We investigate quantum effects in pattern-formation for a degenerate optical parametric oscillator with walk-off. This device has a convective regime in which macroscopic patterns are both initiated and sustained by quantum noise. Familiar methods based linearization about a pseudo-classical field fail in this regime and new approaches are required. We employ a method in which the pump field is treated as a $c$-number variable but is driven by the $c$-number representation of the quantum sub-harmonic signal field. This allows us to include the effects of the fluctuations in the signal on the pump, which in turn act back on the signal. We find that the non-classical effects, in the form of squeezing, survive just above the threshold of the convective regime. Further above threshold the macroscopic quantum noise suppresses these effects.
We introduce a discrete Q-function of N qubit system projected into the space of symmetric measurements as a tool for analyzing general properties of quantum systems in the macroscopic limit. For known states the projected Q-function helps to visualize the results of collective measurements, and for unknown states it can be approximately reconstructed by measuring lowest moments of the of collective variables.
We study the fluctuations of the work performed on a driven quantum system, defined as the difference between subsequent measurements of energy eigenvalues. These work fluctuations are governed by statistical theorems with similar expressions in classical and quantum physics. In this article we show that we can distinguish quantum and classical work fluctuations, as the latter can be described by a macrorealistic theory and hence obey Leggett-Garg inequalities. We show that these inequalities are violated by quantum processes in a driven two-level system and in a harmonic oscillator subject to…
Prospects for reaching persistent entanglement between two spatially separated atomic Bose-Einstein condensates are outlined. The system set-up comprises of two condensates loaded in an optical lattice, which, in return, is confined within a high-Q optical resonator. The system is driven by an external laser that illuminates the atoms such that photons can scatter into the cavity. In the superradiant phase a cavity field is established and we show that the emerging cavity mediated interactions between the two condensates is capable of entangling them despite photon losses. This macroscopic ato…
The possibility is discussed of inferring or simulating some aspects of quantum dynamics by adding classical statistical fluctuations to classical mechanics. We introduce a general principle of mechanical stability and derive a necessary condition for classical chaotic fluctuations to affect confined dynamical systems, on any scale, ranging from microscopic to macroscopic domains. As a consequence we obtain, both for microscopic and macroscopic aggregates, dimensional relations defining the minimum unit of action of individual constituents, yielding in all cases Planck action constant.
The Macroscopic Fluctuation Theory is an effective framework to describe transports and their fluctuations in classical out-of-equilibrium diffusive systems. Whether the Macroscopic Fluctuation Theory may be extended to the quantum realm and which form this extension may take is yet terra incognita but is a timely question. In this short introductory review, I discuss possible questions that a quantum version of the Macroscopic Fluctuation Theory could address and how analysing Quantum Simple Exclusion Processes yields pieces of answers to these questions.
We discuss the unitary quantum dynamics of the Dicke model (spin and oscillator coupled). A suitable quasiprobabilty representing the quantum state turns out to obey a Fokker-Planck equation, with drift terms representing the underlying classical Hamiltonian flow and diffusion terms describing quantum fluctuations. We show (by projecting the dynamics onto a co-moving Poincaré section) how the interplay of deterministic drift and quantum diffusion generates equilibration to the microcanonical density, under conditions of global classical chaos. The pertinent photon statistics reveals macroscopi…
We examine the Hall conductivity of macroscopic two-dimensional quantum system, and show that the observed quantities can sometimes violate the fluctuation dissipation theorem (FDT), even in the linear response (LR) regime infinitesimally close to equilibrium. The violation can be an order of magnitude larger than the Hall conductivity itself at low temperature and in strong magnetic field, which are accessible in experiments. We further extend the results to general systems and give a necessary condition for such large-scale violation to happen. This violation is a genuine quantum phenomenon …
We present a scheme for creating quantum entangled atomic states through the coherent spin-exchange collision of a spinor Bose-Einstein condensate. The state generated possesses macroscopic Einstein-Podolsky-Roson correlation and the fluctuation in one of its quasi-spin components vanishes. We show that an elongated condensate with large aspect ratio is most suitable for creating such a state.
Macroscopic Quantum Electrodynamics with Gain: Modified Fluctuations and Their Consequences
RIKEN Centre for Advanced Photonics, RIKEN（RIKEN先进光子学中心）；Instituto Superior Técnico—University of Lisbon and Instituto de Telecomunicações（里斯本高等理工学院与电信研究所）；The Blackett Laboratory, Imperial College London（帝国理工学院布莱克特实验室）
With the slow but constant progress in the coherent control of quantum systems, it is now possible to create large quantum superpositions. There has therefore been an increased interest in quantifying any claims of macroscopicity. We attempt here to motivate three criteria which we believe should enter in the assessment of macroscopic quantumness: The number of quantum fluctuation photons, the purity of the states, and the ease with which the branches making up the state can be distinguished.
