Real space-time imaging of valence electron motion in molecules

a superposition of valence electronic generated by stable laser picometer spatial resolution attosecond temporal

has remained elusive 5,30 . Here we combine CEP stable few-cycle (< 6 fs long) laser pulses with an STM to break this fundamental barrier, and to follow electron motion concurrently with pm spatial and 300 as temporal resolutions.
In our experiments, orthogonally linearly polarised near infrared laser pulses with slightly different carrier frequencies, obtained by selecting the 0 th and 1 st order diffraction beams of the laser pulses passing through an acousto-optic-frequency-shifter (AOFS), were focused at the apex of a W nanotip in tunnel contact with molecular layers of Perylenetetracarboxylic dianhydride (PTCDA) grown on top of a Au (111) surface. The polarization axes of the two laser pulses formed an angle of 45º with respect to the tip axis and their incidence angle at the junction was 7° with respect to the Au (111) surface (see Fig. 1a and section I in methods for details of the experimental set-up). This configuration ensures that the non collinear polarizations of the pulses only overlap with each other through their component along the nanotip axis; this overlap occurs within the small bandwidth of the STM. In this way, we circumvent the use of mechanical modulation to lock-in detect the laser-induced tunneling current in the STM and avoid spatial interferences between the laser pulses, which can make the tunnel junction unstable 31 . The correlation of the laser-induced tunneling current as a function of the delay between the two laser pulses is shown in Fig. 1d. The orange curve shows the variation in the tunnel gap width during the measurement. At zero delay between the two laser pulses, the polarization induced along the nanotip axis resembles the one induced by a single laser pulse at the tunnel junction at the small offset frequency (see section II in methods).
This induced polarization along the tip axis can be assumed to be instantaneous 32 for the timescale of the dynamics presented here. The excellent stability of our interferometric pumpprobe set-up over several hours (Fig. S2, methods) enables the possibility to lock-in detect the tunneling current dynamics induced by a single laser pulse, without the need to mechanically modulate the laser pulses. It is important to note that, for the wavelength ( ∼ 850 nm) and intensities (~ 1 x 10 12 W/cm 2 ) of the laser pulses used in this work, only photon-driven tunneling is possible 21 (Keldysh parameter, γ >1), not field-driven tunneling as it would be the case at higher pulse intensities 21 .
The electronic energy levels of a single monolayer of PTCDA molecules are favorably positioned with respect to the surface state of Au (111). A single photon of ~1.5 eV energy from the laser pulse resonantly couples the highest occupied molecular orbital (HOMO) to the Au (111) surface state as well as the latter to the lowest unoccupied molecular orbital (LUMO) of PTCDA. Thus, with controlled positioning of the electronic levels of the molecule with respect to the Fermi level of the nanotip, enabled by adjustment of the bias at the tunnel junction, a laser pulse can either induce a transition from the HOMO to the surface state, Fig. 1b, or from the surface state to the LUMO, Fig. 1c. In other words, by modulating the bias voltage at the tunnel junction one can control the initial state from which the laser-induced transition takes place.
We consider first the case of zero delay between the two laser pulses (hereafter referred to as a single-pulse experiment). We note that, in this case, the electric-field components of the two pulses cancel each other in the surface plane due to the specific geometric arrangement of the two laser pulses (Fig. 1a), so that the only active electric-field component is that along the tip axis (this is no longer true for non-zero delay between the pulses). As soon as this single pulse reaches the sample, a transfer of population from the lower to the upper level starts. Fig. 1e shows the calculated temporal evolution of the populations in the surface and LUMO states resonantly coupled by our 6 fs long laser pulse obtained from standard two-level Rabi formulas (see section V in methods). As can be seen, at the end of the laser pulse, most of the electronic population remains in the lower state, thus excluding the possibility that a single 6 fs pulse induces Rabi oscillations between those states. This is the obvious consequence of the fact that, for the peak electric field E of the laser pulse used in the experiment and the small value of the dipole coupling between the two levels, μ (see section VI in methods), the Rabi period, 2 ℏ/( ), is much longer than the pulse duration. We note that the transition dipole moment along the tip axis (the only active component of μ in the single-pulse case) is small due to the nearly perfect planar arrangement of the Au (111) atoms and the PTCDA layer. We exclude any further exchange of population between the two states when the pulse is over due to the extremely short tunneling times 21 (< 0.5 fs), from the sample to the STM junction. Therefore, in a single-pulse experiment, tunneling from the sample to the W tip will essentially carry spatial information about the lower electronic state. Spatially resolved topographic scans of the single-pulse induced tunneling current at various bias settings at the tunnel junction are shown in Fig. 1f to Fig. 1i.
