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arXiv 1710.04429quant-ph
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复平面中的振荡势阱与绝热定理

Oscillating potential well in complex plane and the adiabatic theorem

Stefano Longhi

备注：
13 pages, 6 figures
发表信息：
Phys. Rev. A 96, 042101 (2017)
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摘要：

在慢变化势阱$V(x,t)=V(x-x_0(εt))$中的量子粒子，以慢频率$ε$在时间上周期性地振动，提供了一个重要的量子力学系统，其中绝热定理不能预测在比$ \sim 1 / ε$更长的时间尺度上的渐近动力学。具体地说，我们考虑一个双阱势$V(x)$维持两个束缚态的频率间隔为$ω_0$，并在复平面上的振动。假设两个不同的空间位移$x_0(t)$：实空间位移$x_0(εt)=A \sin (εt)$，对应于普通的厄米特振动，和复一个$x_0(εt)=A-A \exp( -i εt)$，对应于非厄米特振动。当粒子最初准备在基态的势阱，击穿的绝热演化被发现为厄米和非厄米振荡的振荡频率$ε$接近$ω_0$的奇共振。然而，在这两种情况下，一个不同的物理机制的非绝热转变。对于厄米振荡，避免交叉的准能量观察到在奇共振和非绝热跃迁之间的两个束缚态，导致拉比flopping，可以解释为一个多光子共振过程。对于复振荡势阱，绝热性的破坏是由于在准能量交叉处出现Floquet例外点引起的。

英文摘要：

A quantum particle in a slowly-changing potential well $V(x,t)=V(x-x_0(εt))$, periodically shaken in time at a slow frequency $ε$, provides an important quantum mechanical system where the adiabatic theorem fails to predict the asymptotic dynamics over time scales longer than $ \sim 1 / ε$. Specifically, we consider a double-well potential $V(x)$ sustaining two bound states spaced in frequency by $ω_0$ and periodically-shaken in complex plane. Two different spatial displacements $x_0(t)$ are assumed: the real spatial displacement $x_0(εt)=A \sin (εt)$, corresponding to ordinary Hermitian shaking, and the complex one $x_0(εt)=A-A \exp( -i εt)$, corresponding to non-Hermitian shaking. When the particle is initially prepared in the ground state of the potential well, breakdown of adiabatic evolution is found for both Hermitian and non-Hermitian shaking whenever the oscillation frequency $ε$ is close to an odd-resonance of $ω_0$. However, a different physical mechanism underlying nonadiabatic transitions is found in the two cases. For the Hermitian shaking, an avoided crossing of quasi-energies is observed at odd resonances and nonadiabatic transitions between the two bound states, resulting in Rabi flopping, can be explained as a multiphoton resonance process. For the complex oscillating potential well, breakdown of adiabaticity arises from the appearance of Floquet exceptional points at exact quasi energy crossing.

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