Relevant bibliographies by topics / Quantum-mechanical oscillator

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  2. Dissertations / Theses
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Academic literature on the topic 'Quantum-mechanical oscillator'

Author: Grafiati
Published: 4 June 2021
Last updated: 4 February 2022

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Journal articles on the topic "Quantum-mechanical oscillator"

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Burd, S. C., R. Srinivas, J. J. Bollinger, et al. "Quantum amplification of mechanical oscillator motion." Science 364, no. 6446 (2019): 1163–65. http://dx.doi.org/10.1126/science.aaw2884.

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Detection of the weakest forces in nature is aided by increasingly sensitive measurements of the motion of mechanical oscillators. However, the attainable knowledge of an oscillator’s motion is limited by quantum fluctuations that exist even if the oscillator is in its lowest possible energy state. We demonstrate a technique for amplifying coherent displacements of a mechanical oscillator with initial magnitudes well below these zero-point fluctuations. When applying two orthogonal squeezing interactions, one before and one after a small displacement, the displacement is amplified, ideally with no added quantum noise. We implemented this protocol with a trapped-ion mechanical oscillator and determined an increase by a factor of up to 7.3 (±0.3) in sensitivity to small displacements.
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Mercier de Lépinay, Laure, Caspar F. Ockeloen-Korppi, Matthew J. Woolley, and Mika A. Sillanpää. "Quantum mechanics–free subsystem with mechanical oscillators." Science 372, no. 6542 (2021): 625–29. http://dx.doi.org/10.1126/science.abf5389.

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Quantum mechanics sets a limit for the precision of continuous measurement of the position of an oscillator. We show how it is possible to measure an oscillator without quantum back-action of the measurement by constructing one effective oscillator from two physical oscillators. We realize such a quantum mechanics–free subsystem using two micromechanical oscillators, and show the measurements of two collective quadratures while evading the quantum back-action by 8 decibels on both of them, obtaining a total noise within a factor of 2 of the full quantum limit. This facilitates the detection of weak forces and the generation and measurement of nonclassical motional states of the oscillators. Moreover, we directly verify the quantum entanglement of the two oscillators by measuring the Duan quantity 1.4 decibels below the separability bound.
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Ikot, Akpan N., Louis E. Akpabio, Ita O. Akpan, Michael I. Umo, and Eno E. Ituen. "Quantum Damped Mechanical Oscillator." International Journal of Optics 2010 (2010): 1–6. http://dx.doi.org/10.1155/2010/275910.

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The exact solutions of the Schrödinger equation for quantum damped oscillator with modified Caldirola-Kanai Hamiltonian are evaluated. We also investigate the cases of under-, over-, and critical damping.
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Sergeev, S. "Quantum curve inq-oscillator model." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–31. http://dx.doi.org/10.1155/ijmms/2006/92064.

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A lattice model of interactingq-oscillators, proposed by V. Bazhanov and S. Sergeev in 2005 is the quantum-mechanical integrable model in2+1dimensional space-time. Its layer-to-layer transfer matrix is a polynomial of two spectral parameters, it may be regarded in terms of quantum groups both as a sum ofsl(N)transfer matrices of a chain of lengthMand as a sum ofsl(M)transfer matrices of a chain of lengthNfor reducible representations. The aim of this paper is to derive the Bethe ansatz equations for theq-oscillator model entirely in the framework of2+1integrability providing the evident rank-size duality.
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BLASONE, MASSIMO, GIUSEPPE VITIELLO, PETR JIZBA, and FABIO SCARDIGLI. "DETERMINISM BENEATH COMPOSITE QUANTUM SYSTEMS." International Journal of Modern Physics A 24, no. 18n19 (2009): 3652–59. http://dx.doi.org/10.1142/s0217751x09047314.

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This paper aims at the development of 't Hooft's quantization proposal to describe composite quantum mechanical systems. In particular, we show how 't Hooft's method can be utilized to obtain from two classical Bateman oscillators a composite quantum system corresponding to a quantum isotonic oscillator. For a suitable range of parameters, the composite system can be also interpreted as a particle in an effective magnetic field interacting through a spin-orbital interaction term. In the limit of a large separation from the interaction region we can identify the irreducible subsystems with two independent quantum oscillators.
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Rath, Biswanath, Pravanjan Mallick, Prachiprava Mohapatra, Jihad Asad, Hussein Shanak, and Rabab Jarrar. "Position-dependent finite symmetric mass harmonic like oscillator: Classical and quantum mechanical study." Open Physics 19, no. 1 (2021): 266–76. http://dx.doi.org/10.1515/phys-2021-0024.

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Abstract We formulated the oscillators with position-dependent finite symmetric decreasing and increasing mass. The classical phase portraits of the systems were studied by analytical approach (He’s frequency formalism). We also study the quantum mechanical behaviour of the system and plot the quantum mechanical phase space for necessary comparison with the same obtained classically. The phase portrait in all the cases exhibited closed loop reflecting the stable system but the quantum phase portrait exhibited the inherent signature (cusp or kink) near origin associated with the mass. Although the systems possess periodic motion, the discrete eigenvalues do not possess any similarity with that of the simple harmonic oscillator having m = 1.
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SISTO, RENATA, and ARTURO MOLETI. "ON THE SENSITIVITY OF GRAVITATIONAL WAVE RESONANT BAR DETECTORS." International Journal of Modern Physics D 13, no. 04 (2004): 625–39. http://dx.doi.org/10.1142/s021827180400475x.

