Part I of this thesis is concerned with cavity optomechanical systems subject to periodic driving. We develop a Floquet approach to solve time-periodic quantum Langevin equations in the steady state, show that two-time correlation functions of system operators can be expanded in a Fourier series, and derive a generalized Wiener-Khinchin theorem that relates the Fourier transform of the autocorrelator to the noise spectrum. Weapply our framework to optomechanical systems driven with two tones. In a setting used to prepare mechanical resonators in quantum squeezed states, we nd and study the general solution in the rotating-wave approximation. In the following chapter, we show that our technique reveals an exact analytical solution of the explicitly time-periodic quantum Langevin equation describing the dual-tone backaction-evading measurement of a single mechanical oscillator quadrature due to Braginsky, Vorontsov, and Thorne [Science 209, 547 (1980)] beyond the commonly used rotating-wave approximation and show that our solution can be generalized to a wide class of systems, including to dissipatively or parametrically squeezed oscillators, as well as recent two-mode backaction-evading measurements. In Part II, we study nonreciprocal optomechanical systems with several optical and mechanical modes. We show that an optomechanical plaquette with two cavity modes coupled to two mechanical modes is a versatile system in which isolators, quantum-limited phase-preserving, and phase-sensitive directional ampliers for microwave signals can be realized. We discuss the noise added by such devices, and derive isolation bandwidth, gain bandwidth, and gain-bandwidth product, paving the way toward exible, integrated nonreciprocal microwave ampliers. Finally, we show that similar techniques can be exploited for current rectication in double quantum dots, thereby introducing fermionic reservoir engineering. We verify our prediction with a weak-coupling quantum master equation and the exact solution. Directionality is attained through the interference of coherent and dissipative coupling. The relative phase is tuned with an external magnetic eld, such that directionality can be reversed, as well as turned on and off dynamically.

During the last years, with the evolution of technology enabling the control of nano-mesoscopic systems, the possibility of experimentally implementing a Maxwell’s demon has aroused much interest. Its classical version has already been implemented, in photonic and electronic systems, and currently its quantum version is being broadly studied. In this context, the purpose of this work is the development of a protocol for the implementation of the quantum version of an autonomous Maxwell’s demon in a system of superconducting qubits. The system is composed of an Asymmetrical Single-Cooper-Pair Transistor, ASCPT, which has its extremities in contact with heat baths, such that the left one has a lower temperature than the right one. And of a device of two interacting Cooper-Pair Boxes, CPB’s, named as an ECPB, for Extended Cooper-Pair Box. The ECPB is also in contact with a heat bath and possess a genuine quantum feature, entanglement, being described by its antisymmetric and symmetric states, that couple capacitively to the ASCPT with different strengths. A specific operating regime was found where the spontaneous dynamics of the tunneling of Cooper pairs through the ASCPT, will led to a heat transport from the bath in contact with the left extremity of the ASCPT to the bath at the right. And so, as in Maxwell’s original thought experiment, the demon, which is composed by the ECPB and the island of the ASCPT, mediates a heat flux from a cold to a hot bath, without the expense of work. However as expected, the violation of the 2nd law of thermodynamics does not occur, as during the dynamics heat is also released to the bath in contact with the ECPB, compensating the decrease of entropy that occurs in the baths in contact with the ASCPT. / Nos últimos anos, com a evolução da tecnologia que permite o controle de sistemas nano-mesoscópicos, a possibilidade de se implementar um demônio de Maxwell despertou muito interesse. A sua versão clássica já foi realizada experimentalmente com sucesso em sistemas fotônicos e eletrônicos e atualmente a versão quântica tem sido amplamente estudada. Neste contexto, o objetivo deste trabalho é desenvolver um protocolo para a implementação de uma versão quântica de um demônio de Maxwell autônomo utilizando dispositivos supercondutores. O sistema é composto por um Asymmetrical Single-Cooper-Pair Transistor, ASCPT, que possui as suas extremidades em contato com banhos térmicos, sendo que o banho à esquerda possui uma temperatura inferior ao da direita. E por um dispositivo composto por dois Cooper-Pair Boxes, CPB’s, interagentes, denominado ECPB, sigla para Extended Cooper-Pair Box. O ECPB também se encontra em contato com um banho e possui uma característica genuinamente quântica, emaranhamento, sendo descrito por seus estados antissimétrico e simétrico, que se acoplam capacitivamente ao ASCPT com intensidades distintas. Encontrou-se que em um regime de operação específico a dinâmica espontânea de tunelamento de pares de Cooper ao longo do ASCPT origina o transporte de calor do banho à esquerda do ASCPT, ao banho à direita. Desta forma, assim como proposto originalmente por Maxwell, o demônio, composto pelo ECPB e pela ilha do ASCPT, media um fluxo de calor de um banho frio para um banho quente, sem a realização alguma de trabalho. Contudo como esperado, a violação da 2ª lei da termodinâmica não ocorre, já que durante a dinâmica calor é liberado ao banho em contato com o dispositivo de CPB’s, compensando a diminuição de entropia que ocorre nos banhos em contato com o ASCPT.

