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Journal of Physics B Atomic Molecular and Optical Physics

Magnetic phase transitions of nonuniform spin-tensor-momentum coupled Bose–Einstein condensates

Jie Wang, Ning Yue, Ai‐Xia Zhang, Xin Qiao, Ji-Ming Gao, Zi-Fa Yu, Xiaobo Zhang, Ju-Kui Xue

Published Apr 15, 2026• 1 citation
Publisher

Abstract

Abstract Spin-tensor-momentum coupling (STMC) induces dramatic change of the single-particle energy spectrum, resulting in rich and novel quantum ground state phases. Here, considering the atomic interactions, the STMC induced Z 2 symmetry breaking of the energy band, the tricritical point and the magnetic phase transitions in trapped STMC Bose–Einstein condensates are presented analytically and numerically. We demonstrate that the ground state momentum and spin tensor are coupled by STMC and the asymmetry of the energy band is persistent in STMC system, resulting in phase transition between magnetized and unmagnetized plane wave phases or between the two unmagnetized plane wave phases. The critical conditions for the phase transitions are obtained analytically, clarifying the physical mechanisms behind the phase transitions. Particularly, a tricritical point is predicted, where different types of energy band merge and the first-order phase transition and the second-order phase transition meet. Interestingly, it is shown that the ground state strongly depends on the external trapping potential, establishing a potential method for manipulating the phase transitions of the system. We provide a theoretical evidence for deep understanding and experimental manipulation of novel quantum phases in STMC systems.