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Different theoretical estimates of the sensitivity of gravitational wave resonant bar detectors, which have been published in the last decades, are reviewed and discussed. The "classical" cross-section estimate is obtained considering the bar as a classical or quantum oscillator, whose initial thermal state is that of a single oscillator driven by a single external stochastic force. Other theoretical studies computed a much larger cross-section, using a variety of quantum-mechanical arguments. The review of the existing literature shows that there is no well established model for the response of a resonant detector to gravitational waves. The resonant, yet random, nature of the Brownian thermal motion may justify considering the bar response at the fundamental longitudinal eigenfrequency as that of a large number of effective quantum mechanical oscillators. Assuming this hypothesis, quantum coherence effects, as first suggested by Weber, lead to a much larger cross-section than that "classically" predicted. The reduction of this amplification due to thermal noise itself is also computed.
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Trifonov, E. D. "Quantum-mechanical oscillator in a uniform force field." Russian Journal of Physical Chemistry B 6, no. 2 (2012): 205–9. http://dx.doi.org/10.1134/s1990793112020248.

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Hardy, L., D. Home, E. J. Squires, and M. A. B. Whitaker. "Realism and the quantum-mechanical two-state oscillator." Physical Review A 45, no. 7 (1992): 4267–70. http://dx.doi.org/10.1103/physreva.45.4267.

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Floratos, E. G., and T. N. Tomaras. "A quantum mechanical analogue for the q-oscillator." Physics Letters B 251, no. 1 (1990): 163–66. http://dx.doi.org/10.1016/0370-2693(90)90247-4.

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Dissertations / Theses on the topic "Quantum-mechanical oscillator"

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Neuhaus, Leonhard. "Cooling a macroscopic mechanical oscillator close to its quantum ground state." Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066555/document.

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Ce travail s'attaque à la mise en évidence expérimentale d'effets quantiques dans le mouvement d'un résonateur mécanique macroscopique avec une masse effective de 33 microgrammes, soit 3 ordres de grandeur au-dessus de celle du système mécanique le plus massif observé à ce jour dans son état quantique fondamental. Nous avons conçu, fabriqué et fait fonctionner un résonateur optomécanique à 3,6 MHz avec une finesse optique de 100.000 et un facteur de qualité mécanique proche de 100 millions, inséré dans l'environnement à 100 mK d'un réfrigérateur à dilution. Nous présentons un montage optique complètement automatisé incluant une cavité de filtrage, une détection homodyne et plusieurs asservissements, implémentés dans un FPGA avec le programme PyRPL développé spécifiquement pour cette expérience. Nous avons refroidi par laser le mode de compression de notre résonateur mécanique jusqu'à un nombre moyen d'occupation thermique de 20 phonons. Le refroidissement est limité par l'apparition d'une instabilité optomécanique de plusieurs modes des suspensions, au-dessous de 100 kHz. Un filtre digital particulier pour supprimer cette instabilité nous a permis d'atteindre le régime où l'action en retour quantique contribue à hauteur d'environ 30 % au bruit de force total de l'oscillateur mécanique. Pour atteindre des contributions encore plus importantes à l'avenir, nous présentons la conception d'un miroir d'entrée à cristal phononique, caractérisé par un plancher de bruit de mouvement Brownien réduit<br>In this work, we attempt the experimental demonstration of quantum effects in the motion of a macroscopic mechanical resonator with a mass of 33 micrograms, about 3 orders of magnitude above the mass of the heaviest system demonstrated so far in the quantum ground state. We have designed, fabricated, and operated an optomechanical resonator at 3.6 MHz, with an optical finesse of 100,000 and a mechanical quality factor near 100 million, embedded in the 100 mK environment of a dilution refrigerator. We present a fully automatized optical measurement setup, including a filter cavity, a homodyne detector, and various feedback controllers implemented in an FPGA with the custom-developed software PyRPL. We have laser-cooled the compression mode of our mechanical resonator to a mean thermal occupation number of 20 phonons. Cooling is limited by the onset of an optomechanical instability of suspension modes with frequencies below 100 kHz. A custom-tailored digital filter to suppress this instability has enabled us to reach a regime where quantum backaction amounts to about 30 % of the total force noise on the mechanical resonator. For even higher ratios in the future, we present the design of a phononic-crystal input mirror with a reduced Brownian motion displacement noise floor
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Vaidya, Nikhilesh Avanish. "NOISE SPECTRUM OF A QUANTUM POINT CONTACT COUPLED TO A NANO-MECHANICAL OSCILLATOR." Diss., Temple University Libraries, 2017. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/447885.

