My Ph.D dissertation is on the fundamental effects in optomechanical systems (OMS) and their important applications. The OMS are based on the possibility of the mechanical motion produced by few photons incident on the mechanical device. This dissertation presents several applications of the OMS in the area of storage of light in long-lived phonons, single mode optomechanical Ramsey interferometry, and generation of large amount of squeezing in the output radiation. The long-lived phonons can be monitored and controlled via optical means as was experimentally demonstrated. To show this, I develop the theory of transient electromagnetically induced transparency (EIT). For further applications like state transfer, especially over very different frequency regimes, I consider double-cavity OMS, where the two cavities can correspond to different spectral domains, yet the state transfer is possible via phonons. The state transfer is based on a new effect, electromagnetically induced absorption (EIA), where one uses a second control field from the other cavity to produce an absorption peak inside the EIT window. All these involve the interference of various path ways via which a final state is reached. The following chapter shows how Fano-like interference can arise in OMS. A Fano asymmetry parameter for OMS was defined.
My Ph.D dissertation is on the fundamental effects in optomechanical systems (OMS) and their important applications. The OMS are based on the possibility of the mechanical motion produced by few photons incident on the mechanical device. This dissertation presents several applications of the OMS in the area of storage of light in long-lived phonons, single mode optomechanical Ramsey interferometry, and generation of large amount of squeezing in the output radiation. The long-lived phonons can be monitored and controlled via optical means as was experimentally demonstrated. To show this, I develop the theory of transient electromagnetically induced transparency (EIT). For further applications like state transfer, especially over very different frequency regimes, I consider double-cavity OMS, where the two cavities can correspond to different spectral domains, yet the state transfer is possible via phonons. The state transfer is based on a new effect, electromagnetically induced absorption (EIA), where one uses a second control field from the other cavity to produce an absorption peak inside the EIT window. All these involve the interference of various path ways via which a final state is reached. The following chapter shows how Fano-like interference can arise in OMS. A Fano asymmetry parameter for OMS was defined.
Cavity-optomechanics, a tool to manipulate mechanical effects of light to couple optical field with other physical objects, is the subject of increasing investigations, especially with regards to electromagnetically induced transparency (EIT). EIT, a result of Fano interference among different atomic transition levels, has acquired a significant importance in many areas of physics, such as atomic physics and quantum optics. However, controllability of such multi-dimensional systems has remained a crucial issue. In this report, we investigate the controllability of EIT and Fano resonances in hybrid optomechanical system composed of cigar-shaped Bose-Einstein condensate (BEC), trapped inside high-finesse Fabry-Pérot cavity with one vibrational mirror, driven by a single mode optical field and a transverse pump field. The transverse field is used to control the phenomenon of EIT. It is detected that the strength of transverse field is not only efficiently amplifying or attenuating out-going optical mode but also providing an opportunity to enhance the strength of Fano-interactions which leads to the amplification of EIT-window. To observe these phenomena in laboratory, we suggest a certain set of experimental parameters. The results provide a route for tunable manipulation of optical phenomena, like EIT, which could be a significant step in quantum engineering.
In this thesis we have focused on the study of various systems which are presently widely studied in different areas of quantum optics and quantum information sciences. These, for example, include the coupled system of photonic waveguides which are known to be highly efficient in manipulating the flow of light. The Hamiltonian describing the evolution of field mode in coupled waveguides is effectively identical to the well-known tight binding Hamiltonian used in solid state physics. The advantage of waveguide system is the possibility to control various interactions by design and their low decoherence rate. The excellent stability offered by coupled waveguides has led to the observation of many key coherent effects such as quantum walk, Bloch oscillation, and discrete Talbot effect. For example, Bloch oscillations have been investigated in coupled waveguides using coherent beam of light. We wanted to inquire whether coherent phenomena such as Bloch oscillations can be possible with incoherent single photon sources. We discovered that Bloch oscillations are indeed possible with single photons provided we prepare single photons in a W state. Moreover, coupled waveguides also find applications in the field of quantum information processing. Since entanglement plays a prominent role in all these applications, it is important to understand the entanglement dynamics in these structures. We considered the case of squeezed input in one of the waveguide and showed that one can generate entanglement between the waveguide modes. We further continued our work on the entanglement generation in coupled waveguides by incorporating the effect of loss in the waveguide structure for the squeezed and photon number input states. We considered relevant experimental parameters and showed that waveguide structures are reasonably robust against the effect of loss. Another system which has attracted a great deal of interest is the optomechanical system. We consider an optomechanical system where an optical cavity mode is coupled to the square of the position of a mechanical oscillator. The optomechanical system can then be regarded as a quantum optical spring, i.e., a spring whose spring constant depends on the quantum state of another system. In particular, we consider the situation where the field inside the cavity is in a coherent state and the oscillator is prepared in its ground state. The quantized nature of the field produces new features in the optomechanical system.
Controlling the interaction between localized optical and mechanical excitations is now possible following advances in micro- and nano-fabrication techniques. To date, most experimental studies of optomechanics have focused on measurement and control of the mechanical subsystem through its interaction with optics, and have led to the experimental demonstration of dynamical back-action cooling and optical rigidity of the mechanical system. However, the optical response of these systems is also modified in the presence of mechanical interactions, leading to effects such as Electromagnetically Induced Transparency (EIT) and parametric normal-mode splitting, and thus a platform for strongly nonlinear optics. In this talk we propose and demonstrate the use of the optomechanical nonlinearity as a new way of controlling the velocity of light via engineered photon-phonon interactions. Our results demonstrate EIT and tunable optical delays on a nanoscale optomechanical crystal device, fabricated by simply etching holes into a thin film of Silicon. At low temperature (8.7 K), we show an optically-tunable delay of 50 ns with near-unity optical transparency, and superluminal light with a 1.4 μs signal advance. These results, while indicating significant progress towards an integrated quantum optomechanical memory, are also relevant to classical signal processing applications.
Recently Qu and Agarwal [Phys. Rev. A 22, 031802 (2013)] found a three-pathway electromagnetically induced absorption (TEIA) phenomenon within a mechanically coupled two-cavity system, where there exist a sharp EIA dip in the broad electromagnetically induced transparency peak in the transmission spectrum. In this work, we study the response of a probe light in a pair of directly coupled microcavities with one mechanical mode. We find that in addition to the sharp TEIA dip within a broad EIT window as found by Qu and Agarwal, three-pathway electromagnetically induced transparency (TEIT) within the broad EIT window could also exist under certain conditions. We give explicit physical explanations and detailed calculations. Our results provide a method for controlling transition between TEIA and TEIT in coupled optomechanical systems, and reveal the multiple pathways interference is versatile for controlling light.
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.
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.