Topics in multi-component ultracold gases and gauge fields

Ozawa, Tomoki

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Description

Title

Topics in multi-component ultracold gases and gauge fields

Author(s)

Ozawa, Tomoki

Issue Date

2012-05-22T00:22:12Z

Director of Research (if dissertation) or Advisor (if thesis)

Baym, Gordon A.

Doctoral Committee Chair(s)

Vishveshwara, Smitha

Committee Member(s)

• Baym, Gordon A.
• DeMarco, Brian L.
• Gilbert, Matthew J.

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• ultracold gas
• artificial gauge field
• multi-component fermion
• double-slit interference

Abstract

In this thesis, we present theoretical studies on three topics related to multi-component ultracold gases and gauge fields. The first topic that we discuss is artificial gauge fields in ultracold gases. Recently, methods to create artificial gauge fields coupled to neutral ultracold systems using a light-induced Berry's connection have been rapidly developing. These methods are not only capable of creating Abelian gauge fields, such as a conventional magnetic field, but also non-Abelian gauge fields, which opens a way to explore and simulate a wide variety of physical models. In this thesis, we discuss various properties of bosons with Rashba-Dresselhaus spin-orbit coupling, which is a special type of non-Abelian gauge field. We investigate the stability of Bose-Einstein condensates with Rashba-Dresselhaus spin-orbit coupling, and show that the condensates are stable against quantum and thermal fluctuations. We also consider the renormalization of the bare interaction by calculating the t-matrix and its consequence on the ground state phase diagrams. The second topic discussed here is three-component ultracold fermionic systems. It is known that ferromagnetism and superfluidity can coexist at low enough temperature in three-component ultracold fermions. In this thesis, we elucidate how fermionic pairing and population imbalance enhance each other. We also describe a crossover from Bardeen-Cooper-Schrieffer state of fermionic pairing state to the limit of Bose-Einstein condensate of three weakly interacting species of molecules, as the interaction increases. Furthermore, we find an interesting similarity in the free energies between three-component ultracold fermions and quantum chromodynamics. The last topic discussed here is Niels Bohr's double-slit interference gedankenexperiment with charged particles, which argues that the consistency of elementary quantum mechanics requires that the electromagnetic field must be quantized. In the experiment a particle's path through the slits is determined by measuring the Coulomb field that it produces at large distances. Under these conditions the interference pattern must be suppressed; otherwise quantum mechanics is not consistent. The mechanism for the suppression of the interference pattern is that, as the particle's trajectory is bent in diffraction by the slits, it must radiate and the radiation must carry away phase information. Thus, the radiation field must be a quantized dynamical degree of freedom. We also consider the related setup in which one attempts to determine the path of a massive particle through an interferometer by measuring the Newtonian gravitational potential the particle produces. In this case, we show that the interference pattern would have to be finer than the Planck length and thus indiscernible. Therefore, unlike for the electromagnetic field, Bohr's argument does not imply that the gravitational field must be quantized.

Graduation Semester

2012-05

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http://hdl.handle.net/2142/31021

Copyright and License Information

Copyright 2012 Tomoki Ozawa

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