arXiv subjects

Alexander Friedrich

Publications and source records attributed to Alexander Friedrich.

At least 19 recordsLinked to original sources

arXiv2026

Fermion quantum field theory on curved and non-inertial backgrounds in standard-Minkowski form

Quantum field theory on curved and non-inertial backgrounds contains background- and foliation-dependent quantities in the canonical Lagrangian, the hypersurface inner product and bilinear form, as well as in the equal-time anti-commutation relations. In this work, we determine a local fermion-field redefinition that brings these canonical structures into their standard-Minkowski forms, i. e., the forms they assume in Cartesian inertial coordinates on Minkowski spacetime, where the zeroth world coordinate is identified as the coordinate of time. Starting from the generally covariant Dirac action minimally coupled to a spin-1 gauge field, we derive the corresponding Lagrangian, fermionic inner product, and quantization rule in an Arnowitt-Deser-Misner decomposition, formulated in arbitrary world coordinates. We identify the generalized temporal gamma matrix as the common geometric factor governing the canonical temporal structure of all three quantities. Using a field redefinition, we transform this generalized temporal gamma matrix to its standard-Minkowski form, thereby mapping the fermionic inner product and the equal-time anti-commutation relation to their standard-Minkowski expressions, while transferring the explicit background and foliation dependence to the transformed Lagrangian and fermion-field operators. We show that such a field redefinition necessarily consists of a local rescaling and a fixing of the local Lorentz frame. This procedure restores the conventional canonical normalization from standard-Minkowski spacetime used for fermionic mode quantization and occupation-number operators. The transformed Lagrangian consequently assumes a generalized first-order Schr\"odinger form, leading to the familiar rest-energy term and spacetime-magnetic couplings, as well as to the leading non-relativistic limit, in which temporal derivatives are separated from spatial ones.

hep-th↗

arXiv2026

PolyNODE: Variable-dimension Neural ODEs on M-polyfolds

Neural ordinary differential equations (NODEs) are geometric deep learning models based on dynamical systems and flows generated by vector fields on manifolds. Despite numerous successful applications, particularly within the flow matching paradigm, all existing NODE models are fundamentally constrained to fixed-dimensional dynamics by the intrinsic nature of the manifold's dimension. In this paper, we extend NODEs to M-polyfolds (spaces that can simultaneously accommodate varying dimensions and a notion of differentiability) and introduce PolyNODEs, the first variable-dimensional flow-based model in geometric deep learning. As an example application, we construct explicit M-polyfolds featuring dimensional bottlenecks and PolyNODE autoencoders based on parametrised vector fields that traverse these bottlenecks. We demonstrate experimentally that our PolyNODE models can be trained to solve reconstruction tasks in these spaces, and that latent representations of the input can be extracted and used to solve downstream classification tasks. The code used in our experiments is publicly available at https://github.com/turbotage/PolyNODE .

cs.LG↗

arXiv2025

Multi-Photon Quantum Rabi Models with Center-of-Mass Motion

The precise control of light-matter interaction serves as a cornerstone for diverse quantum technologies, spanning from quantum computing to advanced atom optics. Typical experiments often feature multi-mode fields and require atoms with intricate internal structures to facilitate e.g., multi-photon interactions or cooling. Moreover, the development of high-precision cold-atom sensors necessitates the use of entangled atoms. We introduce a rigorous, second-quantized framework for describing multi-$\Lambda$-atoms in a cavity, encompassing their center-of-mass motion and interaction with a two-mode electromagnetic field. A key feature of our approach is the systematic application of a Hamiltonian averaging theory to the atomic field operators, enabling the derivation of a compact and physically insightful effective Hamiltonian governing the system's time evolution. This effective Hamiltonian not only incorporates the AC-Stark and Bloch-Siegert shifts, augmented by contributions from all involved ancillary states, but also includes effects from counter-rotating terms, offering a more complete description than conventional RWA-based models. A significant finding is the emergence of a particle-particle interaction mediated by ancillary states, stemming directly from the combined quantum nature of the coupled electromagnetic field and atomic system. We illustrate the practical implications of our model through an analysis of atomic Raman diffraction, determining the time evolution for a typical initial state and demonstrating the resulting Rabi oscillations. Furthermore, our results confirm that both the atomic and optical Hong-Ou-Mandel effect can be observed within this Raman configuration, utilizing a specific two-particle input state, thereby extending the utility of Raman diffraction for quantum interference phenomena and providing a microscopic model of the effect.

