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Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

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Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
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Atomic Nuclei: Nuclear Spin State Overview01:03

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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 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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Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
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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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Superradiant Quantum Phase Transition for an Exactly Solvable Two-Qubit Spin-Boson Model.

Roberto Grimaudo1, Davide Valenti1, Alessandro Sergi2,3

  • 1Dipartimento di Fisica e Chimica "Emilio Segrè", Group of Interdisciplinary Theoretical Physics, Università degli Studi di Palermo, Viale delle Scienze Ed. 18, 90128 Palermo, Italy.

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This study analyzes an exactly solvable two-qubit model, revealing first-order quantum phase transitions. These transitions manifest as abrupt changes in entanglement and magnetization.

Keywords:
entanglementexactly solvable modelsopen quantum systemsquantum phase transitionssuperradiancetwo-qubit spin-boson model

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Area of Science:

  • Quantum mechanics
  • Quantum optics
  • Condensed matter physics

Background:

  • The spin-boson model is a fundamental model in quantum mechanics describing the interaction between a quantum system and a bath.
  • Interacting qubit systems are crucial for quantum computing and quantum information processing.
  • Quantum phase transitions (QPTs) represent fundamental changes in the ground state of quantum systems.

Purpose of the Study:

  • To analyze a specific spin-boson-like model with two interacting qubits.
  • To investigate the possibility of exactly solving the model due to its inherent symmetry.
  • To analytically identify and characterize quantum phase transitions within this system.

Main Methods:

  • The study employs an exactly solvable model characterized by exchange symmetry between two spins.
  • Explicit expressions for eigenstates and eigenenergies are derived.
  • The analysis focuses on identifying abrupt changes in key quantum properties.

Main Results:

  • The model is shown to be exactly solvable due to exchange symmetry.
  • First-order quantum phase transitions are analytically identified.
  • These transitions are linked to significant changes in two-spin concurrence, net spin magnetization, and mean photon number.

Conclusions:

  • The analyzed two-qubit model provides an exactly solvable platform for studying quantum phase transitions.
  • The identified QPTs are physically relevant, demonstrating abrupt changes in measurable quantum properties.
  • This work contributes to the understanding of quantum phase transitions in interacting qubit systems.