Quantum Mechanics PROJECT, fall 2003
Below, please find a list of possible topics for the PROJECT. I've listed one introductory article for each topic (typically from Physics Todayor Physics World- two excellent monthly publications reporting on recent developments in Physics), to help you get started. However, for a satisfactory project you need to do some literature search on your own, maybe with a little guidance from the contact persons listed
below.
HAVE FUN!
ON THE MEANING OF QUANTUM MECHANICS
In most text books (including Sakurai!) the mathematical structures of quantum mechanics are connected to physical reality through the concept of measurement.This is the legacy of the Bohr-Heisenberg-Pauli ”Copenhagen interpretation”. However, as we have discussed in class, turning the notion of measurement into a central axiom of interpretation raises a number of problems. What’s special with a measurement? Why shouldn't it be included from scratch in the quantum mechanical formalism? A novel approach - the so called ”consistent-histories approach” - seeks a sensible remedy to the paradoxes of the traditional interpretation.
”Consistent Histories and Quantum Measurements” by Robert. B. Griffiths and Roland Omnes, Physics Today, August 1999.
contact: Henrik Johannesson, Theoretical Physics, johannesson@fy.chalmers.se
QUANTUM SYNTHESIS
Life on earth is fueled by the energy of the Sun, essentially via
photosynthesis. Photosynthetic organisms - plants, algae and
photosynthetic bacteria - have developed efficient systems to collect the
light of
the Sun and to use its energy to drive their metabolic reactions. Purple
bacteria are great masters of harvesting light, exploiting subtle quantum
mechanical effects to convert light energy for photosynthesis.
”How Nature Harvests Sunlight” by Xiche Hu and Klaus Schulten,
Physics Today, August 1997.
contact: Peter Apell, Applied Physics,
apell@fy.chalmers.se
FROM QUANTUM MECHANICS TO STRINGS... AND BACK
”The second superstring revolution” 1994-95 amalgated a number of themes that had developed independently in theoretical physics for several decades: electric-magnetic duality, gauge theories, symmetries of supergravity and dualities of string theory. The result is the still mysterious ”M-theory” (Magic, Mystery, Membrane,...). Will it revise our understanding of quantum mechanics?
”Duality, Spacetime and Quantum Mechanics” by Edward Witten, Physics Today, May 1997
contact: Bengt Nilsson, Theoretical Physics, tfebn@fy.chalmers.se
MACROSCOPIC QUANTUM PHENOMENA
Bose-Einstein condensation is a macroscopic quantum phenomenon that was first predicted by Albert Einstein in the 1920s. He applied the new concept of Bose statistics to an ideal gas of identical particles with integer spin, trapped in a box at thermal equilibrium. Einstein predicted that at sufficiently low temperatures the particles would accumulate in the lowest quantum state in the box, giving rise to a new state of matter where quantum effects appear on macroscopic scales. Since the first observation in 1995 of ideal Bose-Einstein condensation in dilute atomic gases, many remarkable properties of this quantum state have been unearthed.
"Bose Condensates Make Quantum Leaps and Bounds" by Yvan Castin, Ralph Dum and Alice Sinatra, Physics World, August 1999
contact: Stellan Östlund, Theoretical Physics, ostlund@fy.chalmers.se
APPROACHING THE QUANTUM LIMIT
In many condensed matter systems the electrons are so strongly correlated that they cannot be treated individually. Such correlations give rise to fundamentally altered behaviors - from heavy-fermion physics to the self-organized striped structures recently discovered in the high-temperature superconductors. In the presence of strong magnetic fields, the interactions between magnetic flux quanta and electrons in these systems are expected to produce some rather weird phenomena - watch out for the quantum limit!
"Correlated Electrons in a Million Gauss" by Greg Boebinger, Physics Today, June 1996
contact: Stellan Östlund, Theoretical Physics, ostlund@fy.chalmers.se
QUANTUM TRANSPORT IN OPTICAL LATTICES
Recent advances in techniques for laser manipulation and laser cooling of atoms make it possible to study the quantum motion of atoms in a periodic light field - an optical lattice.
This enables high-precision measurements of some of the most remarkable quantum transport effects predicted by elementary quantum mechanics: Bloch oscillations, Wannier-Stark ladders and Landau-Zener tunneling.
"New Light on Quantum Transport" by Mark Raizen, Christophe Salomon and Qian Niu,
Physics Today, July 1997
contact: Dag Hanstorp, Experimental Physics, dag.hanstorp@fy.chalmers.se
QUANTUM CORRELATIONS OF SQUEEZED LIGHT
The amplitude and phase of electromagnetic fields such as light are subject to intrinsic quantum fluctuations. By "squeezing" the light (using sophisticated spectroscopic techniques) the uncertainty in the field amplitude can be reduced below the "quantum noise level" by a Heisenberg trade-off with the uncertainty in the frequency. The photons produced in squeezed light experiments have strong nonlocal correlations
that cannot be explained by conventional semi-classical electromagnetic theory.
