We analyze a modified version of the Coleman-Hepp model, that is able to take into account energy-exchange processes between the incoming particle and the linear array made up of $N$ spin-1/2 systems. We bring to light the presence of a Wiener dissipative process in the weak-coupling, macroscopic ($N \rightarrow \infty$) limit. In such a limit and in a restricted portion of the total Hilbert space, the particle undergoes a sort of Brownian motion, while the free Hamiltonian of the spin array serves as a Wiener process. No assumptions are made on the spectrum of the Hamiltonian of the spin system, and no partial trace is computed over its states. The mechanism of appearance of the stochastic process is discussed and contrasted to other noteworthy examples in the literature. The links with van Hove's ``$λ^2 T$ limits are emphasized.
We investigate the influence of environmental noise on polarization entangled light generated by parametric emission in a cavity. By adopting a recently developed separability criterion, we show that: i) self-stimulation may suppress the detrimental influence of noise on entanglement; ii) when self-stimulation becomes effective, a classical model of parametric emission incorporating noise provides the same results of quantum theory for the expectation values involved in the separability criterion. Moreover we show that, in the macroscopic limit, it is impossible to observe violations of local …
Macroscopic systems are described most completely by local densities (particle number, momentum and energy) yet the superposition states of such physical variables, indicated by the Everett interpretation, are not observed. In order to explain this, it is argued that histories of local number, momentum and energy density are approximately decoherent when coarse-grained over sufficiently large volumes. Decoherence arises directly from the proximity of these variables to exactly conserved quantities (which are exactly decoherent), and not from environmentally-induced decoherence. We discuss the …
Quantum electrodynamics under conditions of distinguishability of interacting matter entities, and of controlled actions and back-actions between them, is considered. Such "mesoscopic quantum electrodynamics" is shown to share its dynamical structure with the classical stochastic electrodynamics. In formal terms, we demonstrate that all general relations of the mesoscopic quantum electrodynamics may be recast in a form lacking Planck's constant. Mesoscopic quantum electrodynamics is therefore subject to "doing quantum electrodynamics while thinking classically," allowing one to substitute esse…
We consider the claim that decoherence explains the emergence of classicality in quantum systems, and conclude that it does not. We show that, given a randomly chosen universe composed of a variety of subsystems, some of which are macroscopic and subject to decoherence-inducing interactions, and some of which are microscopic, the macroscopic subsystems will not display any distinctively classical behavior. Therefore, a universe in which macroscopic and microscopic do display distinct behavior must be in a very special, highly nongeneric quantum state.
The main argument by proponents of Many-World interpretations of quantum mechanics is that as more and more previously disentangled degrees of freedom become entangled with the microscopic degree we measure, there is no way of telling when the measurement (in the sense of a collapse of the wave function) should occur. Here, we introduce the concept of quantum interlinking, and argue that all macroscopic objects in the universe are connected through links of mutual entanglement while the objects themselves are (for the most part) not entangled. The measurement occurs when the degree we measure …
Classical physics is approached from quantum mechanics in the macroscopic limit. The technical device to achieve this goal is the quantum version of the central limit theorem, derived for an observable at a given time and for the time-dependent expectation value of the coordinate. The emergence of the classical trajectory can be followed for the average of an observable over a large set of independent microscopical systems, and the deterministic classical laws can be recovered in all practical purposes, owing to the largeness of Avogadro's number. This result refers to the observed system with…
Emergence of a Macroscopic Cat State and Multi-Channel Entanglement in a Frustrated Cluster Spin Chain
Universidad de Valencia-CSIC（瓦伦西亚大学-西班牙科学技术委员会）；Universitat Politècnica de València（瓦伦西亚理工大学）；Universidad CEU Cardenal Herrera（CEU卡迪纳尔埃雷拉大学）；IUMPA - Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València（瓦伦西亚理工大学纯数学与应用数学研究所）；Queensland Quantum and Advanced Technologies Research Institute, Griffith University（格里菲斯大学昆士兰量子与先进技术研究院）；VTT Technical Research Centre of Finland（芬兰技术研究中心）
We study the process of observation (measurement), within the framework of a `perspectival' (`relational', `relative state') version of the modal interpretation of quantum mechanics. We show that if we assume certain features of discreteness and determinism in the operation of the measuring device (which could be a part of the observer's nerve system), this gives rise to classical characteristics of the observed properties, in the first place to spatial localization. We investigate to what extent semi-classical behavior of the object system itself (as opposed to the observational system) is ne…
