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.
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.
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.
The field of cavity optomechanics is based on the coupling of optical cavities to mechanical degrees of freedom. Over the past two decades, it has led to remarkable and surprising discoveries. A cavity optomechanical system enabled the first observation of gravitational waves, a discovery awarded with the 2017 Nobel prize, confirming Einstein's 100-year-old prediction. It was also a cavity optomechanical system that has for the first time enabled ground state cooling of the motion of an object containing ~1012 atoms, and entanglement of mechanical oscillators of similar size. Moreover, cavity optomechanical systems have facilitated significant progress in precision-sensing technologies, with diverse applications such as biosensing, magnetometry, and many more.But this may only be the beginning. The field is still in its early days and experimental capabilities are improving fast. For instance, cavity optomechanical systems have the potential to test predicted signatures of quantum gravity such as modifications to the canonical commutator, short-distance modifications to Newtonian gravity, dark matter and dark energy, and even extra dimensions. In this sense, they form an economical platform with a short experimental turnover time, that can compete in its predictive power with mega-scale, multi-billion-dollar experiments such as the Large Hadron Collider.This thesis is dedicated to utilizing cavity optomechanics to explore the maybe most challenging and unexplored frontier in quantum mechanics: The dynamics of macroscopic quantum systems. Quantum physics, since its discovery in the early 20th century, has revolutionized our understanding of the microworld, but has long been thought to apply exclusively to extremely small objects. However, over the past decades, ever-larger quantum systems have emerged in laboratories around the world. On one hand, these are collective, macroscopic quantum phenomena such as superfluidity, superconductivity, and Bose-Einstein condensation. On the other hand, they are quantum states of relatively massive mechanical objects. While our understanding of the interplay of quantum mechanical and classical systems has greatly improved over the past decades, as described by theories of decoherence and open quantum systems, many basic questions about macroscopic quantum systems still remain unanswered. Quantum fluids such as Bose-Einstein condensates and superfluid helium are inherently hard to understand due to their complex dynamics, and difficult to probe experimentally due to the weakness of their interactions with the environment and their fragile nature. This is especially true in the strongly-interacting regime, which is, for instance, found in superfluid helium.Another long-standing, unanswered set of questions in quantum mechanics is related to the quantum measurement problem. What constitutes a quantum measurement? What happens if we engineer a quantum state that is large enough to be, in principle, part of our everyday world? What if we attempt to create a quantum superposition of a living being? Do the laws of physics even permit either of these scenarios?Cavity optomechanics is a unique and powerful platform to investigate macroscopic quantum systems. The extreme sensitivity of cavity optomechanical sensors in readout of mechanical motion makes them susceptible to minute quantum effects. The strong coupling between single photons and phonons in these systems allows engineering and measurement of quantum states of mechanical systems. Furthermore, most cavity optomechanical experiments are cryo-compatible and small in size, which allows integration with other quantum systems to be analyzed, such as superfluid helium.
In this dissertation, I theoretically investigate the open system dynamics of cavity optomechanical systems in the quantum limit, where a mechanical resonator couples to a cavity mode via radiation pressure force. Recent developments in nano-fabrication and cooling techniques make it possible to optically control and manipulate the motion of micro- and nano-mechanical resonator. Several experiments have demonstrated the possibility of preparing macroscopic mechanical resonators into their quantum ground state, which makes optomechanical systems an ideal candidate for studying the quantum behavior of macroscopic objects. One important direction in quantum optomechanics is the study of the decoherence of optomechanical system due to the interaction with their external environments. This dissertation explores the decoherence effects by considering the influence of the radiation pressure coupling on the interaction between optomechanical system and its environments. Because the effects of the nonlinear interaction vary with the optomechanical coupling strength, three different interaction regimes are fully studied here: the weak coupling, the intermediate coupling and the strong coupling.