quant-ph↗

arXiv2024

Decoupling of External and Internal Dynamics in Driven Two-level Systems

We show how a laser driven two-level system including quantized external degrees of freedom for each state can be decoupled into a set of oscillator equations acting only on the external degrees of freedom with operator valued damping representing the detuning. We give a way of characterizing the solvability of this family of problems by appealing to a classical oscillator with time-dependent damping. As a consequence of this classification we (a) obtain analytic and representation-free expressions for Rabi oscillations including external degrees of freedom with and without an external linear potential, (b) show that whenever the detuning operator can be diagonalized (analytically or numerically) the problem decomposes into a set of classical equations and (c) we can use the oscillator equations as a perturbative basis to describe Rabi oscillations in weak but otherwise arbitrary external potentials. Moreover, chirping of the driving fields phase emerges naturally as a means of compensating the Ehrenfest/mean-value part of the detuning operator's dynamics while the presence of driving phase noise leads to a stochastic evolution equation of Langevin type. Lastly, our approach is representation free with respect to the external degrees of freedom and as consequence a suitable representation or basis expansion can be chosen a posteriori depending on the desired application at hand.

quant-ph↗

arXiv2023

Terrestrial Very-Long-Baseline Atom Interferometry: Workshop Summary

This document presents a summary of the 2023 Terrestrial Very-Long-Baseline Atom Interferometry Workshop hosted by CERN. The workshop brought together experts from around the world to discuss the exciting developments in large-scale atom interferometer (AI) prototypes and their potential for detecting ultralight dark matter and gravitational waves. The primary objective of the workshop was to lay the groundwork for an international TVLBAI proto-collaboration. This collaboration aims to unite researchers from different institutions to strategize and secure funding for terrestrial large-scale AI projects. The ultimate goal is to create a roadmap detailing the design and technology choices for one or more km-scale detectors, which will be operational in the mid-2030s. The key sections of this report present the physics case and technical challenges, together with a comprehensive overview of the discussions at the workshop together with the main conclusions.

hep-ex↗

arXiv2023

Finite Pulse-Time Effects in Long-Baseline Quantum Clock Interferometry

Quantum-clock interferometry has been suggested as a quantum probe to test the universality of free fall (UFF) and the universality of gravitational redshift (UGR). In typical experimental schemes it seems advantageous to employ Doppler-free E1-M1 transitions which have so far been investigated in quantum gases at rest. Here, we consider the fully quantized atomic degrees of freedom and study the interplay of the quantum center-of-mass (COM) $-$ that can become delocalized $-$ together with the internal clock transitions. In particular, we derive a model for finite-time E1-M1 transitions with atomic intern-extern coupling and arbitrary position-dependent laser intensities. We further provide generalizations to the ideal expressions for perturbed recoilless clock pulses. Finally, we show at the example of a Gaussian laser beam that the proposed quantum-clock interferometers are stable against perturbations from varying optical fields for a sufficiently small quantum delocalization of the atomic COM.

quant-ph↗

arXiv2023

Optimal baseline exploitation in vertical dark-matter detectors based on atom interferometry

Several terrestrial detectors for gravitational waves and dark matter based on long-baseline atom interferometry are currently in the final planning stages or already under construction. These upcoming vertical sensors are inherently subject to gravity and thus feature gradiometer or multi-gradiometer configurations using single-photon transitions for large momentum transfer. While there has been significant progress on optimizing these experiments against detrimental noise sources and for deployment at their projected sites, finding optimal configurations that make the best use of the available resources are still an open issue. Even more, the fundamental limit of the device's sensitivity is still missing. Here we fill this gap and show that (a) resonant-mode detectors based on multi-diamond fountain gradiometers achieve the optimal, shot-noise limited, sensitivity if their height constitutes 20% of the available baseline; (b) this limit is independent of the dark-matter oscillation frequency; and (c) doubling the baseline decreases the ultimate measurement uncertainty by approximately 65%. Moreover, we propose a multi-diamond scheme with less mirror pulses where the leading-order gravitational phase contribution is suppressed, compare it to established geometries, and demonstrate that both configurations saturate the same fundamental limit.

quant-ph↗

arXiv2023

The Wave Functional of the Vacuum in a Resonator

We show that despite the fundamentally different situations, the wave functional of the vacuum in a resonator is identical to that of free space. The infinite product of Gaussian ground state wave functions defining the wave functional of the vacuum translates into an exponential of a sum rather than an integral over the squares of mode amplitudes weighted by the mode volume and a power of the mode wave number. We express this sum by an integral of a bilinear form of the field containing a kernel given by a function of the square root of the negative Laplacian acting on a transverse delta function. For transverse fields it suffices to employ the familiar delta function which allows us to obtain explicit expressions for the kernels of the vector potential, the electric field and the magnetic induction. We show for the example of the vector potential that different mode expansions lead to different kernels. Lastly, we show that the kernels have a close relationship with the Wightman correlation functions of the fields.

