)-Rb-87-K-40.

We experimentally observe the collective excitation (called surface-mode excitation) of Bose–Einstein condensate of 23 Na by ramping the external magnetic field across the high-partial wave magnetic Feshbach resonance corresponding to vary the atomic interaction. We check the collective surface mode excitation of | 1 , 1 ⟩ state for the three d-wave and three g-wave Feshbach resonances below 600 G and find that only two d-wave resonances present the strong excitation, another d-wave resonance only creates a weak excitation, and all g-wave resonances do not, which reflects the strength of these magnetic Feshbach resonances. For the collective excitation, the excitation of surface modes along the axial weak-confinement and radial strong-confinement of optical dipole trap shows different characteristics. We also study the lifetime of the collective oscillation by measuring the damping rate of the oscillation amplitude, which is caused by the mechanisms of dephasing effect and collisional relaxation. This excitation method gives us a new tool for investigating the properties of ultracold quantum gases without changing the trap frequencies.

We report a compact experimental setup for producing a quantum degenerate mixture of Bose 23 Na and Fermi 40 K gases. The atoms are collected in dual dark magneto–optical traps (MOT) with species timesharing loading to reduce the light-induced loss, and then further cooled using the gray molasses technique on the D 2 line for 23 Na and D 1 line for 40 K. The microwave evaporation cooling is used to cool 23 Na in | F = 2, m F = 2〉 in an optically plugged magnetic trap, meanwhile, 40 K in | F = 9/2, m F = 9/2〉 is sympathetically cooled. Then the mixture is loaded into a large volume optical dipole trap where 23 Na atoms are immediately transferred to |1,1〉 for further effective cooling to avoid the strong three-body loss between 23 Na atoms in |2,2〉 and 40 K atoms in |9/2,9/2〉. At the end of the evaporation in optical trap, a degenerate Fermi gas of 40 K with 1.9 × 10 5 atoms at T / T F = 0.5 in the |9/2,9/2〉 hyperfine state coexists with a Bose–Einstein condensate (BEC) of 23 Na with 8 × 10 4 atoms in the |1,1〉 hyperfine state at 300 nK. We also can produce the two species mixture with the tunable population imbalance by adjusting the 23 Na magneto–optical trap loading time.

Observation of strong correlations and superconductivity in twisted-bilayer graphene1-4 has stimulated tremendous interest in fundamental and applied physics5-8. In this system, the superposition of two twisted honeycomb lattices, generating a moiré pattern, is the key to the observed flat electronic bands, slow electron velocity and large density of states9-12. Extension of the twisted-bilayer system to new configurations is highly desired, which can provide exciting prospects to investigate twistronics beyond bilayer graphene. Here we demonstrate a quantum simulation of superfluid to Mott insulator transition in twisted-bilayer square lattices based on atomic Bose-Einstein condensates loaded into spin-dependent optical lattices. The lattices are made of two sets of laser beams that independently address atoms in different spin states, which form the synthetic dimension accommodating the two layers. The interlayer coupling is highly controllable by a microwave field, which enables the occurrence of a lowest flat band and new correlated phases in the strong coupling limit. We directly observe the spatial moiré pattern and the momentum diffraction, which confirm the presence of two forms of superfluid and a modified superfluid to insulator transition in twisted-bilayer lattices. Our scheme is generic and can be applied to different lattice geometries and for both boson and fermion systems. This opens up a new direction for exploring moiré physics in ultracold atoms with highly controllable optical lattices.

We report on the efficient creation of a sample of 2.2×104 fermionic polar molecules 23Na40K in their rovibrational ground state X1Σ+ |ν = 0, J = 0〉 at 247 nK via an intermediate state of the spin-orbit coupled complex B1Π |ν = 4〉 ∼ c3Σ+ |ν = 25〉. Compared with the intermediate state of the coupled complex B1Π |ν = 12〉 ∼ c3Π+ |ν = 35〉, this intermediate state has the larger Franck-Condon factors for up- and down-leg coupling of stimulated Raman adiabatic passage (STIRAP). We demonstrate this two-photon pathway to the 23Na40K ground state molecules and find that the one-way STIRAP transfer efficiency reaches 75

