Time-Resolved Tunneling (trSTM)

• Time-Resolved Tunneling (trSTM) is a technique that harnesses pump-probe, phase-sensitive, and waveform-controlled methods to reconstruct ultrafast tunneling dynamics from delay-dependent signals.
• trSTM employs diverse experimental modalities such as STM, nanocavity photon detection, and AFM force measurements to access processes spanning picoseconds to attoseconds.
• The approach integrates conceptual, experimental, and theoretical advances to reveal detailed tunneling behavior in semiconductor dynamics, molecular junctions, and collective electronic modes.

Searching arXiv for recent and foundational papers on time-resolved tunneling and STM-related implementations. Time-resolved tunneling, often discussed in scanning-probe contexts as trSTM, comprises pump-probe, phase-sensitive, and waveform-controlled methods that reconstruct tunneling dynamics as an explicit function of delay time, carrier phase, or optical waveform rather than inferring them solely from stationary $I(V)$ or $dI/dV$. In STM-derived implementations, the primary observable can be a delay-dependent tunneling current, a point-contact current, a time-correlated photon signal from an STM nanocavity, or a force signal in an AFM extension; closely related work applies the same logic to molecular double wells, Landau-Zener transitions, strong-field ionization, and planar tunnel junctions. This suggests that trSTM is best regarded as one branch of a broader time-domain tunneling framework (Iwaya et al., 2023, Sun et al., 2024).

1. Conceptual foundations

At the most general level, time-resolved tunneling separates three operations: preparation of a non-equilibrium or phase-coherent state, controlled evolution under a tunneling Hamiltonian, and delayed readout of the resulting populations or coherences. In the clearest two-level realization, a tunneling doublet with even and odd eigenstates $|+\rangle$ and $|-\rangle$ is described by

$H=\frac{\Delta E}{2}\sigma_z,$

and a coherent superposition of the two eigenstates produces oscillatory relocalization between localized states. For the $1_{01}$ rotational tunneling doublet of 3-fluorobenzyl alcohol, the populations obey

$$P_R(t)=\cos^2\left(\frac{\Delta E\, t}{2\hbar}\right),\qquad P_S(t)=\sin^2\left(\frac{\Delta E\, t}{2\hbar}\right),$$

with tunneling period $T=1/\nu_\pm$; the measured tunneling frequency is $\nu_\pm=0.827(15)\ \mathrm{MHz}$, corresponding to $T\approx1.2\ \mu\mathrm{s}$ (Sun et al., 2024).

A second foundational theme is that “tunneling time” is operational rather than unique. Landau-Zener measurements on a Bose-Einstein condensate in a tilted lattice show that time-resolved tunneling depends on whether populations are read out in the adiabatic basis or the diabatic basis, and the post-crossing dynamics differ strongly between them (Tayebirad et al., 2010). Strong-field ionization work reaches a related conclusion from a different direction: the relevant delay can be defined from the phase of the fixed-energy Green’s function, leading to a Wigner trajectory, a non-zero tunneling time delay, and a non-zero longitudinal exit momentum (Camus et al., 2016). These results do not collapse to a single universal clock, but they do converge on a shared principle: time-resolved tunneling is always tied to a specified preparation, Hamiltonian, and readout basis.

2. Experimental architectures

The STM implementations span several hardware classes. An RF-optimized UHV STM with in-situ exchangeable tips and standard sample holders demonstrated a time resolution of $dI/dV$0 by exploiting the nonlinear $dI/dV$1-characteristic of highly oriented pyrolytic graphite, and atomically resolved images were obtained in pulse mode; noise analysis showed that changes in the tunneling junction of $dI/dV$2 are dynamically detectable at $dI/dV$3 time resolution (Saunus et al., 2013). Externally-triggerable optical pump-probe STM on GaAs(110) introduced electrical control of laser-pulse timing and measured a pump-probe cross-correlation of $dI/dV$4, establishing a tens-picosecond regime in an all-electrically timed architecture (Iwaya et al., 2023).

