This thesis investigates three aspects of nonclassicality. The first aspect is macroscopic quantumness, a field which considers the properties of macroscopic superpositions. The various measures of macroscopicity are reviewed. An optomechanical system is described which enables us to study nonclassicality in macroscopic mechanical oscillators. We analyse the impact of different measurement settings on the macroscopicity of the mirror and the Wigner functions of the mechanical state. The same system is also considered under open system dynamics. The second nonclassical concept is the violation of macrorealism. It is shown that a two-level system can violate the Leggett-Garg inequality, thereby demonstrating that the assumptions of macrorealism do not hold. Similar dynamics are then replicated in a macroscopic mechanical system through the use of a hybrid optomechanical system in which an atom interacts with the mechanical oscillator through an optical mode. Mechanical damping is then factored into the dynamics to examine its effect on the violation of the Leggett-Garg inequality for different parameter ranges. The third is nonclassical correlations. Quantum discord and quantum entanglement are defined and several measures are explained. Entanglement distribution via separable states is introduced and then built on by adding imperfections to the operations in the protocol. It is found that the protocol is still successful in spite of the errors in the operations, both when they are unitary and non-unitary. We also develop a method of generating entanglement between two bosons through mediation with two spin systems. Through this system we demonstrate the creation of both entangled coherent states and NOON states.
This thesis investigates three aspects of nonclassicality. The first aspect is macroscopic quantumness, a field which considers the properties of macroscopic superpositions. The various measures of macroscopicity are reviewed. An optomechanical system is described which enables us to study nonclassicality in macroscopic mechanical oscillators. We analyse the impact of different measurement settings on the macroscopicity of the mirror and the Wigner functions of the mechanical state. The same system is also considered under open system dynamics. The second nonclassical concept is the violation of macrorealism. It is shown that a two-level system can violate the Leggett-Garg inequality, thereby demonstrating that the assumptions of macrorealism do not hold. Similar dynamics are then replicated in a macroscopic mechanical system through the use of a hybrid optomechanical system in which an atom interacts with the mechanical oscillator through an optical mode. Mechanical damping is then factored into the dynamics to examine its effect on the violation of the Leggett-Garg inequality for different parameter ranges. The third is nonclassical correlations. Quantum discord and quantum entanglement are defined and several measures are explained. Entanglement distribution via separable states is introduced and then built on by adding imperfections to the operations in the protocol. It is found that the protocol is still successful in spite of the errors in the operations, both when they are unitary and non-unitary. We also develop a method of generating entanglement between two bosons through mediation with two spin systems. Through this system we demonstrate the creation of both entangled coherent states and NOON states.
The extraordinary success of quantum mechanics and its formalism has been established thanks to countless experiments with microscopic systems. Nevertheless, it is still not clear whether and when the quantum world ends, allowing for the emergence of classical phenomena. The extension of quantum properties to macroscopic system gives rise to paradoxes, as the well-known Schrödinger’s cat example. Among the alternatives to quantum mechanics, collapse models propose an objective modification of standard quantum theory to restore macrorealism at large scale. They predict a loss of coherence when scaling towards macroscopic systems, due to a spontaneous collapse mechanism included into the dynamics through non-linear stochastic modifications of the Schrödinger equation. Assessing and characterizing these models is a noteworthy endeavour in the exploration of the quantum-to-classical transition. The overarching goal of this Thesis is to address some of these fundamental issues, by exploring the concept of macrorealism and probing collapse models, making use of optomechanical setups. To answer the question whether a system has a quantum or classical dynamics, we will propose a theoretical test of Leggett-Garg inequalities, as tool to probe the macrorealism of an optomechanical system. We will investigate collapse models through the study of the dynamics of an optomechanical cavity, looking for signatures in the noise spectrum. Further, we will use the hypothesis testing framework and quantum metrology tools to distinguish dynamical channels encoding the presence or the lack of the collapse. Our findings show a violation of Leggett-Garg inequalities, suggesting that the demarcation line of the quantum domain can be pushed further to include larger systems. Our approaches for testing collapse models provide novel methodologies to better discriminate these effects and the results represent another step forward in the attempt of gaining a better understanding of the foundations of physics.
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.
Abstract We discuss a scheme for macrorealistic theories of the Leggett–Garg form (Leggett and Garg 1985 Phys. Rev. Lett. 54 857). Our scheme is based on a hybrid optomechanical system. It seems reasonable to test these inequalities with an optomechanical system, since in an optomechanical cavity it is possible to create non-classical states of the mirror through a projective measurement on the cavity field. We will present the protocol to generate such non-classicality for a general optomechanical cavity and after we will carry out a theoretical test for one of the possible formulations of these inequalities using a hybrid optomechanical system. Specifically, the inequality will be investigated for an harmonic oscillator coupled to a two-level system, which replaces the light field of the cavity. The aim is to reproduce, with this system, the evolution of a single spin-1/2 for which the inequality is violated; this is achievable through the conditioning of the two-level system which will be used as an ancilla.