As can be seen, when the HOMO of the PTCDA molecules is aligned with the Fermi level of the W nanotip, the laser-driven tunneling current images the spatial profile of the HOMO orbitals (Fig.   1f). When it is the Au (111) surface state that is aligned with the Fermi level, the majority of the laser-driven tunneling current arises from the surface state, so that the intensity of the current is much higher on the metallic surface than on the molecules (Fig. 1g). At a bias where not one, but two dipole transitions are possible, e.g., one transition from the surface state to the LUMO and another from the Fermi level of the tip to the LUMO (processes (1) and (2) in Fig. 1c prior to the interaction with the laser pulse. Based on the above arguments, the laser-driven imaging of the surface state and the LUMO has to be symmetric around a range of bias voltages at the tunnel junction, from -200 mV to +200 mV, due to the fact that we access the same initial and final states (see Fig. S3 and S4 in methods). In order to visualize electron dynamics involving two dipole-coupled states of the PTCDA/Au (111) system, we have varied the delay between the two orthogonally polarized laser pulses (hereafter called pump and probe pulses) and performed space-resolved topographic scans of the laser-induced tunneling current. For the laser parameters used in this work and the specific electronic states involved in the process, the optimum conditions to induce such dynamics correspond to the case in which the pump and probe pulses overlap in time. In this case, the populations for the upper (u) and lower (l) states as a function of the pump-probe delay are approximately given by (see section V in methods): where ℰ = /√2, with E being the peak electric field of the laser pulse, T is the pulse duration, , an impinging photon from the pump pulse will coherently couple the HOMO and the surface state. A probe pulse at a certain delay from the pump pulse will then induce a transition between the two states. If the electronic density is concentrated in the surface state, it will stimulate the transition back to the HOMO and vice-versa, akin to quantum beating between the two states (see section V in methods for more details). In this way the electronic density will resemble that of either one of the two states depending on the delay between the two pulses, and electrons will eventually tunnel carrying the spatial information of the state where they tunnel from. A schematic illustration of this process is shown in Fig. 2b. At zero delay (τ1) between the two pulses, the spatially resolved laser-induced imaging maps the spatial profile of the HOMO (Fig. 2d), whereas at a delay of 1.2 fs (τ2) the intensity of the tunnel current maps the Au (111) surface state in between the molecules (Fig. 2c). The laser-induced tunneling current for the latter is much higher than for the former, which is consistent with the single-pulse spatial imaging discussed above (Fig. 1g).
The spatially resolved laser-induced tunneling current as a function of the delay between pump and probe pulses is shown in Fig. 2e. Electron dynamics arising from the interaction of the laser pulses with a monolayer of PTCDA molecules on Au (111) involves both molecular and surface states. In order to observe pure molecular electron dynamics, we have grown multilayers of PTCDA molecules on top of the Au (111) surface. Weak van der Waals coupling between the molecular layers ensures that the upper layer can be sufficiently decoupled from the Au (111) surface state, so that the latter can neither contribute to the induced dynamics nor to the tunneling current 35 . We have found that these conditions are met for four or more PTCDA monolayers. The scanning tunneling spectrum for the 4-monolayer system is shown in Fig. 4a. As can be seen, there is no longer any trace of the surface state and the HOMO-LUMO gap is of the order ~ 2.5-3.0 eV. This energy gap can be overcome by single-photon transitions involving the blue tail of the pulses or two-photon transitions 21,36 involving the pulses' peak frequency. However, in the present weak-field (perturbative) conditions and in the absence of the surface state, which precludes resonant enhanced multiphoton processes, two-photon transitions should be much less likely than one-photon transitions. Hence, according to equation (1), when a laser pulse interacts with upper-layer PTCDA molecules whose HOMOs have been lifted close to the Fermi level of the nanotip (-1.8 V), oscillations between HOMO and LUMO, i.e. between pure molecular states, are expected, but with a frequency that will be significantly different from that of the one-monolayer case due to a different energy gap. This strategy allows for laser-induced spatial imaging of the frontier molecular orbitals as shown in Fig.   3e and Fig. 3f. At variance with the one-monolayer case, not all molecules lead to the same laserinduced tunneling current: half of the molecules, organized in parallel rows, lead to considerably higher currents than the other half. The rows reflecting the HOMOs are accompanied by rows with very low laser-induced tunneling current in the LUMOs (Fig. 3f). In contrast, when the LUMOs of the latter rows become apparent, the HOMOs in the former rows are nearly invisible (Fig. 3e).
As shown by extensive DFT calculations for the four-monolayer PTCDA/Au (111) system (see section VI in methods), this behavior is the consequence of the specific vertical stacking of the PTCDA molecules: the delicate balance between intra-layer hydrogen bonding and inter-layer ππ interactions forces PTCDA molecules in the higher layers to displace horizontally (~ 1Å) with respect to molecules in the lower layers. This leads to a local density of states (DOS) where molecules in one of the rows have a higher DOS than those in the adjacent rows (see