具有大磁场的两足梯中的玻色子理论
Theory of Bosons in two-leg ladders with large magnetic fields
摘要：
我们计算了囚禁在两个阶梯上的玻色气体的基态，其中拉曼诱导的跳跃模拟了大磁场的作用。在平均场的极限下，每个位置有大量的粒子，这映射到一个均匀受挫的双腿阶梯经典自旋模型。净粒子流在基态总是消失，但一般有一个有限的"手征电流"，对应于两个腿上的相等和相反的流动。我们改变了阶梯上跳跃的强度和玻色子之间的相互作用。我们发现三个阶段：（1）"饱和手征电流相"（SCCP），其中密度是均匀的并且手征电流简单地与磁场的强度有关。在这种状态下，唯一的对称性破缺是$U(1)$凝聚相。(2)一个"偏置梯形相位"（BLP），其中一条腿上的密度高于另一条腿。在低密度段，流体速度较高，因此净流为零。除了$U(1)$凝聚相之外，它还具有破缺的$Z_2$反射对称性。(3)“调制密度相位”（MDP），其中原子密度沿阶梯调制。除了$U(1)$凝聚相之外，它还有一个对应于密度波平移的第二个破缺的$U(1)$对称性。我们进一步研究了BLP中凝聚态的涨落，发现了一个类似于Roton-Maxon的激发谱。减少沿梯级的跳变会使频谱变软。当“旋子”的能量达到零时，BLP变得不稳定。我们描述了这些阶段的实验签名，包括改变拉曼跃迁的频率的响应。
英文摘要：
We calculate the ground state of a Bose gas trapped on a two-leg ladder where Raman-induced hopping mimics the effect of a large magnetic field. In the mean-field limit, where there are large numbers of particles per site, this maps onto a uniformly frustrated two-leg ladder classical spin model. The net particle current always vanishes in the ground state, but generically there is a finite "chiral current", corresponding to equal and opposite flow on the two legs. We vary the strength of the hopping across the rungs of the ladder and the interaction between the bosons. We find three phases: (1) A "saturated chiral current phase" (SCCP), where the density is uniform and the chiral current is simply related to the strength of the magnetic field. In this state the only broken symmetry is the $U(1)$ condensate phase. (2) A "biased ladder phase" (BLP), where the density is higher on one leg than the other. The fluid velocity is higher on the lower density leg, so the net current is zero. In addition to the $U(1)$ condensate phase, this has a broken $Z_2$ reflection symmetry. (3) A "modulated density phase" (MDP), where the atomic density is modulated along the ladder. In addition to the $U(1)$ condensate phase, this has a second broken $U(1)$ symmetry corresponding to translations of the density wave. We further study the fluctuations of the condensate in the BLP, finding a roton-maxon like excitation spectrum. Decreasing the hopping along the rungs softens the spectrum. As the energy of the "roton" reaches to zero, the BLP becomes unstable. We describe the experimental signatures of these phases, including the response to changing the frequency of the Raman transition.
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