AI 中文总结
该研究针对光晶格中具有密度依赖规范场的超冷玻色子，采用离散玻戈留波夫理论探究其从玻色-爱因斯坦凝聚体到孤子的一阶量子相变过程，揭示了准粒子模式演化及孤子独特的动力学特性。
AI 中文摘要
被限制在一维光晶格中的超冷玻色子的隧穿会产生一种非平凡的规范场，该规范场取决于所涉及格点之间的密度差。密度依赖隧穿（DDT）会引发从玻色-爱因斯坦凝聚体到局域孤子的一阶量子相变。本文中，我们在弱相互作用极限下研究了整个相变过程中低能准粒子模式的演化。为此，我们采用离散玻戈留波夫理论和色散曲线，发现在孤子相中，偶极（及更高阶）激发的准粒子能量随DDT增加，同时零能模式得以保留。这是由于有效隧穿减小，导致孤子移动的能量代价增大，进而引发更快的偶极振荡。排斥性的格点内原子相互作用通过稳定晶格孤子，进一步将DDT的临界规范场移至更大值，这一点由复规范场平面中的相图和准粒子的模式能隙所证实。我们还表明，由于有效动量具有密度依赖性并会改变孤子的内部结构，孤子不会表现出布洛赫振荡。阱淬灭的动力学响应不会激发局域波包的宽度，且呼吸振荡被抑制。凝聚体的后两种动力学特性因密度依赖规范场的存在而与孤子状态形成独特对比。
英文摘要
Tunneling of ultracold bosons confined in a one-dimensional optical lattice results in a nontrivial gauge field depending on density-difference between the sites involved. The density dependent tunneling (DDT) causes a first-order quantum phase transition from the Bose-Einstein condensate to the localized soliton. Here, we examine the low-lying quasiparticle mode evolution across the transition in the weakly-interacting limit. To this end, we employ the discrete Bogoliubov theory and dispersion curves to reveal an increase in the quasiparticle energies of dipole (and higher) excitations with DDT in the soliton phase while preserving the zero-energy mode. This is due to the decrease in effective tunneling, resulting in a larger energy cost to move the soliton, and causes faster dipole oscillations. The repulsive on-site atomic interaction further shifts the critical gauge field of DDT to a larger value by stabilizing the lattice soliton. The latter is corroborated by a phase diagram in the complex gauge field plane and mode energy gap of quasiparticles. We further show that the soliton does not exhibit Bloch oscillations as the effective momentum becomes density-dependent and deforms its internal structure. The dynamical response of the trap quench does not excite the width of localized wave-packet, and the breathing oscillations are suppressed. The latter two dynamical properties of the condensate uniquely contrast the soliton state due to the density-dependent gauge field.
Comments10 pages, 8 figures
