Vibrational motion in the quantum world requires a superposition of different quantum states - so-called coherences or wave packets. The superposition of two adjacent oscillator states corresponds to a one-quantum coherence, in which the atomic motion is very similar to the classical pendulum. Much more interesting are two-quantum coherences, a true non-classical excitation in which an atom can be in two different places at the same time. Its speed also behaves non-classical, which means that it moves from left to right and from right to left at the same time (see Movie). Such movements exist only for very short times, because the well-defined superposition of the quantum states due to the so-called decoherence within a few picoseconds (1 picosecond = 10^-12s) decays. Such two-phonon coherences are extremely important in the new research field of so-called quantum phononics. There, non-classical atomic movements such as "pinched" or "entangled" phonons are studied.

In the latest issue of the journal Physical Review Letters, researchers at the Max Born Institute in Berlin have used the new method of two-dimensional (2D) terahertz spectroscopy to generate and detect non-classical two-phonon coherences with large spatial amplitudes , In the experiments, a sequence of three phase-locked THz pulses interacts with a 70-μm-thick crystal of the semiconductor indium antimonide (InSb). The electric field emitted by the moving atoms serves as a probe for the atomic movement in real time. A two-dimensional scanning method (a so-called 2D scan), in which the time delay between the three THz pulses is varied, showed pronounced two-phonon signals and was able to reveal their time structure [Fig. 1]. A detailed theoretical analysis has revealed that nonlinear multiple interactions of all three THz pulses are needed to induce such strong two-phonon coherences.

The new experimental method allowed for the first time to detect two-phonon coherences of large amplitude in a crystal. All experimental observations are in excellent agreement with quantum theory. This new type of 2D THz spectroscopy points the way to the generation, analysis, and manipulation of other low-energy excitations in solids, such as, for example. Magnons or optical transitions in excitons or bound to impurities electrons.