# Fundamental Problems in Quantum Physics 2023

Third school on quantum foundations dedicated to Prof. GianCarlo Ghirardi.

Quantum Mechanic is extremely successful in predicting experimental results and has a vast range of applications. Nonetheless, many unanswered questions remain. The school will introduce Master and PhD students to the still outstanding problems in our understanding of quantum foundations.

To give a deep look into the foundations of quantum mechanics, lectures will be given by experts in the field. An extensive time will be dedicated to selected contributed talks.

Registration is mandatory (use form below). There is no fee; participants will have to cover their travel and local expenses.

Registration open till **September 1 ^{st} 2023**.

**Registrations are currently closed.**

The participation is limited to 50 people.

## Location

**The school will take place in Room F of the G building at the University of Trieste. **

## List of lecturers

Stefano Ansoldi (University of Udine)

Nicola Poli (Universtiy of Florence)

Ward Struyve (KU Leuven)

Andrea Trombettoni (University of Trieste)

## List of speakers

Steve Campbell (University College Dublin)

Dario Chisholm (Queen's University Belfast)

Mario Arnolfo Ciampini (University of Vienna)

Lajos Diósi (Wigner Research Centre)

Laria Figurato (University of Trieste)

José Luis Gaona Reyes (University of Trieste)

Giulio Gasbarri (Universitát Autonoma de Barcelona)

Anirudh Gundhi (University of Trieste)

Lucía Menendez-Pidal de Cristina (Complutense University of Madrid)

Giuseppe Antonio Nisticò (University of Calabria)

Kyrilo Simonov (University of Vienna)

Andrea Smirne (University of Milan)

Giovanni Spaventa (Ulm University)

Hendrik Ulbricht (University of Southampton)

Linda van Manen (University of Jena)

Andrea Vinante (CNR - Istituto di Fotonica e Nanotecnologie)

## Program

Dates: Wednesday,** September 13 **to Friday,** September 15**, 2023

The scientific program will develop from Wednesday morning to Friday afternoon. Participants are strongly encouraged to attend all three days of the school. We specifically choose these dates to allow the interested participants to attend also the IQIS conference that will take place in Trieste the following week: www.iqis2023.it.

## Abstracts lectures:

**Stefano Ansoldi **(University of Udine): **The Fulling-Davies-Unruh effect**

We discuss field quatization in a uniformly accelerated system as a proxy to understand fundamental challenges of quantum field theory on curved background.

**Nicola Poli **(University of Florence & LENS): **Precision test of fundamental physics with matter-wave interferometers**

Today, matter-wave interferometers such as clocks and gravimeters allow for precision measurements of time and gravity at unprecedented levels. In all these sensors, the exquisite control of both internal (electronic) and external (center of mass motion) degrees of freedom of ultra-cold atomic samples, enable us to study interactions at their most basic, quantum level, paving the way for new tests of fundamental physics.

In this talk, I’ll focus on all possible implementations of alkali-earth atoms in atom interferometry schemes involving two-photon and single-photon transitions. Moreover, the experimental results toward the production of ultra-cold cadmium for atom interferometry and prospects for tests of fundamental physics will also be discussed.

**Ward Struyve** (KU Leuven): **Introduction to Bohmian mechanics**

Bohmian mechanics is an alternative to standard quantum mechanics which describes particles moving under the influence of the wave function. I will provide an introduction to the theory, with an explanation how it reproduces the usual quantum predictions and possible practical applications. I will also (briefly) discuss how it deals with relativity, quantum field theory and quantum gravity.

**Andrea Trombettoni **(University of Trieste): **Ultracold atoms for quantum simulations**

The goal of the lecture is to provide an introduction to the field of quantum simulations with ultracold atoms. After a brief discussion of the physical properties of such systems, I discuss the basic ingredients currently available to perform quantum simulations. I finally point out the main applications, discussing in particular the case of lattice models and low-dimensional systems.

## Abstracts talks:

**Steve Campbell** (University College Dublin):** Thermodynamics of coherent control**

The steady interest in understanding the thermodynamics of quantum systems has led to several approaches to defining work and heat in a quantum mechanically consistent way (at least almost consistent!). Quantum thermodynamics as subfield has grown steadily in the last 15 years, revealing the impact that coherence can have on the energetics of quantum systems. Concurrently, the rapid development of techniques to coherently manipulate quantum systems has come to the forefront of research as the race to develop useful quantum devices pushes on. At the intersection of these two fields lies both practical and fundamental insights. In this talk I will briefly review some of approaches to examining the resource consumption of quantum control, aiming to motivate why I think examining the thermodynamics of coherent control is proving to be a particularly fruitful direction to explore.

