Here, we describe the ''temporal lens'' concept that can be used for the focus and magnification of ultrashort electron packets in the time domain. The temporal lenses are created by appropriately synthesizing optical pulses that interact with electrons through the ponderomotive force. With such an arrangement, a temporal lens equation with a form identical to that of conventional light optics is derived. The analog of ray diagrams, but for electrons, are constructed to help the visualization of the process of compressing electron packets. It is shown that such temporal lenses not only compensate for electron pulse broadening due to velocity dispersion but also allow compression of the packets to durations much shorter than their initial widths. With these capabilities, ultrafast electron diffraction and microscopy can be extended to new domains,and, just as importantly, electron pulses can be delivered directly on an ultrafast techniques target specimen.attosecond imaging ͉ ultrafast techniques W ith electrons, progress has recently been made in imaging structural dynamics with ultrashort time resolution in both microscopy and diffraction (ref. 1 and references therein). Earlier, nuclear motions in chemical reactions were shown to be resolvable on the femtosecond (fs) time scale using pulses of laser light (ref. 2 and references therein), and the recent achievement of attosecond (as) light pulses (for recent reviews, see refs. 3-6) has opened up this temporal regime for possible mapping of electron dynamics. Electron pulses of femtosecond and attosecond duration, if achievable, are powerful tools in imaging. The ''electron recombination'' techniques used to generate such attosecond electron pulses require the probing electron to be created from the parent ions (to date no attosecond electron pulses have been delivered on an arbitrary target) and for general applications it is essential that the electron pulse be delivered directly to the specimen.In ultrafast electron microscopy (UEM) (7), the electron packet duration is determined by the initiating laser pulse, the dispersion of the electron packet due to an initial energy spread and electron-electron interactions (see, e.g., ref. 8). Because packets with a single electron can be used to image (1, 7), and the initiating laser pulse can in principle be made very short (Ͻ10 fs), the limiting factor for the electron pulse duration is the initial energy spread. In photoelectron sources this spread is primarily due to the excess energy above the work function of the cathode (8), and is inherent to both traditional photocathode sources (9) and optically induced field emission sources (10-13). Energytime uncertainty will also cause a measurable broadening of the electron energy spread, when the initiating laser pulse is decreased below Ϸ10 fs. For ultrafast imaging techniques to be advanced into the attosecond temporal regime, methods for dispersion compensation and new techniques to further compress electron pulses to the attosecond regime need to be developed.A rec...

To achieve high temporal resolution for ultrafast electron diffraction, Zewail (Proc. Natl Acad. Sci. USA 102, 7069 (2005)) has proposed to use high repetition rate, ultrafast electron sources. Such electron sources emitting one electron per pulse eliminate Coulomb broadening. High repetition rates are necessary to achieve reasonable data acquisition times. We report laser-induced emission from a nanometre-sized tip at one electron per pulse with a 1 kHz repetition rate in the femtosecond regime. This source, combined with 1 MHz repetition rate lasers that are becoming available, will be a primary candidate for next generation ultrafast, high-coherence electron diffraction experiments. We also report that the measured energy bandwidth of our electron source does not support sub-cycle electron emission. This result addresses a current debate on ultrafast nanotip sources. Regardless of the limited bandwidth, this source may be used in conjunction with a recently proposed active dispersion compensation technique (Proc. Natl Acad. Sci. USA 104, 18409 (2007)) to deliver attosecond electron pulses on a target.

We demonstrate a time-of-flight electron energy analyzer that operates at an 80MHz repetition rate. The analyzer yields an energy resolution of 40meV for 3eV electrons. The energy resolution limit is dominated by the detector time (or temporal) resolution. With a currently available detector with a temporal resolution of 100ps, we predict an energy resolution of less than 1meV for 200meV electrons. This makes high repetition rate time-of-flight energy analyzers a promising low-technology alternative to current state-of-the-art techniques.

The three-qubit space of entanglement types is the orbit space of the local unitary action on the space of three-qubit pure states, and hence describes the types of entanglement that a system of three qubits can achieve. We show that this orbit space is homeomorphic to a certain subspace of R 6 , which we describe completely. We give a topologically based classification of three-qubit entanglement types, and we argue that the nontrivial topology of the three-qubit space of entanglement types forbids the existence of standard states with the convenient properties of two-qubit standard states.

Electrons in an atom are confined to distinct, quantized energy levels. When atoms form solids, the interaction of the electrons causes their energy levels to split into multiple closely spaced levels, or bands, separated by forbidden regions called band gaps. Each band contains a number of energy levels equal to the number of atoms in the solid. This model of the origin of band structure can be reproduced by using a classical array of harmonic oscillators (masses connected by springs). In this system, each oscillator plays the role of an atom and its resonant frequencies play the roles of electronic energy levels. When coupled, a system of oscillators yields a spectrum of resonant frequencies and when the number of oscillators becomes sufficiently large, the system exhibits the formation of “resonant frequency bands,” similar in structure to the energy bands of an atomic solid. We experimentally demonstrate band formation using coupled harmonic oscillators and highlight the effects of both number of oscillators and coupling strength on the band structure. Additionally, we show that experimental results of this band formation follow a theoretical analysis of the system.