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Physics<br>Ph.D.<br>With the advance in nanotechnology, we are more interested in the "smaller worlds". One of the practical applications of this is to measure a very small displacement or the mass of a nano-mechanical object. To measure such properties, one needs a very sensitive detector. A quantum point contact (QPC) is one of the most sensitive detectors. In a QPC, electrons tunnel one by one through a tunnel junction (a "hole"). The tunnel junction in a QPC consists of a narrow constriction (nm-wide) between two conductors. To measure the properties of a nano-mechanical object (which acts as a harmonic oscillator), we couple it to a QPC. This coupling effects the electrons tunneling through the QPC junction. By measuring the transport properties of the tunneling electrons, we can infer the properties of the oscillator (i.e. the nano-mechanical object). However, this coupling introduces noise, which reduces the measurement precision. Thus, it is very important to understand this source of noise and to study how it effects the measurement process. We theoretically study the transport properties of electrons through a QPC junction, weakly coupled to a vibration mode of a nano-mechanical oscillator via both the position and the momentum of the oscillator. %We study both the position and momentum based coupling. The transport properties that we study consist of the average flow of current through the junction, given by the one-time correlation of the electron tunneling event, and the current noise given by the two-time correlation of the average current, i.e, the variance. The first comprehensive experimental study of the noise spectrum of a detector coupled to a QPC was performed by the group of Stettenheim et al. Their observed spectral features had two pronounced peaks which depict the noise produced due to the coupling of the QPC with the oscillator and in turn provide evidence of the induced feedback loop (back-action). Benatov and Blencowe theoretically studied these spectral features using the Born approximation and the Markovian approximation. In this case the Born approximation refers to second order perturbation of the interaction Hamiltonian. In this approximation, the electrons tunnel independently, i.e., one by one only, and co-tunneling is disregarded. The Markovian approximation does not take into account the past behavior of the system under time evolution. These two approximations also enable one to study the system analytically, and the noise is calculated using the MacDonald formula. Our main aim for this thesis is to find a suitable theoretical model that would replicate the experimental plots from the work of Stettenheim et al. Our work does not use the Markovian approximation. However, we do use the Born approximation. This is justified as long as the coupling between the oscillator and QPC is weak. We first obtain the non-Markovian unconditional master equation for the reduced density matrix of the system. Non-Markovian dynamics enables us to study, in principle, the full memory effects of the system. From the master equation, we then derive analytical results for the current and the current noise. Due to the non-Markovian nature of our system, the electron tunneling parameters are time-dependent. Therefore, we cannot study the system analytically. We thus numerically solve the current noise expression to obtain the noise spectrum. We then compare our noise spectrum with the experimental noise spectrum. We show that our spectral noise results agree better with the experimental evidence compared to the results obtained using the Markovian approximation. We thus conclude that one needs non-Markovian dynamics to understand the experimental noise spectrum of a QPC coupled to a nano-mechanical oscillator.<br>Temple University--Theses
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Capelle, Thibault. "Electromechanical cooling and parametric amplification of an ultrahigh-Q mechanical oscillator." Thesis, Sorbonne université, 2020. http://www.theses.fr/2020SORUS045.

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Dans cette thèse, nous avons étudié un système mécanique de très haut facteur de qualité couplé à une cavité micro-onde supraconductrice. Nous présenterons une technique originale de caractérisation des pertes des cavités micro-ondes planaires, ainsi qu’une technique de refroidissement par bande latérale résolue utilisée pour refroidir activement cet oscillateur mécanique à l’aide de la cavité micro-onde. Enfin, nous présenterons des optimisations de cette expérience qui ouvrent la voie au refroidissement de l'oscillateur mécanique dans son état quantique fondamental. Un tel système hybride pourrait jouer le rôle de mémoire quantique sur puce, permettant de stocker les états quantiques non-gaussiens générés par des circuits quantiques supraconducteurs dans des vibrations mécaniques avec des temps de cohérence approchant la seconde<br>In this thesis, we have studied an ultrahigh quality factor mechanical oscillator coupled to a microwave cavity. We will present an original technique to probe the losses of planar microwave cavities, as well as a resolved sideband cooling technique to actively cool this mechanical oscillator using the microwave cavity. Finally, we will present some optimizations of this experiment which open the path towards the ground state cooling of the mechanical oscillator. Such a hybrid quantum system could be used as an on-chip quantum memory, able to store fragile quantum states generated by superconducting quantum circuits for coherence times approaching a second
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Vaish, Nitika. "Optomechanical transducer based on a single quantum dot." Thesis, Université Grenoble Alpes (ComUE), 2019. http://www.theses.fr/2019GREAY074.

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Dans le contexte de la nanomécanique, les systèmes hybrides quantiques sont des oscillateurs mécaniques couplés à un seul objet quantique individuel. Ces systèmes offrent des possibilités radicalement nouvelles pour la fabrication de transducteurs optomécaniques extrêmement sensibles et ultra-compacts, qui peuvent servir de capteurs de position ou de nano-moteurs.L’objet étudié dans ce travail est un système hybride constitué d’une boite quantique semi-conducteur unique couplée aux vibrations d’un fil photonique. Il a été démontré dans l'équipe, il y a quelques années, que l'énergie de transition de la boite quantique dépend de la contrainte générée par les oscillations du fil.Dans cette thèse, nous démontrons l'effet inverse, où chaque photon émis par la boite quantique s'accompagne d'une force qui entraîne l’oscillations du fil photonique. Ceci permet de réaliser un nano moteur fonctionnant grâce à la contrainte générée par une seule boite quantique pilotée par laser. L'effet est appelé "effet marteau quantique". Ce résultat ouvre la possibilité de la réalisation future d’un état quantique du mouvement par le transfert de la « quanticité » d'un système à deux niveaux vers le mouvement d’un oscillateur mécanique macroscopique<br>In the context of nanomechanics, quantum hybrid systems are mechanical oscillators coupled to a single individual quantum system. These systems offer radically new possibilities for the fabrication of extremely sensitive and ultra-compact optomechanical transducers, which can serve as position sensors or nano engines.The hybrid system investigated in this work consists of a single semiconducting quantum dot (QD) embedded in a vibrating photonic wire. It has been shown in the team, a few years ago, that the transition energy of the QD depends on the strain generated by the wire oscillations.In this thesis, we demonstrate the reverse effect, where each photon emitted by the QD comes along with a strain-induced force which drives the oscillations of the photonic wire. This realizes a nano engine run by a laser-driven single quantum object. The effect has been coined “Quantum Hammer effect”. This result opens the possibility for the future realization of a quantum state of motion via the transfer of the ”quantumness” of a two-level system towards the motion of a macroscopic mechanical oscillator
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Jason, Peter. "Comparisons between classical and quantum mechanical nonlinear lattice models." Licentiate thesis, Linköpings universitet, Teoretisk Fysik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-105817.

