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Related Concept Videos

Sound Waves: Resonance01:14

Sound Waves: Resonance

Resonance is produced depending on the boundary conditions imposed on a wave. Resonance can be produced in a string under tension with symmetrical boundary conditions (i.e., has a node at each end). A node is defined as a fixed point where the string does not move. The symmetrical boundary conditions result in some frequencies resonating and producing standing waves, while other frequencies interfere destructively. Sound waves can resonate in a hollow tube, and the frequencies of the sound...
Double Resonance Techniques: Overview01:12

Double Resonance Techniques: Overview

Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved by...
¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene π orbitals.
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...
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...
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.
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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Published on: June 8, 2018

Nonlinear mode coupling and resonant excitations in two-component Bose-Einstein condensates.

Ju-Kui Xue1, Guan-Qiang Li, Ai-Xia Zhang

  • 1College of Physics and Electronics Engineering, Northwest Normal University, Lanzhou, 730070, China. xuejk@nwnu.edu.cn

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 21, 2008
PubMed
Summary

Investigating nonlinear excitations in two-component Bose-Einstein condensates (BECs) reveals parametric resonance can create complex multisoliton configurations. This study offers a method for forming these structures in BECs.

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Last Updated: Jul 6, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Microwave Photonics Systems Based on Whispering-gallery-mode Resonators
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Area of Science:

  • Quantum physics
  • Atomic physics
  • Nonlinear dynamics

Background:

  • Two-component Bose-Einstein condensates (BECs) exhibit complex nonlinear behaviors.
  • Understanding these excitations is crucial for quantum simulation and atom optics.

Purpose of the Study:

  • To analytically and numerically investigate nonlinear excitations in two-component BECs.
  • To explore the effects of parametric resonance on excitation dynamics.
  • To demonstrate a method for generating multisoliton configurations.

Main Methods:

  • Variational approximation for analytical insights.
  • Numerical simulations of coupled Gross-Pitaevskii equations.
  • Time-periodic modulation of intercomponent interactions to induce parametric resonance.

Main Results:

  • Identified beating phenomena, higher-harmonic generation, and mode mixing.
  • Derived analytical resonance conditions for parametric excitation.
  • Observed periodic phase separation and diverse multisoliton configurations (soliton trains, pairs, domain walls) via numerical simulations.
  • Confirmed analytical resonance conditions with numerical results.

Conclusions:

  • Parametric resonance provides a controllable pathway to excite and form complex multisoliton structures in two-component BECs.
  • The findings offer insights into controlling quantum matter waves and developing novel quantum devices.