Wave Function Collapse Models Research Articles

Optimization of a BEGe Detector Setup for Testing Quantum Foundations in the Underground LNGS Laboratory

In this work, we report on tests performed with an experimental apparatus prototype based on a broad-energy germanium detector aimed at investigating topical, foundational issues in quantum mechanics: i.e., possible violations of the spin-statistics connection and models of dynamical wave function collapse. Our recent phenomenological analyses demonstrated the importance of pushing the research of new physics signal, predicted in these fields, to an energy range below 10 keV. We describe the development of the dedicated data acquisition system and of the pulse shape discrimination algorithm, which have already allowed us to get a factor two improvement in the lower energy threshold. Future plans are discussed to further improve the lower energy threshold to the level of a few keV.

Collapse Dynamics Are Diffusive.

Noninterferometric experiments have been successfully employed to constrain models of spontaneous wave function collapse, which predict a violation of the quantum superposition principle for large systems. These experiments are grounded on the fact that, according to these models, the dynamics is driven by noise that, besides collapsing the wave function in space, generates a diffusive motion with characteristic signatures, which, though small, can be tested. The noninterferometric approach might seem applicable only to those models that implement the collapse through noisy dynamics, not to any model, that collapses the wave function in space. Here, we show that this is not the case: under reasonable assumptions, any collapse dynamics (in space) is diffusive. Specifically, we prove that any space-translation covariant dynamics that complies with the no-signaling constraint, if collapsing the wave function in space, must change the average momentum of the system and/or its spread.

Neo-Aristotelian Metaphysics and the Theology of Nature edited by William M.R. Simpson, Robert C. Koons, and James Orr, Routledge, 2022, pp. 446, £118.82, hbk

Neo-Aristotelian Metaphysics and the Theology of Nature edited by William M.R. Simpson, Robert C. Koons, and James Orr, Routledge, 2022, pp. 446, £118.82, hbk

A Novel Approach to Parameter Determination of the Continuous Spontaneous Localization Collapse Model

Models of dynamical wave function collapse consistently describe the breakdown of the quantum superposition with the growing mass of the system by introducing non-linear and stochastic modifications to the standard Schrödinger dynamics. Among them, Continuous Spontaneous Localization (CSL) was extensively investigated both theoretically and experimentally. Measurable consequences of the collapse phenomenon depend on different combinations of the phenomenological parameters of the model-the strength λ and the correlation length rC-and have led, so far, to the exclusion of regions of the admissible (λ-rC) parameters space. We developed a novel approach to disentangle the λ and rC probability density functions, which discloses a more profound statistical insight.

Possible limits on superconducting quantum computers from spontaneous wave-function collapse models

The continuous spontaneous localization (CSL) model is an alternative formulation of quantum mechanics, which introduces a noise-coupled nonlinearly to the wave function to account for its collapse. We consider CSL effects on quantum computers made of superconducting transmon qubits. As a direct effect CSL reduces quantum superpositions of the computational basis states of the qubits: we show the reduction rate to be negligibly small. However, an indirect effect of CSL, dissipation induced by the noise, also leads transmon qubits to decohere, by generating additional quasiparticles. Since the decoherence rate of transmon qubits depends on the quasiparticle density, by computing their generation rate induced by CSL, we can estimate the corresponding quasiparticle density and thus the limit set by CSL on the performances of transmon quantum computers. We show that CSL could spoil the quantum computation of practical algorithms on large devices. We further explore the possibility of testing CSL effects on superconducting devices.

Search for Spontaneous Radiation from Wave Function Collapse in the Majorana Demonstrator.

The Majorana Demonstrator neutrinoless double-beta decay experiment comprises a 44kg (30kg enriched in ^{76}Ge) array of p-type, point-contact germanium detectors. With its unprecedented energy resolution and ultralow backgrounds, Majorana also searches for rare event signatures from beyond standard model physics in the low energy region below 100keV. In this Letter, we test the continuous spontaneous localization (CSL) model, one of the mathematically well-motivated wave function collapse models aimed at solving the long-standing unresolved quantum mechanical measurement problem. While the CSL predicts the existence of a detectable radiation signature in the x-ray domain, we find no evidence of such radiation in the 19-100keV range in a 37.5kg-y enriched germanium exposure collected between December 31, 2015, and November 27, 2019, with the Demonstrator. We explored both the non-mass-proportional (n-m-p) and the mass-proportional (m-p) versions of the CSL with two different assumptions: that only the quasifree electrons can emit the x-ray radiation and that the nucleus can coherently emit an amplified radiation. In all cases, we set the most stringent upper limit to date for the white CSL model on the collapse rate, λ, providing a factor of 40-100 improvement in sensitivity over comparable searches. Our limit is the most stringent for large parts of the allowed parameter space. If the result is interpreted in terms of the Diòsi-Penrose gravitational wave function collapse model, the lower bound with a 95%confidence level is almost an order of magnitude improvement over the previous best limit.

