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NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of...
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In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
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Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
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In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
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Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Superconducting circuits

Background:

  • Superconducting circuits are a key platform for exploring many-body physics.
  • Nonlinear elements in these circuits are often simplified as two-level qubits.
  • The spin-boson model describes quantum dissipation in systems like charge qubits coupled to transmission lines.

Purpose of the Study:

  • To investigate the impact of the intrinsic multilevel structure of superconducting qubits on the validity of the spin-boson paradigm.
  • To explore how multilevel effects influence quantum dissipation and critical phenomena in these circuits.

Main Methods:

  • Theoretical analysis of phase localization in multilevel superconducting qubits.
  • Numerical renormalization group (NRG) simulations to study quantum critical points.
  • Variational state calculations incorporating charge discreteness.

Main Results:

  • The multilevel structure of superconducting qubits restricts the applicability of the spin-boson model due to phase localization.
  • Wave function delocalization across multiple charge states is observed.
  • NRG simulations indicate that quantum critical points shift out of accessible ranges in the multilevel regime.

Conclusions:

  • The conventional spin-boson description is insufficient for multilevel superconducting qubits.
  • Phase localization and charge discreteness are crucial factors in understanding dissipation and criticality.
  • These findings are relevant for a broad range of superconducting quantum devices.