The ability to coherently control mechanical systems with optical fields has made great strides over the past decade, and now includes the use of photon counting techniques to detect the nonclassical nature of mechanical states. These techniques may soon be used to perform an optomechanical Bell test, hence highlighting the potential of cavity optomechanics for device-independent quantum information processing. Here, we propose a witness which reveals optomechanical entanglement without any constraint on the global detection efficiencies in a setup allowing one to test a Bell inequality. While our witness relies on a well-defined description and correct experimental calibration of the measurements, it does not need a detailed knowledge of the functioning of the optomechanical system. A feasibility study including dominant sources of noise and loss shows that it can readily be used to reveal optomechanical entanglement in present-day experiments with photonic crystal nanobeam resonators.
The ability to coherently control mechanical systems with optical fields has made great strides over the past decade, and now includes the use of photon counting techniques to detect the nonclassical nature of mechanical states. These techniques may soon be used to perform an optomechanical Bell test, hence highlighting the potential of cavity optomechanics for device-independent quantum information processing. Here, we propose a witness which reveals optomechanical entanglement without any constraint on the global detection efficiencies in a setup allowing one to test a Bell inequality. While our witness relies on a well-defined description and correct experimental calibration of the measurements, it does not need a detailed knowledge of the functioning of the optomechanical system. A feasibility study including dominant sources of noise and loss shows that it can readily be used to reveal optomechanical entanglement in present-day experiments with photonic crystal nanobeam resonators.
In the past two decades, the union of quantum mechanics and information science has led to significant progress in our understanding of the quantum world and in our ability to coherently control individual quantum systems. New technologies have appeared, and some of them, such as quantum key distribution (QKD), are now commercially available. We are now envisioning quantum networks that could allow us to communicate over intercontinental scales, as the internet does, but with a provable security. An open question in this framework is how to certify that a given quantum network performs well, i.e. how to detect entanglement between 2, 5, 10 or 100 nodes located far away from each other. Bell tests are appealing for such a task as they allow one to certify the presence of entanglement deviceindependently, i.e. without assumptions on the Hilbert space dimension or on the proper alignment of the measurement devices. In the first chapter, I start by examining in depth the most standard approach to perform a Bell test in which a source based on spontaneous parametric down conversion (SPDC) is used to create photon pairs entangled in polarization. I show, in particular, that in this case the Bell inequality violation is fundamentally limited by vacuum and multi-photon emissions. In the second part of this thesis, I show how to overcome this limitation by using the SPDC source to create single photon entanglement, i.e. entanglement between two paths sharing a single photon, or two-mode squeezed states. Here, the non local content of the states is revealed using photon counting techniques preceded by small displacements in phase space. In the third part, I show how these measurements can be used for an optomechanical Bell test. This opens the way for device-independent quantum information processing with optomechanical systems and might be relevant to test collapse models in a theory independent manner. In the fourth chapter, the same measurements are used to build up a witness that can reveal genuine path entanglement. This witness has triggered an experiment which highlights its potential for network certification. I conclude the thesis by showing how path entanglement can be revealed with the human eye by exploiting these displacement operations.
Over the past few decades, experimental tests of Bell-type inequalities have been at the forefront of understanding quantum mechanics and its implications. These strong bounds on specific measurements on a physical system originate from some of the most fundamental concepts of classical physics-in particular that properties of an object are well-defined independent of measurements (realism) and only affected by local interactions (locality). The violation of these bounds unambiguously shows that the measured system does not behave classically, void of any assumption on the validity of quantum theory. It has also found applications in quantum technologies for certifying the suitability of devices for generating quantum randomness, distributing secret keys and for quantum computing. Here we report on the violation of a Bell inequality involving a massive, macroscopic mechanical system. We create light-matter entanglement between the vibrational motion of two silicon optomechanical oscillators, each comprising approx. 10^{10} atoms, and two optical modes. This state allows us to violate a Bell inequality by more than 4 standard deviations, directly confirming the nonclassical behavior of our optomechanical system under the fair sampling assumption.
The outstanding progress in nanostructure fabrication and cooling technologies allows what was unthinkable a few decades ago: bringing single-mode mechanical vibrations to the quantum regime. The coupling between photon and phonon excitations is a natural source of nonclassical states of light and mechanical vibrations, and its study within the field of cavity optomechanics is developing lightning fast. Photonic crystal cavities are highly integrable architectures that have demonstrated the strongest optomechanical coupling to date and should therefore play a central role for such hybrid quantum-state engineering. In this context, we propose a realistic heralding protocol for the on-chip preparation of remotely entangled mechanical states, relying on the state-of-the-art optomechanical parameters of a silicon-based nanobeam structure. Pulsed sideband excitation of a Stokes process, combined with single-photon detection, allows the writing of a delocalized mechanical Bell state in the system, signatures of which can then be read out in the optical field. A measure of entanglement in this protocol is provided by the visibility of a characteristic quantum interference pattern in the emitted light.
Quantum optomechanics uses optical means to generate and manipulate quantum states of motion of mechanical resonators. This provides an intriguing platform for the study of fundamental physics and the development of novel quantum devices. Yet, the challenge of reconstructing and verifying the quantum state of mechanical systems has remained a major roadblock in the field. Here, we present a novel approach that allows for tomographic reconstruction of the quantum state of a mechanical system without the need for extremely high quality optical cavities. We show that, without relying on the usual state transfer presumption between light an mechanics, the full optomechanical Hamiltonian can be exploited to imprint mechanical tomograms on a strong optical coherent pulse, which can then be read out using well-established techniques. Furthermore, with only a small number of measurements, our method can be used to witness nonclassical features of mechanical systems without requiring full tomography. By relaxing the experimental requirements, our technique thus opens a feasible route towards verifying the quantum state of mechanical resonators and their nonclassical behaviour in a wide range of optomechanical systems.
Photons of a laser beam driving the upper motional sideband of an optomechanical cavity can decay into photon-phonon pairs by means of an optomechanical parametric process. The phononic state can subsequently be mapped to a photonic state by exciting the lower sideband, hence creating photon-photon pairs out of an optomechanical system. Here we show that these pairs can violate a Bell inequality when they are measured with photon counting techniques preceded by small displacement operations in phase space. The consequence of such a violation as well as the experimental requirements are intensively discussed.
Quantum entanglement, has been acknowledged as a precious resource due to its inherent nonclassical correlations between subsystems. These quantum correlations have the potential for many quantum processes, including canonical ones: quantum cryptography, quantum teleportation, and dense coding. To exploit the advantages of quantum entanglement, two essential premises are required, i.e., to prepare high-quality entanglement and characterize quality level of prepared entanglement. Thus far, quantum entanglement can be produced in various quantum systems; however, it appears that this new resource is complex and difficult to characterize. The standard methods to characterize multipartite entanglement, e.g., entanglement witness, state tomography, or quantum state verification, require full knowledge of the Hilbert space dimension and precise calibration of measurement devices, which are usually difficult to acquire in experiment. The most radical way to overcome these problems is to detect entanglement solely based on the Bell-like correlations of measurement outcomes collected in the experiment, namely, device-independent characterization of entanglement. This article reviews the recently developed device-independent methods to characterize entanglement, including self-testing and device-independent certification of entanglement. These approaches can be widely applied in kinds of quantum information processing, especially for those with security demands.