physics.gen-ph↗

arXiv2022

Tunneling Gravimetry

We examine the prospects of utilizing matter-wave Fabry-Pérot interferometers for enhanced inertial sensing applications. Our study explores such tunneling-based sensors for the measurement of accelerations in two configurations: (a) a transmission setup, where the initial wave packet is transmitted through the cavity and (b) an out-tunneling scheme with intra-cavity generated initial states lacking a classical counterpart. We perform numerical simulations of the complete dynamics of the quantum wave packet, investigate the tunneling through a matter-wave cavity formed by realistic optical potentials and determine the impact of interactions between atoms. As a consequence we estimate the prospective sensitivities to inertial forces for both proposed configurations and show their feasibility for serving as inertial sensors.

quant-ph↗

arXiv2022

Light propagation and atom interferometry in gravity and dilaton fields

Dark matter or violations of the Einstein equivalence principle influence the motion of atoms, their internal states as well as electromagnetic fields, thus causing a signature in the signal of atomic detectors. To model such new physics, we introduce dilaton fields and study the modified propagation of light used to manipulate atoms in light-pulse atom interferometers. Their interference signal is dominated by the matter's coupling to gravity and the dilaton. Even though the electromagnetic field contributes to the phase, no additional dilaton-dependent effect can be observed. However, the light's propagation in gravity enters via a modified momentum transfer and its finite speed. For illustration, we discuss effects from light propagation and the dilaton on different atom-interferometric setups, including gradiometers, equivalence principle tests, and dark matter detection.

quant-ph↗

arXiv2022

Universality-of-clock-rates test using atom interferometry with $T^{3}$ scaling

Metric descriptions of gravitation, among them general relativity as today's established theory, are founded on assumptions summarized by the Einstein equivalence principle (EEP). Its violation would hint at unknown physics and could be a leverage for the development of quantum gravity. Atomic clocks are excellent systems to probe aspects of EEP connected to (proper) time and have evolved into a working horse for tests of local position invariance (LPI). Even though the operational definition of time requires localized and idealized clocks, quantum systems like atoms allow for spatial superpositions that are inherently delocalized. While quantum experiments have tested other aspects of EEP, no competitive test of LPI has been performed or proposed allowing for an intrinsic delocalization. We extend the concepts for tests of the universality of clock rates (one facet of LPI) to atom interferometry generating delocalized quantum clocks. The proposed test depends on proper time with a favorable scaling and is, in contrast to fountain clocks, robust against initial conditions and recoil effects. It enables optical frequencies so that the projected sensitivity exceeds the one of state-of-the-art localized clocks. These results extend our notion of time, detached from classical and localized philosophies.

quant-ph↗

arXiv2022

SCoT: Sense Clustering over Time: a tool for the analysis of lexical change

We present Sense Clustering over Time (SCoT), a novel network-based tool for analysing lexical change. SCoT represents the meanings of a word as clusters of similar words. It visualises their formation, change, and demise. There are two main approaches to the exploration of dynamic networks: the discrete one compares a series of clustered graphs from separate points in time. The continuous one analyses the changes of one dynamic network over a time-span. SCoT offers a new hybrid solution. First, it aggregates time-stamped documents into intervals and calculates one sense graph per discrete interval. Then, it merges the static graphs to a new type of dynamic semantic neighbourhood graph over time. The resulting sense clusters offer uniquely detailed insights into lexical change over continuous intervals with model transparency and provenance. SCoT has been successfully used in a European study on the changing meaning of `crisis'.

cs.CL↗

arXiv2021

Gravitational Redshift Tests with Atomic Clocks and Atom Interferometers

Atomic interference experiments can probe the gravitational redshift via the internal energy splitting of atoms and thus give direct access to test the universality of the coupling between matter-energy and gravity at different spacetime points. By including possible violations of the equivalence principle in a fully quantized treatment of all degrees of freedom, we characterize how the sensitivity to gravitational redshift violations arises in atomic clocks and atom interferometers, as well as their underlying limitations. Specifically, we show that: (i.) Contributions beyond linear order to trapping potentials lead to such a sensitivity of trapped atomic clocks. (ii.) While Bragg-type interferometers, even with a superposition of internal states, with state-independent, linear interaction potentials are at first insensitive to gravitational redshift tests, modified configurations, for example by relaunching the atoms, can mimic such tests tests under certain conditions. (iii.) Guided atom interferometers are comparable to atomic clocks. (iv.) Internal transitions lead to state-dependent interaction potentials through which light-pulse atom interferometers can become sensitive to gravitational redshift violations.

