Mechanical properties of metallic-nanowire self-oscillations are investigated through a coherent-state analysis. We focus on elucidating the time behavior of quantum energy in such oscillations, in addition to the analysis of fluctuations, evolution of eigenstates, and oscillatory trajectories. The quantum energy varies somewhat randomly at first, but, at a later time, it undergoes a stable periodical oscillation; the mean energy in the stabilized motion is large when the frequency of the driving force is resonated with that of the intrinsic oscillation of the nanowire. We confirmed that when the oscillatory amplitude is sufficiently low, the quantum energy is quite different from the classical one due to zero-point energy which appears in the quantum regime. Because the power in such an oscillation is typically ultra low, quantum effects in the nanowire oscillations are non-negligible. Detailed analysis for the evolution of the probability densities and their relation with the oscillation trajectories of the nanowire are also carried out. Characterizing quantum effects in the actual oscillatory motions and clarifying their difference from the classical ones are important in understanding nanowire self-oscillations.
Mechanical properties of metallic-nanowire self-oscillations are investigated through a coherent-state analysis. We focus on elucidating the time behavior of quantum energy in such oscillations, in addition to the analysis of fluctuations, evolution of eigenstates, and oscillatory trajectories. The quantum energy varies somewhat randomly at first, but, at a later time, it undergoes a stable periodical oscillation; the mean energy in the stabilized motion is large when the frequency of the driving force is resonated with that of the intrinsic oscillation of the nanowire. We confirmed that when the oscillatory amplitude is sufficiently low, the quantum energy is quite different from the classical one due to zero-point energy which appears in the quantum regime. Because the power in such an oscillation is typically ultra low, quantum effects in the nanowire oscillations are non-negligible. Detailed analysis for the evolution of the probability densities and their relation with the oscillation trajectories of the nanowire are also carried out. Characterizing quantum effects in the actual oscillatory motions and clarifying their difference from the classical ones are important in understanding nanowire self-oscillations.
The coupling of nanomechanical resonators to controllable quantum systems represents a growing and promising area of research. Recent advances in this field have brought to astonishing results, such as the initialization of a mechanical resonator into its quantum ground state and even the preparation of non-classical coherent states of motion. These achievements open up appealing scenarios to quantum information technologies and to the exploration of the quantum-classical boundary. From an application perspective, such quantum-mechanical hybrid systems provide a versatile and attractive tool for a variety of precision measurements, like ultra-sensitive detection of force, mass, and displacement. \n \nQuantum control over a mechanical resonator, or, conversely, the prospect of using resonator's motion for probing quantum states, both involve some tight requirements. First of all, the interaction between the mechanics and its quantum partner has to be large on the scale of the decoherence rates of the coupled systems. In most cases, the coupling mechanism has to be activated by engineering the resonator with electrodes, magnets, or mirrors, or by using tailored laser fields. For this reason, the search for a strong coupling typically competes with the requirement of overcoming decoherence effects. In addition, for quantum effects to be observable, strong coupling has to be accompanied by the preparation of zero entropy initial states, for instance by cooling the resonator into its ground state of motion. \n \nThe motivation pursued by this thesis is to contribute to the inspiring field of hybrid systems by walking through each of the aforementioned directions. We in fact demonstrate a promising system in which optically active quantum dots, embedded in fully self-assembled core-shell nanowires, are coupled to the nanowire motion. Mechanical vibrations of the nanowire modulate the quantum dot emission energy over a broad range exceeding 14 meV, by means of deformation potential coupling. In our system, therefore, both the coupling mechanism and the quantum states themselves are intrinsic to the resonator's structure. Besides revealing unusually strong, such a built-in opto-mechanical interaction produces a hybrid system whose inherent coherence is unspoiled by any functionalization or external field and whose fabrication is simpler than top-down techniques. \n \nWe further demonstrate the use of a quantum point contact as a displacement transducer to measure and control the low-temperature thermal motion of a nearby micromechanical cantilever. We show that by including the QPC in a suitable feedback loop, we are able to cool the cantilever's fundamental mechanical mode down to the level of the measurement noise, achieving a squashing of the QPC noise at high gain. Due to its off-board design, our system is particularly versatile and suitable to force-sensing applications. Since the QPC transducer is sensitive to local modifications of the nearby electric field, our approach is in principle compatible with any nanoscale resonator, without requiring any functionalization to activate the coupling. By improving the performance of the QPC as a one-dimensional conductor and the cantilever-QPC capacitive coupling, our system has the potential to achieve quantum-limited displacement resolution and ground state cooling. We then report on some ongoing attempts to overcome the current limitations of our system and couple mechanical motion to different mesoscopic transport devices. \n \nWe remark that our demonstration of an as-grown quantum-dot-in-nanowire hybrid system opens up bright prospects on future experiments, as also testified by the very recent ferment of the scientific community around this topic. We find that the opto-mechanical