"Nonclassical Excitation in Spectroscopy with Squeezed Light" by Zbigniev Ficek and Peter D. Drummond, Physics Today, September 1997
contact: Dag Hanstorp, Experimental Physics, dag.hanstorp@fy.chalmers.se
QUANTUM CRITICALITY
Phase transitions - where matter goes from one state to another - is normally associated with changes of temperature. However, a new type of transition - driven by quantum fluctuations - is possible, leading to all sorts of intriguing physics. This is a new area of theoretical research where quantum mechanics combined with the sophisticated tools of the renormalization group open up a new vista on the collective behavior of matter.
”Quantum Phase Transitions” by Subir Sachdev, Physics World, April 1999
contact: Henrik Johannesson, Theoretical Physics, johannesson@fy.chalmers.se
QUANTUM CHROMODYNAMICS
Quantum chromodynamics - "QCD" for short - is the modern theory of the strong interactions. Whereas the fundamentals of QCD are simple and elegant, the theory leads to mathematical equations that are notoriusly hard to solve. Still, the theory has an enormous predictive power, and is used to describe most of what goes on at high-energy accelerators. The high-density limit of the theory reveals that nominally weak correlations between baryons can have big effects: the signature of degenerate perturbation theory! As in condensed matter systems this may lead to a drastic restructuring of the ground state... In QCD: color superconductivity.
"QCD Made Simple" by Frank Wilczek, Physics Today, August 2000
contact: Gabriele Ferretti, Theoretical Physics, ferretti@fy.chalmers.se
EXOTIC QUANTUM PARTICLES
Electrons under extreme conditions - confined to a two-dimensional interface at low temperatures and very high magnetic fields - participate in a collective dance which produces one of the most remarkable phases of matter ever discovered: the quantum Hall effect. When dancing, an electron sucks up bits and pieces of the magnetic field and effectively gets transformed into a new kind of particle: a composite fermion.This is a case where
quantum mechanics is not only required to describe the particle dynamics, but where the very definition of a particle requires quantum mechanics!
"The Composite Fermion: A Quantum Particle and its Quantum Fluids" by Jainendra Jain, Physics Today, April 2000
contact: Henrik Johannesson, Theoretical Physics, johannesson@fy.chalmers.se
COSMOLOGICAL QUANTUM WIRES
Current theories of particle physics predict that a variety of so called topological defects formed when the early universe cooled down - in analogy with the defects appearing when cooling a melt into a crystal. Among these defects, the most thoroughly studied are the phenomena called cosmic strings.This is a research area at the intersection of particle physics, cosmology and condensed matter physics: Laboratory experiments yield many examples of analogous phenomena in condensed matter systems that can provide a bridge to understanding the very early universe. Cosmic strings are narrow filaments of enormous lengths, filled with unconverted matter from the early moments of cosmic history. Current theories predict that at a certain stage of their evolution, the strings become giant quantum wires - actually superconducting.This may explain some puzzles of observational cosmology.
"Superconducting Cosmic Strings" by Alejandro Gangui, American Scientist, May-June 2000
contact: Ulf Torkelsson, Astrophysics, torkel @fy.chalmers.se
MOLECULAR QUANTUM WIRES
Carbon nanotubes are cylindrical molecules with a diameter of as little as 1 nanometer and a length up to many micrometers. Essentially, they can be thought of as a single layer of graphite that has been wrapped into a cylinder. Nanotubes exhibit unique quantum properties that derive from the tube's nanometer diameters in combination with the special electronic structure of graphite. There appears to be no material in the world that is as strong, conducting, and inert, all at the same time... This can be put to use: nanotubes provide a showcase where fundamental science and applications go side by side!
"Carbon Nanotubes as Molecular Wires" by Cees Dekker, Physics Today, May 1999
contact: Alex Kleiner, Theoretical Physics, alexkl@fy.chalmers.se
QUANTUM POINT CONTACTS
Electrons confined to nanoscale geometries reveal their quantum mechanical wave-nature by strong interference effects. Enter the world of Mesoscopia! One of the simplest examples is the ballistic transport of electrons through a narrow constriction,
leading to quantization of the conductance.
"Quantum Point Contacts" by Henk van Houten and Carlo Beenakker, Physics Today, July 1996
contact: Mats Jonson, Applied Physics, jonson@fy.chalmers.se
COMPUTATIONAL QUANTUM MECHANICS
Recent progress in large-scale numerical simulations of quantum mechanical systems have accelerated the pace of discoveries in materials science and quantum chemistry.
Today many properties of new and artificially structured materials can be predicted and explained entirely by computations, using atomic numbers as the only input. Major industrial firms such as Motorola and Dow Chemical are setting up their own applied quantum mechanics research departments!
