arXiv subjects

Christian Schubert

Publications and source records attributed to Christian Schubert.

At least 19 recordsLinked to original sources

arXiv2026

Worldline representation of multiloop amplitudes in quantum electrodynamics

The worldline approach to quantum electrodynamics allows one to construct integral representations combining large numbers of Feynman diagrams. Here I review the state-of-the-art of a long-term effort to make this fact useful for actual multiloop calculations, such as of the scalar and spinor QED vacuum polarization functions and the electron anomalous magnetic moment. After a short historical introduction, and a discussion of the non-standard mathematical challenges involved, I focus on a recent calculation of the two-loop vacuum polarisation in scalar QED and some master integral formulas obtained in this context.

hep-th↗

arXiv2026

Integration techniques for worldline integrals

The worldline formalism allows one to obtain compact integral representations combining the information of large numbers of Feynman diagrams. However, their analytic calculation leads to a non-standard integration problem for which existing mathematical algorithms are of little help. Here I will summarize the state-of-the-art of worldline integration focusing on examples from QED in vacuum and in constant external fields.

hep-th↗

arXiv2025

Space magnetometry with a differential atom interferometer

Atom interferometers deployed in space are excellent tools for high precision measurements, navigation, or Earth observation. In particular, differential interferometric setups feature common-mode noise suppression and enable reliable measurements in the presence of ambient platform noise. Here we report on orbital magnetometry campaigns performed with differential single- and double-loop interferometers in NASA's Cold Atom Lab aboard the International Space Station. By comparing measurements with atoms in magnetically sensitive and insensitive states, we have realized atomic magnetometers mapping magnetic field curvatures. Our results pave the way towards precision quantum sensing missions in space.

physics.atom-ph↗

arXiv2025

Large, ultra-flat optical traps for uniform quantum gases

Ultracold atomic gases with uniform density can be created by flat-bottom optical traps. These gases provide an ideal platform to study many-body physics in a system that allows for simple connections with theoretical models and emulation of numerous effects from a wide range of fields of physics. In Earth-bound laboratories the trap sizes, number of species and states, as well as the range of physical effects are largely restricted by the adopted levitation technique. Homogeneous ultracold gases in microgravity simulators and space however offer an interesting perspective which is actively being pursued. To exploit the full potential of any gravity-compensated laboratory the box potentials created need to be as large as possible. By using two orthogonally aligned acousto-optic deflectors, we create large time-averaged optical potentials with trapping volumes a thousandfold larger than conventional setups, described by power-law scalings with exponents of up to $152$. We verify the performance of our setup by simulating the mean-field behaviour of a quantum gas ground state in conjunction with dynamical excitations due to the realistic time-dependent painting potentials. The implementation of this setup may open new directions at the interface with condensed matter, few-body Efimov physics or the exploration of critical, non-equilibrium phenomena.

cond-mat.quant-gas↗

arXiv2024

Worldline integration of photon amplitudes

It has been known for many years that methods inspired by string theory, such as the worldline formalism, allow one to write down integral representations that combine large numbers of Feynman diagrams of different topologies. However, to make this fact useful for state-of-the-art calculations one has to confront non-standard integration problems where neither the known integration techniques for Feynman diagrams nor algebraic manipulation programs are of much help. Here I will give a progress report on this long-term project focussing on photon amplitudes at one and two loops, in vacuum and in external fields.

hep-th↗

arXiv2024

Pair creation in electric fields

Sauter-Schwinger pair creation in electromagnetic fields is a fundamental prediction of QED and one of the motivations for the present efforts in constructing super-strong lasers. I will give a historical review of the subject, and then focus on two recent developments. The first one is the worldline instanton formalism, a sophisticated version of the WKB approximation that makes it possible to calculate the pair creation rate for complicated field configurations. The second one is an adaptation of the Dirac-Heisenberg-Wigner formalism suitable for a detailed study of the formation of real particles in time and space.

hep-ph↗

arXiv2024

Interferometry of Atomic Matter Waves in the Cold Atom Lab onboard the International Space Station

Ultracold atomic gases hold unique promise for space science by capitalizing on quantum advantages and extended freefall, afforded in a microgravity environment, to enable next-generation precision sensors. Atom interferometers are a class of quantum sensors which can use freely falling gases of atoms cooled to sub-photon-recoil temperatures to provide unprecedented sensitivities to accelerations, rotations, and gravitational forces, and are currently being developed for space-based applications in gravitational, earth, and planetary sciences, as well as to search for subtle forces that could signify physics beyond General Relativity and the Standard Model. NASA's Cold Atom Lab (CAL) operates onboard the International Space Station as a multi-user facility for studies of ultracold atoms and to mature quantum technologies, including atom interferometry, in persistent microgravity. In this paper, we report on path-finding experiments utilizing ultracold $^{87}$Rb atoms in the CAL atom interferometer, which was enabled by an on-orbit upgrade of the CAL science module: A three-pulse Mach-Zehnder interferometer was studied to understand limitations from the influence of ISS vibrations. Additionally, Ramsey shear-wave interferometry was used to manifest interference patterns in a single run that were observable for over 150 ms free-expansion time. Finally, the CAL atom interferometer was used to remotely measure the photon recoil from the atom interferometer laser as a demonstration of the first quantum sensor using matter-wave interferometry in space.