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In the mid-1920s, the great Albert Einstein proposed that at extremely low temperatures, a gas of bosonic particles will enter a new phase where a large fraction of them occupy the same quantum state. This state would bring many of the peculiar features of quantum mechanics, previously reserved for small samples consisting only of a few atoms or molecules, up to a macroscopic scale. This is what we today call a Bose-Einstein condensate. It would take physicists almost 70 years to realize Einstein's idea, but in 1995 this was finally achieved. The research on Bose-Einstein condensates has since taken many directions, one of the most exciting being to study their behavior when they are placed in optical lattices generated by laser beams. This has already produced a number of fascinating results, but it has also proven to be an ideal test-ground for predictions from certain nonlinear lattice models. Because on the other hand, nonlinear science, the study of generic nonlinear phenomena, has in the last half century grown out to a research field in its own right, influencing almost all areas of science and physics. Nonlinear localization is one of these phenomena, where localized structures, such as solitons and discrete breathers, can appear even in translationally invariant systems. Another one is the (in)famous chaos, where deterministic systems can be so sensitive to perturbations that they in practice become completely unpredictable. Related to this is the study of different types of instabilities; what their behavior are and how they arise. In this thesis we compare classical and quantum mechanical nonlinear lattice models which can be applied to BECs in optical lattices, and also examine how classical nonlinear concepts, such as localization, chaos and instabilities, can be transfered to the quantum world.
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Volmer, Julia Louisa. "New attempts for error reduction in lattice field theory calculations." Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/19350.

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Gitter QCD ist ein erfolgreiches Instrument zur nicht-perturbativen Berechnung von QCD Observablen. Die hierfür notwendige Auswertung des QCD Pfadintegrals besteht aus zwei Teilen: Zuerst werden Stützstellen generiert, an denen danach das Pfadintegral ausgewertet wird. In der Regel werden für den ersten Teil Markov-chain Monte Carlo (MCMC) Methoden verwendet, die für die meisten Anwendungen sehr gute Ergebnisse liefern, aber auch Probleme wie eine langsame Fehlerskalierung und das numerische Vorzeichenproblem bergen. Der zweite Teil beinhaltet die Berechnung von Quark zusammenhängenden und unzusammenhängenden Diagrammen. Letztere tragen maßgeblich zu physikalischen Observablen bei, jedoch leidet deren Berechnung an großen Fehlerabschätzungen. In dieser Arbeit werden Methoden präsentiert, um die beschriebenen Schwierigkeiten in beiden Auswertungsteilen des QCD Pfadintegrals anzugehen und somit Observablen effizienter beziehungsweise genauer abschätzen zu können. Für die Berechnung der unzusammenhängenden Diagramme haben wir die Methode der exakten Eigenmodenrekonstruktion mit Deflation getestet und konnten eine 5.5 fache Verbesserung der Laufzeit erreichen. Um die Probleme von MCMC Methoden zu adressieren haben wir die rekursive numerische Integration zur Vereinfachung von Integralauswertungen getestet. Wir haben diese Methode, kominiert mit einer Gauß-Quadraturregel, auf den eindimensionalen quantenmechanischen Rotor angewandt und konnten exponentiell skalierende Fehlerabschätzungen erreichen. Der nächste Schritt ist eine Verallgemeinerung zu höheren Raumzeit Dimensionen. Außerdem haben wir symmetrisierte Quadraturregeln entwickelt, um das Vorzeichenproblem zu umgehen. Wir haben diese Regeln auf die eindimensionale QCD mit chemischem Potential angewandt und konnten zeigen, dass sie das Vorzeichenproblem beseitigen und sehr effizient auf Modelle mit einer Variablen angewendet werden können. Zukünftig kann die Effizienz für mehr Variablen verbessert werden.<br>Lattice QCD is a very successful tool to compute QCD observables non-perturbatively from first principles. The therefore needed evaluation of the QCD path integral consists of two parts: first, sampling points are generated at which second, the path integral is evaluated. The first part is typically achieved by Markov-chain Monte Carlo (MCMC) methods which work very well for most applications but also have some issues as their slow error scaling and the numerical sign-problem. The second part includes the computation of quark connected and disconnected diagrams. Improvements of the signal-to-noise ratio have to be found since the disconnected diagrams, though their estimation being very noisy, contribute significantly to physical observables. Methods are proposed to overcome the aforementioned difficulties in both parts of the evaluation of the lattice QCD path integral and therefore to estimate observables more efficiently and more accurately. For the computation of quark disconnected diagrams we tested the exact eigenmode reconstruction with deflation method and found that this method resulted in a 5.5-fold reduction of runtime. To address the difficulties of MCMC methods, we tested the recursive numerical integration method, which simplifies the evaluation of the integral. We applied the method in combination with a Gauss quadrature rule to the one-dimensional quantum-mechanical rotor and found that we can compute error estimates that scale exponentially to the correct result. A generalization to higher space-time dimensions can be done in the future. Additionally, we developed the symmetrized quadrature rules to address the sign-problem. We applied them to the one-dimensional QCD with a chemical potential and found that this method is capable of overcoming the sign-problem completely and is very efficient for models with one variable. Improvements of the efficiency for multi-variable scenarios can be made in the future.
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Aoust, Guillaume. "Développements de sources infrarouges et de résonateurs en quartz pour la spectroscopie photoacoustique." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX067/document.