**Dario Alexander Chisholm** (Queen's University Belfast): **Quantum objectivity**

Quantum objectivity aims to explain the emergence of classical objectivity from a quantum substrate, one of the key aspects of the quantum-to-classical transition. It does so by giving a definition of objectivity for quantum systems, more specifically, a quantum state is said to be objective if multiple observers are able to recover information about the state and agree among themselves. This is in turn possible only if said information was encoded multiple times into the surrounding environment. After an initial introduction to the main frameworks used in this context, namely quantum Darwinism and spectrum broadcast structure, I will give an overview of some recent results in this area of research.

**Mario Arnolfo Ciampini** (University of Vienna): **Macroscopic quantum mechanics using levitated optomechanics**

Massive systems and quantum objects do not go well together. As the mass grows larger, the coherence of a quantum system is readily lost through the many interactions with the environment.

However, if we want to probe first hand the interconnection between quantum theory and gravity interactions, then the dream would be generating a genuine macroscopic superposition in space of a massive object. Today, levitated nanoparticles trapped in high vacuum have emerged as a promising and versatile optomechanical platform, where techniques coming from cold atoms, optomechanical systems, biological systems and control theory, come together to allow for preparation of nearly pure quantum state of motion of sub-micron particles, along with fast dynamical control of the forces acting on them. In this presentation, I will start from a general introduction of optomechanics as the platform of choice, I will briefly show what amazing physics can be probed with it, and finally I will show the path toward observing for the first time matter-wave interference of the center of mass motion of a levitated nanoparticle, along with the obvious roadblocks to solve in the way there.

**Lajos Diósi** (Eötvös Loránd University & Wigner Research Center): **Wavefunction collapse in hybrid formalism: GRW hybrid master equation**

Hybrid quantum-classical formalism is a simple alternative to textbook formalism of the wavefunction's random collapse. This alternative applies when the simple von Neumann collapse is upgraded to time-continuous collapse. The usual stochastic equations of the conditional quantum state and the measured signal can be rewritten in a single hybrid master equation. As a specific example, we consider the GRW stochastic equations of the wavefunction's conjectured spontaneous dynamical collapse and construct the theory's hybrid master equation.

**Laria Figurato** (University of Trieste): **On the testability of the Károlyházy model**

One of the first proposals in the context of gravitational decoherence was formulated by Károlyházy. He suggested that there is a fundamental limitation in the precision with which a length can be measured by means of a quantum probe, a limitation which he interpreted as arising due to stochastic fluctuations of the spacetime metric, which prevent measurements from being too sharply defined. Consequence of these fluctuations is decoherence in space and that charged particles, being accelerated by the metric fluctuations, emit radiation. Actually, Károlyházy's original paper resorted an additional ingredient, besides spacetime fluctuations: it was assumed that these fluctuations have the form of gravitational waves. This poses a severe constraint on the correlation function of the fluctuations, which is ultimately responsible for predicting a large photon emission rate from matter, which in turn is excluded by experimental evidence. Yet, gravitational wave are not necessary but spacetime fluctuations alone, with a more general correlation function, suffice. We explore what happens to Károlyház's model when a more general correlations functions for the gravitational fluctuations is taken into account.

**José Luis Gaona Reyes** (University of Trieste): **Implementation of Newtonian Gravity through Gaussian Continuous Measurements**

I will describe basic concepts of Quantum Measurement Theory, with particular focus on the construction of the Wiseman-Milburn master equation. Then, I will proceed to describe some models which incorporate Newtonian gravity through a continuous measurement and feedback mechanism. In particular, I will discuss the models due to Kafri, Taylor and Milburn (KTM) and Tilloy and Diósi (TD). I will analyse the differences between the KTM and TD models, and discuss the robustness of the later.

**Giulio Gasbarri** (Universitát Autonoma de Barcelona): **Sequential Hypothesis Testing for Continuosly monitored Quantum Systems**

Opto- and magneto-mechanical devices have emerged as highly promising platforms for constructing ultraprecise sensors, as well as for investigating quantum mechanics and its interplay with gravity.

Despite significant progress in developing these devices and a substantial body of theoretical research in this field, there remains a vast area to explore regarding effective strategies for utilizing the collected time-series data, especially in protocols requiring real-time data assessment.

In this talk, we address the hypothesis testing problem and propose the application of sequential strategies, as these strategies allow for the identification of underlying hypotheses with certified success probabilities. Traditional statistical inference methods that process measurement data only after the experiment has concluded. However, in the context of continuously monitored sensors and numerous real-life applications, it becomes crucial to employ sequential strategies that process resources in real-time and make decisions based on the data accumulated up to that point.

Our focus is on integrating sequential analysis methodologies into continuously monitored quantum systems, with a specific emphasis on a fundamental statistical inference aspect: binary hypothesis testing.

