Coherent collective oscillations of electrons in metallic nanostructures, known as localized surface plasmons (LSPs), are crucial for confining light to atomic scales and enabling strong light-matter interactions. These interactions exhibit nonlinear dependence on the local field, making direct real-time sampling of the electron oscillations essential for developing petahertz-scale optical modulation, control, and readout in quantum nanodevices. Previous studies have relied on spectral measurements (absorption spectroscopy, transient reflectivity) or ultrafast techniques like time-resolved two-photon photoemission (TR-2PPE) and time-resolved scanning near-field optical microscopy (TR-SNOM) to investigate light-matter interactions. However, these methods either lack time-domain resolution or fail to capture the phase information of plasmon oscillations. While recent experiments have demonstrated control over photo-assisted tunneling currents using the carrier-envelope phase (CEP) of driving laser pulses, a direct time-domain sampling of ultrafast coherent collective electron oscillations and the resulting local electric field has remained elusive. This research addresses this gap by presenting a novel approach to directly trace both plasmon oscillations and nonlinear electron oscillations induced by ultrashort laser pulses in a strongly light-interacting quantum nanodevice.

The interaction of light with metallic nanostructures generates collective oscillations of conduction electrons. When the light frequency matches the LSP resonance frequency, these oscillations are dramatically amplified, leading to strong electromagnetic fields with applications in nano-optics and single-molecule sensing. This strong field interaction also reveals the nonlinear optical response of matter, resulting in anharmonic electron motion and oscillations at multiples of the driving frequency. Traditional spectroscopic methods and ultrafast techniques like TR-2PPE and TR-SNOM have been used to study these interactions, revealing ultrafast plasmon dynamics. However, these techniques have limitations in resolving the phase information of the frequency-dependent plasmon oscillations. Recent work utilizing photo-assisted tunneling currents and CEP control of driving laser pulses has shown promise, yet direct time-domain sampling of coherent electron oscillations remained a challenge.

The study utilizes an array of Au bowtie nanoantennas with sub-nanometer junction gaps fabricated on a fused silica substrate. Electron oscillations are traced by recording photo-assisted tunneling currents. Two ultrashort laser pulses (7 fs duration) with slightly different carrier frequencies are used for homodyne beating, a self-referencing technique to measure the phase of plasmon oscillations. These pulses are generated by using an acousto-optic frequency shifter (AOFS) to create a small frequency offset (f0 ~ 700 Hz) between the pulses. The pulses are combined and focused onto the nanoantenna junctions, exciting collective electron oscillations. The resulting photocurrent is measured using lock-in detection at the offset frequency f0. The homodyne beating signal, which is proportional to the square of the electric field and contains both amplitude and phase information, provides a time-resolved characterization of the plasmon oscillations. Nonlinear electron oscillations are investigated by measuring the photocurrent at harmonic frequencies of f0 (2f0, 3f0). To analyze the contributions of linear and nonlinear processes, the photocurrent is measured as a function of increasing laser pulse intensity, allowing separation of linear and nonlinear components by analyzing the lock-in signals at different frequencies. A model based on a driven damped harmonic oscillator describes the plasmon oscillations. The mechanism of photocurrent generation is explained via a photo-assisted tunneling model, which accounts for electrons being photo-excited and tunneling across the nanoantenna junction. CEP control of plasmon oscillations is demonstrated by varying the CEP of one laser pulse using a radio frequency phase shifter, altering the phase of the plasmon oscillations.

The experiments revealed a non-instantaneous response of the plasmon oscillations to the driving laser field, with a T2 decay time of approximately 8 fs. The plasmon oscillation period was approximately 2.6 fs. The spectral phase of the plasmonic field was highly dispersive, consistent with a driven harmonic oscillator. The study successfully decoupled the contributions of linear and nonlinear electron oscillations in the generated tunneling currents. The second and third order nonlinear oscillations showed oscillation periods of approximately 1.3 fs and 0.9 fs respectively. Power scaling experiments, measuring the photocurrent as a function of increasing laser intensity, confirmed the contributions of both linear and nonlinear polarization responses. The photocurrent showed a transition from linear (slope of 1) to quadratic (slope of 2) scaling with increasing intensity. The mechanism of photocurrent generation was identified as photo-assisted tunneling, dependent on the bias voltage across the nanoantenna junction. Finally, the study demonstrated real-time phase control of localized plasmon oscillations by varying the CEP of the driving laser pulses.

The findings directly address the challenge of real-time sampling of ultrafast coherent collective electron oscillations. The observed non-instantaneous response and the dispersive phase behavior of the plasmon oscillations confirm the resonant nature of the excitation. The ability to separate the linear and nonlinear contributions to the photocurrent provides valuable insights into the nature of light-matter interactions in this regime. The photo-assisted tunneling mechanism explains the observed nonlinear dependence of the photocurrent on bias voltage. The successful demonstration of CEP control opens possibilities for active control over plasmon oscillations. These results have significant implications for the development of ultrafast optical devices, particularly in the context of on-chip light-wave electronics.

This work presents a significant advancement in the field of strong light-matter interaction by achieving real-time tracking of coherent electron oscillations in a quantum nanodevice. The successful decoupling of linear and nonlinear contributions, combined with the demonstration of phase control, opens new avenues for developing petahertz-scale optical devices. Future research could explore the application of this technique to study single-molecule interactions, investigate other nanostructures, and further enhance control over plasmon dynamics.

The current study focuses on a specific type of nanoantenna (Au bowtie). The generalizability to other nanostructures needs further investigation. The measurements at higher pulse energies were less stable due to the risk of nanodevice damage. The exact gap sizes in the nanoantennas were not perfectly controlled and might have varied slightly. The simple model used for the plasmon oscillations might need refinement to capture more complex behaviors.