All fields of physics - be it nuclear, atomic and molecular, solid state, or optical - offer examples of systems which are strongly influenced by the environment of the actual system under investigation. The scope of what is called "the environment" may vary, i.e., how far from the system of interest an interaction between the two does persist. Typically, however, it is much larger than the open system itself. Hence, a fully quantum mechanical treatment of the combined system without approximations and without limitations of the type of system is currently out of reach. With the single assumption of the environment to consist of an internally thermalized set of infinitely many harmonic oscillators, the seminal work of Stockburger and Grabert [Chem. Phys., 268:249-256, 2001] introduced an open system description that captures the environmental influence by means of a stochastic driving of the reduced system. The resulting stochastic Liouville-von Neumann equation describes the full non-Markovian dynamics without explicit memory but instead accounts for it implicitly through the correlations of the complex-valued noise forces. The present thesis provides a first application of the Stockburger-Grabert stochastic Liouville-von Neumann equation to the computation of the dynamics of anharmonic, continuous open systems. In particular, it is demonstrated that trajectory based propagators allow for the construction of a numerically stable propagation scheme. With this approach it becomes possible to achieve the tremendous increase of the noise sample count necessary to stochastically converge the results when investigating such systems with continuous variables. After a test against available analytic results for the dissipative harmonic oscillator, the approach is subsequently applied to the analysis of two different realistic, physical systems. As a first example, the dynamics of a dissipative molecular oscillator is investigated. Long time propagation - until thermalization is reached - is shown to be possible with the presented approach. The properties of the thermalized density are determined and they are ascertained to be independent of the system's initial state. Furthermore, the dependence on the bath's temperature and coupling strength is analyzed and it is demonstrated how a change of the bath parameters can be used to tune the system from the dissociative to the bound regime. A second investigation is conducted for a dissipative tunneling scenario in which a wave packet impinges on a barrier. The dependence of the transmission probability on the initial state's kinetic energy as well as the bath's temperature and coupling strength is computed. For both systems, a comparison with the high-temperature Markovian quantum Brownian limit is performed. The importance of a full non-Markovian treatment is demonstrated as deviations are shown to exist between the two descriptions both in the low temperature cases where they are expected and in some of the high temperature cases where their appearance might not be anticipated as easily.

The 20th century saw the first revolution of quantum mechanics, setting the rules for our understanding of light, matter, and their interaction. The 21st century is focused on using these quantum mechanical laws to develop technologies which allows us to solve challenging practical problems. One of the directions is the use quantum devices which promise to surpass the best computers and best known classical algorithms for solving certain tasks. Crucial to the design of realistic devices and technologies is to account for the open nature of quantum systems and to cope with their interactions with the environment. In the first part of this dissertation, we show how to tackle classical optimization problems of interest in the physical sciences within one of these quantum computing paradigms, known as quantum annealing (QA). We present the largest implementation of QA on a biophysical problem (six different experiments with up to 81 superconducting quantum bits). Although the cases presented here can be solved on a classical computer, we present the first implementation of lattice protein folding on a quantum device under the Miyazawa-Jernigan model. This is the first step towards studying optimization problems in biophysics and statistical mechanics using quantum devices. In the second part of this dissertation, we focus on the problem of excitonic energy transfer. We provide an intuitive platform for engineering exciton transfer dynamics and we show that careful consideration of the properties of the environment leads to opportunities to engineer the transfer of an exciton. Since excitons in nanostructures are proposed for use in quantum information processing and artificial photosynthetic designs, our approach paves the way for engineering a wide range of desired exciton dy- namics. Finally, we develop the theory for a two-dimensional electronic spectroscopic technique based on fluorescence (2DFS) and challenge previous theoretical results claiming its equivalence to the two-dimensional photon echo (2DPE) technique which is based on polarization. Experimental realization of this technique confirms our the- oretical predictions. The new technique is more sensitive than 2DPE as a tool for conformational determination of excitonically coupled chromophores and o↵ers the possibility of applying two-dimensional electronic spectroscopy to single-molecules.

