A two-level system resonantly interacting with an ac magnetic or electric field constitutes the physical basis of diverse phenomena and technologies. However, Schrödinger's equation for this seemingly simple system can be solved exactly only under the rotating wave approximation, which neglects the counter-rotating field component. When the ac field is sufficiently strong, this approximation fails, leading to a resonance-frequency shift known as the Bloch-Siegert (BS) shift. Here, we report the vacuum BS shift, which is induced by the ultrastrong coupling of matter with the counter-rotating component of the vacuum fluctuation field in a cavity. Specifically, an ultra-high-mobility 2D electron gas inside a high-Q terahertz cavity in a quantising magnetic field revealed ultra-narrow Landau polaritons, which exhibited a vacuum BS shift up to 40 GHz. This shift, clearly distinguishable from the photon-field selfinteraction effect, represents a unique manifestation of a strong-field phenomenon without a strong field. sions. We thank Yoichi Kawada, Hironori Takahashi, and Hamamatsu Photonics K.K. for fabricating the achromatic THz quarter wave plate. J.K.

The ultrafast coherent manipulation of electrons using waveform-controlled laser pulses 1-9 is a key issue in the development of modern electronics 10,11. Developing such an approach for a tunnel junction will provide a new platform for governing ultrafast currents on an ever smaller scale, which will be indispensable for the advancement of next-generation quantum nanocircuits 12-15 and plasmonic devices 16-18. Here, we demonstrate that carrier-envelope phase controlled single-cycle terahertz electric fields can coherently drive electron tunnelling either from a nanotip to a sample or vice versa. Spatially confined electric fields of more than 10 V/nm strongly modulate the potential barrier at a nanogap in a scanning tunnelling microscope (STM) within a sub-picosecond time scale and can steer a huge number of electrons in an extremely nonlinear regime, which is not possible using a conventional STM. Our results are expected to pave the way for the future development of nanoscale science and technologies.

The recent development of optical technology has enabled the practical use of a carrier-envelope phase-controlled monocycle electric field in the terahertz (THz) regime. By combining this technique with metal nanostructures such as nanotips, which induce near-field enhancement, the development of novel applications is anticipated. In particular, THz scanning tunneling microscopy (THz-STM) is a promising technique for probing ultrafast dynamics with the spatial resolution of STM. However, the modulation of the THz waveform is generally accompanied by an enhancement of the electric field, which is unknown in actual measurement environments. Here, we present a method enabling direct evaluation of the enhanced near field in the tunnel junction in THz-STM in the femtosecond range, which is essential for the use of the THz near field. In the tunneling regime, it was also demonstrated that the transient electronic state excited by an optical pulse can be evaluated using the THz-STM, and the ultrafast carrier dynamics in 2H-MoTe2 excited by an optical pulse was reproducibly probed.

Light-field-driven processes occurring under conditions far beyond the diffraction limit of the light can be manipulated by harnessing spatiotemporally tunable near fields. A tailor-made carrier envelope phase in a tunnel junction formed between nanogap electrodes allows precisely controlled manipulation of these processes. In particular, the characterization and active control of near fields in a tunnel junction are essential for advancing elaborate manipulation of light-field-driven processes at the atomic-scale. Here, we demonstrate that desirable phase-controlled near fields can be produced in a tunnel junction via terahertz scanning tunneling microscopy (THz-STM) with a phase shifter. Measurements of the phase-resolved subcycle electron tunneling dynamics revealed an unexpected large carrier-envelope phase shift between far-field and near-field single-cycle THz waveforms. The phase shift stems from the wavelength-scale feature of the tip-sample configuration. By using a dual-phase double-pulse scheme, the electron tunneling was coherently manipulated over the femtosecond time scale. Our new prescription-in situ tailoring of single-cycle THz near fields in a tunnel junction-will offer unprecedented control of electrons for ultrafast atomic-scale electronics and metrology.

Improved control over the electromagnetic properties of metal nanostructures is indispensable for the development of next-generation integrated nanocircuits and plasmonic devices. The use of terahertz (THz)-field-induced nonlinearity is a promising approach to controlling local electromagnetic properties. Here, we demonstrate how intense THz electric fields can be used to modulate electron delocalization in percolated gold (Au) nanostructures on a picosecond time scale. We prepared both isolated and percolated Au nanostructures deposited on high resistivity Si(100) substrates. With increasing the applied THz electric fields, large opacity in the THz transmission spectra takes place in the percolated nanostructures; the maximum THz-field-induced transmittance difference, 50% more, is reached just above the percolation threshold thickness. Fitting the experimental data to a Drude-Smith model, we found furthermore that the localization parameter and the damping constant strongly depend on the applied THz-field strength. These results show that ultrafast nonlinear electron delocalization proceeds via strong electric field of THz pulses; the intense THz electric field modulates the backscattering rate of localized electrons and induces electron tunneling between Au nanostructures across the narrow insulating bridges without any material breakdown.

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Coupling an intense electric field of terahertz (THz) pulse to a scanning tunneling microscope (STM) has opened new avenues for conducting ultrafast electron manipulation and tracking quantum dynamics at the nanometer spatial resolution. Here we combined the THz-field-driven STM with a photon detection system and demonstrated nanospectroscopic investigations of STM-induced luminescence triggered by THzfield-driven electrons. Owing to the abundant spectral information on photons, we were able to separately measure and characterize luminescence from a localized plasmon excited by THz-field-and DC-field-driven inelastic electron tunneling. We revealed that the plasmon excitation by THz-field-driven electrons in our experiment occurred at an extremely high voltage and current region due to the use of intense THz pulses, which would provide a unique experimental platform for exploring the light−matter interactions in a plasmonic nanocavity. Our method also paves the way for investigating quantum energy dynamics accompanying quantum conversions with subpicosecond time and atomic-scale spatial resolution.

We report results of terahertz Faraday and Kerr rotation spectroscopy measurements on thin films of Bi1−xSbx, an alloy system that exhibits a semimetal-to-topological-insulator transition as the Sb composition x increases. By using a single-shot time-domain terahertz spectroscopy setup combined with a table-top pulsed mini-coil magnet, we conducted measurements in magnetic fields up to 30 T, observing distinctly different behaviors between semimetallic (x < 0.07) and topological insulator (x > 0.07) samples. Faraday and Kerr rotation spectra for the semimetallic films showed a pronounced dip that blue-shifted with the magnetic field, whereas spectra for the topological insulator films were positive and featureless, increasing in amplitude with increasing magnetic field and eventually saturating at high fields (>20 T). Ellipticity spectra for the semimetallic films showed resonances, whereas the topological insulator films showed no detectable ellipticity. To explain these observations, we developed a theoretical model based on realistic band parameters and the Kubo formula for calculating the optical conductivity of Landau-quantized charge carriers. Our calculations quantitatively reproduced all experimental features, establishing that the Faraday and Kerr signals in the semimetallic films predominantly arise from bulk hole cyclotron resonances while the signals in the topological insulator films represent combined effects of surface carriers originating from multiple electron and hole pockets. These results demonstrate that the use of high magnetic fields in terahertz magnetopolarimetry, combined with detailed electronic structure and conductivity calculations, allows us to unambiguously identify and quantitatively determine unique contributions from different species of carriers of topological and nontopological nature in Bi1−xSbx. arXiv:1907.00137v1 [cond-mat.mes-hall]