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Nonlinear and Quantum Optics Near Nanoparticles

Suman S. Dhayal

Published Dec 1, 2015• 0 citations
Publisher

Abstract

We study the behavior of electric fields in and around dielectric and metal nanoparticles, and prepare the ground for their applications to a variety of systems viz. photovoltaics, imaging and detection techniques, and molecular spectroscopy. We exploit the property of nanoparticles being able to focus the radiation field into small regions and study some of the interesting nonlinear, and quantum coherence and interference phenomena near them. The traditional approach to study the nonlinear light-matter interactions involves the use of the slowly varying amplitude approximation (SVAA) as it simplifies the theoretical analysis. However, SVVA cannot be used for systems which are of the order of the wavelength of the light. We use the exact solutions of the Maxwell's equations to obtain the fields created due to metal and dielectric nanoparticles, and study nonlinear and quantum optical phenomena near these nanoparticles. We begin with the theoretical description of the electromagnetic fields created due to the nonlinear wavemixing process, namely, second-order nonlinearity in an nonlinear sphere. The phase-matching condition has been revisited in such particles and we found that it is not satisfied in the sphere. We have suggested a way to obtain optimal conditions for any type and size of material medium. We have also studied the modifications of the electromagnetic fields in a collection of nanoparticles due to strong near field nonlinear interactions using the generalized Mie theory for the case of many particles applicable in photovoltaics (PV). We also consider quantum coherence phenomena such as modification of dark states, stimulated Raman adiabatic passage (STIRAP), optical pumping in $4$-level atoms near nanoparticles by using rotating wave approximation to describe the Hamiltonian of the atomic system. We also considered the behavior of atomic and the averaged atomic polarization in $7$-level atoms near nanoparticles. This could be used as a prototype to study any $n-$level atomic system experimentally in the presence of ensembles of quantum emitters. In the last chapter, we suggested a variant of a pulse-shaping technique applicable in stimulated Raman spectroscopy (SRS) for detection of atoms and molecules in multiscattering media. We used discrete-dipole approximation to obtain the fields created by the nanoparticles.