"Computational Materials Science: The Era of Applied Quantum Mechanics" by Jerzy Bernholc, Physics Today, September 1999
contact: Göran Wahnström, Applied Physics, wahnstrom@fy.chalmers.se
QUANTUM FRACTIONALIZATION
Quantum mechanics is a strange business, and the quantum physics of strongly correlated many-electron systems can be stranger still. Examples are the fractional quantum-Hall effect, organic conductors and the high-temperature superconductors. One of the most striking features, demonstrated rigorously in an exactly solvable model, is that correlated electrons living in one dimension behave as if their charge and spin have separated dynamically: the electrons together conspire to form new effective particles carrying only charge orspin, and these particles move independent of each other!Could something similar happen in higher dimensions? Do we have to rewrite the textbooks from scratch?
"When the Electron Falls Apart" by Philip W. Anderson, Physics Today, October 1997
contact: Henrik Johannesson, Theoretical Physics, johannesson@fy.chalmers.se
SPIN-POLARIZED QUANTUM TRANSPORT
Electrons have spin as well as charge, and this make all the difference in future electronics. Spin polarized conduction electrons in ferromagnetic materials can be manipulated by putting in tunneling barriers that act as "spin polarizers" when a magnetic field is applied to the structure. The fundamental quantum mechanical nature of spin places it out of reach of many of the forces in a solid, suggesting that a spin-polarized current in a device could have sufficiently long relaxation times to make it useful for practical purposes. Enter the spin transistor!
"Spin-Polarized Transport" by Gary A. Prinz, Physics Today, April 1995
contact: Per Delsing, MINA, delsing@fy.chalmers.se
QUANTUM ORGANICS
Interacting electrons behave quite bizarre when confined to low dimensions. An example are the Bechgaard salts , where the conducting molecules stack in 1D structures. These organic materials exhibit a wealth of quantum effects which cannot be explained by ordinary text-book theory. Instead one has to invoke a new theory that treats the electrons as a strongly correlated composite: the Luttinger liquid.
"One-Dimensional Conductors" by Claude Bourbonnais and Denis Jerome, Physics World, September 1998
contact: Sebastian Eggert, Theoretical Physics, eggert@fy.chalmers.se
QUANTUM CRYPTOGRAPHY
Over the last few years, rapid progress has been made in the field of quantum cryptography in which information is carried by single quantum states. This technology, which is a direct outcome from the foundations of quantum mechanics, has great advantages over traditional approaches. In particular, it guarantees that the key needed to encrypt and decrypt a message can be safeguraded to 100%. Quantum cryptography has recently been demonstrated by sending polarized photons through optical fibers that are tens of kilometers in length!
"Quantum Cryptography Takes to the Air" by Richard Hughes and Jane Nordholt,
Physics World, May 1999
contact: Göran Wendin, MINA, wendin@fy.chalmers.se
QUANTUM COMPUTING
If the progress in computer technology continues with the current rate, by the year 2020 the basic memory components of a computer will be the size of individual atoms. At such scales, conventional theories of computation break down. A new field called "quantum computing" is emerging that is reinventing the foundations of computer science and information theory in a way that is fully consistent wth quantum mechanics. This new theory predicts that quantum computers can perform certain tasks incredibly much faster than classical computers, and even accomplish mind-boggling feats such as teleporting information, breaking "unbreakable" codes and generate true random numbers.
"Quantum Information and Computation" by Charles H. Bennett, Physics Today, October
1995
contact: Andreas Käck, MINA, anka@fy.chalmers.se
QUANTUM TELEPORTATION
Teleportation is a popular artifice in science fiction stories for beaming action heroes around the Universe and introducing all kinds of identity paradoxes into a story line: The destruction of the original object at the source is accompanied by the creation of an exact replica at the intended destination. Science fiction? Maybe
not much longer! In 1997 physicists in
Insbruck and Rome independently accomplished the feat of teleporting the quantum state of a single photon! What lies ahead? Teleporting atomic states? The quantum state of a molecule? And then...?
"Quantum Teleportation" by Anton Zeilinger, Scientific American, April 2000
contact: Henrik Johannesson, Theoretical Physics, johannesson@fy.chalmers
QUANTUM TRICKERY
The closest thing we have to a probability distribution in quantum phase space is the so called Wigner distribution,which maps onto the usual phase space probability distribution in the classical limit. In a recent tour de forceof experimentation, the Wigner distribution of a quantum particle has been measured. This makes possible a complete picture of the underlying wave function, opening the door to experimental studies of a quantum state as it loses coherence when interacting with its environment.
"The Art of Measuring Quantum States" by Matthias Freyberger et al., Physics World,
November 1997
contact: Henrik Johannesson, Theoretical Physics, johannesson@fy.chalmers.se
QUANTUM GRAVITY
Quantum mechanics and general relativity are the two great pillars that form the foundation of modern physics, and ultimately, of all science. Yet the two pillars stand in two different worlds: quantum and classical... Are the two theories compatible? Can they ever be reconciled in a self-consistent theory of quantum gravity?
"Quantum Gravity" by Paul Renteln, American Scientist, November-December 1991
contact: Bengt Nilsson, Theoretical Physics, tfebn@fy.chalmers.se
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This page was last updated on October 19, 2000.