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Related Concept Videos

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

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.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
¹H NMR Signal Multiplicity: Splitting Patterns01:13

¹H NMR Signal Multiplicity: Splitting Patterns

When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

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

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

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 others.
Aliasing01:18

Aliasing

Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...
Properties of Fourier Transform II01:24

Properties of Fourier Transform II

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Related Experiment Video

Updated: Jun 2, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Faithful entanglement swapping based on sum-frequency generation.

Nicolas Sangouard1, Bruno Sanguinetti, Noé Curtz

  • 1Group of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland.

Physical Review Letters
|April 27, 2011
PubMed
Summary

We demonstrate a faithful entanglement swapping protocol using sum-frequency generation, eliminating the need for postselection. This breakthrough offers a practical solution for single-photon nonlinear optics, advancing quantum technologies.

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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

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Last Updated: Jun 2, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Area of Science:

  • Quantum optics
  • Nonlinear optics
  • Quantum information science

Background:

  • Entanglement swapping is crucial for quantum networks.
  • Existing methods often require postselection, limiting efficiency.
  • Spontaneous parametric down-conversion is a common source for entanglement.

Purpose of the Study:

  • To develop a postselection-free entanglement swapping protocol.
  • To demonstrate the utility of sum-frequency generation in quantum optics.
  • To provide a practical solution for single-photon nonlinear optics.

Main Methods:

  • Utilizing sum-frequency generation for entanglement swapping.
  • Performing a proof-of-principle experiment.
  • Operating at the single-photon level.

Main Results:

  • Achieved faithful entanglement swapping without postselection.
  • Demonstrated sum-frequency generation as a viable nonlinear optical process at the single-photon level.
  • Established an alternative to complex multi-photon protocols.

Conclusions:

  • Sum-frequency generation offers a realistic pathway for efficient quantum information processing.
  • This method simplifies heralded entanglement creation and device-independent quantum key distribution.
  • The findings pave the way for more robust quantum communication.