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La spectrométrie photoacoustique QEPAS constitue l’une des méthodes les plussensibles pour la détection de gaz à l’état de traces. Ses performances sont étroitement liées àcelles de sa source de lumière infrarouge cohérente et de son résonateur mécanique qui détecteles ondes acoustiques. La thèse a pour objectif de développer ces deux briques élémentaires.Dans un premier temps, les performances des résonateurs mécaniques sont modélisées, permettantde mieux comprendre leur comportement. Une formule analytique originale de leurfacteur de qualité y est incorporée, permettant de prédire avec précision les pertes qu’ils subissentlorsqu’ils résonnent dans un gaz. Grâce à ces modèles, de nouveaux résonateurs optimiséssont conçus et réalisés, aboutissant à des performances améliorées. Dans un secondtemps, les sources cohérentes infrarouges QCL et OPO sont améliorées pour la photoacoustique.L’impulsion de pompe optimale pour un OPO est présentée pour distribuer au mieuxl’énergie de pompe disponible dans le temps, et ainsi maximiser le rendement de rayonnementinfrarouge disponible. Un logiciel de simulation numérique original des OPOs est égalementcréé, et permet de simuler rapidement le spectre d’émission d’un OPO quelconque<br>Infrared photoacoustic spectrometry QEPAS is one of the most sensitive techniquefor trace gas sensing. The goal of the thesis is to improve the two key elements of the instrument: the mechanical resonator and the coherent infrared light source.First, the use of resonators as an acoustic waves sensor is investigated, allowing to better understandtheir behavior. Our modeling include a new analytical formula of their quality factor,predicting the amount of losses they experience when immersed within a gaz. The models areused to design and fabricate new custom resonators, leading to enhanced performances. Second,two infrared sources named QCL and OPO are optimized for the photoacoustic application.The optimal pump pulse for an OPO is derived to efficiently distribute the available pumpenergy in time, hence maximizing the yield of infrared light. A simulation software has alsobeen created for OPOs, able to quickly predict the spectrum of any type of OPO
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"Time evolution of perturbed quantum mechanical morse oscillator =: 被擾動的Morse諧振子在量子力學中的演化". 2002. http://library.cuhk.edu.hk/record=b5895993.

