Directly Observing Squeezed Phonon States with Femtosecond X-Ray Diffraction

Squeezed states are quantum states of a harmonic oscillator in which the variance of two conjugate variables each oscillate out of phase. Ultrafast optical excitation of crystals can create squeezed phonon states, where the variance of the atomic displacements oscillates due to a sudden change in the interatomic bonding strength. With femtosecond x-ray diffraction we measure squeezing oscillations in bismuth and conclude that they are consistent with a model in which electronic excitation softens all phonon modes by a constant scaling factor.

Figure 1

Sketch of the bismuth unit cell, showing directions used for the diffraction measurements.

Figure 2

(a) Time-resolved diffraction from the (111) lattice planes, showing the coherent $A_{1g}$ mode. The solid line shows a fit using a constant frequency model [18] which is also used to estimate the pump pulse arrival time $t=0$. (b) Diffraction signal from the $(10\overline{1})$ planes at room temperature (purple triangles) and the $(11\overline{2})$ planes at both room temperature (blue circles) and at 170 K (green diamonds). (c) Change in the direction-projected mean-square atomic displacement for $[10\overline{1}]$ at room temperature (purple triangles), and $[11\overline{2}]$ at room temperature (blue circles) and at 170 K (green diamonds). For clarity, the data for $[10\overline{1}]$ and $[11\overline{2}]$ at 170 K have been displaced vertically. The solid lines are the results of the fit discussed in the text. The dashed blue line is the prediction for the $[11\overline{2}]$ direction at room temperature based on DFT [26].