| Majorana fermions(MFs) are exotic particles that are their own anti-particles. One predicts that neutrinos may be MFs. In the past few decades, particle physicists have been looking for MFs, however, there are no definite experimental evidences to demonstrate neutrinos are MFs up to now. Currently, MFs signatures occurring as quasiparticle excitations in condensed matter systems have attracted widespread interest, because of their importance in fundamental physics and potential applications in topological quantum computation based on solid-state devices. This exotic particle obeys non-Abelian statistics, and MFs will appear at the end of the nanowire in the hybrid semiconductor nanowire/superconductor(SNW/SC) heterostructures biased with an external magnetic field. However, other physical mechanisms, such Kondo effect, and disorder or band bending in the SNW, will result in similar Majorana signature. Furthermore, most of the schemes to detect MFs have focused on the electronic transport properties at present. Therefore, to obtain definitive signatures of MFs, alternative setups or proposals for detecting MFs are necessary. In this thesis, we propose all-optical scheme for detecting the possible Majorana signature.In recent years, benefiting from the advances in modern nanoscience, various nanostructures such as semiconductor quantum dots(SQDs), SNW, metal nanoparticles(MNP), nano-superconductor, optical cavity at nanoscale, have obtained remarkable progress, paving a way to investigate the kinds of quantum phenomena in nanoscale system. Meanwhile, the radiation pressure has been obtained based on the nanoscale optical cavity, which opens another door to investigate optomechanical system. In addition, layered nanomaterial, such as grapheme, carbon nanotube, and Mo S2, due to their low mass density, high quality-factor, high frequency, and intrinsically small size, are considered as the ideal nanomaterial for fabricating nanomechanical systems(NMSs). In this thesis, we present an all-optical means for detecting novel physical phenomenon based on the pump-probe technique. The whole thesis includes the following six chapters.The first chapter is the introduction, we firstly introduce the basic information about SQD and MNP, and briefly describe the manufacture methods and their various applications. Then we introduce that Majorana signature is observed in the hybrid semiconductor nanowire/superconductor(SNW/SC) heterostructures and several celebrated experiments for search MFs in condensed matter systems in recent three years. In addition, we introduce the layered nanomaterial, such as grapheme, carbon nanotube, and Mo S2, and give a detailed description about the production of Mo S2 and its potential application in the future. Further, we introduce the hybrid nanomechanical system(such as SQD coupled to the nanomechanical resonator system) and optomechanical system(such as whispering gallery mode cavity optomechanical system). In the last, we introduce the pump-probe technique.In Chapter Two, we propose an all-optical means for detecting MFs in condensed matter systems. SQD as a two-level system, which offers a beneficial medium to detect MFs. When there is a coupling between the SQD and MFs, the Majorana signature will be carried out via the probe absorption spectrum and nonlinear optical Kerr effect of the SQD with the pump-probe technique. We further consider a hybrid system consisting of a MNP and a SQD to detect MFs. The surface plasmon enhanced effect will significantly enhance the probe absorption spectrum and eventually make MFs more sensitive to be detectable. When we implant the SQD into a nanomechanical resonator(NR) system, the vibration of the NR will enhance the nonlinear optical effect, which makes the MFs more sensitive for detection, and the nonlinear optical scheme for detecting MFs maybe immune to detection noises. Compared with the SQD, a single electron spin can be considered as an ideal two-level system, which can behave as a sensitive probe. We further consider implanting a single electron spin into a suspended carbon nano tube(CNT), and decete MFs with a single electron spin. With this scheme, the coupling strength between MFs and a single electron spin is also determined, and the CNT resonator behaved as a phonon cavity is robust for detecting of MFs. This optical scheme will provide another method for the detection MFs and will open the door for new applications ranging from robust manipulation of MFs to quantum information processing based on MFs.In Chapter Three, we propose a nano-optomechanical system based on a plate-like circular monolayer Mo S2 suspended on the Si/Si O2 substrate. We investigate the linear and nonlinear coherent optical properties of this system, present a scheme for measuring the coupling strength of exciton–nanoresonator, and demonstrate the phenomenon of phonon-induced transparency. With manipulating the power of the pump field, the system indicates a promising candidate for an optical transistor. We also investigate the nonlinear effect of the system which can be regulated under different parameter regimes, and propose a nonlinear optical scheme for measuring the frequency of the Mo S2 nanoresonator. Based on the coherent optical spectrum, we further propose a nonlinear optical scheme to determine the mass of the biomolecules(such as single influenza virus and HIV virus) with the resonance frequency shift of the resonator. This scheme proposed here may have potential applications in quantum sensing and all-optical Mo S2-based devices.In Chapter Four, we propose two kinds of nanomechanical systems which are carbon nanotube mechanical resonator and Z-shaped graphene nanoribbon mechanical resonator systems, and compare to the two systems. Based on a doubly clamped suspended carbon nanotube resonator, we firstly present a nonlinear optical mass sensor. The masses of external particles(such as nitric oxide molecules) landing onto the surface of carbon nanotube can be determined directly and accurately via using the nonlinear optical spectroscopy. To compare with carbon nanotube resonator, we further put forward a nonlinear optical mass sensing based on a doubly-clamped Z-shaped graphene nanoribbon. Due to its property of low mass density, single nano-particles, such as such as NH3 and NO2, can be identified with grapheme mechanical resonator. The nonlinear optical mass sensing may be immune to detection noises, which will improve the sensitivity of detection. The phenomena of phonon-induced transparency, electromagnetically-induced absorption, parametric amplification, and nonlinear optical Kerr effect are also demonstrated in the graphene nanoribbon mechanical resonator system. The grapheme and carbon nanotube based mechanical resonator system may provide a nonlinear optical measurement technique in quantum measurements, environmental pollutant monitoring and trace chemical detection.In Chapter Five, in microwave frequency, we first consider graphene resonator coupled to a microwave on-chip cavity based on a bilayer graphene. We theoretically demonstrate the phenomenon of optomechanically induced transparency and the slow light effect based on the coupled graphene nanomechanical resonator-microwave cavity system under red sideband regime. Compared with the general optomechanical system, in which the optically tunable delay is about nanosecond, while the group velocity delay of microwave in the graphene resonator-microwave cavity system can reach 0.4 ms. When the system is driven on its blue sideband, the phenomena of optomechanically induced absorption and fast-light effect are also obtained. We further investigate the nonlinear effects such as four-wave mixing(FWM) and present a nonlinear means to measure the vibrational frequency of the resonator. In optical wave frequency, We present a generalized three-mode cavity optomechanical system, where two cavity modes with strong control fields and weak signal fields are coupled to a common mechanical resonator. We find that the weak input signal fields will be entirely absorbed by the system without generating any energy output from each of the cavity modes termed coherent perfect absorption(CPA), and the two cavity modes and mechanical mode will share the input probe fields energy when CPA occurs under parameter regimes. With changing the parameter conditions, a weak input signal field will transmit from one cavity to the other cavity without undergoing any energy loss termed coherent perfect transmission(CPT). Moreover, the above phenomena are dependent on the coupling strength between the two cavity modes in this optomechanical systems. The origin and conditions that enable these phenomena to achieve are analyzed, and potential applications in switches, modulators, and filters may be realized in all-optical domain based on such phenomena.In Chapter Six, it is the main conclusions and the prospst. |
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