In this work the semiclassical hybrid dynamics is extended in order to be capable of treating open quantum systems considering finite baths. The corresponding phenomena, i.e. decoherence and dissipation, are investigated for various scenarios.

The work summarizes basic theory of relaxation, energy transfer and decoher- ence in photosynthetic molecular aggregates described as open quantum systems and basic theory of third order coherent non-linear spectroscopy. The work presents two methods for calculation of photo-induced dynamics of molecular aggregates. The methods relax certain approximations of the theories commonly used to model the relaxation and energy transfer in the molecular systems on the sub-picosecond time scale. The first theory derived in the formalism of para- metric projection operators accounts for correlations in a second-order non-linear response-function that are usually neglected in the formalism of master equations. The second theory represents stochastic model of exact dynamics via the cumulant expansion. The work also presents an analysis of importance of the secular and the Markov approximations in the description of dynamics derived in the second-order perturbation theory in the system-bath coupling with emphasis on the excitonic coherence lifetime.

Na primeira parte deste trabalho empregamos a equação estocástica de Itô para obter uma interpretação generazilada de be-ables, que engloba dissipação, decoerência e a transição da dinâmica quântica para clássica. Ao escolher uma fonte de estocasticidade que leva à correção dissipativa da dinâmica hamiltoniana na forma de Lindblad, obtemos uma nova classe de trajetórias que incorpora às trajetórias de Bohm o termo difusivo presente na formulação de Nelson. Utilizando nossa formulação extendida dos be-ables identificamos o processo de decoerência e verificamos que este encontra-se em concordância com o formalismo quântico usual. Na segunda parte deste trabalho analisamos a dinâmica de um sistema quântico sob a competição de dois sistemas multimodais contra-atuantes: um atenuador ou reservatório térmico e um amplificador de Glauber. Mapeamos o comportamento dinâmico deste sistema, identificando diferentes regimes de parâmetros. Calculamos o processo de decoerência emergente da ação dos sistemas multimodais e discutimos aplicações para o nosso sistema. Na terceira parte deste trabalho, usamos a abordagem de campo médio para a obtençãoo da equação mestra que descreve o problema da superradiância sob a ação de flutuações térmicas do reservatório. Desejamos com isso explorar a possibilidade de se verificar o processo de ressonância estocástica no âmbito da superradiância. / In the first part of this work we employ the Itô stochastic equation to extend Bells be-able interpretation of quantum mechanics to encompass dissipation, decoherence and quantum-to-classical transition through quantum trajectories. For a particular choice of the source of stochasticity, the one leading to a dissipative Lindblad type correction to the Hamiltonian dynamics, we verify that the diffusive term in Nelson´s formalism is naturally incorporated into Bohm´s one, rendering a unified Bohm-Nelson theory. Mainly, analyzing the intereference between quantum trajectories, we clearly identify the decoherence time, as estimated from the usual quantum formalism. We also observe the quantum-to-classical transition through the convergence of the infinite possible quantum trajectories to their associated classical counterparts. In the second part of this work we analyze the dynamical behavior of a quantum system under the actions of two counteracting baths: the inevitable energy draining reservoir and, oppositly, an enginereed Glauber amplifier feeding the system excitation. We trace the system dynamics towards equilibrium to mapp its distinct behaviors following from the attenuation × amplification interplay. The decoherence process emerging from the action of both counteracting baths is also computed and, finally, applications of such an attenuation × amplification competition is discussed. Finally, in the third part of this work we employ the mean field approximation to derive the master equation describing the process of superradiant emission under the presence of thermal fluctuation. We envisage to explore the possibility of observe stochastic resonance within the superradiant process.