coupling rate is not far from the nanowire mechanical frequency. This fact makes our system particularly promising for the quantum non-demolition readout of a quantum dot state through a measurement of the nanowire position. On the other hand, we show that the coupling can be further optimized, and the nanowire mechanical heating rate reduced, thus disclosing the captivating perspective of using quantum dots to probe and control the mechanical state of a nanowire. In this context, it would be important to investigate a possible spin-oscillator coupling in our system, given the long coherence time offered by a spin state in a quantum dot. The wide range of control over the quantum dots emission energy and the ability to tune two neighboring dots into resonance pave the way to mechanically induced emitter-emitter coupling. In addition, our monolithic opto-mechanical system constitutes a good candidate for recent proposals of a tripartite hybrid system, which would integrate an optical cavity, a quantum two-level system and a mechanical resonator. The intrinsically strong coupling between the quantum dots and the nanowire motion would enhance the interaction between the mechanics and the cavity field, leading for instance to efficient cooling of the resonator to the ground state. Finally, the quantum dot sensitivity to the nanowire resonant vibration could also support the use of our system as an integrated force probe or as a nanomechanical mass sensor. In other words, the results reported in this dissertation constitute not only a relevant proof-of-principle, moreover they open up intriguing challenges for future research.
Transport-induced self-sustained oscillations in electromechanical systems convert a static electrochemical bias into robust, autonomous oscillatory motion in the absence of any external periodic drive. However, an exact description of such self-oscillations remains challenging in nanoscale electromechanical devices featuring a simultaneously large bosonic Hilbert space, strong interactions, and structured fermionic leads. We formulate a tensor-network framework that combines a binary representation of the vibrational mode with mesoscopic reservoir embeddings that enable controlled access to the self-oscillatory steady states and relevant transport observables without explicit real-time propagation. We demonstrate the emergence of mechanical self-oscillations across a broad set of operating conditions, in which strong electromechanical backaction, nonadiabatic oscillator dynamics, and energy-dependent electronic tunneling processes compete. Furthermore, we observe that for both slow and fast vibrating mechanical modes, suppressed vibrational occupation fluctuations in the self-oscillation window along the electromechanical coupling strength sweep are preceded by a peak in the occupation fluctuations. Collectively, we explore how both intrinsic system properties and environmental parameters govern such autonomous oscillations over a broad range of operating conditions. The broad applicability of our framework will facilitate further extension of the method to more complex and experimentally relevant scenarios to study the thermodynamics of quantum autonomous devices with potential applications in quantum sensing, timekeeping, information processing, and energy conversion.
Among the various nanoscale systems operating in the quantum limit, nanomechanical oscillators have emerged as particularly powerful platforms. They constitute highly sensitive sensors and can mediate interactions between light and localized quantum systems, playing a central role in various quantum information processing architectures. Due to their relatively large mass, they also serve as ideal platforms for investigating the transition between classical and quantum behavior. This thesis examines the dynamics of a nanomechanical oscillator coupled to a driven two-level system. The analysis focuses on the resolved sideband limit, where the twolevel system’s damping rate Γ is much smaller than the mechanical frequency ωm, and explores both the strong coupling (ωm ≫ g0 ≫ Γ) and ultra-strong coupling (g0 ∼ ωm ≫ Γ) regimes, where g0 denotes the coupling strength. These regimes enable coherent manipulation of the mechanical state while preserving its quantum coherence. Under blue-detuned driving of the two-level system and assuming low mechanical damping, the system exhibits a dynamical instability marked by the emergence of limit cycles in the mechanical oscillator. The onset of this regime is accompanied by pronounced fluctuations in the photon emission from the two-level system, indicated by a large deviation from Poissonian statistics. The phonon statistics display a similar behavior, offering an additional experimental signature. As the coupling strength approaches ωm, the mechanical oscillator reaches a steady state with non-classical feature. The phonon number distribution in this regime resembles that of Fock states, and the corresponding quasi-probability distribution in phase space displays negative regions, a signature of nonclassicality. A method is proposed to detect this non-classicality experimentally through measurements of the emitted light, from which the full quantum state of the coupled system can be reconstructed. The robustness of this approach is analyzed in the presence of realistic noise sources. The thesis further investigates the response of the system under two-tone driving. A tailored model is developed to describe this regime at strong coupling. When the driving frequencies are tuned to the first blue and red sidebands, the mechanical oscillator reaches a steady state exhibiting quadrature squeezing. In the case where both driving frequencies are red-detuned, the oscillator evolves into a superposition of coherent states, analogous to the behavior of a parametrically driven resonator. In both configurations, non-classical features become prominent when g0 approaches ωm. These results provide new insights into the generation and stabilization of non-classical and squeezed mechanical states. We outline feasible strategies for their detection, offering potential applications in hybrid quantum systems and foundational tests of quantum mechanics.
