Shawn A. Hilbert

Temporal lenses for attosecond and femtosecond electron pulses

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.

Exploring temporal and rate limits of laser-induced electron emission

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.

Topology of the three-qubit space of entanglement types

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{sup 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.

A high repetition rate time-of-flight electron energy analyzer

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.

Acoustic analog to quantum mechanical level splitting

A simple physical system is discussed that mirrors the quantum mechanical infinite square well with a central delta well potential. The physical realization consists of a continuous sound wave traveling in a pair of tubes separated by an adjustable diaphragm. The equivalence between the quantum system and the acoustic system is explored. The analytic solution to the quantum system exhibits level splitting as does the acoustic system.

An acoustic analog for a quantum mechanical level-splitting route to band formation

This paper explores band structure in a simple acoustic apparatus that acts as an analog to the quantum infinite square well with multiple delta-function perturbations. The apparatus can be used to visualize abstract quantum phenomena in a concrete and easily understandable way. It consists of regular sections of PVC pipes connected by variable aluminum diaphragms to allow coupling between the pipe sections. The equivalence between standing waves in the acoustic system and stationary states in the quantum system is examined for multiple-cavity situations. We show that the experimental results from the acoustic system and the analytic solutions of the quantum system demonstrate the same resonance structure. We also experimentally show that the acoustic system supports band structure and that the band width is dependent on the hole size of the diaphragms.

An acoustic demonstration of an avoided crossing

We experimentally demonstrate an avoided crossing in an acoustic system, consisting of two coupled PVC tube sections. One section has a fixed length, while the other has a variable length. Coupling between these tube sections is controlled by an aluminum diaphragm with a variable hole size. The avoided crossings in the acoustic system are compared to those of a quantum infinite square well split into two regions—one of fixed length and another of variable length. The two regions are separated by a delta potential well that controls the coupling between the two regions. We demonstrate that the acoustic and quantum systems exhibit similar avoided crossing behaviors.

Experimental Observation of Time-Delays Associated with Electric Matteucci–Pozzi Phase Shifts

In 1985, Matteucci and Pozzi (1985 Phys. Rev. Lett. 54 2469) demonstrated the presence of a quantum mechanical phase shift for electrons passing a pair of oppositely charged biprism wires. For this experimental arrangement no forces deflect the electrons. Consequently, the result was reported as a non-local type-2 Aharonov-Bohm effect. Boyer (2002 Found. Phys. 32 41-50; 1987 Nuovo Cimento B 100 685-701) showed theoretically that the Matteucci-Pozzi effect could be associated with a time delay caused by a classical force. We present experimental data that confirm the presence of a time delay. This result is in contrast to the situation for the original magnetic Aharonov-Bohm effect. On similar theoretical grounds, Boyer has also associated classical forces and time delays with the magnetic Aharonov-Bohm effect. Recently, we reported the absence of such observable time delays. The contrast with our current work illustrates the subtle nature of Aharonov-Bohm effects.