This thesis concentrates on generating and measuring non-classical states of mechanical oscillators by coupling them to atomic and molecular quantum systems. We start with a discussion of what novel physics can be explored by mechanical systems operating in the quantum regime. We then discuss one technique making it a possibility- cavity optomechanics, particularly optomechanical cooling. We investigate the limits of optomechanical cooling and review how the coupling of mechanical oscillators to external heat baths limits the minimum attainable phonon occupation number. As a possible alternative for circumventing clamping losses, we consider an all-optical approach where the mechanical element (in this case, a Bragg mirror) is suspended via optical forces, and discuss some limitations of this approach. We explore several schemes aimed at the generation of quantum states in mechanical oscillators. We consider specifically two examples: one in which the mechanical oscillator is coupled to polar molecules via dipole-dipole interaction, and another where it is magnetically coupled to a Bose condensate. The first example emphasizes that such an interaction can generate parametric squeezing and entanglement. The second scheme demonstrates that the back action of BEC spin measurements can be used to generate quantum states of motion of a mechanical oscillator. We then discuss possible methods for measuring the entire density matrix of a mechanical oscillator. The first method achieves the tomographic reconstruction of the mechanical Wigner function by coupling it simultaneously to a classical optical oscillator and a qubit. The second approach involves a state transfer scheme between momentum excitations of a bose-condensate in a cavity and a moving mirror of the cavity that is entirely mediated by the light field. We conclude with a discussion of the broader implications of this work, and some future research directions.
This thesis concentrates on generating and measuring non-classical states of mechanical oscillators by coupling them to atomic and molecular quantum systems. We start with a discussion of what novel physics can be explored by mechanical systems operating in the quantum regime. We then discuss one technique making it a possibility- cavity optomechanics, particularly optomechanical cooling. We investigate the limits of optomechanical cooling and review how the coupling of mechanical oscillators to external heat baths limits the minimum attainable phonon occupation number. As a possible alternative for circumventing clamping losses, we consider an all-optical approach where the mechanical element (in this case, a Bragg mirror) is suspended via optical forces, and discuss some limitations of this approach. We explore several schemes aimed at the generation of quantum states in mechanical oscillators. We consider specifically two examples: one in which the mechanical oscillator is coupled to polar molecules via dipole-dipole interaction, and another where it is magnetically coupled to a Bose condensate. The first example emphasizes that such an interaction can generate parametric squeezing and entanglement. The second scheme demonstrates that the back action of BEC spin measurements can be used to generate quantum states of motion of a mechanical oscillator. We then discuss possible methods for measuring the entire density matrix of a mechanical oscillator. The first method achieves the tomographic reconstruction of the mechanical Wigner function by coupling it simultaneously to a classical optical oscillator and a qubit. The second approach involves a state transfer scheme between momentum excitations of a bose-condensate in a cavity and a moving mirror of the cavity that is entirely mediated by the light field. We conclude with a discussion of the broader implications of this work, and some future research directions.
Cavity optomechanics originated from the research of interferometric detection of gravitational waves, and later became a fast-growing area of techniques and approaches ranging from the fields of atomic, molecular, and optical physics to nano-science and condensed matter physics as well. Recently, it focused on the exploration of operating mechanical oscillators deep in the quantum regime, with an interest ranging from quantum-classical interface tests to high-precision quantum metrology. In this paper, recent theoretical work of our group in the field of quantum measurement with cavity optomechanical systems is reviewed. We explore the quantum measurement theory and its applications with several unconventional cavity optomechanical schemes working in the quantum regime. This review covers the basics of quantum noises in the cavity optomechanical setups and the resulting standard quantum limit of precision displacement and force measurement. Three novel quantum measurement proposals based on the hybrid optomechanical system are introduced. First, we describe a quantum back-action insulated weak force sensor. It is realized by forming a quantum-mechanics-free subsystem with two optomechanical oscillators of reversed effective mass. Then we introduce a role-reversed atomic optomechanical system which enables the preparation and the quantum tomography of a variety of non-classical states of atoms. In this system, the cavity field acts as a mechanical oscillator driven by the radiation pressure force from an ultracold atomic field. In the end, we recommend a multimode optomechanical transducer that can detect intensities significantly below the single-photon level via adiabatic transfer of the microwave signal to the optical frequency domain. These proposals demonstrate the possible applications of optomechanical devices in understanding of quantum-classical crossover and in achieving quantum measurement limit.
