Hwang Myung-Joong, Plenio Martin B
Institut für Theoretische Physik and IQST, Albert-Einstein-Allee 11, Universität Ulm, D-89069 Ulm, Germany.
Phys Rev Lett. 2016 Sep 16;117(12):123602. doi: 10.1103/PhysRevLett.117.123602. Epub 2016 Sep 13.
Phase transitions are commonly held to occur only in the thermodynamical limit of a large number of system components. Here, we exemplify at the hand of the exactly solvable Jaynes-Cummings (JC) model and its generalization to finite JC lattices that finite component systems of coupled spins and bosons may exhibit quantum phase transitions (QPTs). For the JC model we find a continuous symmetry-breaking QPT, a photonic condensate with a macroscopic occupation as the ground state, and a Goldstone mode as a low-energy excitation. For the two site JC lattice we show analytically that it undergoes a Mott-insulator to superfluid QPT. We identify as the underlying principle of the emergence of finite system QPTs the combination of increasing atomic energy and increasing interaction strength between the atom and the bosonic mode, which allows for the exploration of an increasingly large portion of the infinite dimensional Hilbert space of the bosonic mode. This suggests that finite system phase transitions will be present in a broad range of physical systems.
通常认为相变仅在大量系统组分的热力学极限中发生。在此，我们以可精确求解的 Jaynes-Cummings（JC）模型及其对有限 JC 晶格的推广为例，说明耦合自旋和玻色子的有限组分系统可能表现出量子相变（QPT）。对于 JC 模型，我们发现了一个连续对称性破缺的 QPT、一个以宏观占据为基态的光子凝聚态以及一个作为低能激发的戈德斯通模式。对于双位点 JC 晶格，我们通过解析表明它经历了从莫特绝缘体到超流体的 QPT。我们确定有限系统 QPT 出现的基本原理是原子能量增加与原子和玻色子模式之间相互作用强度增加的结合，这使得能够探索玻色子模式无限维希尔伯特空间中越来越大的部分。这表明有限系统相变将存在于广泛的物理系统中。
