Performing accurate position measurements of a mechanical resonator by coupling it to some optically driven quantum emitter is an important challenge for quantum sensing and metrology. We fully characterize the quantum noise associated with this measurement process, by deriving master equations for the coupled emitter and the resonator valid in the ultrastrong coupling regime. At short timescales, we show that this noise sets a fundamental limit to the readout sensitivity and that the standard quantum limit can be recovered for realistic experimental conditions. At long timescales, the scattering of the mechanical quadratures leads to the decoupling of the emitter from the driving light, switching off the noise source. This method can be used to describe the interaction of any quantum system strongly coupled to a finite size reservoir.
Performing accurate position measurements of a mechanical resonator by coupling it to some optically driven quantum emitter is an important challenge for quantum sensing and metrology. We fully characterize the quantum noise associated with this measurement process, by deriving master equations for the coupled emitter and the resonator valid in the ultrastrong coupling regime. At short timescales, we show that this noise sets a fundamental limit to the readout sensitivity and that the standard quantum limit can be recovered for realistic experimental conditions. At long timescales, the scattering of the mechanical quadratures leads to the decoupling of the emitter from the driving light, switching off the noise source. This method can be used to describe the interaction of any quantum system strongly coupled to a finite size reservoir.
We present an analytically tractable model of a driven quantum harmonic emitter, such as an oscillating charged dipole, emitting radiation via resonance fluorescence. With this model we are able to characterize the quantum mechanical correlations that are built up at early times between the drive, the resonant emitter, and its fluorescence. We describe detection strategies that can reveal these quantum signatures in experiments by performing joint measurements on the quantum emitter and its fluorescence field. In particular, we show that simultaneous quantum measurements of a driven quantum emitter and its fluorescence can be used to probe the quantum noise of the driving field, relative to the maximally classical coherent state of the driving field, in short-time experiments. We conclude by discussing the applications to quantum sensing in quantum optical, quantum acoustic, and quantum gravitational scenarios of interest.
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.
The radiation pressure interaction of light with a mechanical oscillator leads to a fundamental disturbance on the oscillator. This disturbance - measurement backaction - is due to the quantum fluctuations in the amplitude of the light. When the phase of the light is detected to infer the mechanical position, quantum fluctuations in the phase - measurement imprecision - leads to a further uncertainty in the estimate of the position. In this conventional measurement strategy, these two noise sources impose a fundamental limit on the ability to estimate the position of the mechanical object - the so-called standard quantum limit [1]. However, the two noise contributions are in general correlated. The fluctuations in the amplitude quadrature drive the mechanical oscillator, and this backaction driven motion is transduced into the phase quadrature. Correlations thus established [2] form a valuable quantum mechanical resource that can be directly employed for back-action cancellation in the measurement record via “variational measurements” [3].
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.
Why are classical theories often sufficient to describe the physics of our world even though everything around us is entirely composed of microscopic quantum systems? The boundary between these two fundamentally dissimilar theories remains an unsolved problem in modern physics. Position measurements of small objects allow us to probe the area where the classical approximation breaks down. In quantum mechanics, Heisenbergâ s uncertainty principle dictates that any measurement of the position must be accompanied by measurement induced back-action---in this case manifested as an uncertainty in the momentum. In recent years, cavity optomechanics has become a powerful tool to perform precise position measurements and investigate their fundamental limitations. The utilization of optical micro-cavities greatly enhances the interaction between light and state-of-the-art nanomechanical oscillators. Therefore, quantum mechanical phenomena have been successfully observed in systems far beyond the microscopic world. In such a cavity optomechanical system, the fluctuations in the position of the oscillator are transduced onto the phase of the light, while fluctuations in the amplitude of the light disturb the momentum of the oscillator during the measurement. As a consequence, correlations are established between the amplitude and phase quadrature of the probe light. However, so far, observation of quantum effects has been limited exclusively to cryogenic experiments, and access to the quantum regime at room temperature has remained an elusive goal because the overwhelming amount of thermal motion masks the weak quantum effects. This thesis describes the engineering of a high-performance cavity optomechanical device and presents experimental results showing, for the first time, the broadband effects of quantum back-action at room temperature. The device strongly couples mechanical and optical modes of exceptionally high quality factors to provide a measurement sensitivity ∼104 times below the requirement to resolve the zero-point fluctuations of the mechanical oscillator. The quantum back-action is then observed through the correlations created between the probe light and the motion of the nanomechanical oscillator. A so-called â variational measurementâ , which detects the transmitted light in a homodyne detector tuned close to the amplitude quadrature, resolves the quantum noise due to these correlations at the level of 10\% of the thermal noise over more than an octave of Fourier frequencies around mechanical resonance. Moreover, building on this result, an additional experiment demonstrates the ability to achieve quantum enhanced metrology. In this case, the generated quantum correlations are used to cancel quantum noise in the measurement record, which then leads to an improved relative signal-to-noise ratio in measurements of an external force. In conclusion, the successful observation of broadband quantum behavior on a macroscopic object at room temperature is an important milestone in the field of cavity optomechanics. Specifically, this result heralds the rise of optomechanical systems as a platform for quantum physics at room temperature and shows promise for generation of ponderomotive squeezing in room-temperature interferometers.
Cavity and circuit QED study light-matter interaction at its most fundamental level. Yet, this interaction is most often neglected when considering the coupling of this system with an environment. In this paper, we show how this simplification, which leads to the standard quantum optics master equation, is at the root of unphysical effects. Including qubit relaxation and dephasing, and cavity relaxation, we derive a master equation that takes into account the qubit-resonator coupling. Special attention is given to the ultrastrong coupling regime, where the failure of the quantum optical master equation is manifest. In this situation, our model predicts an asymmetry in the vacuum Rabi splitting that could be used to probe dephasing noise at unexplored frequencies. We also show how fluctuations in the qubit frequency can cause sideband transitions, squeezing, and Casimir-like photon generation.