Mesoscopic quantum thermo-mechanics: A new frontier of experimental physics

In the last decade, experimentalists have demonstrated their impressive ability to control mechanical modes within mesoscopic objects down to the quantum level: it is now possible to create mechanical Fock states, to entangle mechanical modes from distinct objects, and to store quantum information or transfer it from one quantum bit to another, among the many possibilities found in today's literature. Indeed, mechanics is quantum, very much like spins or electromagnetic degrees of freedom; and all of this is, in particular, referred to as a new engineering resource for quantum technologies. However, there is also much more beyond this utilitarian aspect: invoking the original discussions of Braginsky and Caves, where a quantum oscillator is thought of as a quantum detector for a classical field, namely, a gravitational wave, which is also a unique sensing capability for quantum fields. The subject of study is then the baths to which the mechanical mode is coupled to, let them be known or unknown in nature. This Perspective is about this new potentiality that addresses stochastic thermodynamics, potentially down to its quantum version, the search for a fundamental underlying (random) field postulated in recent theories that can be affiliated to the class of the wave-function collapse models, and more generally open questions of condensed matter like the actual nature of the elusive (and ubiquitous) two-level systems present within all mechanical objects. However, such research turns out to be much more demanding than the use of a few quantum mechanical modes: all the known baths have to be identified, experiments have to be conducted in-equilibrium, and the word “mechanics” needs to be justified by a real ability to move substantially the center-of-mass when a proper drive tone is applied to the system.

Present status and future challenges of non-interferometric tests of collapse models

The superposition principle is the cornerstone of quantum mechanics, leading to a variety of genuinely quantum effects. Whether the principle applies also to macroscopic systems or, instead, there is a progressive breakdown when moving to larger scales is a fundamental and still open question. Spontaneous wavefunction collapse models predict the latter option, thus questioning the universality of quantum mechanics. Technological advances allow to increasingly challenge collapse models and the quantum superposition principle, with a variety of different experiments. Among them, non-interferometric experiments proved to be the most effective in testing these models. We provide an overview of such experiments, including cold atoms, optomechanical systems, X-ray detection, bulk heating and comparisons with cosmological observations. We also discuss avenues for future dedicated experiments, which aim at further testing collapse models and the validity of quantum mechanics.

Non-Markovian wave-function collapse models are Bohmian-like theories in disguise

Spontaneous collapse models and Bohmian mechanics are two different solutions to the measurement problem plaguing orthodox quantum mechanics. They have, a priori nothing in common. At a formal level, collapse models add a non-linear noise term to the Schrödinger equation, and extract definite measurement outcomes either from the wave function (e.g. mass density ontology) or the noise itself (flash ontology). Bohmian mechanics keeps the Schrödinger equation intact but uses the wave function to guide particles (or fields), which comprise the primitive ontology. Collapse models modify the predictions of orthodox quantum mechanics, whilst Bohmian mechanics can be argued to reproduce them. However, it turns out that collapse models and their primitive ontology can be exactly recast as Bohmian theories. More precisely, considering (i) a system described by a non-Markovian collapse model, and (ii) an extended system where a carefully tailored bath is added and described by Bohmian mechanics, the stochastic wave-function of the collapse model is exactly the wave-function of the original system conditioned on the Bohmian hidden variables of the bath. Further, the noise driving the collapse model is a linear functional of the Bohmian variables. The randomness that seems progressively revealed in the collapse models lies entirely in the initial conditions in the Bohmian-like theory. Our construction of the appropriate bath is not trivial and exploits an old result from the theory of open quantum systems. This reformulation of collapse models as Bohmian theories brings to the fore the question of whether there exists `unromantic' realist interpretations of quantum theory that cannot ultimately be rewritten this way, with some guiding law. It also points to important foundational differences between `true' (Markovian) collapse models and non-Markovian models.