DOI
10.12794/metadc822820

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We study the behavior of electric fields in and around dielectric and metal nanoparticles, and prepare the ground for their applications to a variety of systems viz. photovoltaics, imaging and detection techniques, and molecular spectroscopy. We exploit the property of nanoparticles being able to focus the radiation field into small regions and study some of the interesting nonlinear, and quantum coherence and interference phenomena near them. The traditional approach to study the nonlinear light-matter interactions involves the use of the slowly varying amplitude approximation (SVAA) as it simplifies the theoretical analysis. However, SVVA cannot be used for systems which are of the order of the wavelength of the light. We use the exact solutions of the Maxwell's equations to obtain the fields created due to metal and dielectric nanoparticles, and study nonlinear and quantum optical phenomena near these nanoparticles. We begin with the theoretical description of the electromagnetic fields created due to the nonlinear wavemixing process, namely, second-order nonlinearity in an nonlinear sphere. The phase-matching condition has been revisited in such particles and we found that it is not satisfied in the sphere. We have suggested a way to obtain optimal conditions for any type and size of material medium. We have also studied the modifications of the electromagnetic fields in a collection of nanoparticles due to strong near field nonlinear interactions using the generalized Mie theory for the case of many particles applicable in photovoltaics (PV). We also consider quantum coherence phenomena such as modification of dark states, stimulated Raman adiabatic passage (STIRAP), optical pumping in 444-level atoms near nanoparticles by using rotating wave approximation to describe the Hamiltonian of the atomic system. We also considered the behavior of atomic and the averaged atomic polarization in 777-level atoms near nanoparticles. This could be used as a prototype to study any n−n-n−level atomic system experimentally in the presence of ensembles of quantum emitters. In the last chapter, we suggested a variant of a pulse-shaping technique applicable in stimulated Raman spectroscopy (SRS) for detection of atoms and molecules in multiscattering media. We used discrete-dipole approximation to obtain the fields created by the nanoparticles.
Optical properties of ensembles of realistic quantum emitters coupled to plasmonic systems are studied by using adequate models that can take into account full atomic geometry. In particular, the coherent effects such as forming ``dark states,'' optical pumping, coherent Raman scattering, and the stimulated Raman adiabatic passage (STIRAP) are revisited in the presence of metallic nanoparticles. It is shown that the dark states are still formed but they have more complicated structure, and the optical pumping and the STIRAP cannot be employed in the vicinity of plasmonic nanostructures. Also, there is a huge difference in the behavior of the local atomic polarization and the atomic polarization averaged over an ensemble of atoms homogeneously spread near nanoparticles. The average polarization is strictly related to the polarization induced by the external field, while the local polarization can be very different from the one induced by the external field. This is important for the excitation of single molecules, e.g., different components of scattering from single molecules can be used for their efficient detection.
The coherent effects such as forming “dark states,” optical pumping, and the stimulated Raman adiabatic passage (STIRAP) are studied in the presence of dielectric and/or metalic nanoparticles. It is shown that the “dark states” are still formed but they have more complicated atomic structure, the optical pumping and the STIRAP cannot be employed in the vicinity of plasmonic nanostructures. Also we show difference of the local atomic polarization and the atomic polarization averaged over ensemble of atoms homogeneously spread near nanoparticles.
This thesis is an attempt at studying quantum coherence effects coupled via plasmons. After introducing the quantum coherence in atomic systems in Chapter 1, we utilize it in Chapter 2 to demonstrate a new technique of detection of motion of single atoms or irons inside an optical cavity. By taking into account the interaction of coherences with surface plasmonic waves excited in metal nanoparticles, we provide a theoretical model along with experimental data in Chapter 3 to describe the modification of Raman spectra near metal nanoparticles. We show in chapter 4 that starting from two emitters, coupled via a plasmonic field, the symmetry breaking occurs, making detectable the simultaneous existence of the fast super-radiance and the slow sub-radiance emission of dye fluorescence near a plasmonic surface. In Chapter 5, we study the photon statistics of a group of emitters coupled via plasmons and by the use of quantum regression theorem, we provide a theoretical model to fully investigate the dependence of photon bunching and anti-bunching effects to the interaction between atoms, fields and surrounding mediums.
Optically controlled dipole-dipole interaction at submicrometers and subwavelength scales leads to many interesting phenomenon and remarkable potential applications in quantum optics, condensed matter physics, and today’s micro-devices. In this dissertation, we study the applications of quantum optical coherence to nano-optics in the following systems and aspects. On the one hand, chiral metamaterials has been previously reported as excellent candidates to realize both attractive and repulsive Casimir forces, where the existence of a repulsive Casimir force depends upon the strength of the chirality. On the other hand, nanoscale integration of metal nanoparticles and semiconductors is particularly interesting because the strengths of both materials are combined in such a hybrid system. In the first part of this work, we proposed a technical scheme to coherently control of the Casimir interaction energy with two identical chirality mediums. We took explicit caution regarding the requirements of passivity and causal response of the materials, since these requirements are essential for the application of the Lifshitz formula. The rare-earth metals’ atomic species, for instance, dysprosium, is proposed as an applicable medium for the forthcoming studies of possible experimental implementation of our technique. Secondly, we fully investigated the coherent control of the quantum optical properties of spontaneous emission spectra of a semiconductor quantum dot coupled to a metallic nanoparticle. The properties of the spontaneous emission spectra of such a system are studied in detail with and without involving the coherent field. The Rabi splitting effect in the spectrum emitted by the quantum dot under particular conditions is predicted for different sizes of the metal nanoparticles. We show that the spontaneous emission spectra of the transition coupled to surface plasmons may be further modified by adjusting the external coherent control on the adjacent transitions. In the third part, we propose a robust protocol to study the entanglement generation in a hybrid structure consisting of two quantum dots in the proximity of a metallic nanoshell. The entanglement arises impulsively due to common coupling to the plasmonic nanostructure, without demanding postselective measurement or mediating the dissipative environment. The long-lived entangled states can be created deterministically by optimizing the shell thickness as well as the ratio of the distances between the quantum dots and the surface of the shell. The loss of the system is greatly reduced even when the quantum dots are ultraclose to the shell, which signifies a slow decay rate of the coherence information and longtime entanglement preservation.
In this work, we present numerical results on the influence of a spherical metallic nanoparticle to the population transfer in a Λ-type quantum system under conditions of Stimulated Raman Adiabatic Passage (STIRAP). For the study of the system’s dynamics, we use the density matrix approach for the quantum system, where the parameters for the electric field amplitudes and the spontaneous decay rates have been calculated using ab initio electromagnetic calculations for the plasmonic nanoparticle. We present results for the evolution of the populations of the different levels of the quantum system as a function of different parameters, in the presence and the absence of the plasmonic nanoparticle. We find that the presence of the plasmonic nanoparticle and the polarization of the pump and Stokes fields with respect to the surface of the nanoparticle, affect the efficiency of the population transfer inside the three-level quantum system. For the right combination of the values of the modified spontaneous decay rates and the fields intensities, high efficiency population transfer is obtained in the quantum system near a plasmonic nanoparticle using STIRAP process.