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Physical Review A

Non-Hermitian spin-orbit-coupling-induced unique dispersion relation and collective dynamics in nonuniform Bose-Einstein condensates

Juncheng Liang, Ai‐Xia Zhang, Ju-Kui Xue

Published Mar 12, 2025• 1 citation
Publisher

Abstract

The interplay of non-Hermiticity and spin-orbit (SO) coupling has attracted great interest in condensed-matter physics, ultracold atomic physics, optics, and other fields. Here we study the ground states, collective modes, and free-expansion dynamics of non-Hermitian SO-coupled Bose-Einstein condensates (BECs) with momentum-dependent gain and loss in a harmonic trap. An efficient analytical method for revealing the impact of non-Hermiticity on the ground states and dynamics of SO-coupled BECs is proposed. A dispersion relation with effective mass ${m}_{2}$ that can be larger than 1, less than 1, or negative is engineered by the momentum-dependent gain and loss, which is distinct from the ordinary SO-coupled BECs, where ${m}_{2}>1$ always holds. Negative effective mass can lead to the self-interference effect of condensates, while ${m}_{2}<1$ means that condensates can gain a larger acceleration when they are subjected to a constant force. Interestingly, the high-order zero-point kinetic energies are derived analytically and confirmed numerically, establishing a link between the zero-point kinetic energy and dispersion relation. In particular, the second-order zero-point kinetic energy can be controlled by the effective mass ${m}_{2}$, which has an important impact on many phenomena of ultracold atomic physics. In addition, another key result is that the frequencies of dipole and breathing modes can exceed the values of traditional BECs without SO coupling when the effective mass ${m}_{2}<1$, showing that gain (loss) is a powerful tool for probing and controlling quantum systems. Moreover, the asymmetric free expansion and self-interference effect of the condensates caused by negative effective masses are observed, and it is found that the rate of expansion is controlled by the effective mass ${m}_{2}$. Our results show that the controllable gain-loss engineering in SO-coupled BECs provides a prospect to explore novel quantum many-body physics.

DOI
10.1103/physreva.111.033309

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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.
In this paper, we bring out several potential signatures of negative mass regimes while investigating an expanding spin-orbit-coupled spinor F=1F=1F=1 Bose-Einstein condensate by analyzing the dispersion relation of the single-particle quantum system. In spin-orbit-coupled spinor condensates, a negative-mass parameter generates a wave packet that propagates in the opposite direction of the momentum. We analyze the dynamics of spin waves analytically and present a simple approach to investigate the expansion of spinor condensates. In particular, we examine the dynamics when both masses are negative, which results in the spinor condensates splitting into two counterpropagating self-interfering packets. Using numerical simulations of the coupled Gross-Pitaevskii equations, we demonstrate the density expansion and self-interference patterns with and without magnetization for repulsive and attractive interactions with different coupling parameters. The highlight of our investigation is that we are able to unearth several phenomena observed in experiments, such as self-interfering packets, pileup, modulation instability, slow down, self-trapping, and gap solitons. In particular, the gap soliton exists at the gap created by the intersection of two negative masses.
We study analytically and numerically the nonlinear collective dynamics of quasi-one-dimensional spin–orbit coupled spin-1 Bose–Einstein condensates trapped in harmonic potential. The ground state of the system is determined by minimizing the Lagrange density, and the coupled equations of motions for the center-of-mass coordinate of the condensate and its width are derived. Then, two low energy excitation modes in breathing dynamics and dipole dynamics are obtained analytically, and the mechanism of exciting the anharmonic collective dynamics is revealed explicitly. The coupling among spin–orbit coupling, Raman coupling and spin-dependent interaction results in multiple external collective modes, which leads to the anharmonic collective dynamics. The cooperative effect of spin momentum locking and spin-dependent interaction results in coupling of dipolar and breathing dynamics, which strongly depends on spin-dependent interaction and behaves distinct characters in different phases. Interestingly, in the absence of spin-dependent interaction, the breathing dynamics is decoupled from spin dynamics and the breathing dynamics is harmonic. Our results provide theoretical evidence for deep understanding of the ground sate phase transition and the nonlinear collective dynamics of the system.
Abstract In this paper, we investigate the spin and tunneling dynamics of a spin–orbit-coupled noninteracting Bose–Einstein condensate in a periodically driven non-Hermitian double-well potential. Under high-frequency driving, we obtain the effective time-averaged Hamiltonian by using the standard time-averaging method, and analytically calculate the Floquet quasienergies, revealing that the parity-time ( )-breaking phase transition appears even for arbitrarily small non-Hermitian parameters when the spin–orbit coupling strength takes half-integer value, irrespective of the values of other parameters used. When the system is -symmetric with balanced gain and loss, we find numerically and analytically that in the broken -symmetric regions, there will exist the net spin current together with a vanishing atomic current, if we drop the contribution of the exponential growth of the norm to the current behaviors. When the system is non- -symmetric, though the quasienergies are partial complex, a stable net spin current can be generated by controlling the periodic driving field, which is accompanied by a spatial localization of the condensate in the well with gain. The results deepen the understanding of non-Hermitian physics and could be useful for engineering a variety of devices for spintronics.