One of the main goals of the theory of open quantum systems is to devise methods which help preserve the quantum properties of a system interacting with its environment. One possible pathway to achieve this goal is to use non-Markovian reservoirs, characterized by information backflows and revivals of certain quantum properties. These reservoirs usually require advanced engineering techniques, which may turn their implementation impractical. In this dissertation we propose an alternative technique: the injection of a classical colored noise, which induces the desired quantum non-Markovianity. In order to do that, we investigate the dynamics of a quantum system interacting with its surrounding environment and under the injection of a classical stochastic colored noise. A time-local master equation for the system is derived by using the stochastic wave function formalism and functional calculus. Afterwards, the non-Markovianity of the evolution is detected by using the Andersson, Cresser, Hall and Li measure, which is based on the decay rates of the master equation in canonical Lindblad-like form. Finally, we evaluate the measure for three different colored noises and study the interplay between environment and noise pump necessary to induce quantum non-Markovianity, as well as the energy balance of the system. / Um dos objetivos principais da teoria de sistemas quânticos abertos é desenvolver métodos que ajudem a preservar as propriedades quânticas de um sistema interagindo com o ambiente. Um possível caminho para alcançar essa meta é usar reservatórios não-Markovianos, caracterizados por refluxos de informação e renascimento de certas propriedades quânticas. Esses reservatóris geralmente requerem o uso de técnicas avançadas de engenharia, o que pode tornar sua implementação impraticável. Nessa dissertação nós propomos uma técnica alternativa: a injeção de um ruído colorido clássico, o qual induz a desejada não-Markovianidade quântica. De modo a fazer isso, nós investigamos a dinâmica de um sistema quântico interagindo com o ambiente e sob a injeção de um ruído colorido clássico estocástico. Uma equação mestra local no tempo é derivada usando-se do formalismo da função de onda estocástica e de técnicas de cálculo funcional. Após isso, a não-Markovianidade da evolução é detectada através da medida de Andersson, Cresser, Hall e Li, a qual é baseada nos coeficientes da equação mestra na forma de Lindblad-like canônica. Finalmente, nós calculamos a medida para três diferentes ruídos coloridos e estudamos a relação entre o ambiente e o bombeio estocástico necessária para induzir não-Markovianidade quântica, assim como o balanço de energia do sistema.

Orientador: Prof. Dr. Gabriel Teixeira Landi / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, Santo André, 2018. / Em sistemas microscópicos, grandezas como calor e trabalho devem ser tratadas como variáveis aleatórias. Neste trabalho foram estudados os fluxos de calor e de partículas entre dois sistemas unidimensionais fermiônicos A eB, inicialmente preparados separadamente em equilíbrio térmico com reservatórios de calor e partículas preparados a diferentes temperaturas e diferentes potenciais químicos. Calculando a evolução da matriz densidade, foram analisadas as implicações da presença de um ruído de dephasing no sistema, tais como a termalização, a produção de entropia e a evolução da informação mútua como uma forma de analisar a correlação entre os sistemas. Além disso, foi estudado também uma forma do teorema de flutuação do calor no caso onde há fluxo de partículas. / In microscopic systems, heat and work must be treated as random variables. In this work I studied the fluxes of heat and particles between two unidimentional fermionic systems A and B, initially prepared in thermal equilibrium with a reservoir of particles and heat, kept at diferent temperatures and chemical potentials. Computing the evolution of the density matrix, the implications of the presence of a dephasing noise in the system were analyzed, such as thermalization, entropy production and the evolution of mutual information as a way to analyze the correlation between the systems. Moreover, a shape for fluctuation theorems of the heat in the case where there is also a ?ux of particles and its validity was also studied.

Fenômenos que ocorrem a tempos curtos em sistemas quânticos abertos são caracterizados por possuírem um tempo característico de uma ordem muito menor que o tempo de relaxação do sistema. Como exemplos podemos citar o efeito de decoerência, que em resumo tenta explicar como a natureza quântica de um sistema é perdida ao longo da interação com o ambiente e o fenômeno de superradiância, onde estuda-se como alguns sistemas emitem um pulso energético muito rápido gerando um pico de intensidade fino localizado muito antes da relaxação do sistema. O objetivo desse trabalho é não só estudar esses fenômenos mas como apresentar uma técnica alternativa para a quantificação das medidas associadas e de seus tempos característicos. A técnica apresentada se baseia em fazer uma expansão perturbativa no tempo para o operador densidade a partir de uma equação mestra quântica e com seu uso calcular grandezas físicas relevantes a fenômenos que ocorrem a tempos curtos. A simplicidade da técnica e seu uso abrangente são os principais fatores motivadores deste trabalho. / Short-time phenomena in open quantum systems are characterized by having a characteristic time of a much lower order than the relaxation time of the system. As examples we can mention the effect of decoherence, which in summary tries to explain how the quantum nature of a system is lost along the interaction with the environment and the superradiance phenomenon, where is studied how some systems emit a very fast energy pulse generating a peak of fine intensity located long before the relaxation of the system. The aim of this work is not only study these phenomena but to present an alternative technique for quantifying the associated measures and their characteristic times. The presented technique is based on making a perturbative expansion in time for the density operator from a quantum master equation and use it to calculate physical quantities relevant to phenomena occurring at short times. The simplicity of the technique and its widespread use are the main motivating factors of this work.