Other architectures use the STM junction in less conventional ways. In a tunable STM nanocavity, time-resolved single-molecule photoluminescence from MgPc and ZnPc on NaCl/Ag(111) was measured by TCSPC with an effective instrument response function $dI/dV$5; the cavity reduced molecular lifetimes from nanoseconds to a few picoseconds, with $dI/dV$6 inferred from peak-shift analysis (Doležal et al., 2023). At the opposite temporal extreme, two-color waveform-controlled STM generated directional attosecond tunneling bursts with durations on the order of $dI/dV$7, $dI/dV$8 lateral spatial resolution, and sub-ångström topographic sensitivity under ambient conditions (Davidovich et al., 14 Jul 2025). Multimodal ultrafast STM on $dI/dV$9 combined trSTM, time-resolved point contact, and optical pump-probe reflectance in one instrument, while a compact next-generation pump-probe module extended the same logic to AFM force detection on insulating materials (Bae et al., 15 Jul 2025, Iwaya et al., 2024).

This diversity matters conceptually. It shows that trSTM does not refer to a single instrument topology, nor even always to direct current readout from a tunneling junction. In some implementations the junction is a GHz-capable nonlinear mixer, in others a nanocavity, in others one channel within a multimodal pump-probe platform.

3. Signal formation and readout

In optical pump-probe STM, ultrafast information is typically encoded into a slowly varying average current. For GaAs(110), the measured observable is

$|+\rangle$0

where $|+\rangle$1 is the delay of interest and $|+\rangle$2 is a long delay, typically half the repetition period. Delay-time modulation rather than intensity modulation keeps the average optical power constant and suppresses thermal expansion artifacts; $|+\rangle$3 is the OPP tunneling current–delay time curve (Iwaya et al., 2023). In multimodal ultrafast STM on $|+\rangle$4, the pair-pulse correlation observable is written

$|+\rangle$5

with the “infinite” delay realized by a $|+\rangle$6 separation between pulse pairs (Bae et al., 15 Jul 2025).

A different readout logic appears in pump-probe spin-resolved tunneling spectroscopy. For a magnetic adatom excited by a spin-polarized tunneling pulse, the experimentally relevant quantity is the total number of transmitted electrons during the combined pump and probe sequence,

$|+\rangle$7

with $|+\rangle$8 developing a positive overlap peak for $|+\rangle$9 and a relaxation-controlled dip for $|-\rangle$0 (Schüler et al., 2012). In microwave six-wave mixing on a chiral molecular double well, the emitted listen-line phase rather than the current is the crucial observable: $|-\rangle$1 with opposite slopes for the two listen frequencies, so that phase-delay linearity directly yields the tunneling frequency (Sun et al., 2024). In time-resolved STM nanocavity spectroscopy, the observable is instead the photon arrival-time histogram in TCSPC, and lifetimes shorter than the $|-\rangle$2 IRF are inferred from the shift of the molecular decay peak relative to the plasmon IRF (Doležal et al., 2023).

The common feature across these readouts is indirectness. “Time-resolved” frequently means that an ultrafast process is reconstructed from a delay-dependent average current, phase, or photon distribution, not that the instantaneous tunneling current is directly digitized in real time.

4. Representative regimes and results

Semiconductor carrier dynamics were the first major current-based application domain. On GaAs(110), all-electronic optical pump-probe STM resolved biexponential dynamics with $|-\rangle$3 and $|-\rangle$4, attributed to bulk-side and surface-side decay, and later accessed a $|-\rangle$5 carrier timescale in low-temperature-grown GaAs with $|-\rangle$6 delay steps (Iwaya et al., 2023). For magnetic adatoms, pump-probe tunneling pulses traced the nanosecond relaxation of a single Fe atom on Cu$|-\rangle$7N/Cu(100), with relaxation dynamics manifested in the spin-dependent tunneling current and characteristic times $|-\rangle$8 in the modeled Fe/Cu$|-\rangle$9N system (Schüler et al., 2012).

