Symmetry breaking with ultrashort light pulses opens up new quantum pathways for coherent phonons

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The magenta dashed lines with arrows illustrate the diffraction of hard femtosecond X-ray pulses from the lattice planes of the Bi crystal. Red spheres connected by red lines: Unit cell of an unexcited bismuth crystal containing two Bi atoms with one atom at the origin. The second atom is shown as green balls in panel (b) and is indicated as small balls in panels (c) and (d). Blue spheres connected by blue lines: Unit cell of the photoexcited crystal with reduced symmetry containing four Bi atoms. (c) Orange curve: electric field of the optical excitation pulse. Weak and/or short wavelength pulses can only excite coherent phonons with identical motions in all unit cells indicated by light red balls and arrows. (d) Strong excitation with femtosecond mid-infrared pulses reduces the symmetry of the crystal and allows opposing atomic motions (light blue spheres and arrows) in adjacent unit cells. Credit: MBI/M. runge

The atoms in a crystal form a regular lattice, in which they can move small distances from their equilibrium positions. Such phonon excitations are represented by quantum states. A superposition of phonon states defines a so-called phonon wave packet, which is connected to the collective coherent oscillations of the atoms in the crystal.

Coherent phonons can be generated by excitation of the crystal with a femtosecond light pulse, and their movements in space and time can be followed by scattering an ultrashort X-ray pulse from the excited material. The scattered X-ray pattern provides a direct view of the momentary position and distances between atoms. A sequence of such patterns provides a “movie” of atomic motions.

The physical properties of coherent phonons are determined by the symmetry of the crystal, which represents a periodic arrangement of identical unit cells. Weak optical excitation does not change the symmetry properties of the crystal. In this case, coherent phonons with identical atomic motions in all unit cells are excited. Conversely, strong optical excitation can break the symmetry of the crystal and cause the atoms in adjacent unit cells to oscillate differently.

While this mechanism has the potential to access other phonons, it has not been explored so far.

In the diary Physical review b, researchers from the Max-Born-Institute in Berlin, in collaboration with researchers from the University of Duisburg-Essen, demonstrated a new concept for excitation and probing coherent phonons in transiently broken symmetry crystals. The key to this concept lies in reducing the symmetry of a crystal by appropriate optical excitation, as has been demonstrated with the prototype crystalline semimetallic bismuth (Bi).






(a) Coherent phonon oscillations with a frequency of 2.6 THz observed in optical pump/femtosecond X-ray diffraction probe experiments for different pump fluences of mid-infrared excitation pulses centered on a wavelength of 5 m. Phononic wave packets are only observed for strong excitation pulses, i.e. they are absent for pump fluences below 1.9 mJ/cm2. Thus, reduction of the unit cell symmetry via strong optical pumping is necessary to gain access to the motion of the phonon. (b) Spectrum of the phonon oscillation obtained from a Fourier transform of the transient at a fluence of 2.9 mJ/cm2 shown in panel (a). Credit: MBI/M. runge

The ultrafast mid-infrared excitation of electrons in Bi changes the spatial distribution of charge and, therefore, transiently reduces the crystalline symmetry. In reduced symmetry new quantum pathways are opened up for the excitation of coherent phonons. Symmetry reduction causes a doubling of the unit cell size from the red structure with two Bi atoms to the blue structure with four Bi atoms. In addition to unidirectional atomic motion, the unit cell with four Bi atoms allows for coherent phonon wave packets with bidirectional atomic motions.

Probing of the transient crystal structure directly by femtosecond X-ray diffraction reveals oscillations of diffracted intensity, which persist on a picosecond time scale. The oscillations result from coherent motions of the wave packet along the phonon coordinates in the crystal of reduced symmetry.

Their frequency of 2.6 THz is different from that of low excitation level phonon oscillations. Interestingly, this behavior occurs only above a threshold of the optical pump fluence and reflects the highly non-linear, so-called non-perturbative, character of the optical excitation process.

In summary, optically induced symmetry breaking allows the excitation spectrum of a crystal to be changed on ultrashort time scales. These results may pave the way for transient driving material properties and thus for the implementation of new functions in optoacoustics and optical switching.

More information:
Azize Ko et al, Quantum pathways of carrier and coherent phonon excitation in bismuth, Physical review b (2023). DOI: 10.1103/PhysRevB.107.L180303

About the magazine:
Physical review b

Provided by the Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy (MBI)

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