Quantum Interference Visibility Spectroscopy in Two-Color Photoemission from Tungsten Needle Tips

When two-color femtosecond laser pulses interact with matter, electrons can be emitted through various multiphoton excitation pathways. Quantum interference between these pathways gives rise to a strong oscillation of the photoemitted electron current, experimentally characterized by its visibility. In this Letter, we demonstrate the two-color visibility spectroscopy of multiphoton photoemissions from a solid-state nanoemitter. We investigate the quantum pathway interference visibility over an almost octave-spanning wavelength range of the fundamental ($\omega$) femtosecond laser pulses and their second harmonic ($2\omega$). The photoemissions show a high visibility of 90% $\pm 5\%$, with a remarkably constant distribution. Furthermore, by varying the relative intensity ratio of the two colors, we find that we can vary the visibility between 0% and close to 100%. A simple but highly insightful theoretical model allows us to explain all observations, with excellent quantitative agreements. We expect this work to be universal to all kinds of photo-driven quantum interference, including quantum control in physics, chemistry, and quantum engineering.

Figure 1

Experimental setup and multiphoton absorption in a metallic needle tip. (a) Femtosecond laser pulses ($\omega$) and their second harmonic ($2\omega$) are focused onto a tungsten needle tip with an off-axis parabola (OAP). Photoelectrons from the tip biased with $U_{\text{d}\text{c}}$ are detected on an MCP with a phosphor screen and are imaged on a CCD camera. (b) Schematic energy diagram of photoemission processes through three pathways (I, II, III). The green dotted frame marks the substitution of one ($2\omega$) photon for two $\omega$ photons in the absorption pathways.

Figure 2

Visibility of the two-color coherent control in multiphoton photoemissions. The visibilities of the photocurrent oscillations are plotted as a function of the corresponding second-harmonic wavelength of the applied wavelength pairs, which are varied from 590 nm ($2\omega$) and 1180 nm ($\omega$) to 1000 nm ($2\omega$) and 2000 nm ($\omega$). A high visibility of 90% $\pm 5\%$ with a roughly constant distribution is found. The visibilities calculated from the theory [Eq. (5)] are shown as pink triangles. Insets: Typical photocurrent oscillations when the needle tip is illuminated by the two-color laser field. Photocurrent intensities detected on the MCP detector screen are shown depending on the time delay $\tau$ between $\omega$ and $2\omega$ pulses. Sine fits to the data are displayed as red solid lines, clearly revealing an oscillation frequency of $2\omega$.

Figure 3

Comparison of theory and observations of the visibility scaling as a function of the laser intensities. (a)–(c) Visibility scaling depending on the intensity branching ratio $\tilde{I}=I_{2\omega }/I_{\omega }^2$, measured by varying the second-harmonic intensity $I_{2\omega }$. The data in (b) are taken from [29]. The color coding of the circles also represents the measured visibilities corresponding to the color bar in (d). Red solid lines in (a)–(c) depict fit curves using Eq. (5), whereas the blue solid lines show the calculated visibility using Eqs. (5) and (6). The blue band indicates the uncertainty of the calculated visibility obtained from the 10% uncertainty assumed in the field enhancement factors. (d) The calculated visibility as a function of fundamental intensity $I_{\omega }$ and second-harmonic intensity $I_{2\omega }$ using Eq. (4) for the wavelength pair of 720 nm and 1440 nm (color map). The measured visibilities of (a)–(c) are plotted as colored circles in (d) (black dashed frames) as well as in (f) and (g). (e) The data points show a consistently larger visibility and hence deviate from the theory color map (background color) as they do in (a). (f), (g) Two enlarged insets for better visualization where the background color in (f) is calculated for 850 nm and 1700 nm, while the background color in (g) is calculated for 780 nm and 1560 nm, with experimental data points (colored circles) that are the same as shown in (b) and (c). We note the excellent agreement of the experimentally measured visibility (circles) and the theoretical visibility (background color).