Lotte Mertens Articles

Lotte Mertens

PhD student theoretical physics

Articles

Anisotropic optics and gravitational lensing of tilted Weyl fermions (May 2023) (Article) Viktor Koenye, Lotte Mertens, Corentin Morice, Dmitry Chernyavsky, Ali G. Moghaddam, Jasper van Wezel, Jeroen van den Brink

We show that tilted Weyl semimetals with a spatially varying tilt of the Weyl cones provide a platform for studying analogs to problems in anisotropic optics as well as curved spacetime. Considering particular tilting profiles, we numerically evaluate the time evolution of electronic wave packets and their current densities. We demonstrate that electron trajectories in such systems can be obtained from Fermat's principle in the presence of an inhomogeneous, anisotropic effective refractive index. On the other hand, we show how the electron dynamics reveal gravitational features and use them to simulate gravitational lensing around a synthetic black hole. These results bridge optical and gravitational analogies in Weyl semimetals, suggesting different pathways for experimental solid-state electron optics.

An objective collapse model without state dependent stochasticity (May 2023) (Article) Lotte Mertens, Matthijs Wesseling, Jasper van Wezel

The impossibility of describing measurement in quantum mechanics while using a quantum mechanical model for the measurement machine, remains one of its central problems. Objective collapse theories attempt to resolve this problem by proposing alterations to Schrödinger's equation. Here, we present a minimal model for an objective collapse theory that, in contrast to previous proposals, does not employ state dependent stochastic terms in its construction. It is an explicit proof of principle that it is possible for Born's rule to emerge from a stochastic evolution in which no properties of the stochastic process depend on the state being evolved. We propose the presented model as a basis from which more realistic objective collapse theories can be constructed.

Environment-assisted invariance does not necessitate Born’s rule for quantum measurement (March 2023) (Article) Lotte Mertens, Jasper van Wezel

The argument of environment-assisted invariance (known as envariance) implying Born’s rule is widely used in models for quantum measurement to reason that they must yield the correct statistics, specifically for linear models. However, it has recently been shown that linear collapse models can never give rise to Born’s rule. Here, we address this apparent contradiction and point out an inconsistency in the assumptions underlying the arguments based on envariance. We use a construction in which the role of the measurement machine is made explicit and shows that the presence of envariance does not imply that every measurement will behave according to Born’s rule. Rather, it implies that every quantum state allows a measurement machine to be constructed, which yields Born’s rule when measuring that particular state. This resolves the paradox and is in agreement with the recent result of objective collapse models necessarily being nonlinear.

Quantum state reduction of general initial states through spontaneous unitarity violation (January 2023) (Article) Aritro Mukherjee, Srinivas Gotur, Jelle Aalberts, Rosa van den Ende, Lotte Mertens, Jasper van Wezel

The inability of Schrodinger's unitary time evolution to describe measurement of a quantum state remains a central foundational problem. It was recently suggested that the unitarity of Schrodinger dynamics can be spontaneously broken, resulting in measurement as an emergent phenomenon in the thermodynamic limit. Here, we introduce a family of models for spontaneous unitarity violation that apply to generic initial superpositions over arbitrarily many states, using either single or multiple state-independent stochastic components. Crucially, we show that Born's probability rule emerges spontaneously in all cases.

Thermalization by a synthetic horizon (June 2022, (Article)) Lotte Mertens, Ali G. Moghaddam, Dmitry Chernyavsky, Corentin Morice, Jeroen van den Brink, Jasper van Wezel

Synthetic horizons in models for quantum matter provide an alternative route to explore fundamental questions of modern gravitational theory. Here, we apply these concepts to the problem of emergence of thermal quantum states in the presence of a horizon, by studying ground-state thermalization due to instantaneous horizon creation in a gravitational setting and its condensed matter analogue. By a sudden quench to position-dependent hopping amplitudes in a one-dimensional lattice model, we establish the emergence of a thermal state accompanying the formation of a synthetic horizon. The resulting temperature for long chains is shown to be identical to the corresponding Unruh temperature, provided that the post-quench Hamiltonian matches the entanglement Hamiltonian of the pre-quench system. Based on detailed analysis of the outgoing radiation we formulate the conditions required for the synthetic horizon to behave as a purely thermal source, paving a way to explore this interplay of quantum-mechanical and gravitational aspects experimentally.

The inconsistency of linear dynamics and Born's rule (June 2021, Editors' Suggestion PRA) Lotte Mertens, Matthijs Wesseling, Niels Vercauteren, Alonso Corrales-Salazar, and Jasper van Wezel

Modern experiments using nanoscale devices come ever closer to bridging the divide between the quantum and classical realms, bringing experimental tests of objective collapse theories that propose alterations to Schrödinger's equation within reach. Such objective collapse theories aim to explain the emergence of classical dynamics in the thermodynamic limit and hence resolve the inconsistency that exists within the axioms of quantum mechanics when assuming measurement can be described by quantum mechanics as well. Here, we show that requiring the emergence of Born's rule for relative frequencies of measurement outcomes without imposing them as part of any axiom implies that such objective collapse theories cannot be linear. Previous suggestions for proof of the emergence of Born's rule in classes of problems that include linear objective collapse theories are analyzed and shown to include hidden assumptions.