Symmetry breaking and quantum correlations in finite systems: studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods
Abstract
Investigations of emergent symmetry breaking phenomena occurring in small finitesize systems are reviewed, with a focus on the strongly correlated regime of electrons in twodimensional semiconductor quantum dots and trapped ultracold bosonic atoms in harmonic traps. Throughout the review we emphasize universal aspects and similarities of symmetry breaking found in these systems, as well as in more traditional fields like nuclear physics and quantum chemistry, which are characterized by very different interparticle forces. A unified description of strongly correlated phenomena in finite systems of repelling particles (whether fermions or bosons) is presented through the development of a twostep method of symmetry breaking at the unrestricted HartreeFock level and of subsequent symmetry restoration via post HartreeFock projection techniques. Quantitative and qualitative aspects of the twostep method are treated and validated by exact diagonalization calculations.
Stronglycorrelated phenomena emerging from symmetry breaking include the following.
Chemical bonding, dissociation and entanglement (at zero and finite magnetic fields) in quantum dot molecules and in pinned electron molecular dimers formed within a single anisotropic quantum dot, with potential technological applications to solidstate quantumcomputing devices.
Electron crystallization, with particle localization on the vertices of concentric polygonal rings, and formation of rotating electron molecules (REMs) in circular quantum dots. Such electron molecules exhibit rovibrational excitation spectra, in analogy with natural molecules.
At high magnetic fields, the REMs are described by parameterfree analytic wave functions, which are an alternative to the Laughlin and compositefermion approaches, offering a new point of view of the fractional quantum Hall regime in quantum dots (with possible implications for the thermodynamic limit).
Crystalline phases of strongly repelling bosons. In rotating traps and in analogy with the REMs, such repelling bosons form rotating boson molecules (RBMs). For a small number of bosons, the RBMs are energetically favored compared with the GrossPitaevskii solutions describing vortex formation.
We discuss the present status concerning experimental signatures of such strongly correlated states, in view of the promising outlook created by the latest experimental improvements that are achieving unprecedented control over the range and strength of interparticle interactions.
 Publication:

Reports on Progress in Physics
 Pub Date:
 December 2007
 DOI:
 10.1088/00344885/70/12/R02
 arXiv:
 arXiv:0711.0637
 Bibcode:
 2007RPPh...70.2067Y
 Keywords:

 Condensed Matter  Mesoscopic Systems and Quantum Hall Effect;
 Condensed Matter  Strongly Correlated Electrons;
 Nuclear Theory;
 Physics  Atomic Physics
 EPrint:
 Review article published in Reports on Progress in Physics. REVTEX4. 95 pages with 37 color figures. To download a copy with highquality figures, go to publication #82 in http://www.prism.gatech.edu/~ph274cy/