Quadratic-exponential coherent feedback control of linear quantum stochastic systems

This paper considers a risk-sensitive optimal control problem for a field-mediated interconnection of a quantum plant with a coherent (measurement-free) quantum controller. The plant and the controller are multimode open quantum harmonic oscillators governed by linear quantum stochastic differential equations, which are coupled to each other and driven by multichannel quantum Wiener processes modelling the external bosonic fields. The control objective is to internally stabilize the closed-loop system and minimize the infinite-horizon asymptotic growth rate of a quadratic-exponential functional which penalizes the plant variables and the controller output. We obtain first-order necessary conditions of optimality for this problem by computing the partial Frechet derivatives of the cost functional with respect to the energy and coupling matrices of the controller in frequency domain and state space. An infinitesimal equivalence between the risk-sensitive and weighted coherent quantum LQG control problems is also established. In addition to variational methods, we employ spectral factorizations and infinite cascades of auxiliary classical systems. Their truncations are applicable to numerical optimization algorithms (such as the gradient descent) for coherent quantum risk-sensitive feedback synthesis.Comment: 29 pages, 3 figure

Modern control approaches for next-generation interferometric gravitational wave detectors

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Multiphoton Quantum Optics and Quantum State Engineering

We present a review of theoretical and experimental aspects of multiphoton quantum optics. Multiphoton processes occur and are important for many aspects of matter-radiation interactions that include the efficient ionization of atoms and molecules, and, more generally, atomic transition mechanisms; system-environment couplings and dissipative quantum dynamics; laser physics, optical parametric processes, and interferometry. A single review cannot account for all aspects of such an enormously vast subject. Here we choose to concentrate our attention on parametric processes in nonlinear media, with special emphasis on the engineering of nonclassical states of photons and atoms. We present a detailed analysis of the methods and techniques for the production of genuinely quantum multiphoton processes in nonlinear media, and the corresponding models of multiphoton effective interactions. We review existing proposals for the classification, engineering, and manipulation of nonclassical states, including Fock states, macroscopic superposition states, and multiphoton generalized coherent states. We introduce and discuss the structure of canonical multiphoton quantum optics and the associated one- and two-mode canonical multiphoton squeezed states. This framework provides a consistent multiphoton generalization of two-photon quantum optics and a consistent Hamiltonian description of multiphoton processes associated to higher-order nonlinearities. Finally, we discuss very recent advances that by combining linear and nonlinear optical devices allow to realize multiphoton entangled states of the electromnagnetic field, that are relevant for applications to efficient quantum computation, quantum teleportation, and related problems in quantum communication and information.Comment: 198 pages, 36 eps figure

Novel approaches to optomechanical transduction

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Thermodynamics and synchronization in open quantum systems