Long-baseline laser-interferometer gravitational-wave detectors are operating at a factor of 10 (in amplitude) above the standard quantum limit (SQL) within a broad frequency band. Such a low classical noise budget has already allowed the creation of a controlled 2.7 kg macroscopic oscillator with an effective eigenfrequency of 150 Hz and an occupation number of 200. This result, along with the prospect for further improvements, heralds the new possibility of experimentally probing macroscopic quantum mechanics (MQM) - quantum mechanical behavior of objects in the realm of everyday experience …
As a universal theory of physics, quantum mechanics must assign states to every level of description of a system -- from a full microscopic description, all the way up to an effective macroscopic characterization -- and also to describe the interconnections among them. Assuming that we only have a coarse-grained access to a physical system, here we show how to assign to it a microscopic description that abides by all macroscopic constraints. In order to do that, we employ general coarse-graining maps, allowing our approach to be used even when the split between system and environment is not ob…
A key feature of non-equilibrium thermodynamics is the Markovian, deterministic relaxation of coarse observables such as, for example, the temperature difference between two macroscopic objects which evolves independently of almost all details of the initial state. We demonstrate that the unitary dynamics for moderately sized spin-1/2 systems may yield the same type of relaxation dynamics for a given magnetization difference. This observation might contribute to the understanding of the emergence of thermodynamics within closed quantum systems.
In this article I aim to provide an intuitive and non-technical introduction to decoherence and quantum Darwinism. Together these theories explain how our classical reality emerges from an underlying quantum mechanical description. Here I focus on two aspects of this and explain, firstly, how decoherence can tell us why we never see macroscopic superpositions, such as dead-and-alive cats, in our classical surroundings; and secondly I describe and then provide a resolution to the so-called preferred basis problem. I then introduce recent results demonstrating that certain aspects of classicalit…
Ever since the advent of quantum mechanics, it has been clear that the atoms composing matter do not obey Newton's laws. Instead, their behavior is described by the Schroedinger equation. Surprisingly though, until recently, no clear explanation was given for why everyday objects, which are merely collections of atoms, are observed to obey Newton's laws. It would seem that, if quantum mechanics explains all the properties of atoms accurately, they, too, should obey quantum mechanics. This reasoning led some scientists to believe in a distinct macroscopic, or ``big and complicated,'' world in w…
It has been claimed that decoherence of open quantum systems explains the tendency of macroscopic systems to exhibit quasiclassical behavior. We show that quasiclassicality is in fact an unremarkable property, characterizing generic subsystems of environments even in the absence of dynamical decoherence. It is suggested that decoherence is best regarded as explaining the persistence of true classicality, rather than the emergence, rather than the emergence of quasiclassicality.
We propose a mechanism where high entanglement between very distant boundary spins is generated by suddenly connecting two long Kondo spin chains. We show that this procedure provides an efficient way to route entanglement between multiple distant sites. We observe that the key features of the entanglement dynamics of the composite spin chain are remarkably well described using a simple model of two singlets, each formed by two spins. The proposed entanglement routing mechanism is a footprint of the emergence of a Kondo cloud in a Kondo system and can be engineered and observed in varied physi…
We study the emergence of macrorealism in a harmonic oscillator subject to consecutive measurements of a squeezed action. Since the harmonic oscillator dynamics admits a hidden trajectory formulation, the assumptions of macrorealism are violated only by the measurement process. We demonstrate a breakdown of macrorealism in a wide parameter range that is maximized in a scaling limit of extreme squeezing. A semiclassical analysis shows that macrorealism is violated even with measurements of classically smooth observables that do not resolve quantum levels. We propose an experimental test of macr…
Models for deterministic quantum mechanics of Cartan-Randers type are introduced, together with the fundamental notions of the concentration of measure theory. We explain how the application of the concentration of measure to Cartan-Randers models provides a framework from which it emerge 1. The invariance under infinitesimal diffeomorphisms of the macroscopic dynamics 2. A mechanism for reduction of the quantum state and 3. The Weak Equivalence Principle.