A multipartite quantum system is entangled when its state cannot be factorized into a product of states or a mixture of such products. Quantum information schemes that exploit this purely quantum mechanical feature have been devised initially for systems with two discrete quantum levels (i.e., qubits), and afterward, extended to continuous-variable (CV) systems characterized by observables with continuous spectra, such as the position and momentum of a particle, or the quadratures of an electromagnetic field. Optomechanical systems, such as a driven optical cavity with vibrating end-mirrors or a classical coherent field scattering sidebands off a freely suspended mirror, hold a promise of being candidates for CV quantum information processing applications. As in most other proposals, light is the information carrier; the difference lies in the choice of a micromirror as a quantum storage device. Desired quantum states can be encoded in acoustic modes. The optomechanical coupling, owing to which quantum state transfer between radiation and mirror is possible, is realized via the radiation pressure effect, which consists in momentum transfer between field and mirror during the scattering process. The use of the vibrational modes of a micromirror as a quantum state encoder system is somehow unexpected because this is a macroscopic ensemble of atoms expected to behave rather classically. However, there are proposals that show that, in principle, the vibrational occupation number of even such a large collection of atoms in a solid can be reduced close to zero, which signifies a clear transition from the classical to the quantum regime. Remarkable progress has been made to experimentally cool the resonator by a few orders of magnitude to quite low occupation numbers. However, in order to approach the quantum limit, one needs to integrate small, light, and flexible micromechanical elements into high-finesse cavities (which are typically much more rigid and massive), which is technically challenging. Furthermore, the mechanical quality factor has to be quite high, but present microfabrication techniques yield a mechanical quality factor scaling down for smaller and smaller microresonators. This chapter starts with developing a general framework for treating the dynamics of a driven optical cavity with a vibrating end-mirror system in which two cooling techniques have been recently demonstrated: (i) cold-damping quantum feedback, where the oscillator position is measured through a phase-sensitive detection of the cavity output and the resulting photocurrent is used for a real-time correction of the dynamics, and (ii) backaction or self-cooling, in which the off-resonant operation of the cavity results in a retarded back action on the mechanical system, and hence, in a “self”-modification of its dynamics. The two situations are illustrated in Fig. 24.1. Analytical results for the final phonon number are obtained for both schemes and their applicability within today's state-of-the-art laboratory setups is analyzed.
In this paper, we propose a new theoretical scheme for generating a macroscopic Schrödinger cat state of a mechanical oscillator in a hybrid optomechanical system where a beam of two-level atoms passes through the cavity. In the model under consideration, the cavity field couples to the macroscopic mirror through the optomechanical interaction while it couples to the atom through a generalized Jaynes–Cummings interaction that involves the cavity-mode structure. The motion of the mirror modifies the cavity-mode function and therefore modulates the atom-field interaction, leading to the three-mode atom-field-mirror coupling or, equivalently, polariton-mirror coupling in a dressed picture. This interaction induces a controllable anharmonicity in the energy spectrum of the mechanical oscillator, which provides the possibility of generating a superposition of two time-dependent coherent states of the mechanical oscillator just by performing a conditional measurement on the internal states of the atoms exiting the optomechanical cavity. We also investigate the tripartite atom-field-mirror entanglement, which is controllable by adjusting the parameters of the system. In addition, we explore the effects of the mechanical dissipation and thermal noise on the tripartite quantum correlation in the system as well as the generated mechanical superposition state.