quant-ph↗

arXiv2020

Atom-interferometric test of the universality of gravitational redshift and free fall

Light-pulse atom interferometers constitute powerful quantum sensors for inertial forces. They are based on delocalised spatial superpositions and the combination with internal transitions directly links them to atomic clocks. Since classical tests of the gravitational redshift are based on a comparison of two clocks localised at different positions under gravity, it is promising to explore whether the aforementioned interferometers constitute a competitive alternative for tests of general relativity. Here we present a specific geometry which together with state transitions leads to a scheme that is concurrently sensitive to both violations of the universality of free fall and gravitational redshift, two premises of general relativity. The proposed interferometer does not rely on a superposition of internal states, but merely on transitions between them, and therefore generalises the concept of physical atomic clocks and quantum-clock interferometry. An experimental realisation seems feasible with already demonstrated techniques in state-of-the-art facilities.

quant-ph↗

arXiv2019

Minimizers of Generalized Willmore Functionals

We introduce a notion of generalized Willmore functionals motivated by the Hawking energy of General Relativity and bending energies of membranes. An example of a bending energy is discussed in detail. Using results of Y. Chen and J. Li, we present a compactness result for branched, immersed, haunted, stratified surface with bounded area and Willmore energy. This allows us to prove the existence of area constrained minimizers for generalized Willmore functionals in the class of haunted, branched, immersed bubble trees by direct minimization. Here a haunted, stratified surfaces are introduced, in order to account for bubbling and vanishing components along the minimization process. Similarly, we obtain the existence of area and volume constrained, minimal, closed membranes for the discussed bending energy. Moreover, we argue that the regularity results of A. Mondino and T. Rivière for Willmore surfaces can be carried over to the setting of generalized Willmore surfaces. In particular, this means that critical points of a generalized Willmore functional are smooth away from finitely many points.

math.DG↗

arXiv2019

Concentration of Small Hawking Type Surfaces

We investigate the Hawking energy of small surfaces in space times without symmetry assumptions by introducing the notion of Hawking type functionals. In particular, we find that Hawking type functionals are generalized Willmore functionals which allows us to find area constrained, minimizing, immersed, haunted bubble trees. These bubble trees are smooth spheres provided their area is small enough. Following a similar analysis of the Willmore functional conducted by T. Lamm and J. Metzger we characterize the concentration points of area constrained, critical surfaces for Hawking type functionals and the Hawking energy. Moreover, we determine their expansion on small surfaces.

math.DG↗

arXiv2019

Interference of Clocks: A Quantum Twin Paradox

The phase of matter waves depends on proper time and is therefore susceptible to special-relativistic (kinematic) and gravitational (redshift) time dilation. Hence, it is conceivable that atom interferometers measure general-relativistic time-dilation effects. In contrast to this intuition, we show: (i.) Closed light-pulse interferometers without clock transitions during the pulse sequence are not sensitive to gravitational time dilation in a linear potential. (ii.) They can constitute a quantum version of the special-relativistic twin paradox. (iii.) Our proposed experimental geometry for a quantum-clock interferometer isolates this effect.

quant-ph↗

arXiv2019

Embodied Neuromorphic Vision with Event-Driven Random Backpropagation

Spike-based communication between biological neurons is sparse and unreliable. This enables the brain to process visual information from the eyes efficiently. Taking inspiration from biology, artificial spiking neural networks coupled with silicon retinas attempt to model these computations. Recent findings in machine learning allowed the derivation of a family of powerful synaptic plasticity rules approximating backpropagation for spiking networks. Are these rules capable of processing real-world visual sensory data? In this paper, we evaluate the performance of Event-Driven Random Back-Propagation (eRBP) at learning representations from event streams provided by a Dynamic Vision Sensor (DVS). First, we show that eRBP matches state-of-the-art performance on the DvsGesture dataset with the addition of a simple covert attention mechanism. By remapping visual receptive fields relatively to the center of the motion, this attention mechanism provides translation invariance at low computational cost compared to convolutions. Second, we successfully integrate eRBP in a real robotic setup, where a robotic arm grasps objects according to detected visual affordances. In this setup, visual information is actively sensed by a DVS mounted on a robotic head performing microsaccadic eye movements. We show that our method classifies affordances within 100ms after microsaccade onset, which is comparable to human performance reported in behavioral study. Our results suggest that advances in neuromorphic technology and plasticity rules enable the development of autonomous robots operating at high speed and low energy consumption.

cs.NE↗