While quantum theory has been tested to an incredible degree on microscopic scales, quantum effects are seldom observed in our everyday macroscopic world. The curious results of applying quantum mechanics to macroscopic objects are perhaps best illustrated by Erwin Schrödinger's famous thought experiment, where a cat can be put into a superposition state of being both dead and alive. Obviously, these quantum predictions are in stark contradiction to our common experience. Even with plenty of theoretical explanations put forward to explain this discrepancy, a large number of questions about the frontier between the quantum and the classical world remain unanswered. To distinguish between classical and quantum behavior, two fundamental concepts inherent to classical physics have been established over the years: The world view of local realism limits the power of classical experiments to establish correlations over space, while the world view of macroscopic realism (or macrorealism) restricts temporal correlations. Necessary conditions for both world views have been formulated in the form of Bell and Leggett-Garg inequalities, and Bell inequalities have been shown to be violated by quantum mechanics through increasingly conclusive experiments. Furthermore, many challenging steps towards convincing violations of macrorealism have been taken in a number of recent experiments. In the first part of this thesis, conditions for macrorealism are analyzed in detail. Two necessary conditions for macrorealism, the original Leggett-Garg inequality and the recently proposed no-signaling in time condition, are presented. It is then shown that a combination of no-signaling in time conditions is not only necessary but also sufficient for the existence of a macrorealistic description. Finally, an operational formulation of no-signaling in time, in terms of positive-operator valued measurements and Hamiltonians, is derived. In the next part, we argue that these results lead to a suitable definition of classical behavior. In particular, we provide a formalism to judge the classicality of measurements and time evolutions. We then proceed to apply it to a number of exemplary measurement operators and Hamiltonians. Finally, we argue for the importance of spontaneously realized Hamiltonians in our intuition of classical behavior. Next, differences between local realism and macrorealism are analyzed. For this purpose, the probability polytopes for spatially and temporally separated experiments are compared, and a fundamental difference in the power of quantum mechanics to build both types of correlations is discovered. This result shows that Fine's theorem, which states that a set of Bell inequalities is necessary and sufficient for local realism, is not transferable to macrorealism. Thus, (Leggett-Garg) inequalities are in principle not well-suited for tests of macrorealism, as they can never form a necessary and sufficient condition, and unnecessarily restrict the violating parameter space. No-signaling in time is both better suited and more strongly motivated from the underlying physical theory. In the final part of this thesis, a concrete experimental setup for implementing quantum experiments with macroscopic objects is proposed. It consists of a superconducting micro-sphere in the Meißner state, which is levitated by magnetic fields. Through its expelled magnetic field, the sphere's center-of-mass motion couples to a superconducting quantum circuit. Properly tuned, ground state cooling can be realized, since the sphere's motion is extremely well isolated from the surrounding environment. This setup therefore is a promising candidate for the observation of quantum effects in macroscopic systems.
The descriptions of the quantum realm and the macroscopic classical world di�er signi
�cantly not only in their mathematical formulations, but also in their foundational concepts
and philosophical consequences. The assumptions of local realism, non-contextuality
and macroscopic realism (macro-realism) along with the quantum mechanical violations
of these assumptions are discussed.
A complete generalization is provided of Wigner's argument inferring quantum nonlocality,
originally restricted for the EPR-Bohm entangled state, based on assuming joint
probability distributions for all the relevant dichotomic observables. Such Generalized
Wigner Inequality (GWI) turns out to be the N-partite local realist inequality which is
violated by quantum mechanics for all pure entangled states for any N.
We then exploit the non-trivial manifestation of quantum non-locality via local contextuality
on three qubit system. Here, we propose an experimental scheme to realize this
feature by deriving a new local realist inequality. The way quantum entanglement can
be used for global contextual value assigning is discussed in a quantum pseudo-telepathy
game.
In the second part of this report, we formulate Leggett-Garg inequality (LGI) in terms
of joint probability and demonstrate its quantum mechanical violation for two state oscillation,
which is initial state dependent, unlike the case of standard LGI. It has been
shown that, the newly formulated LGI reveals robustness against unsharp measurement
for testing compatibility between macro-realism and quantum mechanics. Finally we
show that, the recently proposed No-signaling in time condition, contradicts with quantum
mechanical predictions for any degree of unsharpness in measurement.
According to the world view of macrorealism, the properties of a given system exist prior to and independent of measurement, which is incompatible with quantum mechanics. Leggett and Garg put forward a practical criterion capable of identifying violations of macrorealism, and so far experiments performed on microscopic and mesoscopic systems have always agreed with quantum mechanics. However, a macrorealist can always assign the cause of such violations to the perturbation that measurements effect on such small systems, and hence a definitive test would require using noninvasive measurements, preferably on macroscopic objects, where such measurements seem more plausible. However, the generation of truly macroscopic quantum superposition states capable of violating macrorealism remains a big challenge. In this work we propose a setup that makes use of measurements on the polarization of light, a property that has been extensively manipulated both in classical and quantum contexts, hence establishing the perfect link between the microscopic and macroscopic worlds. In particular, we use Leggett-Garg inequalities and the criterion of no signaling in time to study the macrorealistic character of light polarization for different kinds of measurements, in particular with different degrees of coarse graining. Our proposal is noninvasive for coherent input states by construction. We show for states with well-defined photon number in two orthogonal polarization modes, that there always exists a way of making the measurement sufficiently coarse grained so that a violation of macrorealism becomes arbitrarily small, while sufficiently sharp measurements can always lead to a significant violation.