Professor Steve Simon - The Story of Anyons

The speaker begins by introducing the topic of the lecture, which is about anions and their significance in quantum physics. The lecture is the fifth in a series and the speaker expresses happiness at the turnout. There's a brief mention of the speaker's anticipation for the talk and an apology for a scheduling confusion. The lecture focuses on the work of Professor Simon from the University of Oxford, who specializes in topological phases of matter and their relation to computing. The speaker sets the stage for a historical narrative that starts in 1924 with a significant development in quantum physics.

The paragraph delves into the historical discovery of Bose-Einstein statistics, which describes the behavior of photons as indistinguishable particles. The story begins with a letter from India's Satyendra Nath Bose to Albert Einstein, who derived Max Planck's radiation law using a new approach. Einstein recognized the importance of this work and generalized it to particles with mass, leading to the concept of bosons. The paragraph also touches on the exclusion principle formulated by Wolfgang Pauli, which states that no two electrons can occupy the same quantum state, leading to Fermi-Dirac statistics. The speaker discusses the historical oversight of giving credit to Pascual Jordan for his contribution to Fermi-Dirac statistics, which was overlooked due to his later political affiliations with the Nazi party.

This paragraph discusses the exchange operator, which is used to determine the statistical properties of particles. The speaker explains how the square of the exchange operator must equal one, leading to the classification of particles as bosons or fermions based on whether the exchange results in a plus or minus outcome. The speaker then introduces a critical paper from 1977 that challenged the conventional wisdom by showing that in two dimensions, particles could exist with statistical properties different from both bosons and fermions. This was a groundbreaking discovery that was initially ignored but later gained recognition.

The speaker addresses the oversight in quantum mechanics textbooks regarding the existence of particles beyond bosons and fermions. The conventional argument, which is flawed, is based on the idea that the exchange of identical particles in a two-particle system should always result in a plus or minus one phase shift, depending on whether they are bosons or fermions. The speaker explains that this argument fails to consider the topological properties of particle exchanges in two dimensions, which can lead to different outcomes. The historical neglect of this possibility is attributed to the initial lack of recognition of the 1977 paper and the subsequent rederivation of the results by other physicists.

The speaker transitions to the discussion of the fractional quantum Hall effect, a phenomenon that occurs in two-dimensional electron systems at low temperatures. The fractional quantum Hall effect is highlighted as a key area where anions, particles with fractional statistics, have been theoretically predicted and later experimentally observed. The speaker mentions the work of Frank Wilczek, who coined the term 'anion' and brought significant attention to the field. The paragraph also touches on the experimental breakthroughs in measuring the fractional phase associated with anions, which confirmed their existence and distinct statistical properties.

The speaker elaborates on the fundamental interest in anions, emphasizing their potential existence in various physical systems beyond the fractional quantum Hall effect. The importance of anions in the context of quantum computing and memory is discussed, highlighting their potential as a platform for topological quantum computation. The speaker mentions the investment by Microsoft in developing anion-based quantum computing technology. The paragraph concludes with a reflection on the historical journey of anions from theoretical prediction to experimental confirmation, emphasizing the long-term scientific curiosity and perseverance that led to this discovery.

The speaker describes the anion interferometer experiment, which is designed to measure the fractional phase associated with anions in a fractional quantum Hall system. The experiment involves manipulating quasi-particles with electric fields and observing their interference patterns. The speaker explains the significance of the observed fractional phase, which is a direct experimental observation of anions. The paragraph also touches on the challenges and the innovative solutions used to overcome them, such as the use of image charges to reduce the interaction between quasi-particles and the edges of the system.

The speaker provides an in-depth explanation of the quantum Hall effect, particularly focusing on the fractional quantum Hall effect. The properties of the Nu equals one-third state are discussed, including the superfluid nature of the system and the existence of persistent vortices with fractional charges. The speaker emphasizes the quantization of the Hall resistance and the surprising discovery of quasi-particles with charges that are fractions of an electron's charge. The paragraph concludes with a discussion on the implications of these findings, including the potential for anions to be considered as fundamental particles within the context of the two-dimensional system they inhabit.

The speaker addresses the nature of anions, their interactions, and their fractional statistics. The discussion includes the interaction of anions with other particles, such as phonons and electrons, and the conservation of net charge. The speaker also touches on the concept of Berry's phase, which is a correction to the adiabatic approximation and is related to the fractional phase observed in anion experiments. The paragraph concludes with a reflection on the historical recognition of contributions to the field and the ongoing research into the properties of anions and their potential applications.