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Yuen Pui-Ho.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 2002.<br>Includes bibliographical references (leaves 158-159).<br>Text in English; abstracts in English and Chinese.<br>Yuen Pui-Ho.<br>ACKNOWLEDGEMENTS --- p.1<br>ABSTRACT --- p.2<br>CONTENTS --- p.4<br>LIST OF FIGURES --- p.7<br>Chapter CHAPTER 1 - --- INTRODUCTION --- p.13<br>Chapter 1-1 --- Interaction with EM-field --- p.15<br>Chapter 1-2 --- Objective of this study --- p.17<br>Chapter 1-3 --- Thesis arrangement --- p.18<br>Chapter CHAPTER 2 - --- LITERATURE REVIEW --- p.20<br>Chapter 2-1 --- Numerical Method --- p.20<br>Chapter 2-1-1 --- Classical calculation --- p.20<br>Chapter 2-1-2 --- Quantum mechanical calculation --- p.21<br>Chapter 2-1-2-1 --- Finite Difference Method --- p.21<br>Chapter 2-1-2-2 --- Non-finite difference method --- p.23<br>Chapter 2-1-3 --- Calculation of dissociation probability --- p.24<br>Chapter 2-2 --- Morse oscillator under constant driving frequency --- p.26<br>Chapter 2-2-1 --- Classical and quantum dynamics comparison --- p.26<br>Chapter 2-2-2 --- Resonance condition and factors affecting dissociation probability --- p.27<br>Chapter 2-3 --- MORSE OSCILLATOR UNDER CHIRPED DRIVING FREQUENCY --- p.33<br>Chapter 2-3-1 --- Bucket Dynamics --- p.35<br>Chapter 2-3-2 --- Floquet Analysis --- p.38<br>Chapter 2-4 --- Summaries --- p.43<br>Chapter CHAPTER 3 - --- METHODOLOGY --- p.46<br>Chapter 3-1 --- The model --- p.46<br>Chapter 3-2 --- An approximation to sinusoidal variation --- p.47<br>Chapter 3-3 --- Approximation to chirping frequency --- p.51<br>Chapter 3-4 --- Calculating time evolution operator for piecewise constant --- p.56<br>Chapter 3-5 --- Performance of the piecewise constant approach --- p.58<br>Chapter 3-5-1 --- Error vs. time --- p.59<br>Chapter 3-5-2 --- Accuracy dependence on number of term included --- p.62<br>Chapter 3-5-3 --- Accuracy dependence on applied E-field --- p.64<br>Chapter 3-5-4 --- "Drawbacks of the "" piecewise constant approach ´ح" --- p.65<br>Chapter CHAPTER 4 - --- BEHAVIOR OF MORSE OSCILLATOR UNDER SEMI-CLASSICAL EM- FIELD --- p.67<br>Chapter 4-1 --- Morse oscillator in monochromatic laser light --- p.67<br>Chapter 4-1-1 --- Theoretical analysis --- p.67<br>Chapter 4-1-2 --- Numerical simulation --- p.70<br>Chapter 4-1-2-1 --- Dependence on resonant levels --- p.70<br>Chapter 4-1-2-2 --- Dependence on Intensity --- p.76<br>Chapter 4-1-2-3 --- Frequency deviation from resonant frequency --- p.79<br>Chapter 4-2 --- Morse oscillator driven by chirped laser pulse --- p.89<br>Chapter 4-2-1 --- Chirping scheme --- p.89<br>Chapter 4-2-2 --- Level climbing and residual --- p.92<br>Chapter 4-2-3 --- Factors affecting dissociation probability --- p.98<br>Chapter 4-2-3-1 --- Dependence on driving amplitude --- p.98<br>Chapter 4-2-3-2 --- Dependence on rate of frequency change and initial driving frequency --- p.99<br>Chapter 4-2-3-3 --- Dependency on starting state --- p.104<br>Chapter 4-3 --- Chapter Summary --- p.106<br>Chapter CHAPTER 5 - --- "BUCKET DYNAMICS AND QUANTUM MECHANICAL ""PHASE SPACE""" --- p.108<br>Chapter 5-1 --- Bucket dynamics in classical Morse oscillator --- p.109<br>Chapter 5-2 --- "Quantum mechanical ""phase space""" --- p.114<br>Chapter 5-2-1 --- Wigner function and its properties --- p.115<br>Chapter 5-2-2 --- Q-function and its properties --- p.121<br>Chapter 5-2-3 --- Q-functions of the energy eigenstates of Morse oscillator --- p.123<br>Chapter 5-3 --- Evolution of Wigner function and Q-function --- p.125<br>Chapter 5-3-1 --- Evolution of Wigner function and Q-function under periodic driving field --- p.125<br>Chapter 5-3-2 --- Evolution of Wigner function and Q-function under driving field with chirped frequency --- p.132<br>Chapter 5-4 --- "Bucket dynamics and, quantum mechanical ""phase space""" --- p.138<br>Chapter 5-5 --- Chapter Summary --- p.141<br>Chapter CHAPTER 6 - --- CONCLUSIONS AND FURTHER STUDIES --- p.143<br>Chapter 6-1 --- Morse oscillator driven by monochromic laser light --- p.143<br>Chapter 6-1-1 --- Factors affecting the behavior of Morse oscillator in monochromic laser light --- p.144<br>Chapter 6-1-1-1 --- Effect of laser intensity --- p.144<br>Chapter 6-1-1-2 --- Effect of driving frequency --- p.144<br>Chapter 6-2 --- Morse oscillator driven by chirped laser pulse --- p.145<br>Chapter 6-3 --- "Bucket dynamics and quantum mechanical ""phase space""" --- p.146<br>Chapter 6-4 --- Wigner function and Q-function of driven Morse oscillator --- p.147<br>Chapter 6-5 --- Conclusions and Discussions --- p.149<br>APPENDIX A - EQUIVALENCE OF QUANTUM SYSTEMS WITH DIFFERENT GAUGES --- p.150<br>APPENDIX B - CALCULATION OF TRANSITION MATRIX ELEMENT TMN --- p.152<br>"APPENDIX C - CALCULATION OF PERTURBED MATRIX ELEMENTS, H´ةKN" --- p.154<br>BIBLIOGRAPHY --- p.158
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Hong, Chi-Hauh, and 洪琪華. "A study of anharmonic oscillators and coupled oscillators with various quantum mechanical methods." Thesis, 1996. http://ndltd.ncl.edu.tw/handle/58121293920205137136.

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碩士<br>國立臺灣大學<br>物理研究所<br>84<br>Anharmonic oscillators and coupled oscillators, for obvious reasons, are important physical systems to study in the realm of quantum mechanics. In this thesis we attempt to solve the bound-state eigenvalue problems involving these systems using various quantum mechanical methods. The methods we employ are mainly the equations-of-motion method, the maximal-decoupling- principle variational method and the optimal-expansion-series method. These methods have been successfully applied to some nuclear structure problems as well as some quantum mechanical mechanical problems such as the one-dimensional anharmonic oscillators. Using the one-dimensional anharmonical oscillators as a testing ground, our goal here is to obtain some accurate but non-perturbative approximate results for the coupled oscillator problems in two dimensions. We hope that in this way we may be able to make contribution to the understanding of the quantum chaos behavior existing in these coupled oscillator systems.
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Sanz, Mora Adrián. "Interfacing mechanical resonators with excited atoms." Doctoral thesis, 2018. https://tud.qucosa.de/id/qucosa%3A31833.

