Optomechanical systems are rapidly becoming one of the most promising platforms for observing quantum behaviour, especially at the macroscopic level. Moreover, thanks to their state-of-the-art methods of fabrication, they may now enter regimes of non-linear interactions between their constituent mechanical and optical degrees of freedom. In this work, we show how this novel opportunity may serve to construct a new generation of optomechanical sensors. We consider the canonical optomechanical setup with the detection scheme being based on time-resolved counting of photons leaking from the cavity. By performing simulations and resorting to Bayesian inference, we demonstrate that the non-classical correlations of the detected photons may crucially enhance the sensor performance in real time. We believe that our work may stimulate a new direction in the design of such devices, while our methods apply also to other platforms exploiting non-linear light-matter interactions and photon detection.
Optomechanical systems are rapidly becoming one of the most promising platforms for observing quantum behaviour, especially at the macroscopic level. Moreover, thanks to their state-of-the-art methods of fabrication, they may now enter regimes of non-linear interactions between their constituent mechanical and optical degrees of freedom. In this work, we show how this novel opportunity may serve to construct a new generation of optomechanical sensors. We consider the canonical optomechanical setup with the detection scheme being based on time-resolved counting of photons leaking from the cavity. By performing simulations and resorting to Bayesian inference, we demonstrate that the non-classical correlations of the detected photons may crucially enhance the sensor performance in real time. We believe that our work may stimulate a new direction in the design of such devices, while our methods apply also to other platforms exploiting non-linear light-matter interactions and photon detection.
To operate quantum sensors at their quantum limit in real time, it is crucial to identify efficient data inference tools for rapid parameter estimation. In photodetection, the key challenge is the fast interpretation of click-patterns that exhibit non-classical statistics-the very features responsible for the quantum enhancement of precision. We achieve this goal by comparing Bayesian likelihood-free methods with ones based on deep learning (DL). While the former are more conceptually intuitive, the latter, once trained, provide significantly faster estimates with comparable precision and yield similar predictions of the associated errors, challenging a common misconception that DL lacks such capabilities. We first verify both approaches for an analytically tractable, yet multiparameter, scenario of a two-level system emitting uncorrelated photons. Our main result, however, is the application to a driven non-linear optomechanical device emitting non-classical light with complex multiclick correlations. Although both methods facilitate inference, only DL provides the execution speed required for real-time performance while naturally learning complex multi-photon click-patterns. Our results pave the way for real-time sensing and dynamical control of quantum devices that leverage non-classical effects in photodetection.
In a nutshell, a cavity optomechanical system consists of a mechanical oscillator inside an optical cavity. Cavity optomechanics studies the interplay between the light-matter radiation-pressure interaction and the change in the cavity frequency induced by mechanical motion. By leveraging the tools of quantum optics and quantum measurement, cavity quantum optomechanics enables the engineering of nonclassical quantum states of bulk matter. In this thesis, I present protocols for engineering such nonclassical quantum states in Part II. First, I introduce a scheme to ‘grow’ a quantum kitten state of a mechanical oscillator into a macroscopic Schrödinger cat state using a series of nonlinear pulsed optomechanical interactions. Next, I detail our proposed schemes to generate and verify entanglement between two mechanical oscillators. Moving on from pulsed optomechanics, I describe the theory behind an experiment that achieved multi-phonon subtraction from a mechanical oscillator in a continuously driven Brillouin optomechanical system. In the final chapter of Part II, I provide a theoretical preview of an experiment that investigates the behaviour of the mechanical oscillator when no light is detected at the output. In Part III, I introduce a new framework for nonlinear cavity quantum optomechanics that incorporates the intrinsic nonlinearity of the radiation-pressure interaction, the nonlinearity from the cavity enhancement, and higher-order mechanical position terms in the expansion of the cavity frequency. I then propose a scheme for measuring mechanical position using general-dyne detection, applicable to pulsed and continuous measurements. This predicts a new regime of operation, the “stochastic Gaussian” regime. Finally, I discuss a protocol for deterministic mechanical squeezing that utilizes the cavity response.
