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Symmetry

Maximizing Four-Wave Mixing in Four-Subband Semiconductor Quantum Wells with Optimal-Shortcut Spatially Varying Control Fields

Dionisis Stefanatos, Emmanuel Paspalakis

Published Feb 21, 2024• 3 citations
Publisher

Abstract

In the present article, we derive optimal spatially varying control fields, which maximize the four-wave mixing efficiency in a four-subband semiconductor asymmetric double quantum well, following analogous works in atomic systems. The control fields coherently prepare the medium, where a weak probe pulse is propagated and eventually converted to a signal pulse at the output. The optimal fields, which maximize the conversion efficiency for a given propagation length, are obtained by applying optimal control theory to a simplified form of propagation equations but are tested with numerical simulations using the full set of Maxwell–Schrödinger equations, which accurately describe the propagation of light pulses in the medium. For short propagation distances, the proposed optimal scheme outperforms a simpler spatially changing control protocol that we recently studied, while for larger distances, the efficiency of both protocols approaches unity. The present work is expected to find application in frequency conversion between light beams, conversion between light beams carrying orbital angular momentum, and nonlinear optical amplification.

DOI
10.3390/sym16030261

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In the present article, we derive optimal spatially varying control fields, which maximize the four-wave mixing efficiency in a four-subband semiconductor asymmetric double quantum well, following analogous works in atomic systems. The control fields coherently prepare the medium, where a weak probe pulse is propagated and eventually converted to a signal pulse at the output. The optimal fields, which maximize the conversion efficiency for a given propagation length, are obtained by applying optimal control theory to a simplified form of propagation equations but are tested with numerical simulations using the full set of Maxwell–Schrödinger equations, which accurately describe the propagation of light pulses in the medium. For short propagation distances, the proposed optimal scheme outperforms a simpler spatially changing control protocol that we recently studied, while for larger distances, the efficiency of both protocols approaches unity. The present work is expected to find application in frequency conversion between light beams, conversion between light beams carrying orbital angular momentum, and nonlinear optical amplification.
In this article, we use spatially modulated control fields to increase the four-wave mixing efficiency in a four-subband semiconductor asymmetric double quantum well, motivated by similar works in atomic systems. Using a simplified version of the propagation equations, we show analytically that for control fields with a constant amplitude and linearly varying mixing angles with the propagation distance, a conversion efficiency close to unity can be achieved even for relatively short propagation distances. Subsequently, we confirm these results by numerically simulating the full set of propagation equations.
We show that for the two widely used configurations of the double- Λ atom–light coupling scheme, one where the control fields are applied in the same Λ -subsystem and another where they are applied in different Λ -subsystems, the forward propagation of the probe and signal fields is described by the same set of equations. We then use optimal control theory to find the spatially dependent optimal control fields that maximize the conversion efficiency from the probe to the signal field, for a given optical density. This work can find application in the implementation of efficient frequency and orbital angular momentum conversion devices for quantum information processing, as well as to be useful for many other applications using the double- Λ atom–light coupling scheme.
Orbital angular momentum (OAM) is an important property of vortex light, which provides a valuable tool to manipulate the light-matter interaction in the study of classical and quantum optics. Here we propose a scheme to generate vortex light fields via four-wave mixing (FWM) in asymmetric semiconductor quantum wells. By tailoring the probe-field and control-field detunings, we can effectively manipulate the helical phase and intensity of the FWM field. Particularly, when probe field and control field have identical detuning, we find that both the absorption and phase twist of the generated FWM field are significantly suppressed. Consequently, the highly efficient vortex FWM is realized, where the maximum conversion efficiency reaches around 50%. Our study provides a tool to transfer vortex wavefronts from input to output fields in an efficient way, which may find potential applications in solid-state quantum optics and quantum information processing.
We propose and analyze an efficient way to enhance four-wave mixing (FWM) signals in a four-subband semiconductor quantum well via Fano-type interference. By using Schrödinger-Maxwell formalism, we derive explicitly analytical expressions for the input probe pulse and the generated FWM field in linear regime under the steady-state condition. With the aid of interference between two excited subbands tunneling to the common continuum, the efficiency to generate FWM field is found to be significantly enhanced, up to 35%. More interestingly, a linear growth rate in the FWM efficiency is demonstrated as the strength of Fano-type interference increases in presence of the continuum states, which can be maintained for a certain propagation distance (i.e., 50μm).
In this paper, we propose an effective scheme to create a frequency entangled states based on bound-to-bound inter-subband transitions in an asymmetric three-coupled quantum well structure. A four-subband cascade configuration quantum well structure is illuminated with a pulsed probe field and two continuous wave control laser fields to generate a mixing field. By properly adjusting the frequency detunings and the intensity of coupling fields, the conversion efficiency can reach 100%. A maximum entangled state can be achieved by selecting a proper length of the sample. We also numerically investigate the propagation dynamics of the probe pulse and mixing pulse, the results show that two frequency components are able to exchange energy through a four-wave mixing process. Moreover, by considering special coupling fields, the storage and retrieval of the probe pulse is also numerically simulated.
We propose a scheme to generate spatially dependent four-wave mixing (FWM) in an asymmetric semiconductor three-coupled-quantum-well nanostructure. By adjusting the detuning of the control field, one can effectively manipulate the FWM output field. Specifically, the vortex phase of the FWM field can be modulated. The detailed explanations based on the dispersion relation are given, which are in good agreement with our results. Furthermore, we perform the interference between the FWM field and the same-frequency Gaussian beam. Our results show that the interference patterns can also be modulated via the detuning of the control field, which may provide a way to observe helical phase modulation via the intensity measurement. This work may be useful for investigating the nonlinear optical phenomena based on orbital angular momentum light.