Electron and boson clusters in confined geometries: symmetry breaking in quantum dots and harmonic traps

Abstract

We discuss the formation of crystalline electron clusters in semiconductor quantum dots and of crystalline patterns of neutral bosons in harmonic traps. In a first example, we use calculations for two electrons in an elliptic quantum dot to show that the electrons can localize and form a molecular dimer. The calculated singlet-triplet splitting (J) as a function of the magnetic field (B) agrees with cotunneling measurements, with its behavior reflecting the effective dissociation of the dimer for large B. Knowledge of the dot shape and of J(B) allows determination of the degree of entanglement. In a second example, we study strongly repelling neutral bosons in two-dimensional harmonic traps. Going beyond the Gross-Pitaevskii (GP) mean-field approximation, we show that bosons can localize and form polygonal-ring-like crystalline patterns. The total energy of the crystalline phase saturates in contrast to the GP solution, and its spatial extent becomes smaller than that of the GP condensate.

LATEX, 9 pages with 6 figures. To appear in Proc. Natl. Acad. Sci. (USA). For related papers, see http://www.prism.gatech.edu/~ph274cy/

References in corpus (3)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Controlling Spin Qubits in Quantum Dots
• Wigner molecules and hybrid qubits

Cited by in corpus (11)

• A molecular state of correlated electrons in a quantum dot
• Absence of Wigner molecules in one-dimensional few-fermion systems with short-range interactions
• Rapidly rotating boson molecules with long or short range repulsion: an exact diagonalization study
• Nonuniversal transmission phase lapses through a quantum dot: An exact-diagonalization of the many-body transport problem
• Molecular formations and spectra due to electron correlations in three-electron hybrid double-well qubits
• Quantum Wigner molecules in moiré materials
• Valleytronic full configuration-interaction approach: An application to the excitation spectra of Si double-dot qubits
• Wigner-molecule supercrystal in transition-metal dichalcogenide moiré superlattices: Lessons from the bottom-up approach
• Universality of Many-Body States in Rotating Bose and Fermi Systems
• Crystal-field effects in the formation of Wigner-molecule supercrystals in moiré TMD superlattices
• The Wigner localization of interacting electrons in a one-dimensional harmonic potential