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We investigate two different coupling schemes between a nano-scale mechanical resonator and one-electron atoms. In these schemes, classical electromagnetic radiation mediates a mutual communication between the mechanical resonator and the atoms. In the process it generates atomic coherences, quantum superpositions of excited electronic levels of the atoms. An atomic coherence is highly responsive to subtle variations in the relative frequencies of the levels participating in such superposition state. By exposing the atoms to electromagnetic radiation modulated by the motion of the mechanical resonator, we show how the response of an atomic coherence can, under appropriate conditions, be used to affect on demand the dynamical state of the mechanical resonator. The first scheme realizes a long range interface between a mechanical resonator and an ensemble of three-level atoms. Here, mechanically modulated electromagnetic radiation comes from a laser beam reflected off an oscillating mirror, the mechanical resonator. This light beam drives the transition between an excited level and a hyperfine sublevel of the atoms with a certain detuning. A weaker light beam resonantly couples to the transition between the excited level and another hyperfine sublevel. On full resonance, the atoms evolve into a stationary coherence of the above (non-absorbing) hyperfine sublevels only. The atoms then become transparent to the weaker light beam, in a phenomenon called electromagnetically induced transparency. Off resonance, we find that this transparency is modulated at the mirror frequency with some phase shift, which allows the weaker beam to cause resonant backaction onto the moving mirror. The strength of this backaction is enhanced near atomic resonances and its character can be switched between amplification or damping of mirror vibrations by adjusting the detuning. In contrast, the second scheme accomplishes a closer range interface between a torsion pendulum and guided two level Rydberg atoms. Attaching a point electric dipole to the torsion pendulum allows electromagnetic coupling to two Rydberg levels of a passing atom. This coupling modifies the eigenfrequencies of the Rydberg levels such that they become dependent on the phonon number of the torsion pendulum. Via Ramsey interferometry, we may readout this effect and thus measure the phonon number. We show that, by subjecting several atoms, one by one, to a Ramsey measurement, a quantum non-demolition detection of the phonon number is feasible. Likewise, we show coherent oscillator displacements possible, by driving the atoms with external fields while they interact with the torsion pendulum. We propose a protocol to reconstruct the quantum state of motion of the torsion pendulum, combining these two techniques, Ramsey measurements and oscillator displacements. Our interfaces between a mechanical resonator and atoms provide alternative routes for the control of the state of motion, ultimately quantum mechanical, of a mechanical resonator, in which the latter is not restricted to be part of a cavity. We will thus ease quantum dynamical manipulations of mechanical resonators of sub micron scales, for which an efficient design of cavity opto- and electro-mechanical systems is hard.
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Books on the topic "Quantum-mechanical oscillator"

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Sudhir, Vivishek. Quantum Limits on Measurement and Control of a Mechanical Oscillator. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-69431-3.

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Sudhir, Vivishek. Quantum Limits on Measurement and Control of a Mechanical Oscillator. Springer, 2018.

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Sudhir, Vivishek. Quantum Limits on Measurement and Control of a Mechanical Oscillator. Springer, 2017.

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Book chapters on the topic "Quantum-mechanical oscillator"

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Hotta, Shu. "Quantum-Mechanical Harmonic Oscillator." In Mathematical Physical Chemistry. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-2225-3_2.

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Hotta, Shu. "Quantum-Mechanical Harmonic Oscillator." In Mathematical Physical Chemistry. Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-10-7671-8_2.

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Schmid, Erich W., Gerhard Spitz, and Wolfgang Lösch. "The Quantum Mechanical Harmonic Oscillator." In Theoretical Physics on the Personal Computer. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-75471-5_14.

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Schmid, Erich W., Gerhard Spitz, and Wolfgang Lösch. "The Quantum Mechanical Harmonic Oscillator." In Theoretical Physics on the Personal Computer. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-97088-7_14.

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Otto Cordes, Heinz. "Remarks about Observables for the Quantum Mechanical Harmonic Oscillator." In Modern Analysis and Applications. Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-9921-4_18.

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Onofrio, Roberto. "Macroscopic Distinguishable States of Mechanical Oscillators Generated by Quantum Nondemolition Measurements." In Quantum Measurements in Optics. Springer US, 1992. http://dx.doi.org/10.1007/978-1-4615-3386-3_14.

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Fernández, Francisco M., and Eduardo A. Castro. "The quantum-mechanical harmonic oscillator." In Algebraic Methods in Quantum Chemistry and Physics. CRC Press, 2020. http://dx.doi.org/10.1201/9780367811426-3.

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"The Quantum Mechanical Simple Harmonic Oscillator." In Topics in Contemporary Mathematical Physics. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814667814_0013.

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"The Quantum Mechanical Simple Harmonic Oscillator." In Topics in Contemporary Mathematical Physics. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812775443_0013.

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Treutlein, Philipp. "Atom Optomechanics." In Quantum Optomechanics and Nanomechanics. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198828143.003.0009.

