Time-Resolved Coherent Photoelectron Spectroscopy of Quantized Electronic States on Metal Surfaces

Abstract

Time-resolved two-photon photoemission in combination with the coherent excitation of several quantum states was used to study the ultrafast electron dynamics of imagepotential states on metal surfaces. For a (100) surface of copper, the spectroscopy of quantum beats made previously unresolved high-order states (quantum number n 2 4) experimentally accessible. By exciting electrons close to the vacuum level, electron wave packets could be created and detected that described the uasi-classical periodic motion of weakly bound electrons. They traveled more than 200 1 away from the surface and oscillated back and forth with a period of 800 femtoseconds.Photoelectron spectroscopy has developed into one of the most versatile and successful tools for surface studies. Particularly attractive features of this technique are the high surface sensitivity associated with the low escape depth of the photoelectrons and the capability of angle-resolved photoemission to completely characterize electronic states in energy and momentum space (1). Recently, these features have been combined with ultrafast laser excitation for direct time-domain investigations of electron dynamics at surfaces (2). Here, we demonstrate another facet of this powerful technique, the investigation of coherence phenomena in real time. In contrast to experimental methods that rely merely on intensities, coherent spectroscopies offer the unique capability of accessing not only the amplitudes but also the phases of the wave functions of interest (3). This techniaue dramaticallv increases the amount of infbrmation that dne is able to obtain about the tem~oral evolution of fast Drocesses.In &s report, we discuss thehynamics of image-potential states, that is, the quantized excited states of electrons that exist in front of many metal surfaces (4, 5). Using femtosecond time-resolved two-photon photoemission (2PPE), we observed the interference between the wave functions of neighboring eigenstates and the quasi-classical motion of electron wave packets created by the coherent superposition of several quantum states. Recently, the imaging of the static charge density of related surface electronic (ground) states in real space with the scanning tunneling microscope has attracted considerable interest (6); the present results reveal the dynamical evolution of excited electrons in real time.Image-potential states are conceptually rather simple. An electron at a distance z in front of a conducting metal surface experiences an attractive force F(d = -e2/(2d2 identical to that produced by a positive (mirror image) charge at a distance z inside the metal (Fig. 1A). If the metal has a band gap (in z direction) near the vacuum level E,, = 0, then an electron below E, , may be trapped in the potential well formed by the Coulomb-like attractive image potential V(z) = -e2/4z and the repulsive surface barrier (4). The resulting quantized electronic states form a Rydberg series with energies En converging toward the vacuum energy, where the influence of the surface Dotential o...

Decay of electronic excitations at metal surfaces

“…In general, the various beating frequencies can be obtained from the Fourier transform of the data with the smooth exponential decay subtracted. Numerical modeling with a density-matrix formalism involving several intermediate states allows to extract the decay time of the individual levels [36,236]. The results agree with the asymptotic n À3 dependence of the energy separation E n;nþ1 and inverse lifetime G n ¼ h=t n (see Section 6.2) expected for hydrogen-like states.…”

“…2 in earlier work . [36,218] are systematically shorter than predicted theoretically (see discussion of Table 8 in Section 6.2). High-quality samples are needed to obtain longer lifetimes as shown in Fig.…”

“…41 shows oscillations on top of the exponential decay which are due to quantum interference in the time domain [36]. The energy difference between the n ¼ 3 and n ¼ 4 states, E 3;4 ¼ 34 meV, is comparable to the bandwidth of the femtosecond pump pulses and leads to a coherent excitation of both states.…”

“…The topographical images monitor simultaneously the quality and structures of the surface area under investigation. Two-photon photoemission (2PPE) [4,34] in the time-resolved mode is the only technique which is able to study the decay in the time domain [35,36]. By combining this information with spectroscopic measurements a very detailed picture of the electron dynamics emerges.…”

Resolubility of image-potential resonances

“…In fact, they have attained the role of a kind of drosophila of electron dynamics. As such, they serve as a benchmark system for the development of new ultrafast experimental techniques and as a reference for investigations of more complex electron transfer processes [6][7][8][9][10][11][12][13][14][15].…”