通过超冷原子的空间自由飞行来获取原子云在动量空间的信息，是超冷原子实验研究中一个重要的探测手段。磁Feshbach共振调控相互作用的超冷原子，需要高偏置磁场下空间自由飞行来获得相互作用能的信息，因此磁场的空间均匀分布对原子自由飞行会产生重要影响。本文对两种绕制的线圈进行了数值模拟，计算了在亥姆霍兹组态下的磁场分布产生，并实验研究了钠原子玻色爱因斯坦凝聚体在不同磁场分布下的自由飞行展开，分析给出了影响自由飞行展开原子密度的磁场线圈参数，为今后设计磁Feshbach共振线圈提供了重要依据。

We demonstrate that dual dark magnetic-optical-traps (MOTs) have great importance in the two-species 87 Rb and 40 K mixture compared with dual bright MOTs. The dark MOT has a little improvement in the trapping of single-species 87 Rb or 40 K gases compared with bright MOT. For the case of loading two-species 87 Rb and 40 K simultaneously, the improvement of 40 K in the dual dark MOTs is mainly from the reduction of light-assisted collision losses. The dual dark MOTs employ a pair of conical lenses to produce the hollow beam for repump laser with high efficiency. The number and density of 87 Rb and 40 K atoms after evaporative cooling in the hybrid magnetic trap with dark MOT loading are compared with those in bright MOT. The atoms with large number and high density make it easier to realize the quantum degenerate of Bose–Fermi mixture.

We report experimental realization of the space-dependent interaction by optical controlled narrow p-wave magnetic Feshbach resonance in a K-40 Fermi gas. A space varied optical field at the tune-out wavelength is applied to illuminate the atomic sample, which drives the bound-to-bound molecular transition to shift the energy of a closed-channel molecule state. Due to the position varied atomic interaction induced by the different laser intensity distribution across the entire Fermi atom cloud, the space-dependent atomic loss rate is observed. This scheme provides a control technique to study the Fermi gas with the space-dependent atomic p-wave interaction, and has great potential in quantum simulation.

We experimentally realize two-dimensional（2D） single-layer ultracold gases of 87 Rb by dynamically tuning the periodicity of a standing wave, known as accordion lattice. In order to load 87 Rb Bose–Einstein condensate into single dark fringe node of the blue detuning optical lattice, we reduce the lattice periodicity from 26.7 μm to 3.5 μm with the help of an acousto-optic deflector（AOD） to compress the three-dimensional BEC adiabatically into a flat and uniform quasi-2D single-layer. We describe the experimental procedure of the atoms loading into the accordion lattice in detail and present the characteristics of the quasi-2D ultracold gases. This setup provides an important platform for studying in-and out-of equilibrium physics, phase transition and 2D topological matter.

We report a novel method to prepare a mixture of 40K Fermi gas having an equal population of the two ground magnetic spin states confined in an optical dipole trap, in the presence of an noisy quantization (magnetic) field. We realize the equal population mixture by applying a series of RF pulses. We observe the dependence of the population distribution between two spin states on the number of the applied RF pulses and find that the decoherence effects leading to the population fluctuations are overcome by the high number of RF pules. Our demonstrated technique can be potentially used in the precision measurement experiments with ultracold gases in noisy environments.

The collective spontaneous emission of many atoms is significantly different from that of a single atom, depending on the geometry and the phase correlation of atomic ensembles. However, experimental observation of arbitrary superradiant and subradiant states of atoms remains challenging due to the difficulties in both preparation and detection of those states. Here we report the time-resolved observation of superradiance from a timed Dicke state in a momentum-space superradiance lattice of Bose-Einstein condensates, which enables an in situ measurement of the coherent lattice dynamics involving both superradiant and subradiant states. The long-lasting oscillation in the superradiant emission is contributed by population transport from the subradiant states in the superradiance lattice. This work paves the way to prepare and observe subradiant states, which has promising applications in quantum information processing.

We study the periodic potential of one-dimensional optical lattice originated from scalar shift and vector shift by manipulating the lattice polarizations. The ac Stark shift of optical lattice is measured by Kapitza-Dirac scattering of $^{87}$Rb Bose-Einstein condensate and the characteristics of spin-dependent optical lattice are presented by scanning the lattice wavelength between the D1 and D2 lines. At the same time, tune-out wavelengths that ac Stark shift cancels can be probed by optical lattice. We give the tune-out wavelengths in more general cases of balancing the contributions of both the scalar and vector shift. Our results provide a clear interpretation for spin-dependent optical lattice and tune-out wavelengths, and help to design it by choosing the appropriate lattice wavelength.