Single-molecule and cavity-modified tunneling-related signals occupy another regime. In far-field $H=\frac{\Delta E}{2}\sigma_z,$0PL, MgPc and ZnPc on 3 ML NaCl showed long-lived components of approximately $H=\frac{\Delta E}{2}\sigma_z,$1 and $H=\frac{\Delta E}{2}\sigma_z,$2, respectively, whereas in the STM nanocavity the same emitters exhibited cavity-modified lifetimes $H=\frac{\Delta E}{2}\sigma_z,$3, indicating strong Purcell enhancement without strong coupling (Doležal et al., 2023). At still shorter timescales, waveform-controlled STM used a two-color field to drive non-adiabatic tunneling across a $H=\frac{\Delta E}{2}\sigma_z,$4–$H=\frac{\Delta E}{2}\sigma_z,$5 gap and inferred current bursts with FWHM $H=\frac{\Delta E}{2}\sigma_z,$6, reported as on the order of $H=\frac{\Delta E}{2}\sigma_z,$7 (Davidovich et al., 14 Jul 2025).

Collective electronic modes can also be accessed through trSTM. In $H=\frac{\Delta E}{2}\sigma_z,$8, trSTM and trPC detected current oscillations at $H=\frac{\Delta E}{2}\sigma_z,$9 and $1_{01}$0. The $1_{01}$1 mode was assigned to a massive phason whose temperature dependence matches the theoretically predicted behavior of a phason gaining mass through the Higgs mechanism, while the $1_{01}$2 mode was interpreted as a daughter phason generated by parametric amplification; comparison with optical pump-probe reflectance showed that this daughter phason competes with and suppresses the amplitudon at the same frequency (Bae et al., 15 Jul 2025).

Beyond STM proper, planar pump-probe tunneling in a GaAs bilayer 2DES reached the microsecond regime. Tr-MERTS injected electrons at selected energies, resolved momentum through

$1_{01}$3

and tracked decay processes in Landau levels with lifetimes up to tens of microseconds. Near $1_{01}$4, it revealed a transient spectral splitting attributed by exact diagonalization to a maximally spin-polarized higher-energy state distinct from a conventional equilibrium skyrmion (Yoo et al., 2023).

5. Theoretical descriptions

The simplest time-resolved tunneling theories reduce the problem to a two-level Hamiltonian. In the chiral molecular case, the tunneling doublet is modeled by $1_{01}$5, while the driven stages are naturally described in a density-matrix or Bloch-vector formalism with short pulses, rotating-wave approximation, and negligible decoherence on the $1_{01}$6 timescale (Sun et al., 2024). This same two-level logic underlies Landau-Zener measurements, where the operational tunneling time depends on whether populations are projected onto the adiabatic or diabatic basis (Tayebirad et al., 2010).

For local spin excitations in STM, a nonperturbative scattering theory in wave-packet form has been used. The model Hamiltonian

$1_{01}$7

contains the barrier and Zeeman term in $1_{01}$8, the anisotropic adatom spin Hamiltonian

$1_{01}$9

and an exchange interaction

$$P_R(t)=\cos^2\left(\frac{\Delta E\, t}{2\hbar}\right),\qquad P_S(t)=\sin^2\left(\frac{\Delta E\, t}{2\hbar}\right),$$0

Pump-probe observables are then expressed through channel-resolved scattering amplitudes and, on longer timescales, coupled to phenomenological Bloch-type relaxation equations for the spin populations (Schüler et al., 2012).

THz-driven STM on vibronically active molecular junctions requires a many-body nonequilibrium description. The Anderson-Holstein model treats a localized orbital with on-site interaction $$P_R(t)=\cos^2\left(\frac{\Delta E\, t}{2\hbar}\right),\qquad P_S(t)=\sin^2\left(\frac{\Delta E\, t}{2\hbar}\right),$$1, local phonon frequency $$P_R(t)=\cos^2\left(\frac{\Delta E\, t}{2\hbar}\right),\qquad P_S(t)=\sin^2\left(\frac{\Delta E\, t}{2\hbar}\right),$$2, and electron-phonon coupling $$P_R(t)=\cos^2\left(\frac{\Delta E\, t}{2\hbar}\right),\qquad P_S(t)=\sin^2\left(\frac{\Delta E\, t}{2\hbar}\right),$$3, driven by a time-dependent bias

$$P_R(t)=\cos^2\left(\frac{\Delta E\, t}{2\hbar}\right),\qquad P_S(t)=\sin^2\left(\frac{\Delta E\, t}{2\hbar}\right),$$4

Variational non-Gaussian states then provide real-time access to the current $$P_R(t)=\cos^2\left(\frac{\Delta E\, t}{2\hbar}\right),\qquad P_S(t)=\sin^2\left(\frac{\Delta E\, t}{2\hbar}\right),$$5, occupancy $$P_R(t)=\cos^2\left(\frac{\Delta E\, t}{2\hbar}\right),\qquad P_S(t)=\sin^2\left(\frac{\Delta E\, t}{2\hbar}\right),$$6, and phonon dynamics, including long-lived phonon oscillations after the pulse (Shi et al., 2019).