Decoherence effects in non-classicality tests of gravity

The experimental observation of a clear quantum signature of gravity is believed to be out of the grasp of current technology. However, several recent promising proposals to test the possible existence of non-classical features of gravity seem to be accessible by the state-of-art table-top experiments. Among them, some aim at measuring the gravitationally induced entanglement between two masses which would be a distinct non-classical signature of gravity. We explicitly study, in two of these proposals, the effects of decoherence on the system’s dynamics by monitoring the corresponding degree of entanglement. We identify the required experimental conditions necessary to perform successfully the experiments. In parallel, we account also for the possible effects of the continuous spontaneous localization (CSL) model, which is the most known among the models of spontaneous wavefunction collapse. We find that any value of the parameters of the CSL model would completely hinder the generation of gravitationally induced entanglement.

Testing dissipative collapse models with a levitated micromagnet

We present experimental tests of dissipative extensions of spontaneous wave function collapse models based on a levitated micromagnet with ultralow dissipation. The spherical micromagnet, with radius $R=27$ $\mu$m, is levitated by Meissner effect in a lead trap at $4.2$ K and its motion is detected by a SQUID. We perform accurate ringdown measurements on the vertical translational mode with frequency $57$ Hz, and infer the residual damping at vanishing pressure $\gamma/2\pi<9$ $\mu$Hz. From this upper limit we derive improved bounds on the dissipative versions of the CSL (continuous spontaneous localization) and the DP (Di\'{o}si-Penrose) models with proper choices of the reference mass. In particular, dissipative models give rise to an intrinsic damping of an isolated system with the effect parameterized by a temperature constant; the dissipative CSL model with temperatures below 1 nK is ruled out, while the dissipative DP model is excluded for temperatures below $10^{-13}$ K. Furthermore, we present the first bounds on dissipative effects in a more recent model, which relates the wave function collapse to fluctuations of a generalized complex-valued spacetime metric.

Ultranarrow-linewidth levitated nano-oscillator for testing dissipative wave-function collapse

Levitated nano-oscillators are seen as promising platforms for testing fundamental physics and testing quantum mechanics in a new high mass regime. Levitation allows extreme isolation from the environment, reducing the decoherence processes that are crucial for these sensitive experiments. A fundamental property of any oscillator is its line width and mechanical quality factor, Q. Narrow line widths in the microHertz regime and mechanical Q's as high as $10^{12}$ have been predicted for levitated systems, but to date, the poor stability of these oscillators over long periods have prevented direct measurement in high vacuum. Here we report on the measurement of an ultra-narrow line width levitated nano-oscillator, whose line width of $81\pm\,23\,\mu$Hz is only limited by residual gas pressure at high vacuum. This narrow line width allows us to put new experimental bounds on dissipative models of wavefunction collapse including continuous spontaneous localisation and Di\'{o}si-Penrose and illustrates its utility for future precision experiments that aim to test the macroscopic limits of quantum mechanics.

VIP2 at Gran Sasso - Test of the validity of the spin statistics theorem for electrons with X-ray spectroscopy

In the VIP2 VIolation of the Pauli Exlusion Principle (PEP) experiment at the Gran Sasso underground laboratory (LNGS) we are searching for possible violations of standard quantum mechanics predictions. With high precision we investigate the Pauli Exclusion Principle and the collapse of the wave function (collapse models). We will present our experimental method of searching for possible small violations of the Pauli Exclusion Principle for electrons, via the search for “anomalous” X-ray transitions in copper atoms, produced by “new” electrons (brought inside a copper bar by circulating current) which could have the probability to undergo Pauli-forbidden transition to the ground state (1 s level) already occupied by two electrons. We will describe the concept of the VIP2 experiment taking data at LNGS presently. The goal of VIP2 is to test the PEP for electrons with unprecedented accuracy, down to a limit in the probability that PEP is violated at the level of 10−31. We will show preliminary experimental results obtained at LNGS and discuss implications of a possible violation.

Large spatial Schrödinger cat state using a levitated ferrimagnetic nanoparticle

The superposition principle is one of the main tenets of quantum mechanics. Despite its counter-intuitiveness, it has been experimentally verified using electrons, photons, atoms, and molecules. However, a similar experimental demonstration using a nano or a micro particle is non-existent. Here in this article, exploiting macroscopic quantum coherence and quantum tunneling, we propose an experiment using a levitated magnetic nanoparticle to demonstrate such an effect. It is shown that the spatial separation between the delocalized wavepackets of a 20 nm ferrimagnetic yttrium iron garnet (YIG) nanoparticle can be as large as 5 μm. We argue that, in addition to using for testing one of the most fundamental aspects of quantum mechanics, this scheme can simultaneously be used to test different modifications, such as wavefunction collapse models, to the standard quantum mechanics. Furthermore, we show that the spatial superposition of a core–shell structure, a YIG core and a non-magnetic silica shell, can be used to probe quantum gravity.

