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Related Concept Videos

Quantum Numbers02:43

Quantum Numbers

34.5K
It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
34.5K
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

1.0K
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
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Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

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In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
1.2K
Phase Diagram01:19

Phase Diagram

5.8K
The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).
5.8K
The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

35.7K
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
35.7K
Phase Transitions02:31

Phase Transitions

19.0K
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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Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source
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Distinguishing Quantum Phases through Cusps in Full Counting Statistics.

Chang-Yan Wang1, Tian-Gang Zhou1, Yi-Neng Zhou1

  • 1Institute for Advanced Study, <a href="https://ror.org/03cve4549">Tsinghua University</a>, Beijing 100084, China.

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Full counting statistics reveal quantum fluctuations. Cusp singularities in these statistics can distinguish between superfluid and Mott phases in quantum systems, offering a new diagnostic tool.

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Area of Science:

  • Quantum physics
  • Condensed matter physics

Background:

  • Measuring physical observables typically involves averaging experimental outcomes.
  • Full counting statistics (FCS), the Fourier transform of outcome distributions, offer a deeper insight into quantum fluctuations in many-body systems.
  • FCS are increasingly important in quantum transport research.

Purpose of the Study:

  • To introduce cusp singularities in FCS as a novel method for differentiating between ordered and disordered phases.
  • To investigate the superfluid-to-Mott transition in the Bose-Hubbard model as a specific application.

Main Methods:

  • Analytical analysis of the Bose-Hubbard model.
  • Numerical simulations to study the behavior of FCS.
  • Focusing on the superfluid-to-Mott transition.

Main Results:

  • Full counting statistics exhibit a cusp singularity with respect to the phase angle in the superfluid phase for large subsystem sizes.
  • The FCS remain smooth in the Mott phase.
  • The observed discontinuity signifies a first-order transition between semiclassical vortex configurations.

Conclusions:

  • Cusp singularities in FCS serve as a robust indicator for distinguishing between ordered (superfluid) and disordered (Mott) phases.
  • This finding provides a new experimental tool for phase characterization in quantum systems.
  • The proposed method is experimentally verifiable using ultracold atoms and superconducting qubits.