Two-Color Coherent Control of Femtosecond Above-Threshold Photoemission from a Tungsten Nanotip

We demonstrate coherent control of multiphoton and above-threshold photoemission from a single solid-state nanoemitter driven by a fundamental and a weak second harmonic laser pulse. Depending on the relative phase of the two pulses, electron emission is modulated with a contrast of the oscillating current signal of up to 94%. Electron spectra reveal that all observed photon orders are affected simultaneously and similarly. We confirm that photoemission takes place within 10 fs. Accompanying simulations indicate that the current modulation with its large contrast results from two interfering quantum pathways leading to electron emission.

Figure 1

Experimental setup. The second harmonic of ${\mathrm{Er}}^{3+}$-doped fiber laser pulses is generated in BBO using off-axis parabolas (OAPs) for dispersion-free focusing and collimation. Beams enter a Mach-Zehnder interferometer with dichroic beam splitters (DBS), where the fundamental passes a variable delay stage. Intensities are independently controlled with neutral density filter wheels (ND) and the beams are spectrally filtered (F1, F2). The polarization of the second harmonic is rotated with a half-wave plate (WP). After recombination of the two pulses with variable time delay $\tau$, they are focused onto a tungsten tip with an off-axis parabola. Electrons are detected on a microchannel plate (MCP) or with a spectrometer using single electron pulse counting.

Figure 2

Demonstration of coherent control of the photocurrent. (a) Electron current as a function of delay $\tau$ between $\omega$ and $2\omega$ pulse for $I_{\omega }=330\mathrm{GW}/{\mathrm{cm}}^2$ and $I_{2\omega }=6.6\mathrm{GW}/{\mathrm{cm}}^2$. For positive values of delay the $2\omega$ pulse encounters the tip first. We define $\tau =0$ at a current maximum in temporal overlap. (b) Magnification of the central area of (a). A sine fit to the data is shown as red solid line. (c) Absolute value of the Fourier transform (FT) of the data in (a). The cooperative photocurrent consists almost exclusively of an oscillatory component at $2\omega$ (ROI 1) and a dc component (ROI 0). (d) Inverse Fourier transform (IFT) of data in ROI 0 and IFT and Hilbert transform of data in ROI 1. Gaussian fits to the data are shown in blue. (e) ROI amplitude fit parameters $B_0$ and $B_1$ as a function of the second harmonic intensity for a fundamental intensity of $I_{\omega }=330\mathrm{GW}/{\mathrm{cm}}^2$. $B_0$ and $B_1$ are proportional to $I_{2\omega }$ (red solid line) and $\sqrt{I_{2\omega }}$ (green dashed line), respectively. The contrast (visibility) of the current oscillation calculated using Eq. (1) (black dots) and Eq. (5) (black dotted line) reaches up to 94% in this experiment. (f) $B_0$ (red squares) and $B_1$ (green dots) as a function of the rotation angle $\theta$ of the polarization direction of the second harmonic with respect to the tip axis and the fundamental field for $I_{\omega }=410\mathrm{GW}/{\mathrm{cm}}^2$ and $I_{2\omega }=13\mathrm{GW}/{\mathrm{cm}}^2$.

Figure 3

Experimental electron spectra for $I_{\omega }=410\mathrm{GW}/{\mathrm{cm}}^2$ and $I_{2\omega }=13\mathrm{GW}/{\mathrm{cm}}^2$. Blue: $2\omega$ pulse alone. Black: $\omega$ pulse alone. Red: $\omega$ and $2\omega$ pulses with relative phase locked at photocurrent maximum. Green: $\omega$ and $2\omega$ pulses with relative phase locked at photocurrent minimum.

Figure 4

Local density of states (LDOS) from a ground-state slab calculation (20 layers) for W(310). LDOS at surface (labeled surface, orange line), LDOS for jellium (labeled jellium, green line), and, for comparison, DOS from a bulk calculation (labeled bulk, black line). Intermediate surface and volume states are found at $2\hslash \omega =1.6\mathrm{eV}$ and $4\hslash \omega =3.2\mathrm{eV}$. Three pathways to an energy of $E_F+4\hslash \omega$ are indicated. The two-photon pathway is negligible under our conditions because of the small $2\omega$ intensity. The reduction of the work function due to the bias voltage is indicated by the purple dash-dotted line at 3.6 eV.