O. Nicrosini, A. Rimini
A new proposal for a Lorentz-invariant spontaneous localization theory is presented. It is based on the choice of a suitable set of macroscopic quantities to be stochastically induced to have definite values. Such macroscopic quantities have the meaning of a time-integrated amount of a microscopically defined quantity called stuff related to the presence of massive particles.
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We present an experimental proposal for the generation of photon triplets based on third-order spontaneous para- metric downconversion in thin optical fibers. Our analysis includes expressions for the quantum state, which de- scribes the photon triplets and for the generation rate in terms of all experimental parameters. We also present, for a specific source design, numerically calculated generation rates.
We extend the beable interpretation, due to Bell, to the continuous spontaneous localization model (CSL). Results obtained by Vink are generalized to the modified Schrodinger equation of Ghirardi, Pearle and Rimini (GPR), which allows a beable interpretation for position and momentum.
In his recent paper [arXiv:1104.1938], Bedingham discussed a hybrid between a theory of spontaneous wave function collapse and Bohmian mechanics. I offer a simpler way of conveying the substance of Bedingham's paper.
A change of quantum states for a quantum particle may lead to a change of physical field it exerts to the environment. We discuss such Gedankenexperiment for measuring the magnetic dipole fields associated with the electronic spins. When entangled, electrons are no longer free Dirac electrons but become an excited state in a quantum-electrodynamics sense. A measurement of magnetism associated with entanglement-collapse of electrons becomes a test for Copenhagen interpretation in the reign of quantum-electrodynamics. This proposal is equally applicable to other particles and their associated fi…
We revisit the back-action of emitted photons on the motion of the relative position of two cold atoms. We show that photon recoil resulting from the spontaneous emission can induce the localization of the relative position of the two atoms through the entanglement between the spatial motion of individual atoms and their emitted photons. The result provides a more realistic model for the analysis of the environment-induced localization of a macroscopic object.
For a solid lattice, we rederive the Continuous Spontaneous Localization (CSL) noise total energy gain of a test mass starting from a Lindblad formulation, and from a similar starting point rederive the geometry factor governing center of mass energy gain. We then suggest that the geometry factor can be used as a way to distinguish between low temperature cantilever motion saturation arising from CSL noise, and saturation arising from thermal leakage.
We describe a previously unexplored effect of the continuous spontaneous localization model whereby a correlation develops in the distributions of two nearby non-interacting particles following a period of diffusion. We propose the use of this effect as an experimental test differentiating between the continuous spontaneous localization model and standard quantum theory. The test involves building a joint probability distribution for the locations of the two particles by repeatedly releasing them from two nearby traps and subsequently measuring their positions after a brief period of time. We …
We propose an experimental setup for studying the Anderson localization of light in the continuous transverse spatial degrees of freedom of the photons. This physical phenomenon can be observed in the transverse profile of a paraxial and quasi-monochromatic beam of light using a spatial light modulator. The light modulator acts in the laser beam as a weak random potential. Here, differently from the standard models studied in the literature, our setup splits the dispersion and potential terms along the beam evolution. By numerical simulations we confirm the feasibility of our experimental prop…
We propose to test the theory of continuous spontaneous localization (CSL) in an all-optical time-domain Talbot-Lau interferometer for clusters with masses exceeding 1000000 amu. By assessing the relevant environmental decoherence mechanisms, as well as the growing size of the particles relative to the grating fringes, we argue that it will be feasible to test the quantum superposition principle in a mass range excluded by recent estimates of the CSL effect.
The interaction of a moving charged particle with its coherent electromagnetic field is analysed in the framework of non-relativistic quantum mechanics. It is shown that, when this interaction is taken into account, a spatially localized state may have a mean energy lower than the one corresponding to a delocalized state.
