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Optics Express

Tunable self-focusing and self-defocusing effects in a triple quantum dot via the tunnel-enhanced cross-Kerr nonlinearity

Xiao‐Qing Luo, Zeng-Zhao Li, Tiefu Li, Wei Xiong, J. Q. You

Published Nov 28, 2018• 16 citations

Abstract

Kerr-nonlinearity induced self-focusing or self-defocusing effect provides the opportunity for exploring fundamental phenomena related to the light-matter interactions. Here we show that the linear and nonlinear dispersion responses are significantly sensitive to both the detunings and the tunneling strengths of the indirect-excitonic (IX) states in an asymmetric triple quantum dot system. In particular, the nonlinear dispersion properties are dominated by the tunnel-enhanced cross-Kerr nonlinearity from one of the IX states. Meanwhile, by varying the detunings of other IX states, we reveal that the tunnel-enhanced cross-Kerr nonlinearity gives rise to the realization of the self-focusing and self-defocusing effects. Moreover, by taking into account the effect of the longitudinal-acoustic-phonon induced dephasing of the IX states, it is possible to modulate the height and position of the peak of the self-focusing or self-defocusing effect. Our results may have potential applications in nonlinear-optics and quantum-optics devices based on the tunnel-enhanced nonlinearities in this solid-state system.

DOI: 10.1364/oe.26.032585

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Kerr-nonlinearity induced self-focusing or self-defocusing effect provides the opportunity for exploring fundamental phenomena related to the light-matter interactions. Here we show that the linear and nonlinear dispersion responses are significantly sensitive to both the detunings and the tunneling strengths of the indirect-excitonic (IX) states in an asymmetric triple quantum dot system. In particular, the nonlinear dispersion properties are dominated by the tunnel-enhanced cross-Kerr nonlinearity from one of the IX states. Meanwhile, by varying the detunings of other IX states, we reveal that the tunnel-enhanced cross-Kerr nonlinearity gives rise to the realization of the self-focusing and self-defocusing effects. Moreover, by taking into account the effect of the longitudinal-acoustic-phonon induced dephasing of the IX states, it is possible to modulate the height and position of the peak of the self-focusing or self-defocusing effect. Our results may have potential applications in nonlinear-optics and quantum-optics devices based on the tunnel-enhanced nonlinearities in this solid-state system.

A scheme for giant enhancement of the Kerr nonlinearity in linear triple quantum dot molecules is proposed. In such a system, the tunneling-induced transparency window obtained in double quantum dot molecules splits into two windows, due to the coupling with the third quantum dot. And most important, the Kerr nonlinearity can be enhanced by several orders of magnitude, compared with that generated in double quantum dot molecules. With proper detuning of the tunneling, giant Kerr nonlinearity accompanied by vanishing absorption can be realized, which opens the possibility to enhance self-phase modulation in tunneling controllable semiconductor nanostructures under conditions of low light levels. Quantitative analysis shows that the giant Kerr nonlinearity is attributed to the interacting double dark resonances induced by the tunneling between the triple quantum dots, therefore no extra laser fields are required.

The nonlinearity of semiconductor quantum dots under the condition of low light levels has many important applications. In this study, linear absorption, self-Kerr nonlinearity, fifth-order nonlinearity and cross-Kerr nonlinearity of multiple quantum dots, which are coupled by multiple tunneling, are investigated by using the probability amplitude method. It is found that the linear and nonlinear properties of multiple quantum dots can be modified by the tunneling intensity and energy splitting of the system. Most importantly, it is possible to realize enhanced self-Kerr nonlinearity, fifth-order nonlinearity and cross-Kerr nonlinearity with low linear absorption by choosing suitable parameters for the multiple quantum dots. These results have many potential applications in nonlinear optics and quantum information devices using semiconductor quantum dots.

Abstract An efficient scheme for probing electron tunnelling is proposed based on the enhanced cross-Kerr nonlinearity in a double–dot system. Due to resonant tunnelling, the cross-Kerr nonlinearity arises in a transparency window. Its intensity is nearly two orders of magnitude greater than that of the self-Kerr effect under any given conditions, where residual absorption is suppressed due to the competition of nonlinear gain and absorption. The enhanced cross-Kerr effect is sensitive to the tunnelling, so the probe spectrum can detect subtle tunnelling changes. The simulation results show that the probe sensitivity of the nonlinear phase shift is about 0.28 rad/ μ eV.

The coherent coupling between three quantum dots via tunneling fields leads to double tunneling-induced transparency and giant Kerr nonlinearity with vanishing absorption. This creates the possibility to achieve self-phase modulation in semiconductor nanostructures via controllable tunneling under the conditions of low light levels. As a result, a considerably high refractive index can be obtained. We suggest an intracavity medium which consists of triple quantum dot molecules to control the Goos–Hänchen (GH) shifts in the reflected light. For a suitable design of a triple quantum dot system, our results show that relatively large positive and negative GH shifts are achievable, without significant distortion, using partially coherent incident light fields.

A scheme for giant Kerr nonlinearity via tunneling in triangular triple quantum dot molecules is proposed. In such a system, the linear absorption and the Kerr nonlinearity depend critically on the energy splitting of the excited states and the tunneling intensity. With proper parameters, giant Kerr nonlinearity accompanied by vanishing absorption can be realized. The enhancement of Kerr nonlinearity is attributed to the interacting double dark resonances induced by the tunneling between the quantum dots, requiring no extra coupling laser fields.

We present an alternative scheme for the preparation of the phase grating in quantum-dot molecules, where the tunnel coupling occurs between two quantum dots. In the presence of interdot tunneling, the nonlinear dispersion can be significantly enhanced with nearly vanishing linear and nonlinear absorption due to the tunneling-induced quantum coherence. With the help of a standing-wave control field, the weak probe light could be diffracted into high-order direction. It is shown that parameters such as the weak-driving intensity, driving detuning, tunneling strength, and interaction length could be used to adjust the diffraction intensity effectively. Our scheme is focused on the weak standing-wave driving and weak tunneling strength, which may provide an easy and actual way to obtain the phase grating and may have potential applications in quantum-optics and quantum-information-processing devices in the solid-state system.