The influence of the frequency modulation on the nonclassicality is explored in a system of nanomechanical resonator, which is a promising device in the fields of quantum information engineering. It is shown that the nonclassicality of the quantum state is dependent on the value of the modulation rate during the quantum evolution. A pronounced peak is observed in the curve of the nonclassicality versus the modulation rate. It indicates that the system's nonclassicality can be enhanced by the modulation rate. The enhancement of the nonclassicality by the modulation rate is induced by the effects of the external driving source on the quantum interference between different energy levels. This is supported by the correspondences between the dependence curves of the nonclassicality indicator and the uncertainty of the Wigner distribution function on the modulation rate.
The influence of the frequency modulation on the nonclassicality is explored in a system of nanomechanical resonator, which is a promising device in the fields of quantum information engineering. It is shown that the nonclassicality of the quantum state is dependent on the value of the modulation rate during the quantum evolution. A pronounced peak is observed in the curve of the nonclassicality versus the modulation rate. It indicates that the system's nonclassicality can be enhanced by the modulation rate. The enhancement of the nonclassicality by the modulation rate is induced by the effects of the external driving source on the quantum interference between different energy levels. This is supported by the correspondences between the dependence curves of the nonclassicality indicator and the uncertainty of the Wigner distribution function on the modulation rate.
The time evolution of the nonclassicality is found to have strong dependence on the driving frequency in a Duffing-type driven nonlinear system with the Gaussian state as the initial Wigner function. Its frequency response curve has a remarkable peak, near which the nonclassicality of the state is enhanced. Furthermore, good correspondences are found between the frequency response curves of the time-average of the nonclassicality indicator and those of the classical mean square amplitude. Such correspondences can also be observed, when using a superposition of two coherent states as the initial Wigner function.
In this work we used an arrangement consisting of Cooper pairs (Cooper Pair Box, CPB) interacting with a nanomechanical Resonator (NR) for various studies: to produce controlable holes in the statistical distribution of excitations of the NR, for resonant and non-resonant cases; to study the evolution of the entropy and the inversion of excitations, including losses in the CPB; and to study the evolution of the Wigner function under the infuence of a reservoir. We have obtained the exact solution of the master equation describing the non-degenerate parametric amplifier interacting with a generalized model of linear phase sensitive reservoir, having the form of the equation equivalent to that of the Fokker-Planck propagator for the Wigner function. We have calculated the Wigner function describing the temporal evolution of a state initially in a superposition of two coherent states, a kind of "Schr?odinger cat", and finally, we have also studied the temporal evolution of the negativity of this function, one of the indicators of nonclassicality of vibrational states of the NR.
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 propose measurement-based conditional generation of the superposition of mesoscopic states of a nanomechanical resonator. We consider a two-level quantum mechanical system (qubit) coupled with a nanomechanical resonator through phonon exchange. An interaction, which produces shifts in the state of the nanomechanical resonator depending on the state of the qubit, is realized by driving the qubit through two resonant fields or a single field with controlled phase. The measurement of the state of the qubit produces superposition states of the nanomechanical resonator. We show that the quantum interference between the generated states in the superposition may lead to an arbitrary large displacement in the resonator. We also discuss decoherence of the generated states using the Wigner function.
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.
We address quantitatively the relationship between the nonlinearity of a mechanical resonator and the nonclassicality of its ground state. In particular, we analyze the nonclassical properties of the nonlinear Duffing oscillator (being driven or not) as a paradigmatic example of a nonlinear nanomechanical resonator. We first discuss how to quantify the nonlinearity of this system and then show that the nonclassicality of the ground state, as measured by the volume occupied by the negative part of the Wigner function, monotonically increases with the nonlinearity in all the working regimes addressed in our study. Our results show quantitatively that nonlinearity is a resource to create nonclassical states in mechanical systems.