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Quantum states preparation in cavity optomechanics

Wenchao Ge

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

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.

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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.
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.
We propose a scheme to generate macroscopic superpositions of well-distinguishable coherent states in an optomechanical system via periodic qubit flipping. Our scheme does not require the single-photon strong-coupling rate of an optomechanical system. The generated mechanical superposition state can be reconstructed using mechanical quantum-state reconstruction. The proposed scheme relies on recycling of an atom, fast atomic qubit flipping, and coherent state mapping between a single-photon superposition state and an atomic superposition state. We discuss the experimental feasibility of our proposal under current technology.
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.
Quantum superposition in mechanical systems is not only key evidence for macroscopic quantum coherence, but can also be utilized in modern quantum technology. Here we propose an efficient approach for creating macroscopically distinct mechanical superposition states in a two-mode optomechanical system. Photon hopping between the two cavity modes is modulated sinusoidally. The modulated photon tunneling enables an ultrastrong radiation-pressure force acting on the mechanical resonator, and hence significantly increases the mechanical displacement induced by a single photon. We study systematically the generation of the Yurke-Stoler-like states in the presence of system dissipations. We also discuss the experimental implementation of this scheme.
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.