Quantum entanglement and quantum superposition are fundamental properties of quantum mechanics, which underline quantum information and quantum computation. Preparing quantum states in the macroscopic level is both conceptually interesting for extending quantum physics to a broader sense and fundamentally important for testing the validity of quantum mechanics. In this dissertation, schemes of preparing macroscopic entanglement and macroscopic superposition states in cavity optomechanics are studied using the unitary evolution method in the nonlinear regime or Lyapunov equation in the linearized regime. Quantum entanglement and quantum superposition states can be realized using experimentally feasible parameters with the proposals in this dissertation.\nFirstly, a scheme of entangling two movable end mirrors in a Fabry-Perot cavity that are coupled to a common single photon superposition state is studied. It is shown that strong entanglement can be obtained either in the single-photon strong coupling regime deterministically or in the single-photon weak coupling regime conditionally.\nSecondly, a scheme of entangling two movable end mirrors, that are coupled to two-mode entangled fields generated from a correlated-emission laser is investigated. By tuning the input driving laser frequencies at the Stokes sidebands of the cavity, the radiation-pressure coupling can be linearized as an effective beam-splitter-like interaction. Hence entanglement can be transferred from the two-mode fields to the two mechanical mirrors. Macroscopic entanglement between macroscopic mirrors persists at temperature ~ 1K.\nThirdly, a scheme of creating macroscopic quantum superpositions of a mechanical mirror via periodically flipping a photonic qubit is proposed. Quantum superposition states of a mechanical mirror can be obtained via the nonlinear radiation coupling with a single-photon superposition state. However, the difference between two superposed mechanical states is very small due to the weak single-photon coupling rate available in experiment. By periodically flipping the photonic qubit state, the difference can be magnified. It is shown in detail that this scheme is experimentally feasible under current technology.
In this thesis, I studied two different approaches which are promising for creating macroscopic quantum superpositions. The first approach, which is the main focus of this thesis, is based on optomechanical systems. The basic challenge to realize quantum effects in optomechanical systems, is considered to be the weak optomechanical coupling rate compared to the decoherence rates of the system caused by the cavity and mechanical damping. To enhance the optomechanical coupling it has been suggested to pump the cavity with coherent laser light \cite{Vitali07}. By this method the strong coupling regime in which the optomechanical coupling rate exceeds all decoherence rates has been demonstrated very recently \cite{Verhagen12,Groblacher09}. It is also known that the optomechanical systems may exhibit nonlinear behaviours such as bistability. After introducing the basic ideas of optomechanical systems in chapter 1, in chapter 2 we studied the connection between optomechanical entanglement and bistability. In chapter 3, we studied the drawback of using a laser to enhance the interaction. We studied the effect of the laser phase noise, as an additional decoherence channel, on the optomechanical entanglement. We have shown that the system is very sensitive to this new source of decoherence and the sensitivity is maximum in the bistable threshold. We discussed that our results are independent of how we model the laser phase noise. In chapter 4, we studied single photon optomechanics. In this regime, we proposed a new scheme to enhance the optomechanical coupling based on post selection. Our scheme is potentially promising to create a superposition of the massive oscillator in different motional states. We also discussed the potential application of our scheme to test some decoherence models. The second approach that we consider in this thesis is based on amplifying single photons with high gain to create micro-macro superpositions . In chapter 5, we discussed the De Martini scheme. We then present our scheme for creating optical micro-macro superposition and discussed its experimental realization under realistic conditions when losses are taken into account.
Cavity optomechanics represents a frontier research direction in quantum science and technology, centered on the control and exploration of interactions between electromagnetic fields and mechanical motion. Rooted in quantum mechanics, this field realizes efficient coupling and precise manipulation of optical fields and mechanical vibrations through the structural design and precise regulation of optical microcavities and mechanical oscillators, thereby revealing and harnessing novel quantum phenomena. In recent years, cavity optomechanics has evolved into an interdisciplinary frontier integrating quantum optics, condensed matter physics, and quantum precision measurement, exhibiting profound application in both fundamental physics research and quantum information science. With advancements in technologies such as nanomanufacturing and laser cooling, optomechanical interactions have been successfully demonstrated in various experimental systems. Among these platforms, cavity cold-atom systems stand out as one of the ideal platforms for implementing quantum optomechanics. Featuring exceptional environmental isolation, long quantum coherence times, and strong light-matter interaction, these systems provide a crucial testbed for exploring strong and even ultrastrong optomechanical coupling effects as well as rich nonlinear quantum phenomena. This paper reviews the recent progress in optomechanical control and manipulation based on cavity cold-atom systems. We first outline the fundamental principles of standard cavity optomechanical systems. Then, we describe the experimental realization of linear and nonlinear optomechanical couplings in cold-atom systems. After that, we focus on the representative applications of this platform in high-precision quantum sensing, quantum memory, and the preparation of macroscopic nonclassical states. Finally, we give an outlook and challenges in this field.