In this paper, we develop a new method to adjust the Raman coupling strength by using the relative phase between two pairs of Raman lasers. The stimulated Raman transition process is highly controllable and has the characteristics of multiple degrees of freedom. In experiments on ultracold atoms, the populations of atomic energy levels can be adjusted by taking an appropriate Raman light intensity and interaction time, and by detuning the two-photon frequency. The intensity of the Raman laser is usually changed to adjust the Raman coupling strength. Based on two-level atoms, a new method of accurately controlling the Raman coupling strength by using the relative phase between two pairs of Raman light beams is developed. This technology can achieve coherent manipulation of atomic quantum states, which greatly broadens the ability of ultracold atoms to perform quantum simulations. First, the 87Rb Bose-Einstein condensate is realized by using an optical dipole trap. Then, the two pairs of Raman lasers are designed with a special optical path to keep the relative phase of the two pairs of Raman lasers stable in the transmission process, and can be controlled accurately. Then the two pairs of Raman light beams act on the two ground state hyperfine energy levels \begin{document}$ |1, 1\rangle $\end{document} and \begin{document}$ |1, 0\rangle $\end{document} of the 87Rb atom. In the experiment, we observe the relation between the percentage of atoms in the two quantum states and the relative phase between the two pairs of Raman light beams. This method provides a unique control parameter for ultracold atom quantum simulation experiments, which is the laser phase. It is hoped that this technology can be used to manipulate the interaction between light and atoms in the future to achieve more abundant physical phenomena.

We report the measurement of the Rydberg excitation spectrum by two-photon process in ultracold( 40)K Fermi gases. Two different methods are employed to measure the Rydberg excitation spectrum, depending on the power of the probe laser. One scheme is to reduce atomic losses by means of electromagnetically induced transparency. The other is to enhance the atomic losses by spontaneous avalanche ionization due to the strong Rydberg-Rydberg interactions. We verify the consistency of both of the methods. The highest Rydberg states detectable in our experiment are limited to n <= 62 due to the competition between the long Rydberg blockade effective range and the limited atomic cloud size.

We report the high-resolution photoassociation (PA) spectroscopy of a Rb-87 Bose-Einstein condensate (BEC) to excited molecular states near the dissociation limit of 5P(1/2) + 5S(1/2) by optical Bragg scattering. Since the detection of optical Bragg scattering in the BEC has a high signal-noise ratio, we obtain the high-resolution PA spectrum of excited molecular states in the range of +/- 1 GHz near the dissociation limit of 5P(1/2) + 5S(1/2). We compare the results with the conventional method of trap loss and show that the results agree with each other very well. Many interesting phenomena of excited molecular states are observed, such as light-induced frequency shift and anomalous strong bound molecular lines at the atomic transition from vertical bar F = 1 > to vertical bar F' = 2 >. The observed excited molecular states in the range of +/- 1 GHz near the dissociation limit of 5P(1/2) + 5S(1/2) should help to further improve long-range bound-state models near the dissociation limit.

We report the high resolution photoassociation (PA) spectroscopy of a $^{87}Rb$ Bose-Einstein condensate (BEC) to excited molecular states near the dissociation limit of $5P_{1/2} +5S_{1/2}$ by optical Bragg scattering. Since the detection of optical Bragg scattering in BEC has a high signal-noise ratio, we obtain the high resolution PA spectrum of excited molecular states in the range of $\pm1$ GHz near the dissociation limit of $5P_{1/2} +5S_{1/2}$. We compare the results with the conventional method of trap loss and show that the results agree each other very well. Many interesting phenomena of excited molecular states are observed, such as light-induced frequency shift and the anomalous strong bound molecular lines at the atomic transition from $|F=1\rangle$ to $|F^{\prime}=2\rangle$. The observed excited molecular states in the range of $\pm1$ GHz near the dissociation limit of $5P_{1/2} +5S_{1/2}$ are never reported before, which will help to further improve the long range bound state models near the dissociation limit.