The evolution of a two-level system subjected to stimulated transitions which is undergoing a sequence of measurements of the level occupation probability is evaluated. Its time correlation function is compared to the one obtained through the pure Schroedinger evolution. Systems of this kind have been recently proposed for testing the quantum mechanical predictions against those of macrorealistic theories, by means of temporal Bell inequalities. The classical requirement of noninvasivity, needed to define correlation functions in the realistic case, finds a quantum counterpart in the quantum nondemolition condition. The consequences on the observability of quantum mechanically predicted violations to temporal Bell inequalities are drawn and compared to the already dealt case of the rf-SQUID dynamics.
The evolution of a two-level system subjected to stimulated transitions which is undergoing a sequence of measurements of the level occupation probability is evaluated. Its time correlation function is compared to the one obtained through the pure Schroedinger evolution. Systems of this kind have been recently proposed for testing the quantum mechanical predictions against those of macrorealistic theories, by means of temporal Bell inequalities. The classical requirement of noninvasivity, needed to define correlation functions in the realistic case, finds a quantum counterpart in the quantum nondemolition condition. The consequences on the observability of quantum mechanically predicted violations to temporal Bell inequalities are drawn and compared to the already dealt case of the rf-SQUID dynamics.
Some temporal Bell inequalities are deduced under the assumption of realism and perfect correlation. No locality condition is needed. When the system is macroscopic, the perfect correlation assumption substitutes the noninvasive measurability hypothesis advanteousgely. The new inequalities are violated quantically. This violation is clearly more severe than the similar violation in the case of ordinary Bell inequalities. Some microscopic and macroscopic situations in which these inequalities could be tested are considered.
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.
Temporal Bell inequalities can be violated for sequences of events (histories) for which probabilities satisfying consistent sum rules cannot be defined. We discuss possible experiments in which such violations, never observed so far, may indeed be seen. The basic scheme, which uses three optically driven and mutually interacting two-level systems, could be implemented in a variety of nanostructures. It could even be mapped onto the dynamics of a single electron four-level system thus allowing for a realization in atomic physics.
"According to the quantum superposition principle, quantum mechanics at the macroscopic scale predicts that a macroscopic system can be in more than one distinct state at the same time. Such an extrapolation of quantum mechanics contradicts our everyday instinct, summarized by Leggett and Garg (LG) under the heading of macrorealism (MR) [1]. To resolve the conflict and to determine whether MR or quantum mechanics is the right description of macroscopic objects, in 1985, Leggett and Garg [1] proposed the temporal Bell's inequality (TBI). If a macorealist description is possible, the inequality is satisfied - quantum mechanics, on the other hand, predicts a violation. Thereafter, people were motivated to engineer macroscopic quantum systems and to test the TBI. In the TBI, one of the most critical postulates is that of the noninvasive measurability (NIM) : it is in principle possible to determine which state the system is in with an arbitrarily small e ect on the subsequent system dynamics. To satisfy the NIM postulate in the TBI experiment, the implementation of the ""ideal negative result"" (INR) measurement was also proposed by LG [1]. In a two-state system, an INR measurement is designed to interact (in each run) with only one of two system states. Only runs where the measurement reported no outcome are kept. Although in the last few years there have been tests of the TBI on microscopic systems with the use of INR measurements [4] and on macroscopic systems using weak measurement [5], no one has ever implemented INR measurements on macroscopic systems in TBI tests so far. In addition, the NIM postulate was simply assumed, and not veri ed by an ancillary test [9, 3]. With these considerations in mind, there are two main tasks in this thesis: the rst one is to analyze the realization of an INR measurement on a macroscopic object. I propose an experiment based on coupling a flux-qubit to a dcSQUID, which mirrors the approach of Knee et al. [4], where the system of interest is coupled to another quantum system which acts as a measuring device. In order to accomplish the first task, we analyze the escape dynamics of a flux-qubit SQUID composite system in various limits and discuss the prospects of operating in a regime realizing a von Neumann (""projective"")-like measurement onto the qubit flux basis. Later in the thesis, I discuss current feasibility of the proposed experiment based on the possible measurement error (the ""venality"" [4]) of our INR measurement. The second task is to analyze experimental tests of measurement invasiveness. I propose a concrete protocol, ancillary to the main TBI experiment, which may narrow some loopholes in the test of MR [3]. I generalize the approach of Wilde and Mizel [3], using the behavior of the two-time correlator of a system as an indicator of measurement invasiveness. The measured invasivities can be used to give a improved lower bound for the TBI."
Some new temporal Bell inequalities are deduced under joint realism assumption, using some perfect correlation property. No locality condition is needed. When the measured system is a macroscopic system, joint realism assumption substitutes the non-invasive measurabilioty hypothesis advantegeously, provided that the system satisfies the perfect correlation property. The new inequalities are violated quantically. This violation can be more severe than the similar violation in the case of precedent temporal Bell inequalities. Some microscopic and mesoscopic situations in which these inequalities could be tested are roughly considered.
Following the strategy of showing specific quantum effects by means of the violation of a classical inequality, a pair of Bell-type inequalities is derived on the basis of certain additional assumptions, whose plausibility is discussed in detail. Such inequalities are violated by the quantum mechanical predictions for the interaction of a two-level Rydberg atom with a single mode sustained by a high-Q resonator. The experimental conditions required in order to show the existence of forbidden values, according to a hidden variables formalism, in a real experiment are analyzed for various initial field statistics. In particular, the revival dynamics expected for the interaction with a coherent field leads to classically forbidden values, which would indicate a purely quantum effect. \textcopyright{} 1996 The American Physical Society.