Anderson Wall and Bloch Oscillations in Molecular Rotation

We describe a universal behavior of linear molecules excited by a periodic train of short laser pulses under quantum resonance conditions. In a rigid rotor, the resonance causes an unlimited ballistic growth of the angular momentum. We show that the centrifugal distortion of rotating molecules eventually halts the growth, by causing Anderson localization beyond a critical value of the angular momentum—the Anderson wall. Its position solely depends on the molecular rotational constants and lies in the range of a few tens of $\hslash$. Below the wall, rotational excitation oscillates with the number of pulses due to a mechanism similar to Bloch oscillations in crystalline solids. We suggest optical experiments capable of observing the rotational Anderson wall and Bloch oscillations at near-ambient conditions with the help of existing laser technology.

Figure 1

Selected quasienergy states $|{\chi }_{ϵ}⟩$ (projected on the angular momentum states $|J,0⟩$), for resonantly kicked ${{}^{14}\mathrm{N}}_2$ molecules (kick strength $P=3$). Panel (a) shows extended states in the region of small angular momentum $J$, panel (b) shows localized states close to and above the Anderson wall. The legends depict the quasienergy values (in units of $\hslash /t_{\mathrm{rev}})$ modulo $2\pi$.

Figure 2

Simulated angular momentum distribution as a function of the number of pulses, for resonantly kicked ${{}^{14}\mathrm{N}}_2$ molecules. Each panel shows the result for a different initial state $|{\mathrm{\Psi }}_0⟩$. Pulses are 50 fs long, with kick strength $P=3$. The solid line in panel (a) is a solution of the semiclassical model Eq. (7).

Figure 3

Simulated (a) angular momentum distribution and (b) alignment signal $⟨{\cos }^2\theta ⟩$ as a function of the number of pulses, for resonantly kicked ${{}^{14}\mathrm{N}}_2$ at $T=298\mathrm{K}$. Pulses are 50 fs long with kick strength $P=3$. Nuclear spin statistics cause different intensities of even and odd $J$ [29].