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A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. A building may vibrate for several seconds with a driving frequency matching the building's natural frequency of vibration; this produces a resonance that results in one building collapsing while the neighboring buildings do not. Often, buildings of a certain height are devastated, while other taller buildings remain intact. This...
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The starting point for expressing the modes of standing waves is understanding the boundary conditions that the waves must follow. The boundary conditions are derived from the physical understanding of how the standing waves are sustained, that is, how the vibrating particles of the medium behave at the boundaries imposed on them.
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A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
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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...
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Unitary Subharmonic Response and Floquet Majorana Modes.

Oles Shtanko1,2, Ramis Movassagh3

  • 1Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA.

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|September 10, 2020
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Researchers discovered that Majorana fermions exhibit a unique spin oscillation, known as subharmonic response (SR), which is crucial for topological quantum computing. Engineered disorder can stabilize these Majorana modes, paving the way for quantum advancements.

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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Topological quantum computation

Background:

  • Non-Abelian statistics, exemplified by Majorana fermions, are key for topological quantum computers.
  • Detecting and manipulating these excitations is crucial for advancing quantum computing.

Purpose of the Study:

  • To establish a link between Majorana fermions and unitary subharmonic response (SR) in driven systems.
  • To explore methods for stabilizing Majorana modes for quantum applications.

Main Methods:

  • Investigating nonequilibrium initial states in periodically driven systems.
  • Analyzing spin oscillations and lifetimes of unpaired Majorana modes.
  • Exploring the role of disorder in stabilizing subharmonic response.

Main Results:

  • Unpaired Majorana modes exhibit localized spin oscillations with twice the driving period (SR).
  • These modes can possess exponentially long lifetimes in clean systems.
  • Engineered disorder can stabilize the subharmonic response of Majorana modes, overcoming limitations in translationally invariant systems.

Conclusions:

  • The study reveals a connection between Majorana fermions and subharmonic response, offering a new avenue for their detection and manipulation.
  • Stabilizing Majorana modes via engineered disorder is a promising strategy for robust topological quantum computation.
  • The findings suggest practical observation using current superconducting circuits and cold atomic systems.