Observation of Bloch Oscillations in Molecular Rotation

We report the observation of rotational Bloch oscillations in a gas of nitrogen molecules kicked by a periodic train of femtosecond laser pulses. A controllable detuning from the quantum resonance creates an effective accelerating potential in angular momentum space, inducing Bloch-like oscillations of the rotational excitation. These oscillations are measured via the temporal modulation of the refractive index of the gas. Our results introduce room-temperature laser-kicked molecules as a new laboratory for studies of localization phenomena in quantum transport.

Figure 1

The periodically kicked rotor as a particle in a 1D lattice. (a) For a rotor kicked at the exact quantum resonance, the dynamics can be described by a tight-binding model. The angular momentum levels $J$ form a discrete 1D grid, and the laser pulses couple sites with $\mathrm{\Delta }J=\pm 2$, where the coupling strength is proportional to the effective kick strength $P$ of the pulses (see the text). (b) A detuning from the quantum resonance introduces an effective potential $V(J)$ to the model. The dynamics are then similar to Bloch oscillations: A wave packet (particle) is accelerated by the effective potential, and its wave vector $k$ grows. When it reaches the edge of the Brillouin zone (here at $k=\pi /2$), the wave is reflected by Bragg reflection.

Figure 2

Bloch oscillations in the angular momentum of laser-kicked ${{}^{14}\mathrm{N}}_2$ molecules. The figure displays the simulated population of the angular momentum levels $J$, as a function of the number of laser pulses. The initial rotational temperature is 298 K. The considered pulse train parameters are $\tau =8.36\mathrm{ps}$ (0.2% less than the revival time of 8.38 ps) and an effective interaction strength of $P=5$ (see the text).

Figure 3

Simplified sketch of the experimental setup. A Ti:sapphire source generates an 800 nm pulse that enters a pump-probe setup. The pump is split into an eight pulse train using three nested interferometers. The probe pulse is converted to circularly polarized 400 nm with variable path length. The beams are focused using an off-axis parabola (depicted as a lens). Molecular alignment triggered by the strong pump train causes birefringence that alters the circular polarization of the weak probe pulse. The probe’s polarization is split and measured, yielding a time-dependent molecular alignment signal that can be time-averaged to yield population alignment. The abbreviations used are BS, beam splitter; IF, interferometer; HWP, half wave plate; L, lens; DL, automated delay line; BBO, $\beta$-BBO crystal; QWP, quarter wave plate; BPF, blue pass filter; GC, gas cell; GTP, Glan-Taylor polarizer; and PD, photodiode.

Figure 4

Measured and simulated time-averaged alignment signal. We compare the measured and simulated time-averaged alignment signals for periodically kicked nitrogen molecules, for different values of the kick strength $P$ and the detuning $\delta$. The statistical error of the experimental data is much less than the plot symbols and therefore not plotted.

Figure 5

Period of the Bloch oscillation. The oscillation period is shown as a function of the detuning, for different effective interaction strengths $P$. The lines are the solution of the semiclassical model [Eqs. (3)], and the markers are experimental values (diamonds, $P=5$; squares, $P=4$; circles, $P=3.2$).