The Continuous Spontaneous Localization (CSL) model strives to describe the quantum-to-classical transition from the viewpoint of collapse models. However, its original formulation suffers from a fundamental inconsistency in that it is explicitly energy non-conserving. Fortunately, a dissipative extension to CSL has been recently formulated that solves such energy-divergence problem. We compare the predictions of the dissipative and non-dissipative CSL models when various optomechanical settings are used, and contrast such predictions with available experimental data, thus building the corresp…
The Continuous Spontaneous Localization (CSL) model is the best known and studied among collapse models, which modify quantum mechanics and identify the fundamental reasons behind the unobservability of quantum superpositions at the macroscopic scale. Albeit several tests were performed during the last decade, up to date the CSL parameter space still exhibits a vast unexplored region. Here, we study and propose an unattempted non-interferometric test aimed to fill this gap. We show that the angular momentum diffusion predicted by CSL heavily constrains the parametric values of the model when a…
Continuous spontaneous localization as the white-noise limit of spontaneous unitarity violation
本文证明自发幺正性破坏模型的白噪声极限等价于一类连续自发定域化模型，并保持能量守恒，可推广至任意初始态，且通过涨落-耗散关系确保玻恩规则统计与无超光速信号。
We investigate the effect of the Continuous Spontaneous Localization (CSL) model on light-pulse atom interferometry. Using a path-integral approach with an additional stochastic potential accounting for CSL, we derive an exponential loss of the contrast that scales linearly with the interferometer time $T$ if both interferometer arms are spatially separated. We compare our theoretical results with measurements from a cold rubidium atom interferometer based on counter-propagating two-photon transitions with pulse separation times up to $T$ = 260 ms and obtain the corresponding bounds on the CSL…
We propose a mathematical and a conceptual framework (called the `E-model' and the `event ontology' resp.) that encompasses and generalizes the `flash' ontology discussed in a recent paper by R. Tumulka (arXiv:quant-ph/0602208)
Working in the limit in which the localization length scale is large compared to other relevant length scales we examine three experimental situations with the continuous spontaneous localization (CSL) model---a well-motivated alternative to standard quantum theory. These are the two-slit experiment; scattering from a potential barrier; and the release of two non-interacting particles simultaneously from a potential trap. In each case we calculate the diagonal part of the time evolved density matrix giving a probability density function over final measured states. The case of the two-slit expe…
The spontaneous localization theory of Ghirardi, Rimini, and Weber (GRW) is a theory in which wavepacket reduction is treated as a genuine physical process. Here it is shown that the mathematical formalism of GRW can be given an interpretation in terms of an evolving distribution of particles on configuration space similar to Bohmian mechanics (BM). The GRW wavefunction acts as a pilot wave for the set of particles. In addition, a continuous stream of noisy information concerning the precise whereabouts of the particles must be specified. Nonlinear filtering techniques are used to determine th…
A proposal for a new kind of spontaneous collapse model
本文提出一种以固定时空坐标坍缩点为核心的非相对论自发坍缩模型，兼具 GRW 与 CSL 特征，可处理不可分辨粒子、导出 CSL 主方程、解决测量问题并纳入牛顿引力。
Paul traps are ion traps that are widely used in spectroscopic experiments to confine and stabilize a charged particle within a small region using oscillating electric fields. The dynamics of the particle inside a Paul trap is described by Mathieu equations. It has been proposed that such traps can be used to detect the effects produced by spontaneous collapse of the associated wavefunction, as described by the model of CSL (Continuous Spontaneous Localization). This model is a non-linear, stochastic and non-relativistic modification to the Schrödinger equation which predicts an additional ran…
We give an explicit stochastic Hamiltonian model of discontinuous unitary evolution for quantum spontaneous jumps like in a system of atoms in quantum optics, or in a system of quantum particles that interacts singularly with "bubbles" which admit a continual counting observation. This model allows to watch a quantum trajectory in a photodetector or in a cloud chamber by spontaneous localisations of the momentums of the scattered photons or bubbles. Thus, the continuous reduction and spontaneous localization theory is obtained from a Hamiltonian singular interaction as a result of quantum filt…