Neutron Star Heating Constraints on Wave-Function Collapse Models.

Spontaneous wave-function collapse models, like continuous spontaneous localization, are designed to suppress macroscopic superpositions while preserving microscopic quantum phenomena. An observable consequence of collapse models is spontaneous heating of massive objects. We calculate the collapse-induced heating rate of astrophysical objects, and the corresponding equilibrium temperature. We apply these results to neutron stars, the densest phase of baryonic matter in the Universe. Stronger collapse model parameters imply greater heating, allowing us to derive competitive bounds on model parameters using neutron star observational data, and to propose speculative bounds based on the capabilities of current and future astronomical surveys.

Extreme Decoherence and Quantum Chaos.

We study the ultimate limits to the decoherence rate associated with dephasing processes. Fluctuating chaotic quantum systems are shown to exhibit extreme decoherence, with a rate that scales exponentially with the particle number, thus exceeding the polynomial dependence of systems with fluctuating k-body interactions. Our findings suggest the use of quantum chaotic systems as a natural test bed for spontaneous wave function collapse models. We further discuss the implications on the decoherence of AdS/CFT black holes resulting from the unitarity loss associated with energy dephasing.

Testing spontaneous collapse through bulk heating experiments: An estimate of the background noise

Models of spontaneous wave function collapse predict a small heating rate for a bulk solid, as a result of coupling to the noise field that causes collapse. This rate is small enough that ambient radioactivity and cosmic ray flux on the surface of the earth can mask the heating due to spontaneous collapse. In this paper we estimate the background noise due to gamma-radiation and cosmic ray muon flux, at different depths. We demonstrate that a low-temperature underground experiment at a depth of about 6.5 km.w.e. would have a low enough background to allow detection of bulk heating for a collapse rate $\lambda$ of $10^{-16}$ s$^{-1}$ using presently available technology.

Colored collapse models from the non-interferometric perspective

Models of spontaneous wave function collapse describe the quantum-to-classical transition by assuming a progressive breakdown of the superposition principle when the mass of the system increases, providing a well-defined phenomenology in terms of a non-linearly and stochastically modified Schrödinger equation, which can be tested experimentally. The most popular of such models is the continuous spontaneous localization (CSL) model: in its original version, the collapse is driven by a white noise, and more recently, generalizations in terms of colored noises, which are more realistic, have been formulated. We will analyze how current non-interferometric tests bound the model, depending on the spectrum of the noise. We will find that low frequency purely mechanical experiments provide the most stable and strongest bounds.Graphical abstract

Gravity induced wave function collapse

Starting from an idea of S.L. Adler~\cite{Adler2015}, we develop a novel model of gravity-induced spontaneous wave-function collapse. The collapse is driven by complex stochastic fluctuations of the spacetime metric. After deriving the fundamental equations, we prove the collapse and amplification mechanism, the two most important features of a consistent collapse model. Under reasonable simplifying assumptions, we constrain the strength $\xi$ of the complex metric fluctuations with available experimental data. We show that $\xi\geq 10^{-26}$ in order for the model to guarantee classicality of macro-objects, and at the same time $\xi \leq 10^{-20}$ in order not to contradict experimental evidence. As a comparison, in the recent discovery of gravitational waves in the frequency range 35 to 250 Hz, the (real) metric fluctuations reach a peak of $\xi \sim 10^{-21}$.

VIP-2 at LNGS: An experiment on the validity of the Pauli Exclusion Principle for electrons

We are experimentally investigating possible violations of standard quantum mechanics predictions in the Gran Sasso underground laboratory in Italy. We test with high precision the Pauli Exclusion Principle and the collapse of the wave function (collapse models). We present our method of searching for possible small violations of the Pauli Exclusion Principle (PEP) for electrons, through the search for “anomalous” X-ray transitions in copper atoms. These transitions are produced by “new” electrons (brought inside the copper bar by circulating current) which can have the possibility to undergo Pauli-forbidden transition to the 1s level already occupied by two electrons. We describe the VIP2 (VIolation of the Pauli Exclusion Principle) experimental data taking at the Gran Sasso underground laboratories. The goal of VIP2 is to test the PEP for electrons in agreement with the Messiah-Greenberg superselection rule with unprecedented accuracy, down to a limit in the probability that PEP is violated at the level of 10−31. We show preliminary experimental results and discuss implications of a possible violation.