A growing number of unresolved-sideband optomechanics experiments are now observing nonlinearities, which cannot be described within the linearized approximation. However, a suitable theoretical framework for describing these nonlinearities is needed for optomechanics to advance beyond the current state-of-the-art. In this talk, I will introduce our framework of cavity quantum optomechanics, which captures the nonlinearities of both the radiation-pressure interaction and the cavity response. I will then describe how this framework can be used to perform position measurement well beyond the breakdown of the linearized approximation.
A growing number of unresolved-sideband optomechanics experiments are now observing nonlinearities, which cannot be described within the linearized approximation. However, a suitable theoretical framework for describing these nonlinearities is needed for optomechanics to advance beyond the current state-of-the-art. In this talk, I will introduce our framework of cavity quantum optomechanics, which captures the nonlinearities of both the radiation-pressure interaction and the cavity response. I will then describe how this framework can be used to perform position measurement well beyond the breakdown of the linearized approximation.
Several optomechanics experiments are now entering the highly sought nonlinear regime where optomechanical interactions are large even for low light levels. Within this regime, new quantum phenomena and improved performance may be achieved; however, a corresponding theoretical formalism of cavity quantum optomechanics that captures the nonlinearities of both the radiation-pressure interaction and the cavity response is needed to unlock these capabilities. Here, we develop such a nonlinear cavity quantum optomechanical framework, which we then utilize to propose how position measurement can be performed beyond the breakdown of the linearized approximation. Our proposal utilizes optical general-dyne detection, ranging from single to dual homodyne, to obtain mechanical position information imprinted onto both the optical amplitude and phase quadratures and enables both pulsed and continuous modes of operation. These cavity optomechanical nonlinearities are now being confronted in a growing number of experiments, and our framework will allow a range of advances to be made in, e.g., quantum metrology, explorations of the standard quantum limit, and quantum measurement and control.
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.
Non-Gaussian quantum states of mechanical motion exhibiting Wigner negativity offer promising capabilities for quantum technologies and tests of fundamental physics. Within the field of cavity quantum optomechanics, it is commonly held that deterministic preparation of mechanical Wigner negativity in the unresolved-sideband regime is not possible, as the intracavity interaction Hamiltonian is linear in mechanical position. Here, we show that, despite this, by accounting for the nonlinearity of the cavity response with mechanical position, mechanical Wigner negativity can be prepared deterministically in the unresolved-sideband regime, without additional nonlinearities, nonclassical drives, or conditional measurements. In particular, we find that Wigner negativity can be prepared with an optical pulse, even without single-photon strong coupling, and the negativity persists in the steady state of a continuously driven system. Our results deepen our understanding of cavity-enhanced radiation pressure and establish a pathway for deterministic preparation of nonclassical mechanical states in the unresolved sideband regime.
The nonlinearity is essential for creation of non-classical states of the cavity or mechanical resonator such as squeezed or cat states. A microwave cavity can be made nonlinear by, for instance, adding Josephson junctions. The mechanical resonator is inherently nonlinear. The radiation pressure interaction between cavity and mechanical resonator is also inherently nonlinear but typically under strong drive of the cavity interaction can be linearized. However, if the optomechanical system is in the strong coupling regime nonlinear quantum effects become observable. These three cases provide the motivation for our studies. We start with backaction analysis of the classical regime of a dc SQUID (superconducting quantum interference device) with an embedded mechanical resonator. Then, we perform quantum analysis to understand how the asymmetry of two Josephson junctions influences the coupling strength of optomechanical interactions such as radiation pressure, cross-Kerr and single-photon beam splitter. Using variational method and self-consistent harmonic approximation we estimate the influence of the radiation pressure coupling and Kerr nonlinearity of the cavity on the effective frequency and dissipation of the cavity. The second part of this thesis focuses on the nonlinearity of the mechanical resonator coupled to the optical/microwave cavity. We study in details the nonlinear optomechanical response and draw the response map to summarize all results of the overcoupled and undercoupled cavity for the red and blue sidebands additionally to the weak and strong drive powers. In the end, w e confirm the developed theory by using it to numerically fit the experimental results.
Cavity quantum optomechanics has emerged as a new platform for quantum science and technology and has applications ranging from quantum-information processing to tests of the foundations of physics. Of crucial importance for optomechanics is the generation and verification of non-Gaussian states of motion and a key outstanding challenge is the observation of a canonical two-mode Schrodinger-cat state in the displacement of two mechanical oscillators. In this work, we introduce a protocol that utilizes the nonlinearity of the radiation-pressure interaction combined with photon-counting measurements to generate this bipartite non-Gaussian mechanical state. Our protocol employs short optical pulses to both generate the mechanical quantum state, and to then measure arbitrary mechanical quadrature moments, which we utilize to verify the non-Gaussian entanglement. Our entanglement-verification procedure can be used to evaluate an entire class of inseparability criteria and also provides a route for experimental characterisation of a broad range of single- and multi-partite mechanical states. Key experimental factors, such as optical loss and mechanical decoherence, are carefully analyzed and we show that the scheme is feasible with only minor improvements to current experiments that operate outside the resolved-sideband regime. Our scheme provides a new avenue for quantum experiments with entangled mechanical oscillators and offers significant potential for further research and development that utilizes such non-Gaussian states for quantum-information and sensing applications, and for studying the quantum-to-classical transition.
The quantum nonlinear regime of optomechanics is reached when nonlinear effects of the radiation pressure interaction are observed at the single-photon level. This requires couplings larger than the mechanical frequency and cavity-damping rate, and is difficult to achieve experimentally. Here we show how to exponentially enhance the single-photon optomechanical coupling strength using only additional linear resources. Our method is based on using a large-amplitude, strongly detuned mechanical parametric drive to amplify mechanical zero-point fluctuations and hence enhance the radiation pressure interaction. It has the further benefit of allowing time-dependent control, enabling pulsed schemes. For a two-cavity optomechanical set-up, we show that our scheme generates photon blockade for experimentally accessible parameters, and even makes the production of photonic states with negative Wigner functions possible. We discuss how our method is an example of a more general strategy for enhancing boson-mediated two-particle interactions and nonlinearities.