We consider temporal correlations of particles with arbitrary spin. We show that the Leggett-Garg inequality can be maximally violated irrespective of the value of spin, thus improving upon an earlier result by Kofler and Brukner [Phys. Rev. Lett. \textbf{99}, 180403 (2007)]. Our proof is accomplished through a suitable adoption of a measurement scheme which has previously been employed for studying the spatial correlation in a system with arbitrary spin. We next consider generalized or unsharp measurements as a method for coarse graining in a quantitative manner, and show that classicality em…
We consider finite macroscopic systems, i.e., systems of large but finite degrees of freedom, which we believe are poorly understood as compared with small systems and infinite systems. We focus on pure states that do not have the `cluster property.' Such a pure state is entangled macroscopically, and is quite anomalous in view of many-body physics because it does not approach any pure state in the infinite-size limit. However, we often encounter such anomalous states when studying finite macroscopic systems, such as quantum computers with many qubits and finite systems that will exhibit symme…
Entanglement constitutes a main feature that distinguishes quantum from classical physics and is a key resource of quantum technologies. Here we show, however, that entanglement may also serve as the essential ingredient for the emergence of classical behavior in a composite nonlinear radiating system. We consider the radiation from a macroscopic spin emitter, such as the collective radiation from an atomic ensemble. We introduce a new class of macroscopic spin states, the coherently radiating spin states (CRSS), defined as the asymptotic eigenstates of the SU(2) lowering operator. We find tha…
To help resolve stubborn aporias in quantum mechanics, Kastner, Kauffman and Epperson have recently proposed a new interpretation of Heisenbergs ontological duality of res extensa and res potentia. In related work, Khrennikov and Aerts and their respective associates have explored the intermediate domain of mesoscopic phenomena in which quantum-like behavior can be observed and formalized. We generalize this work to define a third domain, one of macroscopic, interactive processes to which quantum concepts, but not quantum formalism apply. We show that they follow the non-standard logic propose…
We use a master equation to study the dynamics of two coupled macroscopic quantum systems (e.g.\ a Josephson junction made of two Bose-Einstein condensates or two spin states of an ensemble of trapped ions) subject to a weak continuous measurement. If the coupling between the two systems is suddenly switched on the resulting dynamics leads to caustics (fold and cusp catastrophes) in the number-difference probability distribution, and at the same time the measurement gradually induces a quantum-to-classical transition. Decoherence is often invoked to help resolve paradoxes associated with macro…
The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems stop to behave quantum mechanically and begin to behave classically is still heavily debated in the physics community and subject to theoretical and experimental research. This dissertation puts forward an approach to the quantum-to-classical transition fully within quantum theory and conceptually different from already existing models: It neither needs to …
There are various reasons to believe that quantum theory could be an emergent phenomenon. Trace Dynamics is an underlying classical dynamics of non-commuting matrices, from which quantum theory and classical mechanics have been shown to emerge, in the thermodynamic approximation. However, the time that is used to describe evolution in quantum theory is an external classical time, and is in turn expected to be an emergent feature - a relic of an underlying theory of quantum gravity. In this essay we borrow ideas from Trace Dynamics to show that classical time is a thermodynamic approximation to…
In this paper we review recent progress in studying quantum phase transitions in one- and two-component Bose-Einstein condensates (BEC) in optical lattices. These phase transitions involve the emergence and disappearance of quantum coherence over whole optical lattice and of linear superposition of macroscopic quantum states. The latter may provide new means to engineer and to manipulate novel macroscopic quantum states and novel coherent atomic beams for quantum information processing, quantum computing etc.
