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Nanomaterials

Enhancing Third- and Fifth-Order Nonlinearity via Tunneling in Multiple Quantum Dots

Si-Cong Tian, Huanyu Lu, Hang Zhang, Li-Jie Wang, Shi–Li Shu, Xin Zhang, Guanyu Hou, Ziye Wang, Cunzhu Tong, Lijun Wang

Published Mar 12, 2019• 14 citations
Publisher

Abstract

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.

DOI
10.3390/nano9030423

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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.
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.
Schemes for giant fifth-order nonlinearity via tunneling in both linear and triangular triple quantum dots are proposed. In both configurations, the real part of the fifth-order nonlinearity can be greatly enhanced, and simultaneously the absorption is suppressed. The analytical expression and the dressed states of the system show that the two tunnelings between the neighboring quantum dots can induce quantum interference, resulting in the giant higher-order nonlinearity. The scheme proposed here may have important applications in quantum information processing at low light level.
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.
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.
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.
In the present work, the linear and nonlinear optical properties of quantum dot molecules composed of two quantum dots as well as three quantum dots molecules, respectively known as double quantum dot (DQD) molecule and triple quantum dot (TQD) molecules are studied using the probability amplitude method, and the obtained results are discussed and compared. By solving the state equations of these systems in the interaction picture, under the rotating wave approximation and the dipole approximation, the first and third-order susceptibilities for DQD and TQD molecules are calculated. A phenomenon called tunneling-induced transparency (TIT) which is similar to electromagnetically induced transparency (EIT) is studied in these types of quantum dot molecules. The effect of key system parameters such as tunneling couplings between quantum dots and the tunneling intensity on the linear and nonlinear optical response of multiple quantum dot molecules DQD and TQD is investigated. It was shown that the position and the width of the TIT window created in these quantum dot molecules can be tuned by changing the physical parameters.