The laws of quantum physics are not only extraordinary—they also offer some
far-reaching and unique possibilities for advanced information processing,
quantum computing and cryptography. So far, the basic building blocks for
such quantum operations are electric circuitry in form of superconducting
resonators, light in form of photons or atoms in form of ion chains.
However, all these quantum systems have their drawbacks, and scientists are
therefore continuously searching for useful alternatives.
In their recent publication in Physical Review Research, scientists from the
Department of Physics at the University of Konstanz have found a way to
modulate a free electron in vacuum into a so-called qubit, a two-level
quantum bit. Such qubits are the building blocks of information processing
in quantum computers. To generate their free-electron qubits, the
researchers use the electron beam of a transmission electron microscope and
intersect it with the electric field of classical laser light. "The
resulting matter-wave interferences create a periodic modulation of the
electron energy into discrete, well-defined energy levels, which we use as a
resource for the formation of qubits," explains Professor Peter Baum, the
leader of the research team.
The physical background
To generate their qubits from free electrons, the researchers use the
electron beam of a transmission electron microscope as an electron source
and intersect it with the electric field of classical laser light. In the
oscillations of the light wave, the beam electrons are periodically
accelerated and decelerated in very rapid succession. "This rapid
interaction between the electron beam and the optical cycles of the laser
light results in a periodic modulation of the electron energy into discrete,
well-defined energy levels," explains Professor Peter Baum, the leader of
the research team. "We use this quantization, which can be detected with our
instruments, as a resource for the formation of qubits."
Attosecond electron microscopy
Interestingly, the intersection of electron and laser beam in the experiment
does not only lead to the described phenomena in the energy domain, which
are relevant for qubit generation. With the right choice of laser
parameters, additional useful phenomena arise in the time domain: the
electron beam converts into a sequence of extremely short electron pulses
with durations in the attosecond range.
"This corresponds to the millionth of a billionth part of a second and even
light covers only the size of a bigger molecule in such a time span," says
Peter Baum, illustrating these numbers. Such extremely short electron pulses
are useful for ultrafast electron microscopy of complex light-matter
interactions, where they enable maximum temporal resolution in addition to
an enormous spatial resolution at an atomic level.
Qubits in 'mass production'
Another practical feature of the qubits and attosecond electron pulses in
the experiment is their high production rate: about one billion qubits or
electron pulses are generated per second. This high flux is achieved by
using a continuous, non-pulsed electron source and a continuous, non-pulsed
laser beam. In this way, almost every free electron in the electron beam is
modulated, and qubit production is only limited by the performance limit of
modern high-energy electron sources.
However, this is not the only reason why laser-shaped free electrons and
qubits are an interesting and practical object for further investigations.
"In the vacuum of free space, an electron as an elementary particle does not
interact with any material. The so-called decoherence—the loss of
information to the environment—is therefore rather slow," adds Peter Baum.
"In addition, the laser-optical control of electron beams is versatile and
can be quickly switched." Free-electron qubits under laser control could
therefore play an important role in the future for both fundamental research
and applications in quantum information.
Details on the physics of the qubits
When looked at closely, the free electrons from the electron beam used in
the experiment are not point particles, but rather wave functions with a
finite coherence length that covers multiple light oscillations of the laser
beam used. If so, the same final energy is generated coherently by adjacent
optical field cycles at multiple instances in time. Consequently,
matter-wave interferences create a periodic modulation of the energy
spectrum into discrete energy sidebands, which the researchers use as a
resource for a two-level quantum system. Quantum operations are performed by
simple free-space propagation, where different sidebands acquire nonlinear
matter-wave phases due to the rest mass of the electrons, followed by a
second laser interaction and sideband generation some centimeters later in
the beam. In this way, the researchers can reach almost any point on the
Bloch sphere, i.e. the "coordinate system" in which qubit states are
geometrically represented as points on the surface of a unit sphere.
Reference:
M. V. Tsarev et al, Free-electron qubits and maximum-contrast attosecond
pulses via temporal Talbot revivals, Physical Review Research (2021).
DOI: 10.1103/PhysRevResearch.3.043033
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