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, Departamento de Física Atómica Molecular y Nuclear, leída el 11-07-2017Los efectos disipativos tienen profundas consecuencias en el comportamiento y las propiedades de los sistemas cuánticos [72]. La inevitable interacción con el entorno circundante, con el cual los sistemas intercambian continuamente información, energía, momento angular o materia, es la última responsable de los fenómenos de decoherencia y de la emergencia del comportamiento clásico [490, 614]. Sin embargo, existe un amplio régimen intermedio en el cual efectos disipativos y cuánticos coexisten, dando lugar a una amplia gama de ricos y sorprendentes fenómenos que apenas están empezando a ser comprendidos. Además, las innovadoras técnicas desarrolladas recientemente para controlar y manipular sistemas cuánticos en el laboratorio han hecho esta fenomenología accesible experimentalmente y potencialmente aplicable [244, 586]. En esta tesis exploraremos desde un punto de vista teórico algunas de las conexiones entre efectos disipativos y cuánticos en lo concerniente a dos principales aspectos: el comportamiento termodinámico de los sistemas cuánticos y la relación entre las correlaciones dinámicas y cuánticas compartidas por éstos. Las correlaciones cuánticas son una de las características más sorprendentes de la naturaleza y han atraído un notable interés desde la misma formulación de la teoría cuántica. La comprensión de los mecanismos subyacentes que generan, preservan, o destruyen estas correlaciones resulta de gran importancia a la hora de explorar la frontera cuántico-clásica [597], mientras que es esencial en el diseño de esquemas en los que la decoherencia pueda ser evitada en aplicaciones prácticas [35, 143, 562]. Por otra parte, otro tipo importante de correlaciones dinámicas de caracter más tradicionalmente clásico son los fenómenos de sincronización, que han sido estudiados en un amplio rango de sistemas físicos, químicos y biológicos [433]. La sincronización puede aparecer como un comportamiento espontáneo y cooperativo de diferentes unidades que oscilan y que, cuando se acoplan, adaptan sus ritmos a una frecuencia común. Este fenómeno de sincronización mutua ha sido considerado con profusión desde un punto de vista clásico [249, 263, 606], mientras que los rasgos genuinamente cuánticos de la sincronización estan empezando ahora a ser investigados...Dissipation effects have profound consequences in the behavior and properties of quantum systems. The unavoidable interaction with the surrounding environment, with whom systems continuously exchange information, energy, angular momentum or matter, is ultimately responsible of decoherence phenomena and the emergence of classical behavior. However, there exist a wide intermediate regime in which the interplay between dissipative and quantum effects gives rise to a plethora of rich and striking phenomena that has only started to be understood. In addition, the recent breakthrough techniques in controlling and manipulating quantum systems in the laboratory has made this phenomenology accessible in experiments and potentially applicable. In this thesis we aim to explore from a theoretical point of view some of the connections between dissipative and quantum effects. We focus on three main topics: the relation between dynamical and quantum correlations, the thermodynamical properties of fluctuations, and the performance of quantum thermal machines. First, we study the emergence of transient and asymptotic spontaneous synchronization induced by dissipation in harmonic quantum systems and its connections with quantum correlations. Our results show that synchronization may be used a witnesses for the slow decay or even the preservation of quantum discord in many situations of interest. Furthermore, we develop methods for engineering it in complex harmonic networks or selected clusters, where noiseless subsystems can be obtained by tuning one or few system parameters. Second, we explore the quantum versions of work and entropy production fluctuation relations. We derive a general fluctuation theorem valid for a broad class of open systems dynamics and discuss the meaning of the quantity fulfilling it. Importantly, our theorem overcomes the prototypical assumption of ideal thermal reservoirs. We also study the possibility of split entropy production in arbitrary quantum processes into adiabatic and non-adiabatic contributions, each of them fulfilling an independent fluctuation theorem. Contrary to the classical case, quantum effects may break the split, and we discuss the necessary conditions to enforce it. Our findings are illustrated in three relevant examples for quantum thermodynamics. Finally, we focus on the role quantum effects in the performance of quantum thermal machines. We analyze the case of an optimized quantum Otto cycle powered by a squeezed thermal reservoir. Our previous results allow us to characterize the many striking nonequilibrium features that arise, including work extraction from a single reservoir or multi-task regimes combining both refrigeration of a cold reservoir and work extraction at the same time. On the other hand, we also explore the role of the Hilbert space dimension in the performance of autonomous quantum thermal machines. Our results point that adding extra levels constitutes a thermodynamical resource. For the case of autonomous fridges, we further obtain a statement on the third law of thermodynamics in terms of their number of levels: reaching zero temperature requires an infinite Hilbert space dimension. The research results presented in this thesis are complemented with a broad introduction to the field of open quantum systems and quantum thermodynamics. There, we review the state of the art on these topics and the reader will find the main methods and tools used along the thesis.Depto. de Estructura de la Materia, Física Térmica y ElectrónicaFac. de Ciencias FísicasTRUEunpu