DOI
10.1088/1361-6455/ae5ffe

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Abstract Spin-tensor-momentum coupling (STMC) induces dramatic change of the single-particle energy spectrum, resulting in rich and novel quantum ground state phases. Here, considering the atomic interactions, the STMC induced Z 2 symmetry breaking of the energy band, the tricritical point and the magnetic phase transitions in trapped STMC Bose–Einstein condensates are presented analytically and numerically. We demonstrate that the ground state momentum and spin tensor are coupled by STMC and the asymmetry of the energy band is persistent in STMC system, resulting in phase transition between magnetized and unmagnetized plane wave phases or between the two unmagnetized plane wave phases. The critical conditions for the phase transitions are obtained analytically, clarifying the physical mechanisms behind the phase transitions. Particularly, a tricritical point is predicted, where different types of energy band merge and the first-order phase transition and the second-order phase transition meet. Interestingly, it is shown that the ground state strongly depends on the external trapping potential, establishing a potential method for manipulating the phase transitions of the system. We provide a theoretical evidence for deep understanding and experimental manipulation of novel quantum phases in STMC systems.
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Spin-orbit-coupled bosons can exhibit rich equilibrium phases at low temperature and in the presence of particle-particle interactions. In the case with a 1D synthetic spin-orbit interaction, it has been observed that the ground state of a Bose gas can be a normal phase, stripe phase, or magnetized phase in different parameter regimes. The magnetized states are doubly degenerate and consist of a many-particle two-state system. In this work, we investigate the nonequilibrium quantum dynamics by switching on a simple one-dimensional optical lattice potential as external perturbation to induce resonant couplings between the magnetized phases, and predict a quantum spin dynamics which cannot be obtained in the single-particle systems. In particular, due to particle-particle interactions, the transition of the Bose condensate from one magnetized phase to the other is forbidden when the external perturbation strength is less than a critical value, and a full transition can occur only when the perturbation exceeds such critical strength. This phenomenon manifests itself a dynamical phase transition, with the order parameter defined by the time-averaged magnetization over an oscillation period, and the critical point behavior being exactly solvable. The thermal fluctuations are also considered in detail. From numerical simulations and exact analytic studies we show that the predicted many-body effects can be well observed with the current experiments.
The interplay of quantum fluctuation through the Lee-Huang-Yang (LHY) correction and spin-orbit coupling can modify the stability of the ultradilute Bose-Bose mixtures and result in rich nonlinear physics. Here, under the action of spin-orbit coupling, LHY correction, and rotation, the ground state and vortex excitation of spin-orbit coupled Bose-Einstein condensates (BECs) with LHY correction trapped in a rotating potential are studied. Stable isotropic and anisotropic ground states with zero momentum (in the zero-momentum phase) and nonzero momentum (in the plane wave phase) are obtained. It is shown that anisotropic ground states are persistent near the phase boundary. Particularly, unpolarized and polarized vortex states are predicted. The phase transition condition, the effective mass and quadrupole surface mode describing the anisotropic (deformation) of the condensates, and the critical rotation frequency for vortex excitation are provided analytically. Owing to the action of spin-orbit coupling, the effective mass of the condensates is spatially dependent and asymmetric in two phases, resulting in distinct quadrupole modes, deformations, and vortex excitations in the two phases, especially when the LHY correction is present. The LHY correction promotes the system in the zero-momentum phase with unpolarized vortex states, while the spin-orbit coupling promotes the emergence of a plane wave phase with polarized vortex states. The phase transition and vortex excitation can be well manipulated by spin-orbit coupling, Raman coupling, LHY correction, and external potential.
The recent experimental realization of spin-orbit (SO) coupling for spin-1 ultracold atoms opens an interesting avenue for exploring SO-coupling-related physics in large-spin systems, which is generally unattainable in electronic materials. In this paper, we study the effects of interactions between atoms on the ground states and collective excitations of SO-coupled spin-1 Bose-Einstein condensates (BECs) in the presence of a spin-tensor potential. We find that ferromagnetic interaction between atoms can induce a stripe phase exhibiting in-phase or out-of-phase modulating patterns between spin-tensor and zero-spin-component density waves. We characterize the phase transitions between different phases using the spin-tensor density as well as the collective dipole motion of the BEC. We show that there exists a double maxon-roton structure in the Bogoliubov-excitation spectrum, attributed to the three band minima of the SO-coupled spin-1 BEC.
We systematically investigate the weakly trapped spin-1 Bose-Einstein condensates with spin-orbit coupling in an external Zeeman field. We find that the mean-field ground state favors either a magnetized standing-wave phase or plane-wave phase when the strength of the Zeeman field is below a critical value related to the strength of spin-orbit coupling. The Zeeman field can induce a phase transition between standing-wave and plane-wave phases, and we determine the phase boundary analytically and numerically. The magnetization of these two phases responds to the external magnetic field in a very unique manner: the linear Zeeman effect magnetizes the standing-wave phase along the direction of the magnetic field, but the quadratic Zeeman effect demagnetizes the plane-wave phase. When the strength of Zeeman field surpasses the critical value, the system is completely polarized to a ferromagnetic state or polar state with zero momentum.
We investigate the transitions of ground states induced by zero momentum (ZM) coupling in pseudospin-1/2 Rashba spin-orbit coupled Bose-Einstein condensates confined in a harmonic trap. In a weak harmonic trap, the condensate presents a plane wave (PW) state, a stripe state or a spin polarized ZM state, and the particle distribution of the stripe state is weighted equally at two points in the momentum space without ZM coupling. The presence of ZM coupling induces an imbalanced particle distribution in the momentum space, and leads to the decrease of the amplitude of the stripe state. When its strength exceeds a critical value, the system experiences the transition from stripe phase to PW phase. The boundary of these two phases is shifted and a new phase diagram spanned by the ZM coupling and the interatomic interactions is obtained. The presence of ZM coupling can also achieve the transition from ZM phase to PW phase. In a strong harmonic trap, the condensate exhibits a vortex lattice state without ZM coupling. For the positive effective Rabi frequency of ZM coupling, the condensate is driven from a vortex lattice state to a vortex-free lattice state and finally to a PW state with the increase of coupling strength. In addition, for the negative effective Rabi frequency, the condensate is driven from a vortex lattice state to a stripe state, and finally to a PW state. The stripe state found in the strong harmonic trap is different from that in previous works because of its nonzero superfluid velocity along the stripes. We also discuss the influences of the ZM coupling on the spin textures, and indicate that the spin textures are squeezed transversely by the ZM coupling.