Abstract We review the physics of hybrid optomechanical systems consisting of a mechanical oscillator interacting with both a radiation mode and an additional matterlike system. We concentrate on the cases embodied by either a single or a multi-atom system (a Bose-Einstein condensate, in particular) and discuss a wide range of physical effects, from passive mechanical cooling to the set-up of multipartite entanglement, from optomechanical nonlocality to the achievement of non-classical states of a single mechanical mode. The reviewed material showcases the viability of hybridised cavity optomechanical systems as basic building blocks for quantum communication networks and quantum state-engineering devices, possibly empowered by the use of quantum and optimal control techniques. The results that we discuss are instrumental to the promotion of hybrid optomechanical devices as promising experimental platforms for the study of nonclassicality at the genuine mesoscopic level.
Non-relativistic quantum mechanics have proven to be a significant framework to understand the non-classical behaviour of light and the microcosmos. Perhaps, one of the first technological revolutions within quantum theory came with the invention of the transistor, whereby a purely quantum mechanical description was required. Currently, another outstanding revolution is taking place in a crossroad where information science meets quantum mechanics (this being the quantum information field). Such an area of work contemplates both the fascinating theoretical aspect of quantum correlations, as well as implementations towards quantum tasks performed by a universal quantum computer; tasks that cannot be realised (or they are hard to implement) within the classical domain. This Thesis is devoted to study the dynamics of quantum entanglement in spin-optomechanics systems. In particular, we explore the quantum stabilization of quantum entanglement, a quantum concentration scheme in opto-mechanics and an interfacing of matter and light towards quantum networking applications. Additionally, we also investigate theoretical aspects of quantum correlations within thermal environments, as well as the topical area of quantum sudden transitions. In Chapter 1, we provide a brief summary of quantum information and of the quantum optics framework to cover elementary concepts and techniques used subsequently in this work. Subsequently, in Chapter 2 we present the stabilization of quantum entanglement in a non-linear qubit-oscillator system. The inclusion of a modest nonlinearity gives three results, i) the loss of periodicity of the system, ii) the occurrence of quadrature squeezing appearing for a short time, and iii) the quantum entanglement reaches higher values in contrast to the case without non-linearity. In Chapter 3, a technique to concentrate/distill a two-mode vacuum state in optomechanics via unsharp measurements is presented. Here, one of the optical modes is injected into a cavity at first, and thereafter, it is nonlinearly coupled to a mechanical oscillator. Afterwards, the position of the oscillator is measured using pulsed optomechanics and homodyne detection. The results show that this measurement can conditionally increase the initial entanglement. Next, in Chapter 4, stimulated by optomechanical transducers and quantum networking, a light-matter system is constructed where a qubit is coupled to a cavity mode mediated through a mechanical oscillator. The qubit-oscillator conditionally displaced Hamiltonian and the oscillator-cavity radiation-pressure interaction generate a maximal qubit-cavity entanglement. Additionally, we consider the case in which the cavity mode is coupled to a waveguide, numerical calculations show a promising qubit-fibre entanglement under a weak matter-light coupling. For the quantum network case, we coupled a generic qubit in the first node to a second qubit-cavity distant Jaynes-Cummings system coupled through an optical fibre, where qubit-qubit correlations can be achieved in the quantum open systems scenario. In Chapter 5, we study the evolution of an open quantum system within the Born-Markov microscopic master equation (MME). Essentially, two distant two-level atoms are trapped in fibre-coupled cavities. Under the approximation of one-excitation allowed in the atom-cavity-fibre basis, we can obtain quantum correlations induced by thermal fluctuations from the environments. Lastly, in Chapter 6, we bring together previously elements explored in this Thesis. The system is a hybrid atomic-mechanical system formed from two remote qubits interacting with individual harmonic oscillators. This system, as in Chapter 4, explores interesting applications in quantum networking schemes. The two qubits are initially prepared in a Bell-diagonal state, and consequently the two-qubit correlations exhibit few interesting effects such as freezing, sudden changes and revivals in the evolution of the quantum entropic discord. To conclude, I summarize my findings in Chapter 7.
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.