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Related Concept Videos

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

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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...
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¹H NMR: Complex Splitting01:13

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A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
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¹H NMR Chemical Shift Equivalence: Enantiotopic and Diastereotopic Protons00:58

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Replacing each alpha-hydrogen in chloroethane by bromine (or a different functional group) yields a pair of enantiomers. Such protons are called prochiral or enantiotopic and are related by a mirror plane. Enantiotopic protons are chemically equivalent in an achiral environment. Because most proton NMR spectra are recorded using achiral solvents, enantiotopic hydrogens yield a single signal.
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¹H NMR of Conformationally Flexible Molecules: Temporal Resolution00:52

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At room temperature, the chair conformer of cyclohexane undergoes rapid ring flipping between two equivalent chair conformers at a rate of approximately 105 times per second. These two chair conformers are in equilibrium. The rapid ring flipping results in the interconversion of the axial proton to an equatorial proton and an equatorial to the axial proton. Such interconversions are too rapid and cannot be detected on the NMR timescale. Hence, the NMR spectrometer cannot distinguish between the...
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Atomic Nuclei: Nuclear Spin State Population Distribution01:14

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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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¹H NMR of Conformationally Flexible Molecules: Variable-Temperature NMR01:15

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The axial and equatorial protons in cyclohexane can be distinguished by performing a variable-temperature NMR experiment. In this process, except for one proton, the remaining eleven protons are replaced by deuterium. The deuterium substitution avoids the possible peak splitting caused by the spin-spin coupling between the adjacent protons. The remaining proton flips between the axial and equatorial positions.
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Spatial Separation of Molecular Conformers and Clusters
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Chiral prethermalization in supersonically split condensates.

Kartiek Agarwal1, Emanuele G Dalla Torre1, Bernhard Rauer2

  • 1Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA.

Physical Review Letters
|November 22, 2014
PubMed
Summary
This summary is machine-generated.

Phase relaxation in one-dimensional condensates leads to a prethermal state with distinct temperatures for right- and left-moving excitations. This chirality can be experimentally probed using interference fringe contrasts and may reveal a spacelike Unruh effect.

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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Ultracold atoms

Background:

  • One-dimensional (1D) Bose-Einstein condensates (BECs) exhibit unique quantum phenomena.
  • Phase relaxation dynamics are crucial for understanding the stability and behavior of quantum states.

Purpose of the Study:

  • To investigate the phase relaxation dynamics in a pair of 1D condensates.
  • To explore the resulting prethermal state and its properties.
  • To propose experimental methods for probing these phenomena.

Main Methods:

  • Utilizing the Lorentz invariance of the low-energy sector of 1D condensates.
  • Analyzing dephasing effects on excitation temperatures.
  • Proposing experimental measurements of interference fringe contrasts.

Main Results:

  • Dephasing leads to an unusual prethermal state.
  • Right- and left-moving excitations acquire different, Doppler-shifted temperatures.
  • Chirality of modes can be experimentally detected.

Conclusions:

  • The study reveals a novel prethermal state driven by phase relaxation in 1D condensates.
  • Experimental verification of mode chirality and potential observation of a spacelike Unruh effect are proposed.
  • A concrete experimental setup using atom chips is outlined for realization.