page_title: Sound amplification by stimulated emission of radiation
section_title: Coherent terahertz amplification in a Stark ladder superlattice
hierarchical_section_title: Sound amplification by stimulated emission of radiation / Proposed schemes and devices / Coherent terahertz amplification in a Stark ladder superlattice
caption_attribution_description: English: Stimulated emission of phonons. As the electrons hop between GaAs quantum wells in the superlattice they emit phonons. This process is stimulated by other phonons giving rise to the acoustic amplification
context_page_description: Sound amplification by stimulated emission of radiation refers to a device that emits acoustic radiation. It focuses sound waves in a way that they can serve as accurate and high-speed carriers of information in many kinds of applications—similar to uses of laser light.
  Acoustic radiation can be emitted by using the process of sound amplification based on stimulated emission of phonons. Sound can be described by a phonon just as light can be considered as photons, and therefore one can state that SASER is the acoustic analogue of the laser.
  In a SASER device, a source produces sound waves that travel through an active medium. In this active medium, a stimulated emission of phonons leads to amplification of the sound waves, resulting in a sound beam coming out of the device. The sound wave beams emitted from such devices are highly coherent.
  The first successful SASERs were developed in 2009.
context_section_description: The amplification of coherent terahertz sound in a Wannier-Stark ladder superlattice has been achieved in 2009 according to a paper publication from the School of Physics and Astronomy in the University of Nottingham. Wannier-Stark effect, exists in superlattices. Electron states in quantum wells respond sensitively to moderate electric fields either by the quantum confined Stark effect in the case of wide barriers or by Wannier-Stark localization in the case of a superlattice. Both effects lead to large changes of the optical properties near the absorption edge, which are useful for intensity modulation and optical switching. Namely, in a mathematical point of view, if an electric field is applied to a superlattice the relevant Hamiltonian exhibits an additional scalar potential. If an eigenstate exists, then the states corresponding to wave functions are eigenstates of the Hamiltonian as well. These states are equally spaced both in energy and real space and form the so-called Wannier-Stark ladder.
  In the proposed scheme, an application of an electrical bias to a semiconductor superlattice is increasing the amplitude of coherent folded phonons generated by an optical pulse. This increase of the amplitude is observed for those biases in which the energy drop per period of the superlattice is greater than the phonon energy. If the superlattice is biased such that the energy drop per period of the superlattice exceeds the width of electronic minibands (Wannier-Stark regime), the electrons become localized in the quantum wells and vertical electron transport takes place via hopping between neighboring quantum wells, which may be phonon assisted. As it had been shown previously, under these conditions stimulated phonon emission can become the dominant phonon-assisted hoping process for phonons of an energy value close to the Stark splitting. Thus, coherent phonon amplification is theoretically possible in this type of system. Together with the increase in amplitude, the spectrum of the bias-induced oscillations is narrower than the spectrum of the coherent phonons at zero bias.  This shows that coherent amplification of phonons due to stimulated emission takes place in the structure under electrical pumping.
  A bias voltage is applied to a weakly coupled n-doped GaAs/AlAs superlattice and increases the amplitude of the coherent hypersound oscillations generated by a femtosecond optical pulse. An evidence of hypersound amplification by stimulated emission of phonons emerges, in a system where the inversion of the electron populations for phonon-assisted transitions exists. This evidence is provided by the bias-induced amplitude increase and experimentally observer spectral narrowing of the superlattice phonon mode with a frequency of 441 GHz.
  The main target of this type of experiments is to highlight the realization probability of a coherent amplification of THz sound.  The THz stimulated phonon induced transitions between the electron superlattice states lead to this coherent amplification while processing a population inversion.
  An essential step towards coherent generation ("sasing") of THz sound and other active hypersound devices has been provided by this achievement of THz sound amplification. Generally, in a device where the threshold for "sasing" is achieved, the technique described by this proposed scheme could be used to measure the coherence time of the emitted hypersound.
caption: Stimulated emission of phonons. As the electrons hop between GaAs and AlAs quantum wells in the superlattice they emit phonons. This process is stimulated by other phonons giving rise to the acoustic amplification
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