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Related Concept Videos

Crystal Field Theory - Octahedral Complexes02:58

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To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
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Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
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In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
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The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Time-crystalline eigenstate order on a quantum processor.

Xiao Mi1, Matteo Ippoliti2, Chris Quintana1

  • 1Google Research, Mountain View, CA, USA.

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|November 30, 2021
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Summary
This summary is machine-generated.

Researchers experimentally observed a discrete time crystal (DTC) in a many-body localized system. This non-equilibrium phase exhibits unique spatiotemporal order, distinct from equilibrium states, using superconducting qubits.

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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Quantum information science

Background:

  • Quantum many-body systems exhibit complex phases at equilibrium.
  • Non-equilibrium systems can host novel dynamical phases, like discrete time crystals (DTCs).
  • Observing these dynamical phases experimentally is challenging due to transient behaviors.

Purpose of the Study:

  • To experimentally observe a many-body localized discrete time crystal (MBL-DTC).
  • To demonstrate the characteristic spatiotemporal response of MBL-DTCs for generic initial states.
  • To establish a scalable method for studying non-equilibrium phases on quantum processors.

Main Methods:

  • Implementation of tunable controlled-phase (CPHASE) gates on superconducting qubits.
  • Utilizing a time-reversal protocol to assess decoherence effects.
  • Employing quantum typicality to overcome challenges in spectral sampling.
  • Conducting experimental finite-size analysis to locate phase transitions.

Main Results:

  • Experimental observation of an MBL-DTC in a superconducting qubit array.
  • Demonstration of the MBL-DTC's characteristic spatiotemporal response for generic initial states.
  • Successful quantification of decoherence impact and location of the phase transition.

Conclusions:

  • This work provides experimental evidence for MBL-DTCs as a distinct non-equilibrium phase.
  • The developed methods offer a scalable approach for studying novel non-equilibrium phenomena.
  • The findings advance the understanding of quantum phases beyond thermal equilibrium.