Petahertz electronics in diamond
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- Figure 1: Schematic drawing of the experimental setup with the possibility to simultaneously detect photons and electrons. (a) The detection of electrons from neon gas allowed us to characterize the single attosecond pulses and calibrate the infrared-to-XUV-pulse delay axis in the transient absorption measurements. (b) Black line, spectrum of the XUV attosecond pulse; blue line, same spectrum after transmission through a 50-nm thin polycrystalline diamond sample; green line, static absorbance of diamond.
- Figure 2: (a), (b) Experimental and calculated infrared-induced absorbance as measured with the extreme ultraviolet attosecond pulse. A clear red horizontal line appears both in the experiment and the theory. This feature corresponds to an increased absorption and oscillates with a period of ~1.25 fs. Other oscillating structures depart from this central feature and assume a characteristic V-shaped structure (dashed black lines) that is well reproduced by the theoretical calculations.
- Figure 3: (a) Electronic band structure of diamond. The theoretical calculations allowed us to identify the main sub-bands that dominate the optical response of diamond (highlighted by thicker colored lines). (b) Zoom-in of the section marked with the gray rectangle in (a). The cartoon shows the two main physical mechanisms induced by the IR pump: (i) intra-band motion, (ii) inter-band coupling. Our analysis revealed that the former dominates the observed behavior (c) Calculated IR-induced changes in the absorption for the case of a transition between the two highlighted sub-bands in a) (upper panel) and result from a simplified 2-band model (lower panel).
The rapid progress in picosecond and femtosecond ultrafast lasers that happened in the 80’s has allowed bridging the gap between electronics and optics. The new connection between these two fields has since given rise to a wealth of new technologies and scientific insights. Fruits from these pioneering years include the fields of terahertz science and technology and high-speed optoelectronics.
This revolution keeps going beyond the starting expectation with ultrafast laser sources moving from femtosecond (10-15 s) to attosecond (10-18 s) pulses. This expands our possibilities for measurement and control of optoelectronic properties of materials from the now well-established terahertz into the petahertz (1015 Hz) frequency regime and it lets us explore the ultimate speed limits of electronic and optoelectronic components, which we might eventually hit in future device generations.
The electron motion under the influence of a high-frequency electric field ultimately determines the material limit for high-speed device performance. Ultrafast electron dynamics at the basis of light-matter interaction in dielectrics play a fundamental role in the future development of many relevant technological areas like optoelectronics, photovoltaics and signal processing. Electronic devices available today routinely operate at frequencies of several gigahertz (a billion oscillations per second). Future generations of electronics might reach the terahertz to petahertz domain, which is thousands to a million times faster still. Using similar measurement concepts as developed for terahertz electric fields and femtosecond time resolution, we asked ourselves whether there is a fundamental speed limit for how fast the electrons can be controlled by electrical fields in matter. We explored this limit at optical frequencies using the method of attosecond transient absorption spectroscopy (ATAS) [1-3], which has been recently extended from its initial gas phase applications to dielectrics . In this regard, one key point is to understand to what level and through which mechanisms the electronic properties of a dielectric can be optically controlled on sub-femtosecond timescales on which the onset of the interaction between the material and the external field takes place.
In our work, we explore a regime, where the electrons in a dielectric material are exposed to a relatively strong high-frequency optical field. In this regime, the photon energy of the driving laser becomes comparable to the quiver energy (or ponderomotive energy Up) of the electrons in such an oscillating electrical field. The system lies in a transition region between a more quantum-mechanical (photon driven) and a more classical (field driven) regime. In this regime, non-trivial physical mechanisms come into play and many questions remain open.
In our experiment , we use a 50 nm thin film of diamond that we expose to a few-femtosecond infrared laser pulse. The oscillating electric field underlying this light pulse oscillates at a frequency of about three-quarters of a petahertz, thereby exciting the electrons. The interaction of the electrons with the laser field will result in small changes in the optical absorption. We sensitively probe these changes in an energy-resolved way with a synchronized 250-attosecond pulse in the extreme ultraviolet. A technological precondition for such a type of experiment was the ability to control the phase relation of the underlying electric field with respect to the pulse envelope of the infrared laser pulse. Our attosecond experiment builds on a scheme that was proposed by our group in the late 1990’s and allowed to electronically control this phase relation .
A schematic of the experimental setup is shown in Figure 1. The infrared-induced transient absorption features oscillate with twice the IR central frequency, ω0, and fully recover after the interaction with the light pulse. An example of the experimental data is shown in Figure 2a.
Ab initio calculations performed by the group of Prof. Yabana from the University of Tsukuba by coupling time-dependent density functional theory (TDDFT) in real time with Maxwell’s equations reproduce the experimental results (Fig. 2b). Based on this and simplified theoretical models we could identify the V-shaped energy-dependence of the oscillating absorption features as a signature of the so-called dynamical Franz-Keldysh effect. While the Franz-Keldysh effect for static electric fields has been known and understood before, it has never been observed at the fast petahertz oscillation frequencies of an optical field. The fact that this effect can still be seen even at petahertz excitation frequencies confirms that the electrons in solids can, indeed, be steered by external electric fields even at such high frequencies.
Another important finding from our experiment was that the response of the material to the optical field is dominated by electron motion within a single energy band rather than transitions between different bands – so far it had been unclear what exactly was going on in similar experiments (Fig. 3). This question has now been settled through our observations.
To summarize, we observed attosecond dynamics in diamond that are found to fully recover after the interaction with the infrared pulse. Comparison with ab initio calculations and simplified models allowed us to pinpoint the origin of the observed signals, moving us another step towards a full understanding of optical manipulation of carriers in dielectrics in the petahertz regime. While the realization of petahertz electronic devices might still be far away in the future and other physical effects may eventually limit device performance, our experiment showed that there is no fundamental speed barrier that would prevent us from steering and switching electrons in a component at such high frequencies.
M. Lucchini1, L. Gallmann1, U. Keller1
1 Department of Physics, ETH Zurich,
References and Notes:
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- M. Holler, F. Schapper, L. Gallmann, U. Keller, Phys. Rev. Lett. 106, 123601 (2011).
- M. Schultze, et al., Nature 493, 75 (2012).
- M. Lucchini, S. A. Sato, A. Ludwig, J. Herrmann, M. Volkov, L. Kasmi, Y. Shinohara, K. Yabana, L. Gallmann, U. Keller, Science 353, 916 (2016)
- H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, U. Keller, App. Phys. B 69, 327 (1999)