Geometric Effects on Tunneling in Driven Quantum Systems

TL;DR

The paper addresses how geometric effects shape quantum tunneling under external driving by introducing the twisted Landau-Zener (TLZ) model, which embeds a geometric amplitude via the shift vector to modulate tunneling. It derives a closed-form tunneling probability $P(F)=\exp[-\pi (m+\kappa_{\parallel} vF/4)^{2}/(|vF|)]$ and validates it with numerical results, revealing phenomena such as nonreciprocity and perfect tunneling. The TLZ framework is applied to concrete systems including a single spin in a time-dependent field, a saw-tooth chain, and Dirac materials (2D and 3D), uncovering chiral imbalance, rectification, and twist-induced pair production effects. The work also discusses the Keldysh crossover between quantum-tunneling and Floquet/photon-absorption regimes in many-body settings, linking geometric tunneling to nonadiabatic dynamics with potential impact on quantum control and light-driven materials. Overall, the paper provides a unified, geometry-centric approach to nonadiabatic transitions in driven quantum systems, with implications for spintronics, topological pumping, and strong-field physics.

Abstract

We review quantum tunneling provoked by external field driving, focusing on the role of geometric effects. The discussion begins with an overview of tunneling phenomena, including the Landau-Zener model and the Schwinger effect, both of which are essential frameworks to describe the generation of elementary excitation of the system. We also refer to the relation between the modern theory of polarization and the geometry of the system, and introduce the shift vector via adiabatic perturbation theory. Then we introduce the twisted Landau-Zener model and shown how the shift vector modulates tunneling probability, followed by several illustrative applications of this model. We also explain the Keldysh crossover, which is the crossover from a quantum tunneling regime to photon absorption regime in driven systems.

Figures (4)

• Figure 1: Various phenomena provoked by the application of external AC fields in the parameter space of photon energy $\Omega$ and field strength $F$. $\xi$ and $\Delta$ are the correlation length and the gap of the system, respectively. The change of behavior over the Keldysh line $\Omega \simeq \xi F$ is called the Keldysh crossover.
• Figure 2: (a) Time-dependent rotation which transforms the TLZ model into the LZ model. (b) Tunneling probability of the model Eq. \ref{['eq:Hamil_q2']} with $m=0.1$ and $v=1$. Numerically calculated $P(F)$ is shown by circles (the LZ model $\kappa_{\parallel}=0$) and triangles (the TLZ model $\kappa_{\parallel}=0.8$). The dashed and solid lines are the predictions from Eq. \ref{['eq:LZquad']} for the LZ and TLZ models, respectively. The arrow represents the sweeping speed at which the prefect tunneling happens Eq. \ref{['eq:PTspeed']}.
• Figure 3: The schematic picture of the saw-tooth chain model Eq. \ref{['eq:HSaw']}.
• Figure 4: (a) The gap minimum point in the wave number space. (b) The behavior of the total pair production rate $\Gamma_{\xi}$ in the parameter space of $\xi\Omega$ and $E$.