We have studied quantum-mechanical behavior of a driven Morse oscillator coupled to a bath of harmonic oscillators. The purpose is to compare the quantum behavior of such a system with the classical solutions of a driven damped Morse oscillator. We start with the quantum Liouville equation, in which the Hamiltonian of the Morse oscillator is expressed in terms of generators of an su(2) Lie algebra. This algebra and the Markovian approximation allow us to derive the generalized master equation (for the reduced density matrix of the Morse oscillator), which contains level-dependent energy and phase relaxation terms. We have numerically integrated the differential equations of the matrix elements to obtain the time evolution of the reduced density matrix and the energy of the Morse oscillator. We show that the energy of the Morse oscillator in general varies with time and eventually reaches an asymptotic oscillatory state. The mean energy value of the asymptotic oscillatory state is studied as a function of the relaxation rates and laser frequency and amplitude. Vibrational distributions have also been found as functions of laser frequency and amplitude. The shape of the distribution changes gradually as laser amplitude increases; it first peaks at the ground state at a small field amplitude, then it peaks at some excited state at a large field amplitude, and for an amplitude in between it can have two maxima. This bimodal vibrational distribution reflects the bistability observed in the classical and semiclassical models. Thus bistability exists in quantum results, not as a hysteresis loop, but as a bimodal distribution. Finally, we show that as laser intensity increases, the time series of the oscillator energy evolves from regular to quasiperiodic behavior, and eventually a chaotic-looking series appears.
The geometric phase, as well as the familiar dynamical phase, occurs in the evolution of a squeezed state in nano-optics as an extra phase. The outcome of the geometric phase in that state is somewhat intricate: its time behavior exhibits a combination of a linear increase and periodic oscillations. We focus in this work on the periodic oscillations of the geometric phase, which are novel and interesting. We confirm that such oscillations are due purely to the effects of squeezing in the quantum states, whereas the oscillation disappears when we remove the squeezing. As the degree of squeezing increases in q-quadrature, the amplitude of the geometric-phase oscillation becomes large. This implies that we can adjust the strength of such an oscillation by tuning the squeezing parameters. We also investigate geometric-phase oscillations for the case of a more general optical phenomenon where the squeezed state undergoes one-photon processes. It is shown that the geometric phase in this case exhibits additional intricate oscillations with small amplitudes, besides the principal oscillation. Such a sub-oscillation exhibits a beating-like behavior in time. The effects of geometric-phase oscillations are crucial in a wide range of wave interferences which are accompanied by rich physical phenomena such as Aharonov–Bohm oscillations, conductance fluctuations, antilocalizations, and nondissipative current flows.
The standard mathematical formalism of cavity QED leads us to consider photons as excitations of a quantum harmonic oscillator. Although it is one of the most familiar problems of quantum mechanics, some aspects of the quantum harmonic oscillator remain difficult to visualize, particularly in the rather abstract context of an electromagnetic field. Recently, modern microfabrication and refrigeration techniques have begun to allow the creation of nanoscale mechanical oscillators which can be cooled close to the quantum regime. Despite the extreme physical differences between an electromagnetic cavity and a nanomechanical resonator, both systems may be approximated by the same quantum harmonic oscillator model. However, the conceptual consequences of quantum behavior, and the challenges to physical intuition, are quite different in the two cases. Taking a mechanical point of view therefore allows fresh insight into the quantum harmonic oscillator problem. To illustrate the connection and how it may aid our understanding of light, the mathematical parallelism between an electromagnetic cavity and a mechanical resonator is demonstrated. Current nanomechanics experiments are discussed, and some possible quantum measurements are introduced. Finally, the discrepancies between the predictions of quantum mechanics and our experience of classical vibrating beams are considered, with an emphasis on how nanomechanics may be able to offer a new perspective on the nature of photons.