Quantum opto-mechanics is a fast moving, broad research field which aims to investigate and control the interaction of light and the quantized motion of mechanical objects and the coupling between them. This allows one to engineer the mechanical quantum state by controlling and measuring the electromagnetic field, and conversely, to control the dynamical evolution of the optical field via its interaction with a mechanical system. Mechanical resonators are accessible in many different shapes and sizes, from kilogram scales in experiments that test gravitational theories to micro- and nano-scales in resolved sideband regime, where the frequency of the mechanical resonator is larger than the bandwidth of the optical cavity. In this regime, it is possible to cool the mechanical object to the ground state which allows a high degree of control and the ability to prepare interesting non-classical states, states that could aid in investigating the quantum dynamics of macroscopic objects. The field of quantum opto-mechanics is a promising testbed for quantum control technologies, such as fundamental tests of quantum mechanics, ultra-sensitive quantum sensors for precise measurements, phonon lasing, mechanical memories with long lifetime and quantum information processing. Furthermore, experiments are progressing toward strong opto-mechanical coupling regimes with single photons. This creates a platform that can take advantage of the nonlinear optical interactions to generate highly non-classical states in such light-matter interfaces. Photonic systems working in the single photon regime will be promising for low power applications and also for implementations of quantum information and computation. Motivated by these applications, this thesis consists of theoretical studies in the context of single photonics. This includes investigating non-classical mechanical state generation and mechanically controlling the dynamical evolution of optical fields in the strong coupling regime single photon opto-mechanics and furthermore, proposing a quantum sensor using single photonics. In this regard, we employ three important formalisms to treat and measure open quantum systems with non-Gaussian input fields: the conditional and unconditional cascaded master equations, Fock-state master equations and input-output Langevin equations. In the context of opto-mechanics, the system to be investigated is composed of two optical cavities with a coupling modulated via a mechanical resonator. In one case, a sequence of single photons are irreversibly sent to one of the optical cavities. After photons go through the opto-mechanical interaction, photon counting measurements are performed on the cavity output, conditionally steering the mechanical state to a highly non-classical Fock state. Numerical calculations are performed to predict the experimental parameters needed to generate a mechanical Fock state before the mechanical object is thermalized. In another case, the same opto-mechanical scheme is employed to conversely modify the state of the optical mode by engineering the state of the mechanical degree of freedom. In this case, it is shown that the opto-mechanical system operates as an effective beam splitter for the input single photons, with a transmission that can be controlled by tuning the number of excitations in the bulk mechanical resonator. When the mechanical resonator has a small coherent amplitude it acts as a quantum control, entangling the optical and mechanical degrees of freedom. As the coherent amplitude of the resonator increases, it acts as a classical control for the input photons. Finally, we propose a novel multi-purpose sensor architecture that can be used for force, refractive index and possibly local temperature detection. In this scheme, two coupled cavities behave as an effective beam splitter. This sensor is based on fourth order interference (the Hong-Ou-Mandel effect) and requires a sequence of single photon pulses and consequently has low pulse power. Changes in the parameter to be measured induce variations in the effective beam splitter reflectivity and result in changes to the visibility of interference. We propose that this generic scheme could be implemented with coupled L3 photonic crystal cavities and find that this system, which only relies on photon coincidence detection and does not need any spectral resolution, can estimate forces as small as 10-7 Newtons and can measure one part per million change in refractive index using a very low input power of 10-10 W.
Cavity optomechanics has become an established and equally promising branch in quantum optics. Thanks to the interaction between matter and electromagnetic radiation, it has proved to be an optimal platform for a range of scopes, from weak force sensing to the study of non-classicality of mechanical motion. Besides, the capability to isolate genuine quantum features of the interaction represents a test ground to address many important questions regarding decoherence, quantum-to-classical transitions and the interface between quantum mechanics and gravity. The first part of the research embedded in this thesis is addressed towards the clear identification and characterisation of quantum features in optomechanics. The main model we will refer to is a deformable Fabry-P\'erot cavity where one of the two mirrors moves under the radiation pressure of light. After having properly assessed the quantum peculiarities of the system, and also having revised some intakes from past literature, we will focus on the study of mechanical non-linearities, as they have been proved to be a key resource to bring out and enhance quantum properties. These investigations provide the basis to eventually propose a method to deterministically prepare and measure macroscopic quantum superposition states of the movable mirror. Such massive quantum states play a key role to inspect the foundations of physics, e.g. to test the collapse of the wave function and phenomenological models of quantum gravity, as well as to develop new enhanced quantum technologies.
Abstract Entanglement generation at a macroscopic scale offers an exciting avenue to develop new quantum technologies and study fundamental physics on a tabletop. Cavity quantum optomechanics provides an ideal platform to generate and exploit such phenomena owing to the precision of quantum optics combined with recent experimental advances in optomechanical devices. In this work, we propose schemes operating outside the resolved-sideband regime, to prepare and verify both optical–mechanical and mechanical–mechanical entanglement. Our schemes employ pulsed interactions with a duration much less than the mechanical period and, together with homodyne measurements, can both generate and characterize these types of entanglement. To improve the performance of our schemes, a precooling stage comprising prior pulses can be utilized to increase the amount of entanglement prepared, and local optical squeezers may be used to provide resilience against open-system dynamics. The entanglement generated by our schemes is quantified using the logarithmic negativity and is analysed with respect to the strength of the pulsed optomechanical interactions for realistic experimental scenarios including mechanical decoherence and optical loss. Two separate schemes for mechanical entanglement generation are introduced and compared: one scheme based on an optical interferometric design, and the other comprising sequential optomechanical interactions. The pulsed nature of our protocols provides more direct access to these quantum correlations in the time domain, with applications including quantum metrology and tests of quantum decoherence. By considering a parameter set based on recent experiments, the feasibility to generate significant entanglement with our schemes, even with large optical losses, is demonstrated.
The investigation of macroscopic quantum phenomena is a current active area of research that offers significant promise to advance the forefronts of both fundamental and applied quantum science. Utilising the exquisite precision and control of quantum optics provides a powerful toolset for generating such quantum states where the types and 'size' of the states that can be generated are set by the experimental parameter regime available and the resourcefulness of the protocol applied. In this work we present a new multistep scheme to 'grow' macroscopic superposition states of motion of a mechanical oscillator via cavity quantum optomechanics. The scheme consists of a series of optical pulses interacting with a mechanical mode via radiation-pressure followed by photon-counting measurements. The multistep nature of our protocol allows macroscopic superposition states to be prepared with a relaxed requirement for the single-photon optomechanical coupling strength. To illustrate the experimental feasibility of our proposal, we quantify how initial mechanical thermal occupation and mechanical decoherence affects the non-classicality and macroscopicity of the states generated and show that our scheme is resilient to optical loss. The advantages of this protocol provide a promising path to grow non-classical mechanical quantum states to a macroscopic scale under realistic experimental conditions.