Through this discussion, we highlight the advantage of sequential strategies compared to existing approaches reliant on fixed predetermined measurement time.

**Anirudh Gundhi** (University of Trieste): **Constraining collapse models via cosmology**

Cosmological inflation is widely regarded to be a part of standard cosmology. Not only does it

solve several cosmological puzzles, the quantum fluctuations of the inflaton field are also believed

to seed the formation of stars, galaxies and the temperature anisotropy of the CMB radiation.

While the quantum perturbations offer to account for the structure in the universe, they also pose conceptual problems concerning its apparent classicality. Several works have sought a possible resolution by considering the continuous spontaneous localization (CSL) models. The nonlinear evolution of the wavefunction that these models introduce, leads to a continuous localization of the wavefunction within the time intervals which scale inversely with the size (the total mass or the number of particles) of the system so that the quantum-to-classical transition is achieved continuously. In this talk, staying within the framework of standard

cosmological perturbation theory, a possible generalization of the mass proportional CSL model to a cosmological setting is proposed. As a consequence, we shall see how one can also constraint collapse models with the help of cosmological observations. We will also see that a generalization can be constructed which is compatible with the CMB constraints, in contrast to some of the claims made in the literature.

**Lucía Menéndez-Pidal de Cristina **(Complutense University of Madrid): **Quantum Cosmology and the Problem of Time**

General Relativity and Quantum Mechanics are two of the most successful theories in physics, able to predict a very wide range of phenomena. However, when trying to combine these two theories to find a theory of Quantum Gravity, one is faced with all sorts foundational problems. One of the most pressing issues is the Problem of Time. In short, General Relativity is a covariant theory, each observer measures its own proper time. Notions like simultaneity become observer dependent. In Quantum Mechanics, one relies on an external an absolute time parameter to account for evolution. These two views on time seem a priory incompatible. In this talk, I will outline the main reasons that point to the need of a theory of Quantum Gravity. Then, I will introduce one the first Quantum Gravity approaches, Geometrodynamics, and I will outline how the problem of time appears. To do so, I will focus on cosmological highly symmetric models, Minisuperspaces models. Finally, I will point out at the different approaches taken to solve the problem of time, mentioning their strengths and shortcomings, focusing on some of my research results.

**Kyrylo Simonov **(University of Vienna): **Quantum supermaps without definite causal order and their thermodynamic advantages**

The nature of causality remains one of the key puzzles in science. In quantum theory, the causal structure is not subject to quantum uncertainty and plays rather a background role. One can ask whether the background causal structure can be dropped, for example, by respecting causality only locally. Such scenarios of local validity of quantum theory while relaxing the global definite causal order of operations can be described via the machinery of higher-order operations, i.e. supermaps. An important example of scenarios of this kind is quantum SWITCH, a process realizing a quantum superposition of causal orders of operations. Looking for the possible applications of quantum SWITCH has been the subject of growing interest in the scientific community as it could provide communication and computational resources not realizable via standard quantum theory. In the last few years, the benefits potentially offered by quantum SWITCH for thermodynamic tasks have appeared in the spotlight. My talk aims at reviewing thermodynamic aspects and applications of higher-order maps and drawing the perspectives.

**Andrea Smirne **(University of Milan): **Multi-time correlation functions in open quantum systems: fundamental meaning and general non-Markovian regimes**

The complete statistical description of an open quantum system calls for the characterization of multi-time correlation functions. As significant examples, mean values of operators at different times yield optical spectra that are of central interest in many physical applications, while multi-time expectation values of completely positive trace nonincreasing maps define the joint probability distributions associated with sequential measurements at different times. Besides their practical interest, the quantum description of multi-time correlation functions has thus a deep fundamental meaning, related with the unavoidably invasive nature of measurements in quantum mechanics. After reviewing the general properties and physical meaning of quantum multi-time correlation functions, I will present a recently introduced nonperturbative method to treat them in any dynamical regime. On the one hand, this allows us to treat in full generality non-Markovian statistics – beyond the range of validity of the quantum regression theorem – and, on the other hand, it broadens our understanding of the difference between classical and quantum stochastic processes associated with sequential measurements at different times.

**Giovanni Spaventa** (Ulm University): **On tests of the quantum nature of gravitational interactions in presence of non-linear corrections to quantum mechanics**

When two particles interact primarily through gravity and follow the laws of quantum mechanics, the generation of entanglement is considered a hallmark of the quantum nature of the gravitational interaction.

However, we demonstrate that entanglement dynamics can also occur in the presence of a weak quantum interaction and non-linear corrections to local quantum mechanics, even if the gravitational interaction is classical or absent at short distances.

This highlights the importance of going beyond entanglement detection to conclusively test the quantum character of gravity, and it

requires a thorough examination of the strength of other quantum forces and potential non-linear corrections to quantum mechanics in the realm of large masses.