Energy diffusion due to spontaneous localization (SL) for a relativistically-fast moving particle is examined. SL is an alternative to standard quantum theory in which quantum state reduction is treated as a random physical process which is incorporated into the Schrödinger equation in an observer-independent way. These models make predictions in conflict with standard quantum theory one of which is non conservation of energy. On the basis of proposed relativistic extensions of SL it is argued that for a single localized particle, non-relativistic SL should remain valid in the rest frame of th…
Collapse models explain the absence of quantum superpositions at the macroscopic scale, while giving practically the same predictions as quantum mechanics for microscopic systems. The Continuous Spontaneous Localization (CSL) model is the most refined and studied among collapse models. A well-known problem of this model, and of similar ones, is the steady and unlimited increase of the energy induced by the collapse noise. Here we present the dissipative version of the CSL model, which guarantees a finite energy during the entire system's evolution, thus making a crucial step toward a realistic…
Testing Continuous Spontaneous Localization model with charged macro-molecules
提出基于线性Paul阱中囚禁两个离子的方法，结合原子与大分子离子测试连续自发局域化模型，以增强量子实验对坍缩机制的检验能力。
Matter-wave interferometry is a direct test of the quantum superposition principle for massive systems, and of collapse models. Here we show that the bounds placed by matter-wave interferometry depend weakly on the details of the collapse mechanism. Specifically, we compute the bounds on the CSL model and its variants, provided by the the KDTL interferometry experiment of Arndt's group [Phys. Chem. Chem. Phys., 2013, 15, 14696-14700], which currently holds the record of largest mass in interferometry. We also show that the CSL family of models emerges naturally by considering a minimal set of …
We apply the formalism of quantum estimation theory to extract information about potential collapse mechanisms of the continuous spontaneous localisation (CSL) form. In order to estimate the strength with which the field responsible for the CSL mechanism couples to massive systems, we consider the optomechanical interaction between a mechanical resonator and a cavity field. Our estimation strategy passes through the probing of either the state of the oscillator or that of the electromagnetic field that drives its motion. In particular, we concentrate on all-optical measurements, such as homody…
Spontaneous Collapse of the Wavefunction: A Testable Proposal Motivated by Discrete Physics
本研究提出一种含全新波函数坍缩机制的修正量子力学，可解决量子测量问题，其能从全离散物理学自然衍生，且相比既有自发坍缩理论更适配波函数的实在论诠释。
On the basis of a proposed model of wave function collapse, we investigate spontaneous localization of a quantum state. The model is similar to the Ghirardi-Rimini-Weber model, while we postulate the localization functions to depend on the quantum state to suffer collapse. According to the model, dual dynamics in quantum mechanics, deterministic and stochastic time evolution, are algorithmically implemented in tandem. After discussing the physical implications of the model qualitatively, we present numerical results for one-dimensional systems by way of example.
We find an analogy between turbulence and the dynamics of the continuous spontaneous localization model (CSL) of the wave function. The use of a standard white noise in the localization process gives Richardson's t^3 law for the turbulent diffusion, while the introduction of an affine noise in the CSL allows us to obtain the intermittency corrections to this law.
There is a striking convergence between Burgers turbulence and the continuous spontaneous localization [CSL] model of quantum mechanics. In this paper, we exploit this analogy showing the similarities in the physics of these two apparently unrelated problems. It is hoped that the kind of analogy we introduce here may lead to important developments in both areas.
A recent experiment [K. C. Lee et al., Science 334, 1253 (2011)] succeeded in detecting entanglement between two macroscopic specks of diamonds, separated by a macroscopic distance, at room temperature. This impressive results is a further confirmation of the validity of quantum theory in (at least parts of) the mesoscopic and macroscopic domain, and poses a challenge to collapse models, which predict a violation of the quantum superposition principle, which is the bigger the larger the system. We analyze the experiment in the light of such models. We will show that the bounds placed by experi…