The Hilbert space formalism describes causality as a statistical relation between initial experimental conditions and final measurement outcomes, expressed by the inner products of state vectors representing these conditions. This representation of causality is in fundamental conflict with the classical notion that causality should be expressed in terms of the continuity of intermediate realities. Quantum mechanics essentially replaces this continuity of reality with phase sensitive superpositions, all of which need to interfere in order to produce the correct conditional probabilities for the…
In this sequel paper we explore how macroscopic quantum phenomena can be measured or understood from the behavior of quantum correlations which exist in a quantum system of many particles or components and how the interaction strengths change with energy or scale, under ordinary situations and when the system is near its critical point. We use the nPI (master) effective action related to the Boltzmann-BBGKY / Schwinger-Dyson hierarchy of equations as a tool for systemizing the contributions of higher order correlation functions to the dynamics of lower order correlation functions. Together wit…
During the past decade, the experimental development of being able to create ever larger and heavier quantum superpositions has brought the discussion of the connection between microscopic quantum mechanics and macroscopic classical physics back to the forefront of physical research. Under equilibrium conditions this connection is in fact well understood in terms of the mechanism of spontaneous symmetry breaking, while the emergence of classical dynamics can be described within an ensemble averaged description in terms of decoherence. The remaining realm of individual-state quantum dynamics in…
While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the trajectories of the correct classical motion must emerge from quantum mechanics, a process referred to as the quantum to classical transition. Extending previous work [Bhattacharya, Habib, and Jacobs, Phys. Rev. Lett. {\bf 85}, 4852 (2000)], here we elucidate this transition in some detail, showing that once the measurement processes which affect all macroscopic syst…
We study the fidelity approach to quantum phase transitions (QPTs) and apply it to general thermal phase transitions (PTs). We analyze two particular cases: the Stoner-Hubbard itinerant electron model of magnetism and the BCS theory of superconductivity. In both cases we show that the sudden drop of the mixed state fidelity marks the line of the phase transition. We conduct a detailed analysis of the general case of systems given by mutually commuting Hamiltonians, where the non-analyticity of the fidelity is directly related to the non-analyticity of the relevant response functions (susceptib…
Emergence of classicality from quantum mechanics, a hotly debated topic, has had no satisfactory resolution so far. Various approaches including decoherence and gravitational interactions have been suggested. In the present work, the Schrödinger-Newton model is used to study the role of semi-classical self-gravity in the evolution of massive spin-1/2 particles in a Stern-Gerlach experiment. For small mass, evolution of the initial wavepacket in a spin superposition shows a splitting in the magnetic field gradient into two trajectories as in the standard Stern-Gerlach experiment. For larger mas…
The resource theory of thermal operations, an established model for small-scale thermodynamics, provides an extension of equilibrium thermodynamics to nonequilibrium situations. On a lattice of any dimension with any translation-invariant local Hamiltonian, we identify a large set of translation-invariant states that can be reversibly converted to and from the thermal state with thermal operations and a small amount of coherence. These are the spatially ergodic states, i.e., states that have sharp statistics for any translation-invariant observable, and mixtures of such states with the same th…
We consider a bosonic Josephson junction made of $N$ ultracold and dilute atoms confined by a quasi one-dimensional double-well potential within the two-site Bose-Hubbard model framework. The behaviour of the system is investigated at zero temperature by varying the inter-atomic interaction from the strongly attractive regime to the repulsive one. We show that the ground-state exhibits a crossover from a macroscopic Schrödinger-cat state to a separable Fock state through an atomic coherent regime. By diagonalizing the Bose-Hubbard Hamiltonian we characterize the emergence of the mascroscopic c…