We describe macroscopic quantum memory devices based on type-II toroidal superconductors and estimate in one case and compute in another the rates at which quantum information stored in these devices ``degrades'' because of thermal fluctuations. In the case when the entire solid torus is superconducting, the Boltzmann factor in the rate corresponds to a well-defined critical fluctuation, and the rate is suppressed exponentially with the linear size of the system. In the case when superconductivity is confined to the surface of the torus, the rate is determined by diffusive motion of vortices a…
We study the connection between dissipation and reality in macroscopic quantum systems. We present the following scenario; if we consider the dynamics of a `partial' wave function, the dissipation is represented as a nonlocal term and it causes destructive interference to suppress the quantum fluctuation. Using the variational method, we confirm that this dissipation term is a reasonable extension of the standard (Schrödinger) description for isolated systems, from which we also derive the classical action. Consequently, in macroscopic systems, the states whose time-integrated dissipation take…
In quantum systems of a macroscopic size V, such as interacting many particles and quantum computers with many qubits, there exist pure states such that fluctuations of some intensive operator A is anomalously large, <δA^2> = O(V^0), which is much larger than that assumed in thermodynamics, <δA^2> = O(1/V). By making full use of the locality, we show, starting from Hamiltonians of macroscopic degrees of freedom, that such states decohere at anomalously fast rates when they are weakly perturbed from environments.
We study quantum measurements of temporal equilibrium fluctuations in macroscopic quantum systems. It is shown that the fluctuation-dissipation theorem, as a relation between observed quantities, is partially violated in quantum systems, even if measurements are made in an ideal way that emulates classical ideal measurements as closely as possible. This is a genuine quantum effect that survives on a macroscopic scale. We also show that the state realized during measurements of temporal equilibrium fluctuations is a `squeezed equilibrium state,' which is macroscopically identical to the pre-mea…
Quantum fluctuations and chaos in fully connected spin models
Institute of Physics, Johannes Gutenberg University Mainz（美因茨约翰内斯·古腾堡大学物理研究所）；School of Physics and Astronomy, University of St Andrews（圣安德鲁斯大学物理与天文学学院）；Department of Physics, University of Konstanz（康斯坦茨大学物理系）
For macroscopic quantum systems, we study what are measured when equilibrium fluctuations of macrovariables are measured in an ideal way that mimics classical ideal measurements as closely as possible. We find that the symmetrized time correlation (symTC) is always obtained for such measurements. As an important consequence, we show that the fluctuation-dissipation theorem (FDT) is partially violated as a relation between observed quantities in macroscopic quantum systems even if measurements are made in such an ideal way.
We theoretically study the macroscopic quantum tunneling (MQT) in a hetero Josephson junction formed by a conventional single-gap superconductor and a multi-gap one such as ${MgB}_{2}$ and iron-based superconductors. In such a Josephson junction more than one phase differences are defined. We clarify the quantum dynamics of the phase differences and construct a theory for the MQT in the multi-gap Josephson junctions. The dynamics of the phase differences are strongly affected by the Josephson-Leggett mode, which is the out-of-phase oscillation mode of the phase differences. The escape rate is …
The question of Bohr correspondence in quantum field theory is considered from a dynamical point of view. It is shown that the classical description of particle interactions is inapplicable even in the limit of large particles' masses because of finite quantum fluctuations of the fields produced. In particular, it is found that the relative value of the root mean square fluctuation of the Coulomb and Newton potentials of a massive particle is equal to 1/sqrt{2}. It is shown also that in the case of a macroscopic body, the quantum fluctuations are suppressed by a factor 1/sqrt{N}, where N is th…
We study the stabilities of quantum states of macroscopic systems, against noises, against perturbations from environments, and against local measurements. We show that the stabilities are closely related to the cluster property, which describes the strength of spatial correlations of fluctuations of local observables, and to fluctuations of additive operators. The present theory has many applications, among which we discuss the mechanism of phase transitions in finite systems and quantum computers with a huge number of qubits.
In equilibrium, forces induced by fluctuations of the electromagnetic field between electrically polarizable objects (microscopic or macroscopic) in vacuum are always attractive. The force may, however, become repulsive for microscopic particles coupled to thermal baths with different temperatures. We demonstrate that this non-equilibrium repulsion can be realized also between macroscopic objects, as planar slabs, if they are kept at different temperatures. It is shown that repulsion can be enhanced by (i) tuning of material resonances in the thermal region, and by (ii) reducing the dielectric…
We consider a thought experiment where the preparation of a macroscopically massive or charged particle in a quantum superposition and the associated dynamics of a distant test particle apparently allow for superluminal communication. We give a solution to the paradox which is based on the following fundamental principle: any local experiment, discriminating a coherent superposition from an incoherent statistical mixture, necessarily requires a minimum time proportional to the mass (or charge) of the system. For a charged particle, we consider two examples of such experiments, and show that th…