The Continuous Spontaneous Localization (CSL) model predicts a tiny break of energy conservation via a weak stochastic force acting on physical systems, which triggers the collapse of the wave function. Mechanical oscillators are a natural way to test such a force; in particular levitated micro-mechanical oscillator has been recently proposed to be an ideal system. We report a proof-of-principle experiment with a micro-oscillator generated by a micro-sphere diamagnetically levitated in a magneto-gravitational trap under high vacuum. Due to the ultra-low mechanical dissipation, the oscillator p…
A more detailed analysis of the measurement problem continues to support the position taken by Shimony and the author that collapse of the wave function takes place in an objective manner in the rhodopsin molecule of the retina. This casts further doubts on the theories involving a spontaneous localization collapse process or a no-collapse decoherence process taking place in the visual cortex in a subjective fashion. The possibility is then raised, as per Anandan, as to whether the solution of the measurement problem in quantum theory allows one to address the problem of quantizing gravitation…
We propose what we believe to be a novel type of optical source for ultra-cold atomic Far Off-Resonance optical-dipole Traps (FORTs). The source is based on an Erbium Amplified Spontaneous Emission (ASE) source that seeds a high power Erbium Doped Fiber Amplifier (EDFA). The main interest of this source is its very low coherence length, thus allowing an incoherent superposition of several trapping beams without any optical interference. The behavior of the superimposed beams is then a scalar sum greatly simplifying complex configurations. As an illustration, we report an estimation of the inte…
Collapse models describe phenomenologically the quantum-to-classical transition by adding suitable nonlinear and stochastic terms to the Schroedinger equation, thus (slightly) modifying the dynamics of quantum systems. Experimental bounds on the collapse parameters have been derived from various experiments involving a plethora of different systems, from single atoms to gravitational wave detectors. Here, we give a comprehensive treatment of the Continuous Spontaneous Localization (CSL) model, the most studied among collapse models, for Fermi liquids. We consider both the white and non-white n…
Different attempts to solve the measurement problem of the quantum mechanics (QM) by denying the collapse principle, and replacing it with changes in the quantum formalism, failed because the changes in the formalism lead to contradictions with QM predictions. To the difference, Ghirardi, Rimini and Weber took the collapse as a real phenomenon, and proposed a calculus by which the wave-function should undergo a sudden localization. Later on, Ghirardi, Pearle and Rimini came with a change of this calculus into the CSL (continuous spontaneous localization) model of collapse. Both these proposals…
In a recent paper [J. Martin and V. Vennin, Phys. Rev. Lett. 124, 080402 (2020)] it was argued that, for most natural choices, the direct application of the continuous spontaneous localization (CSL) theory to the inflationary case, as it is known to work in non-relativistic laboratory situations, is ruled out by cosmological observational data, thus casting a shadow on models based on CSL theory. We point out that such results are based on the consideration of a rather narrow set of choices for the application of the theory to the cosmological context and that the landscape of open and differe…
We consider the relation between so called continuous localization models - i.e. non-linear stochastic Schrödinger evolutions - and the discrete GRW-model of wave function collapse. The former can be understood as scaling limit of the GRW process. The proof relies on a stochastic Trotter formula, which is of interest in its own right. Our Trotter formula also allows to complement results on existence theory of stochastic Schrödinger evolutions by Holevo and Mora/Rebolledo.
Revisiting astrophysical bounds on continuous spontaneous localization models
本文重新审视并扩展了连续自发定域（CSL）模型在致密天体上的宇宙物理界限，提出了新的测试方法，并比较了各界限的优劣。
Are vacuum fluctuations relevant in absorption dynamics?
本文分析真空涨落影响吸收动力学并破坏线性量子演化叠加性的提议，提出基于双原子单吸收后自发辐射时间依赖性的实验检验方案，并比较真空涨落作为解纠缠机制与辐射触发机制的时间尺度。
Ehrenfest Dynamics with Spontaneous Localization
提出基于量子态扩散方程的退相干修正Ehrenfest动力学扩展（SLED），通过轨迹级随机局域化再现Lindblad型传播，确保物理一致性，并在基准模拟中验证了其有效性。
A High-Contrast Bragg Atom Interferometer for Testing Continuous Spontaneous Localization
本文通过构建高对比度布拉格原子干涉仪，系统分析并校正了影响条纹对比度的主要因素，将CSL坍缩率的上限提高至λ_CSL=1.27×10^{-5} s^{-1}（r_C=10^{-5} m），相比先前原子干涉约束提升了约4倍。
Some versions of quantum theory treat wave function collapse as a fundamental physical phenomenon to be described by explicit laws. One motivation is to find a consistent unification of quantum theory and gravity, in which collapse prevents superpositions of space-times from developing. Another is to invoke collapse to explain our perception of definite measurement outcomes. Combining these motivations while avoiding two different collapse postulates seems to require that perceptibly different physical states necessarily create significantly different mass distributions in our organs of percep…