Interfacing ultracold atoms and mechanical oscillators

In this thesis I present experiments investigating controlled coupling between mechanical oscillators and ultracold atoms. I report on three different coupling mechanisms. In a first experiment, the surface potential experienced by atoms close to the mechanical oscillator is employed to couple the oscillator motion to the center of mass (COM) motion of a trapped Bose-Einstein condensate (BEC). The magnetic trapping potential is modified by the surface potential arising from the oscillator surface which results in a reduced trap depth. Vibration of the oscillator leads to a modulation of the trap frequency and the minimum of the trapping potential. Observing the loss of atoms from the BEC allows us to read out the amplitude of the mechanical oscillator with the atoms. In a second experiment, we study the coupling of a mechanical membrane oscillator and thermal atoms trapped in a 1D optical lattice. The membrane is the end mirror of the lattice, and oscillation of the membrane couples to the COM mode of the atomic ensemble. Conversely, the center of mass motion of the atomic ensemble redistributes photons between the two running waves forming the 1D optical lattice, effectively modulating their power, and hence the radiation pressure acting onto the membrane. We observe the action of the oscillating membrane onto the atoms by detecting the resulting temperature increase of the atomic ensemble in absorption imaging. To observe the backaction of the atoms onto the mechanical oscillator, the mechanical damping is measured in experiments with and without atoms in the lattice, and we measure higher damping in the presence of atoms in agreement with the theoretical predictions. These experiments are the first demonstration of backaction of an atomic system onto a mechanical oscillator. We investigate a third coupling mechanism, where the motion of a mechanical oscillator is coupled to the collective spin of a BEC. The tip of a mechanical oscillator is functionalized with a magnet, which transduces the oscillators' motion into oscillations of the magnetic field. This drives spin-flip transitions of trapped atoms to untrapped motional states. The coupling strength is not limited by the square root of the mass ratio of atoms and oscillator as in the other coupling schemes discussed in this thesis. We investigate this coupling scheme theoretically, and discuss the realization of a nanometer-sized mechanical oscillator with a magnetic island. I report on the status of the fabrication, and propose a simplified fabrication method

Nonlinear frequency conversion in isotropic semiconductor waveguides

This thesis describes an experimental investigation of optical frequency conversion in isotropic semiconductor waveguides by use of several phase-matching approaches. Efficient, type I second harmonic generation of femtosecond pulses is reported in birefringently-phase-matched GaAs/Alox waveguides pumped at 2.01 µm. Practical second harmonic average powers of up to ~ 650 µW are obtained, for an average launched pump power of ~ 5 mW. This corresponds to a waveguide conversion efficiency of ~ 20 % and a normalized conversion efficiency of greater than 1000 % W⁻¹cm⁻². Pump depletion of more than 80 % is recorded. Second harmonic generation by type I, third order quasi-phase-matching in a GaAs- AlAs superlattice waveguide is reported for fundamental wavelengths from ~1480 to 1520 nm. Quasi-phase-matching is achieved through modulation of the nonlinear coefficient χ[sub](zxy)⁽²⁾, which is realised by periodically tuning the superlattice bandgap. An average output power of ~25 nW is obtained for a launched pump power of <2.3 mW. Type I second harmonic generation by use of first order quasi-phase-matching in a GaAs/AlAs symmetric superlattice waveguide is also reported, with femtosecond fundamental pulses at 1.55 µm. A periodic spatial modulation of the bulk-like second- order susceptibility χ[sub](zxy)⁽²⁾ is realized using quantum well intermixing by As⁺ ion implantation. A practical second harmonic average power of ~1.5 µW is detected, for a coupled pump power of ~11 mW. Second harmonic generation through modal-phase-matching in GaAs/AlGaAs semiconductor waveguides is reported. Using femtosecond pulses, both type I and type II second harmonic conversion is demonstrated for fundamental wavelengths near 1.55 µm. An average second harmonic power of ~10.3 µW is collected at the waveguide output for a coupled pump power of <20 mW. For a complete characterisation, the optical loss is measured in these nonlinear GaAs- based waveguides over the spectral range 1.3-2.1 µm in the infrared, by deploying a femtosecond scattering technique. Typical losses of ~5-10 dB/cm are measured for the best of the waveguides, while a systematic intensity and wavelength dependent study revealed the contribution of Rayleigh scattering and two photon absorption in the overall transmission loss