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This chapter gives an introduction to optomechanics with ultracold atoms. The opening half deals with optomechanical atom–light interactions. Section 9.2 introduces atom trapping. Section 9.3 discusses the properties of trapped atoms as mechanical oscillators. Section 9.4 describes optomechanical interactions, treating the atoms as polarizable particles, a model used in section 9.5 to derive optomechanical coupling of atoms and a cavity field and briefly review cavity optomechanics experiments with atoms in the quantum regime. The second half deals with hybrid mechanical-atomic systems. We start with an overview of different coupling mechanisms, then focus on light-mediated interactions and derive the coupling of a membrane to an ensemble of laser-cooled atoms. Section 9.8 reviews experiments on sympathetic cooling of a membrane with cold atoms, with perspectives for mechanical quantum control discussed in section 9.9. Section 9.10 introduces the possibilities that arise if the mechanical oscillator is coupled to the atomic internal state.
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Conference papers on the topic "Quantum-mechanical oscillator"

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Neuhaus, Leonhard, Rémi Metzdorff, Salim Zerkani та ін. "Towards quantum effects with a μg-scale mechanical oscillator". У CLEO: QELS_Fundamental Science. OSA, 2016. http://dx.doi.org/10.1364/cleo_qels.2016.fm1c.6.

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Khoshnoud, Farbod, Houman Owhadi, and Clarence W. de Silva. "Stochastic Simulation of a Casimir Oscillator." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-39746.

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Stochastic simulation of a Casimir Oscillator is presented in this paper. This oscillator is composed of a flat boundary of semiconducting oscillator parallel to a fixed plate separated by vacuum. In this system the oscillating surface is attracted to the fixed plate by the Casimir effect, due to quantum fluctuations in the zero point electromagnetic field. Motion of the oscillating boundary is opposed by a spring. The stored potential energy in the spring is converted into kinetic energy when the spring force exceeds the Casimir force, which generates an oscillatory motion of the moving plate. Casimir Oscillators are used as micro-mechanical switches, sensors and actuators. In the present paper, a stochastic simulation of a Casimir oscillator is presented for the first time. In this simulation, Stochastic Variational Integrators using a Langevin equation, which describes Brownian motion, is considered. Formulations for Symplectic Euler, Constrained Symplectic Euler, Stormer-Verlet and RATTLE integrators are obtained and the Symplectic Euler case is solved numerically. When the moving parts in a micro/nano system travel in the vicinity of 10 nanometers to 1 micrometer range relative to other parts of the system, the Casimir phenomenon is in effect and should be considered in analysis and design of such system. The simulation in this paper considers modeling such uncertainties as friction, effect of surface roughness on the Casimir force, and change in environmental conditions such as ambient temperature. In this manner the paper explores a realistic model of the Casimir Oscillator. Furthermore, the presented study of this system provides a deeper understanding of the nature of the Casimir force.
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Neuhaus, Leonhard, Rémi Metzdorff, Salim Zerkani, et al. "Cooling a Macroscopic Mechanical Oscillator close to its Quantum Ground State." In Quantum Information and Measurement. OSA, 2017. http://dx.doi.org/10.1364/qim.2017.qf2c.3.

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Riviere, R., S. Deleglise, S. Weis, et al. "Cooling of a mechanical oscillator close to the quantum regime." In 12th European Quantum Electronics Conference CLEO EUROPE/EQEC. IEEE, 2011. http://dx.doi.org/10.1109/cleoe.2011.5943652.

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Sudhir, V., D. J. Wilson, S. Fedorov, et al. "Quantum correlations in measurement-based control of a mechanical oscillator." In Frontiers in Optics. OSA, 2016. http://dx.doi.org/10.1364/fio.2016.ff3d.6.

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Sudhir, Vivishek. "Quantum limits on measurement and control of a mechanical oscillator." In Laser Science. OSA, 2017. http://dx.doi.org/10.1364/ls.2017.lm3f.2.

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Schütz, H., V. Sudhir, R. Schilling, S. Fedorov, D. J. Wilson, and T. J. Kippenberg. "Quantum correlations of light due to a room temperature mechanical oscillator." In CLEO: QELS_Fundamental Science. OSA, 2017. http://dx.doi.org/10.1364/cleo_qels.2017.fw4f.1.

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Metzdorff, Remi, Leonhard Neuhaus, Salim Zerkani, et al. "Cooling a macroscopic mechanical oscillator close to its quantum ground state." In 2017 Conference on Lasers and Electro-Optics Europe (CLEO/Europe) & European Quantum Electronics Conference (EQEC). IEEE, 2017. http://dx.doi.org/10.1109/cleoe-eqec.2017.8087320.

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Restrepo, Juan, Julien Gabelli, Cristiano Ciuti, and Ivan Favero. "Classical and quantum theory of photothermal cavity cooling of a mechanical oscillator." In 12th European Quantum Electronics Conference CLEO EUROPE/EQEC. IEEE, 2011. http://dx.doi.org/10.1109/cleoe.2011.5943690.

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Verhagen, Ewold, Samuel Deléglise, Stefan Weis, Albert Schliesser, and Tobias J. Kippenberg. "Quantum-Coherent Coupling of a Mechanical Oscillator to an Optical Cavity Mode." In CLEO: Applications and Technology. OSA, 2012. http://dx.doi.org/10.1364/cleo_at.2012.jm1k.1.

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Reports on the topic "Quantum-mechanical oscillator"

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Parks, A. D., and J. L. Solka. Computing With Quantum Mechanical Oscillators. Defense Technical Information Center, 1991. http://dx.doi.org/10.21236/ada389497.

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