We present a new, falsifiable, quantum theory of gravity, which we name Non-commutative Matter-Gravity. The commutative limit of the theory is classical general relativity. In the first two papers of this series, we have introduced the concept of an atom of space-time-matter [STM], which is described by the spectral action in non-commutative geometry, corresponding to a classical theory of gravity. We used the Connes time parameter, along with the spectral action, to incorporate gravity into trace dynamics. We then derived the spectral equation of motion for the gravity part of the STM atom, w…
Experimental Proposal on Non-Abelian Aharonov-Bohm Caging Effect with a Single Trapped Ion
提出利用单囚禁离子合成非阿贝尔规范场以实现非阿贝尔 AB 笼禁效应的实验方案，发现其发生于干涉矩阵幂零或特定初态设定时，为研究局域化与非阿贝尔物理提供了新工具。
Relativistic model of spontaneous wave-function localization induced by nonHermitian colored noise
本文基于随机非厄米作用量发展相对论量子场论，通过带纯虚数项的狄拉克作用量耦合费米子密度算符与普适有色噪声，推导波包定域化长度并发现其随可观测宇宙增大而减小，为相对论自发波函数坍缩提供潜在框架。
Gravitational Poissonian Spontaneous Localization Model of Hybrid Quantum-Classical Newtonian Gravity: Energy Increase and Experimental Bounds
本文提出一种混合量子-经典引力模型，通过不同空间模糊化减少自发加热，利用中子星数据设定新参数下限。
We propose a dual-pump third-order nonlinear scheme for producing pairs of correlated photons that is less susceptible to Raman noise than typical spontaneous four wave mixing methods (SFWM). Beginning with the full multimode Hamiltonian we derive a general expression for the joint spectral amplitude, from which the probability of producing a pair of photons can be calculated. As an example, we demonstrate that a probability of 0.028 pairs per pulse can be achieved in an appropriately designed fused silica microfiber. As compared with single pump SFWM in standard fiber, we calculate that our p…
In this work we consider a wide variety of alternatives opened when applying the continuous spontaneous localization (CSL) dynamical collapse theory to the inflationary era. The definitive resolution of many of the issues discussed here will have to await, not only for a general relativistic CSL theory, but for a fully workable theory of quantum gravity. Our concern here is to explore these issues, and to warn against premature conclusions. This exploration includes: two different approaches to deal with quantum field theory and gravitation, the identification of the collapse-generating operat…
The efficiency of laser-cooling relies on the existence of an almost closed optical-transition cycle in the energy spectrum of the considered species. In this respect rare-earth elements exhibit many transitions which are likely to induce noticeable leaks from the cooling cycle. In this work, to determine whether laser-cooling of singly-ionized erbium Er$^+$ is feasible, we have performed accurate electronic-structure calculations of energies and spontaneous-emission Einstein coefficients of Er$^+$, using a combination of \textit{ab initio} and least-square-fitting techniques. We identify five…
Each natural mode of the electromagnetic field within a parabolic mirror exhibits spatial localization and polarization properties that can be exploited for the quantum control of its interaction with atomic systems. The region of localization is not restricted to the focus of the mirror leading to a selective response of atomic systems trapped on its vicinity. We report calculations of the spontaneous emission rates for an atom trapped inside the mirror accounting for all atomic polarizations and diverse trapping regions. It is shown that electric dipole transitions can be enhanced near the f…
Proposal for experimental realization of quantum spin chains with quasiperiodic interactions using Rydberg atoms
本研究提出用里德伯原子实现准周期相互作用的量子自旋模型的方法，数值计算发现该模型存在异于遍历区和多体局域化区的多体临界区域，为研究无序量子系统局域化性质提供实验方案。
The inflationary paradigm provides a mechanism to generate the primordial perturbations needed to explain the observed large scale structures in the universe. Inflation traces back all the inhomogeneities to quantum fluctuations although the structures look classical today. Squeezing of primordial quantum fluctuations along with the mechanism of decoherence accounts for many aspects of this quantum to classical transition, although it remains a matter of debate as to whether this is sufficient to explain the issue of realization of a single outcome (i.e. the issue of macro-objectification) fro…
Resurrecting Vanilla Power Law Inflation with the aid of Continuous Spontaneous Localization in the ACT era
针对标准幂律暴胀的优雅退出、数据兼容性及原初量子扰动经典化问题，提出坍缩修正的幂律暴胀模型，解决经典化问题并与Planck、ACT等当前数据兼容，还产生更红移的张量谱且谱指数无跑动。
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