High-harmonic spectroscopy has already proven itself as a tool for probing band structure and topological properties in ordinary semiconductors. In strongly correlated materials such as Mott insulators, theoretical work predicted that high harmonics are produced by the recombination of doublon-holon pairs, but there had been no direct experimental observations of the subcycle dynamics of these quasiparticles. The work sits within a series of studies in which high harmonics were used to track phase transitions and correlation effects, yet neighboring studies were mostly limited to cycle-averaged spectra. Here, for the first time, the chirp of high harmonics in a Mott insulator has been measured, giving access to the motion of doublons and holons on attosecond timescales.
The experiment was performed on a single crystal of Ca0.4Sr0.6CuO2, which consists of weakly coupled Cu-O chains and is described by a one-dimensional Hubbard model with a charge-transfer gap of 2.1 eV. The sample was irradiated with an intense pulse at a wavelength of 3.5 µm (intensity 0.6 TW/cm²) and a weak second-harmonic pulse at 1.75 µm (20 MW/cm²), both polarized along the chains. The two-color field broke inversion symmetry, which allowed even harmonics to be generated. The intensity of the even harmonics (from the 6th to the 12th) was measured as a function of the relative phase between the two pulses. To interpret the data, a semiclassical model of doublon-holon trajectories was used, in which the dispersion of charge excitations was taken from the Bethe ansatz solution of the one-dimensional Hubbard model, and the motion of the pair in the laser field was treated classically. In addition, the temporal profile of harmonic emission was measured by scanning the delay between the pulses.
All above-gap even harmonics (6th, 8th, 10th, 12th) showed intensity modulation with a period of a quarter of an optical cycle, confirming the symmetry breaking by the two-color field. From the shift of the modulation maxima between harmonics, a positive chirp of 0.19 fs/eV was extracted: higher harmonics are emitted later in the optical cycle. This result agrees with the semiclassical calculation (0.206 fs/eV), in which each harmonic is tied to a specific doublon-holon trajectory, and a larger pair separation yields a higher recombination energy. The temporal emission profile showed that as the harmonic order increases, the maximum shifts to earlier cycles of the pulse: the 12th harmonic peaks about 22 fs earlier than the 4th. The asymmetry of the profile, quantified by the skewness coefficient, grows monotonically from 0.0045 for the 4th harmonic to 0.2613 for the 12th. This is explained by the fact that higher harmonics are born on longer trajectories and suffer more from scattering off carriers accumulated during the pulse. An estimate of the characteristic dephasing length gave a value of about 0.5 of the lattice constant.
The work directly demonstrates for the first time that high harmonics in a Mott insulator are indeed generated by the recombination of doublon-holon pairs, and that their chirp reflects the subcycle dynamics of these quasiparticles. Unlike neighboring studies, which measured only averaged spectra, this work provides information about the temporal structure of emission within a single optical cycle. This opens the possibility of using high-harmonic spectroscopy as a probe of correlated electron dynamics in real time. Moreover, the observation of energy-dependent dephasing points to a fundamental limitation for coherent control in strongly correlated systems, which matters for Floquet engineering.
The topic could develop toward separating the contributions of different dephasing mechanisms, such as Bloch oscillations, interchain hopping of doublons and holons, and scattering off spinons. This will require experiments with selective excitation or doping, as well as comparison with full quantum many-body calculations. Also promising is the application of a similar two-color technique to other correlated materials, including high-temperature superconductors and systems with charge ordering, in order to identify universal features of subcycle dynamics.
The results will influence the development of attosecond condensed-matter physics and the understanding of nonequilibrium phenomena in quantum materials, including Floquet engineering and light-induced phase transitions.
Immediate steps include measuring the chirp over a wider range of intensities to test predictions about Bloch oscillations, and performing similar experiments on materials with controlled interchain coupling.
The work is directly connected to the unsolved problem of describing nonequilibrium dynamics in strongly correlated electron systems, where standard band pictures fail. It shows that semiclassical trajectories in the charge sector of the Hubbard model can describe subcycle dynamics, but a full understanding requires accounting for spin degrees of freedom and many-body effects, which remain a challenge for theory.
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What the work does
The work demonstrates a measurement of the chirp of high harmonics in the one-dimensional Mott insulator Ca0.4Sr0.6CuO2 using a two-color laser field to break symmetry. A positive chirp of 0.19 fs/eV was obtained, consistent with the semiclassical model of doublon-holon trajectories, and a harmonic-order-dependent dephasing due to scattering on accumulated carriers was discovered.
Where its strength is
For the first time, experimental access to the subcycle dynamics of doublons and holons in a Mott insulator has been achieved through the chirp of high harmonics, which makes it possible to trace quasiparticle trajectories on attosecond timescales.
Where it could go next
Worth trying
Why this may matter
This method could become a universal tool for probing ultrafast correlated processes in quantum materials, including the dynamics of charge and spin excitations, and could help in understanding the limitations of Floquet engineering.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.52, against a usual 0.64. It looks like few have drilled nearby.
A doublon-holon pair in a one-dimensional Mott insulator resembles an electron-hole pair in a semiconductor, but with a fundamental difference: the doublon and the holon are not independent quasiparticles; their motion is rigidly correlated because of the strong Coulomb interaction. The experiment used a material related to cuprate superconductors, where the same Cu-O chains play a key role in high-temperature superconductivity.