Electron magnetic resonance imaging and spatially selective control over
electrons in a solid state sample, at a sub-micrometer resolution.
OR
Taking photos of electrons, using magnetic fields.
Instructor: Yaron Artzi Department of Physics.
Abstract:
Modern physics reveal that the electron possesses a property, known as a “spin”,
that may be visualized as a sphere of electric charge, spinning at a very high speed.
As a result of this circulating charge, a small magnetic field is produced and
therefore, the electron spin can in fact be thought of as a tiny magnet. It turns out
that when we introduce electrons to a magnetic field, their magnetic north poles
tend to align either in the same direction or opposite to the direction of the
externally applied magnetic field. If we then apply an additional microwave field to
the electrons, in the appropriate conditions (known as resonance conditions), the
electron spins will turn to point in the other direction. (see figure below for further
details).
Figure 1: An illustration showing the basic principles of ESR. In an external magnetic field
the spins of the electrons orient either in the same direction or in the opposite direction as
the external magnetic field. Microwave energy can then be absorbed by the electrons and
cause their spins to change their orientation. In many cases, this absorption of energy by the
electrons can be measured, and a great deal of information can be learned about physical
systems this way
Electron spin resonance (ESR) is a physical method of observing resonance
absorption of microwave energy by such electron spins, when placed in an external
magnetic field. By using methods of ESR, a great deal of information can be
obtained about physical systems, that may not be obtained in any other way.
Moreover, since with methods of ESR one can manipulate directly the direction of
the electron spin, it may be possible to use the electron spin as a new kind of
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information carrier for use in a new and exciting field, known as quantum
computation. In conjunction with methods of magnetic resonance imaging (MRI),
that are used by the medical community, images showing the physical locations of
electrons in a sample can be obtained, which makes ESR an even more powerful
scientific tool.
In this project, we will attempt to prepare and characterize a small sample, with an
unknown number of electron spins in it. We will prepare some additional reference
samples, to compare against, so that we will be able to determine how many
electron spins we have in our sample. We will then perform magnetic resonance
imaging experiments in a state-of-the-art pulsed ESR system, to determine the
spatial locations of the electron spins in our sample. We will also attempt to image
electron spins only in small parts of our sample, to show that we can selectively
manipulate only a fraction of all the electron spins in our sample.
Student mission / Objective:
To learn about, manipulate and probe the spin of the electron by use of a cutting-edge
pulsed Electron Spin Resonance (ESR) imaging system and participate in ongoing
work, to develop tools essential for electron-spin based quantum computation devices.
Requirements:
Math (5 grade) and Physics (5 grade) are mandatory and basic knowledge in Matlab
(data analysis will be done using Matlab) is preferred.
You can read the following paper in order to get a sense about the project (The system
described here is an older version of the system we’ll use in the project. Also, don’t
worry if you don’t understand too much. You can see in this article examples of ESR
imaging results, similar to what we will get in the project):
Paper name:
ESR imaging in solid phase down to sub-micron resolution: methodology and
applications
Also, please read the following required reading material:
1.
First chapter of the book: J. Jin, Electromagnetic Analysis and Design in
Magnetic Resonance Imaging .
Although this chapter discusses nuclear spins, the principles it gives are
completely equivalent to the case of the electron spin and therefore this
information is relevant to this project. I decided to give you this reading material,
because it sticks to a simple explanation of the principles of magnetic resonance,
without requiring a prior knowledge of quantum mechanics!
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2.
Fourier transform
We will use this mathematical tool to some extent, so I want you to read about it
at:
a) https://simple.wikipedia.org/wiki/Fourier_transform
simple definitions, etc. - to begin with.
b) http://www.thefouriertransform.com/
A nice site that gives relevant information, without over complicating things.
Read the following pages:
i.
Introduction to the Fourier Transform
ii.
Fourier Transform - Properties
iii. Mathematical Background (if you need to).
Questions about the reading material:
1.
How do spins in a magnetic field “move” and what is the Larmor frequency?
2.
What does a pulse of magnetic field (B1) that oscillates at the resonance
frequency does to the spins? What is a 90° pulse? What is a 180° pulse?
We will discuss the answers when we meet at the dinner in the opening ceremony.
Please feel free to contact me with questions regarding the project and questions
regarding the reading material, at: [email protected]
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