A complementary line of theory formulates time-resolved tunneling spectroscopy directly in terms of nonequilibrium Green’s functions. In the extended-probe approach for a quenched Mott insulator, the probe occupation obeys

$$P_R(t)=\cos^2\left(\frac{\Delta E\, t}{2\hbar}\right),\qquad P_S(t)=\sin^2\left(\frac{\Delta E\, t}{2\hbar}\right),$$7

so the measured tunneling signal is a double-time functional of the lesser Green’s function (Zawadzki et al., 2019). Tr-MERTS in a bilayer 2DES implements the same principle experimentally in planar form, with tunneling current determined by the overlap of source and target spectral functions and occupations, but with direct momentum selectivity via $$P_R(t)=\cos^2\left(\frac{\Delta E\, t}{2\hbar}\right),\qquad P_S(t)=\sin^2\left(\frac{\Delta E\, t}{2\hbar}\right),$$8 (Yoo et al., 2023).

6. Limits, misconceptions, and outlook

A recurrent misconception is that trSTM must mean direct ultrafast current sampling by a broadband current amplifier. The literature shows otherwise. RF-STM at $$P_R(t)=\cos^2\left(\frac{\Delta E\, t}{2\hbar}\right),\qquad P_S(t)=\sin^2\left(\frac{\Delta E\, t}{2\hbar}\right),$$9, OPP-STM at $T=1/\nu_\pm$0 cross-correlation, multimodal trSTM on $T=1/\nu_\pm$1, and AFM force detection all infer ultrafast dynamics from time-averaged observables modulated by delay, phase, or overlap conditions (Saunus et al., 2013, Iwaya et al., 2023, Bae et al., 15 Jul 2025, Iwaya et al., 2024). A second misconception is that all STM-based time-resolved tunneling measures current. Nanocavity experiments instead measure photons, and AFM extensions measure force, while still using the STM or SPM junction as the nanoscale transducer (Doležal et al., 2023, Iwaya et al., 2024).

The main technical limits are platform-specific. In microwave molecular tunneling, bandwidth and timing resolution determine which tunneling splittings are resolvable: benzyl alcohol at $T=1/\nu_\pm$2 was too fast for the same setup that resolved 3-fluorobenzyl alcohol at $T=1/\nu_\pm$3 (Sun et al., 2024). In nanocavity spectroscopy, the $T=1/\nu_\pm$4 IRF prevents direct fitting of few-picosecond decays, so peak-shift analysis is required (Doležal et al., 2023). In OPP-STM and AFM, long-term optical stability and suppression of thermal expansion artifacts are decisive (Iwaya et al., 2023, Iwaya et al., 2024). In waveform-driven STM, ambient operation is compatible with attosecond burst generation, but direct attosecond gating has not yet replaced theory-assisted reconstruction of the temporal profile (Davidovich et al., 14 Jul 2025).

The current trajectory of the field points in several directions. Microwave coherent control has already demonstrated precise phase control of a chiral wavepacket and suggests coherent inhibition or enhancement of tunneling, dynamic localization, and eventual sensitivity to parity-violating energy differences in molecular double wells (Sun et al., 2024). Attosecond STM has already shown directional control of current bursts and naturally motivates a fully pump-probe attosecond STM in which one waveform-controlled pulse prepares a localized electronic state and a second pulse reads out its evolution (Davidovich et al., 14 Jul 2025). Multimodal ultrafast STM has shown that tunneling, point contact, and optical reflectance can be combined within one instrument, which suggests that future trSTM will increasingly be interpreted not as an isolated microscopy mode but as one channel in a broader correlated measurement stack spanning current, force, and optical observables (Bae et al., 15 Jul 2025, Iwaya et al., 2024).