**Hendrik Ulbricht **(University of Southampton): **Testing quantum mechanics and gravity by levitated mechanics**

I will report on our recent efforts to push levitated experiments in a regime for testing both quantum superpositions of large masses and gravity of small masses. I will show results from non-interferometric experiments in optical and magnetic trapping as well as two-mass gravity by using levitated magnets as probes. I will also show our progress for an upcoming levitated experiment in space.

**Linda van Manen **(FSU Jena): **Stochastic dynamics of quantum systems with switching diffusion coefficient**

In this talk I will discuss open quantum systems in a bath with a fluctuating diffusion constant. The fluctuating environment will correlate two quantum systems and allow us to distinguish internal interactions from system-bath interactions. Furthermore, we can evaluate the quantumness of the correlations. If time permits, I will shortly talk on how this model can be utilized as a test for quantum gravity.

**Andrea Vinante **(CNR - Istituto di Fotonica e Nanotecnologie): **Tests of spontanous collapse models with mechanical and thermal experiments**

Spontaneous collapse models predict a violation of energy conservation, that should manifest as a force noise in mechanical systems or as a tiny spontaneous heating of matter. These effects can be used to perform noninterferometric experimental tests of collapse models and rule out regions of their parameter space. In this talk, I will focus on mechanical and thermal tests at low temperature. I will discuss recent results and future prospects

## Organisers

Angelo Bassi - University of Trieste, Italy

Matteo Carlesso - University of Trieste, Italy

Sandro Donadi - Queen's University Belfast, UK

## Accomodation

Each participant will be responsible for booking their accomodation. Some options include the following:

-Hotel Colombia, Via della Geppa 18, 34132 Trieste

-Palazzo Talenti 1907, Via Saverio Mercadante 1, 34122 Trieste

-Hotel Città di Parenzo, 8 Via degli Artisti 8, 34121 Trieste

## Travel

Arriving by plane, one can choose to land at Trieste Airport, Venice Marco Polo Airport, or Treviso Airport. In addition, trains operated by Trenitalia travel frequently between Trieste and major Italian cities. Moreover, buses are available for local and regional transport.

Airport transit: Trieste is served by the **Ronchi dei Legionari Airport**, the closest and most convenient airport to the city. Visitors can reach the city by either using Bus Line G51 or train.

**From airport to Trieste by bus**: The bus stops are outside the airport terminal building, on the left. Bus 51 runs from the airport to downtown Trieste. At the airport, bus tickets can be purchased at the Agenzia Turismo FVG on the ground floor or from the automatic machine at the arrivals hall. The tickets must be purchased before getting on the bus.

**From airport to Trieste by train**: The train stop is connected to the airport through an elevated corridor. Train tickets can be purchased from the automatic machines at the train stop, or directly from the **Trenitalia website**.

**From Venice Marco Polo airport to Trieste**: Visitors can reach Trieste from **Venice Marco Polo Airport** by bus + train (look at the **Trenitalia website** for train schedules) or via Flixbus. The Mestre-Venezia airport buses take approximately half an hour from the airport to the train station of Venezia Mestre, where passengers switch to trains that run direct to Trieste. Train tickets must be purchased and validated at the validating machines before boarding trains; fines for carrying non-validated tickets are high.

**From Treviso airport to Trieste**: Visitors can reach Trieste from **Treviso Airport** by bus + train (look at the **Trenitalia website** for train schedules). The Treviso airport buses take approximately 15 minutes from the airport to the train station of Treviso, where passengers switch to trains that run direct to Trieste. Train tickets must be purchased and validated at the validating machines before boarding trains; fines for carrying non-validated tickets are high.

## How to reach the venue:

The school will take place in the **lecture room F in the G building** in the central campus of the Trieste University.

Since Trieste is quite a small city, the best way to get around it is to walk. However, take into account that the University is quite uphill and it can take a bit of time to get there.

In alternative, there are several buses that connects the University with the city centre. Tickets for the bus must be purchased in advance, as they are not available onboard. You can purchase them at the main train station in Trieste and at the many local tobacco shops (which are indicated with the symbol T). The cost of a one-way ticket is 1.35 Eur. Remember to validate it at the moment of getting on the bus in the machines located in the interior.

Local Bus No. 17/ departs from Piazza della Libertà (in front of the Trieste Central Station), and arrives at the University. **17/ schedule**

Local Bus No. 17: It is better to take it from the start of Via Coroneo (the bus stop is close to the ALDI supermarket). It also arrives at the University. **17 schedule**

**Contacts**: matteo.carlesso@units.it, s.donadi@qub.ac.uk

This workshop falls within the activities of QuCoM and is kindly sponsored by INFN