Lewis-Riesenfeld invariants and transitionless quantum driving
Lewis-Riesenfeld invariants and transitionless quantum driving
复制标题
刘易斯-里森菲尔德不变量和无过渡量子驱动
DOI：
10.1103/physreva.83.062116
复制
发表时间：
2011-06-22
影响因子：
2.9
通讯作者：
Muga, J. G.
中科院分区：
文献类型：
--
作者：
Chen, Xi;Torrontegui, E.;Muga, J. G.
近年来，人们提出了不同的方法，并通过实验实现了对量子系统中随时间变化的哈密顿量进行逆工程，并通过非绝热捷径加速慢绝热过程。在Berry提出的“无过渡量子驱动”中，设计了快捷哈密顿量，使系统在任意短的时间内精确地遵循参考哈密顿量定义的近似绝热路径。另一种方法是基于首先设计一个Lewis-Riesenfeld不变量来携带哈密顿函数的特征态从指定的初始构型到最终构型，同样是在任意时间内，然后从不变量构造连接这些边界构型的瞬态哈密顿函数。我们表明，这两种方法，在形式上和结果上明显不同，实际上是密切相关的，并且可能是等效的，因此，其中一种方法中的逆向工程操作可以根据另一种方法的概念和操作来重新解释和理解。作为明确的例子，我们研究了时变谐波陷阱的展开和两能级系统的状态制备。
Different methods have been recently put forward and implemented experimentally to inverse engineer the time-dependent Hamiltonian of a quantum system and accelerate slow adiabatic processes via nonadiabatic shortcuts. In the ''transitionless quantum driving'' proposed by Berry, shortcut Hamiltonians are designed so that the system follows exactly, in an arbitrarily short time, the approximate adiabatic path defined by a reference Hamiltonian. A different approach is based on first designing a Lewis-Riesenfeld invariant to carry the eigenstates of a Hamiltonian from specified initial to final configurations, again in an arbitrary time, and then constructing from the invariant the transient Hamiltonian that connects these boundary configurations. We show that the two approaches, apparently quite different in form and so far in results, are, in fact, strongly related and potentially equivalent, so that the inverse-engineering operations in one of them can be reinterpreted and understood in terms of the concepts and operations of the other one. We study, as explicit examples, expansions of time-dependent harmonic traps and the state preparation of two-level systems.