From quarks to cold atoms: the phases of strongly-interacting systems

Powell, Philip

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https://hdl.handle.net/2142/45461 Copy

Description

Title

From quarks to cold atoms: the phases of strongly-interacting systems

Author(s)

Powell, Philip

Issue Date

2013-08-22T16:40:55Z

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

Baym, Gordon A.

Doctoral Committee Chair(s)

Fradkin, Eduardo H.

Committee Member(s)

• Baym, Gordon A.
• MacDougall, Gregory
• Grosse Perdekamp, Matthias

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• dense quark matter
• phase diagrams
• strongly-interacting matter
• neutron stars
• quantum chromodynamics
• ultracold atomic gases
• degenerate Fermi gas

Abstract

In this thesis we investigate the phase structure of dense quark matter, the structure and stability of neutron and quark stars, and the phases of ultracold fermions in the presence of an artificial spin-orbit coupling. While spanning an extraordinary twenty orders of magnitude in energy scales, these systems exhibit some remarkable similarities including non-perturbative many-body interactions, perfect fluid behavior, the formation of Cooper pairs, and the possibility of BCS-BEC crossovers between weakly and strongly interacting regimes. Moreover, due to phenomenal advancements in laser cooling techniques and the ability to exert an unprecedented level of control over the interactions of ultracold atomic gases, the possibility of using these systems to simulate the complex behavior of systems not easily realized in the laboratory (e.g., non-Abelian gauge fields, quantum chromodynamics) is becoming increasingly real. Despite the widespread success of quantum chromodynamics (QCD), the theory of the strong nuclear force, much remains unknown about the properties of strongly-interacting quark matter. In large part, this continued ignorance is a result of the mathematical intractability of QCD and the limitations of current numerical techniques to very low densities. In the first part of this thesis, in order to gain some insight into the phase structure of dense quark matter we therefore apply an effective field theory which is built upon the symmetries of QCD, the Polyakov–Nambu–Jona-Lasinio (PNJL) model. We construct the QCD phase diagram for two and three quark flavors, giving special attention to the effect of the intermediate strange quark mass on the preferred quark pairing structure at intermediate to high density. In addition, we investigate the impact of the strange quark mass and axial anomaly on a recently proposed low temperature critical point, which may allow for a smooth crossover between hadronic and color superconducting matter. Finally, we investigate the impact of a local color neutrality constraint on phases of asymmetric quark pairing. While the Relativistic Heavy Ion Collider (RHIC) continues to probe the QCD phase diagram at ever-higher temperatures and researchers await the completion of the highly anticipated Facility for Antiprotons and Ion Research (FAIR), the only known “laboratories” in which low temperature dense quark matter is encountered are the cores of neutron stars. Fortunately, the structure of these astrophysical objects is highly dependent upon the properties of the dense matter in their cores, and observations of the mass-radius relationship of these stars impose constraints on the quark matter equation of state. In the second part of this thesis we investigate the possibility of realizing massive neutron stars, such as the recently observed PSRs J1614-2230, J0348+0432, and J1311-3430 with masses of two solar masses or larger, by including a flavor-symmetric vector coupling within an NJL model description of quark matter. By extracting the quark matter equation of state we show that in the absence of diquark pairing, a reasonable magnitude vector repulsion can to stabilize neutron stars against gravitational collapse up to 2.34 solar masses. We also investigate the possibility of realizing stable quark stars with densities much higher than those obtained in conventional neutron stars, but find that stars with central densities much greater than ten times nuclear density are always unstable to gravitational collapse. In the third part of this thesis we study the properties of ultracold atomic gases in the presence of artificial gauge fields. While neutral atoms do not naturally couple to the gauge fields in nature (e.g., magnetic fields, the strong nuclear force), recent advancements in laser techniques have led to the realization of synthetic gauge fields in which ultracold atoms behave as if they were charged. Combined with the Feshbach resonance, through which the two-body interactions which dominate these dilute gases can be arbitrarily tuned, these gases can be used to simulate a wide variety of systems, including those that occur naturally and those that do not. We study the phase structure of a two-species mixture of fermions in the presence of Rashba-Dresselhaus (RD) spin-orbit coupling, which is induced by a specific type of non-Abelian gauge field. In particular, we compute the dependence of the superfluid critical temperature on the RD coupling strength and the tunable two-body interaction. We also investigate the effects of the spin-orbit coupling on the crossover between weakly bound (BCS) atomic pairs and strongly bound (BEC) molecules and the effects of fluctuations on the stability of the superfluid phase.

Graduation Semester

2013-08

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http://hdl.handle.net/2142/45461

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Copyright 2013 by Philip D. Powell. All rights reserved.

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