Bound state in the continuum explained

A bound state in the continuum (BIC) is an eigenstate of some particular quantum system with the following properties:

  1. Energy lies in the continuous spectrum of propagating modes of the surrounding space;
  2. The state does not interact with any of the states of the continuum (it cannot emit and cannot be excited by any wave that came from the infinity);
  3. Energy is real and Q factor is infinite, if there is no absorption in the system.

BICs are observed in electronic, photonic, acoustic systems, and are a general phenomenon exhibited by systems in which wave physics applies.

Bound states in the forbidden zone, where there are no finite solutions at infinity, are widely known (atoms, quantum dots, defects in semiconductors). For solutions in a continuum that are associated with this continuum, resonant states are known, which decay (lose energy) over time. They can be excited, for example, by an incident wave with the same energy. The bound states in the continuum have real energy eigenvalues and therefore do not interact with the states of the continuous spectrum and cannot decay.[1]

Classification of BICs by mechanism of occurrence

Source:[1]

BICs arising when solving the inverse problem

Wigner-von Neumann's BIC (Potential engineering)

The wave function of one of the continuum states is modified to be normalizable and the corresponding potential is selected for it.

Hopping rate engineering

In the tight binding approximation, the jump rates are modified so that the state becomes localized

Notes and References

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