A negative effective mass can be realized in quantum systems by engineering the dispersion relation. A powerful method is provided by spin-orbit coupling, which is currently at the center of intense research efforts. Here we measure an expanding spin-orbit coupled Bose-Einstein condensate whose dispersion features a region of negative effective mass. We observe a range of dynamical phenomena, including the breaking of parity and of Galilean covariance, dynamical instabilities, and self-trapping. The experimental findings are reproduced by a single-band Gross-Pitaevskii simulation, demonstrating that the emerging features—shock waves, soliton trains, self-trapping, etc.—originate from a modified dispersion. Our work also sheds new light on related phenomena in optical lattices, where the underlying periodic structure often complicates their interpretation.

Relative chlorophyll content (SPAD) is an important index for characterizing the nitrogen nutrient status of plants. Continuous, rapid, nondestructive, and accurate estimation of SPAD values in wheat after heading stage can positively impact subsequent nitrogen fertilization management strategies, which regulate grain filling and yield quality formation. In this study, the estimation of SPAD of leaf relative chlorophyll content in spring wheat was conducted at the experimental base in Wuyuan County, Inner Mongolia in 2021. Multispectral images of different nitrogen application levels at 7, 14, 21, and 28 days after the wheat heading stage were acquired by DJI P4M UAV. A total of 26 multispectral vegetation indices were constructed, and the measured SPAD values of wheat on the ground were obtained simultaneously using a handheld chlorophyll meter. Four machine learning algorithms, including deep neural networks (DNN), partial least squares (PLS), random forest (RF), and Adaptive Boosting (Ada) were used to construct SPAD value estimation models at different time from heading growth stages. The model’s progress was evaluated by the coefficient of determination (R²), root mean square error (RMSE), and mean absolute error (MAPE). The results showed that the optimal SPAD value estimation models for different periods of independent reproductive growth stages of wheat were different, with PLS as the optimal estimation model at 7 and 14 days after heading, RF as the optimal estimation model at 21 days after heading, and Ada as the optimal estimation model at 28 d after heading. The highest accuracy was achieved using the PLS model for estimating SPAD values at 14 d after heading (training set R² = 0.767, RMSE = 3.205, MAPE = 0.060, and R² = 0.878, RMSE = 2.405, MAPE = 0.045 for the test set). The combined analysis concluded that selecting multiple vegetation indices as input variables of the model at 14 d after heading stage and using the PLS model can significantly improve the accuracy of SPAD value estimation, provides a new technical support for rapid and accurate monitoring of SPAD values in spring wheat.

We study the phase diagram of a Rashba spin-orbit-coupled Bose-Einstein condensate confined in a two-dimensional toroidal trap. In the immiscible regime we find an azimuthally periodic density distribution, with the periodicity highly tunable as a function of the spin-orbit-coupling strength and which favors an odd number of petals in each component. This allows for a wide range of states that can be created. We further show that in the miscible regime, both components possess states with persistent flows with a unit winding number difference between them and with the absolute values of these winding numbers depending on the spin-orbit-coupling strength. All features of the odd-petal and the persistent flow states can be explained using a simple but effective model.

While a spin–orbit-coupled spin-1 Bose–Einstein condensate (BEC) has been experimentally observed, its elementary excitations remain unclear in the stripe phase. Here, we systematically study the elementary excitations in three distinct phases of a spin–orbit-coupled spin-1 BEC. We find that the excitation spectrum as well as the corresponding static response function and structure factor depend strongly on spin–orbit coupling parameters such as the quadratic Zeeman field and the Rabi frequency. In the stripe phase, besides two gapless Goldstone modes, we show the existence of roton excitations. Finally, we demonstrate that quantum phase transitions between these different phases including the zero-momentum, plane wave and stripe phases are characterized by the sound velocities and the quantum depletion.

Single-particle dynamics of a spin-orbit-coupled Bose-Einstein condensate has recently been investigated in experiments that explore the physics of Landau-Zener tunneling and of the Zitterbewegung. In this paper, we study the influence of a nonlinearity due to interactions on these dynamics and show that the dispersion relation develops interesting loop structures. The atoms can move along the nonlinear dispersion curve in the presence of a weak acceleration force, and we show that the loops lead to straightforward nonlinear Landau-Zener tunneling. However, we find that for the Zitterbewegung, induced by a sudden quench in the spin-orbit-coupling parameters, the nonlinear dispersion is irrelevant.

Synthetic spin-tensor-momentum coupling has recently been proposed for realization in atomic Bose-Einstein condensates. Here we study bright solitons in Bose-Einstein condensates with spin-tensor-momentum coupling and spin-orbit coupling. The properties and dynamics of spin-tensor-momentum-coupled and spin-orbit-coupled bright solitons are identified to be different, which are contributed from the different symmetries.