Abstract We address the macroscopic quantumness of the state of mechanical systems subjected to conditional protocols devised for state engineering in cavity optomechanics. We use a measure of macroscopicity based on phase-space methods. We cover the transition regime into strong single-photon coupling, illustrating how measurements performed over the cavity field that drives the dynamics of a mechanical system are able to steer the latter toward large quantum coherent states. The effect of losses is evaluated for the case of an open cavity and analyzed in terms of the features of the Wigner functions of the state of the mechanical system. We also address the case of engineered phonon-subtracted mechanical systems, in full open-system configuration, demonstrating the existence of optimal working points for the sake of mesoscopic quantumness. Our study is relevant for and applicable to a broad range of settings, from clamped to levitated mechanical systems.
Abstract We address the macroscopic quantumness of the state of mechanical systems subjected to conditional protocols devised for state engineering in cavity optomechanics. We use a measure of macroscopicity based on phase-space methods. We cover the transition regime into strong single-photon coupling, illustrating how measurements performed over the cavity field that drives the dynamics of a mechanical system are able to steer the latter toward large quantum coherent states. The effect of losses is evaluated for the case of an open cavity and analyzed in terms of the features of the Wigner functions of the state of the mechanical system. We also address the case of engineered phonon-subtracted mechanical systems, in full open-system configuration, demonstrating the existence of optimal working points for the sake of mesoscopic quantumness. Our study is relevant for and applicable to a broad range of settings, from clamped to levitated mechanical systems.
Optomechanics is currently believed to provide a promising route towards the achievement of genuine quantum effects at the large, massive-system scale. By using a recently proposed figure of merit that is well suited to address continuous-variable systems, in this paper we analyze the requirements needed for the state of a mechanical mode (embodied by an end-cavity cantilever or a membrane placed within an optical cavity) to be qualified as macroscopic. We show that according to the phase-space-based criterion that we have chosen for our quantitative analysis, the state achieved through strong single-photon radiation-pressure coupling to a quantized field of light and conditioned by measurements operated on the latter might be interpreted as macroscopically quantum. In general, though, genuine macroscopic quantum superpositions appear to be possible only under quite demanding experimental conditions.
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.
Quantum opto-mechanics is a fast moving, broad research field which aims to investigate and control the interaction of light and the quantized motion of mechanical objects and the coupling between them. This allows one to engineer the mechanical quantum state by controlling and measuring the electromagnetic field, and conversely, to control the dynamical evolution of the optical field via its interaction with a mechanical system. Mechanical resonators are accessible in many different shapes and sizes, from kilogram scales in experiments that test gravitational theories to micro- and nano-scales in resolved sideband regime, where the frequency of the mechanical resonator is larger than the bandwidth of the optical cavity. In this regime, it is possible to cool the mechanical object to the ground state which allows a high degree of control and the ability to prepare interesting non-classical states, states that could aid in investigating the quantum dynamics of macroscopic objects. The field of quantum opto-mechanics is a promising testbed for quantum control technologies, such as fundamental tests of quantum mechanics, ultra-sensitive quantum sensors for precise measurements, phonon lasing, mechanical memories with long lifetime and quantum information processing. Furthermore, experiments are progressing toward strong opto-mechanical coupling regimes with single photons. This creates a platform that can take advantage of the nonlinear optical interactions to generate highly non-classical states in such light-matter interfaces. Photonic systems working in the single photon regime will be promising for low power applications and also for implementations of quantum information and computation. Motivated by these applications, this thesis consists of theoretical studies in the context of single photonics. This includes investigating non-classical mechanical state generation and mechanically controlling the dynamical evolution of optical fields in the strong coupling regime single photon opto-mechanics and furthermore, proposing a quantum sensor using single photonics. In this regard, we employ three important formalisms to treat and measure open quantum systems with non-Gaussian input fields: the conditional and unconditional cascaded master equations, Fock-state master equations and input-output Langevin equations. In the context of opto-mechanics, the system to be investigated is composed of two optical cavities with a coupling modulated via a mechanical resonator. In one case, a sequence of single photons are irreversibly sent to one of the optical cavities. After photons go through the opto-mechanical interaction, photon counting measurements are performed on the cavity output, conditionally steering the mechanical state to a highly non-classical Fock state. Numerical calculations are performed to predict the experimental parameters needed to generate a mechanical Fock state before the mechanical object is thermalized. In another case, the same opto-mechanical scheme is employed to conversely modify the state of the optical mode by engineering the state of the mechanical degree of freedom. In this case, it is shown that the opto-mechanical system operates as an effective beam splitter for the input single photons, with a transmission that can be controlled by tuning the number of excitations in the bulk mechanical resonator. When the mechanical resonator has a small coherent amplitude it acts as a quantum control, entangling the optical and mechanical degrees of freedom. As the coherent amplitude of the resonator increases, it acts as a classical control for the input photons. Finally, we propose a novel multi-purpose sensor architecture that can be used for force, refractive index and possibly local temperature detection. In this scheme, two coupled cavities behave as an effective beam splitter. This sensor is based on fourth order interference (the Hong-Ou-Mandel effect) and requires a sequence of single photon pulses and consequently has low pulse power. Changes in the parameter to be measured induce variations in the effective beam splitter reflectivity and result in changes to the visibility of interference. We propose that this generic scheme could be implemented with coupled L3 photonic crystal cavities and find that this system, which only relies on photon coincidence detection and does not need any spectral resolution, can estimate forces as small as 10-7 Newtons and can measure one part per million change in refractive index using a very low input power of 10-10 W.
We prepare single phonon Fock state of mechanical mode in optomechanical system based on photon subtraction process in the linear regime of optomechanical interaction. The correlation set between cavity and field modes is utilized to recast the state of a pre-cooled mechanical mode into a single phonon Fock state as the field mode is subjected to a photon subtraction type measurement at a dynamical instant of interaction time. The resultant conditional state of mechanical mode quantified by its Wigner function, exhibits an excellent compatibility with the standard single quantum Fock state. We confirm the nature of obtained state by calculating the phonon statistics, and conditional fidelity which approaches to unity for an instantaneous measurement time within an appropriate choice of parametric regime. Moreover, we also study the effects of temperature parameter for the preparation of target state. The present scheme can be realized to engineer the single quantum Fock state of macroscopic mechanical mode with currently available technology.
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.
Optomechanics is currently believed to provide a promising route towards the achievement of genuine quantum effects at the large, massive-system scale. By using a recently proposed figure of merit that is well suited to address continuous-variable systems, in this paper we question such expectation. We quantify the degree of macroscopicity of the state of a vibrating mechanical mode (embodied by an end-cavity cantilever or a membrane placed within an optical cavity) achieved through its radiation-pressure coupling to a quantized field of light. By showing that quite demanding conditions should be met in order to be able to claim for genuine macroscopic quantum superpositions, our investigation poses substantial doubts on the suitability of current experimental configurations in optomechanics.