physics.atom-ph↗

arXiv2023

Low-energy limit of N-photon amplitudes in a constant field

While the QED photon amplitudes at full momentum so far have been calculated only up to the six-photon level, in the low-energy limit there are explicit formulas for all helicity components even at the N-photon level, obtained by Martin et al. in 2002. Here we use the worldline formalism to extend that result to the N-photon amplitudes in a generic constant field. For both scalar and spinor QED, we obtain compact representations for the low-energy limits of these amplitudes involving only simple algebra and a single global proper-time integral with trigonometric integrand.

hep-th↗

arXiv2023

Optimal squeezing for high-precision atom interferometers

We show that squeezing is a crucial resource for interferometers based on the spatial separation of ultra-cold interacting matter. Atomic interactions lead to a general limitation for the precision of these atom interferometers, which can neither be surpassed by larger atom numbers nor by conventional phase or number squeezing. However, tailored squeezed states allow to overcome this sensitivity bound by anticipating the major detrimental effect that arises from the interactions. We envisage applications in future high-precision differential matter-wave interferometers, in particular gradiometers, e.g., for gravitational-wave detection.

physics.atom-ph↗

arXiv2023

Generalized Gelfand-Dikii equation and solitonic electric fields for fermionic Schwinger pair production

In previous work on Schwinger pair creation in purely time-dependent fields, it was shown how to construct ``solitonic'' electric fields that do not create scalar pairs with an arbitrary fixed momentum. We show that this construction can be adapted to the fermionic case in two inequivalent ways, both closely related to supersymmetric quantum mechanics for reflectionless potentials, and both leading to the vanishing of the density of created pairs at certain values of the Pöschl-Teller like index $p$ of the associated Schrödinger equation. For one of them, we are able to demonstrate that the pair non-creation can be interpreted as a quantum interference effect using the phase-integral formalism. Asymptotically for large $p$, here scalar particles are not created for integer $p$ and fermions are not created for half integer $p$. Thus for any given momentum we can construct electric fields that create scalar particles but not spinor particles, and vice versa. In the scalar QED case, the solitonic fields had originally been found using the Gelfand-Dikii equation, which is related to the resolvent of the mode equation, and through it to the (generalized) KdV equation [38]. This motivates us to develop for the spinor QED case, too, an evolution equation that can be considered as a fermionic generalization of the Gelfand-Dikii equation.

hep-th↗

arXiv2023

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↗

arXiv2023

The QED four -- photon amplitudes off-shell: part 1

The QED four-photon amplitude has been well-studied by many authors, and on-shell is treated in many textbooks. However, a calculation with all four photons off-shell is presently still lacking, despite of the fact that this amplitude appears off-shell as a subprocess in many different contexts, in vacuum as well as with some photons connecting to external fields. The present paper is the first in a series of four where we use the worldline formalism to obtain this amplitude explicitly in terms of hypergeometric functions, and derivatives thereof, for both scalar and spinor QED. The formalism allows us to unify the scalar and spinor loop calculations, to avoid the usual breaking up of the amplitude into three inequivalent Feynman diagrams, and to achieve manifest transversality as well as UV finiteness at the integrand level by an optimized version of the integration-by-parts procedure originally introduced by Bern and Kosower for gluon amplitudes. The full permutation symmetry is maintained throughout, and the amplitudes get projected naturally into the basis of five tensors introduced by Costantini et al. in 1971. Since in many applications of the "four-photon box" some of the photons can be taken in the low-energy limit, and the formalism makes it easy to integrate out any such leg, apart from the case of general kinematics (part 4) we also treat the special cases of one (part 3) or two (part 2) photons taken at low energy. In this first part of the series, we summarize the application of the worldline formalism to the N-photon amplitudes and its relation to Feynman diagrams, derive the optimized tensor-decomposed integrands of the four-photon amplitudes in scalar and spinor QED, and outline the computational strategy to be followed in parts 2 to 4.

hep-th↗

arXiv2023

The worldline formalism in strong-field QED

The worldline formalism provides an alternative to Feynman diagrams that has been found particularly useful for external-field calculations in quantum electrodynamics. Here I summarize its present range of applications, which includes Schwinger pair creation, photon splitting in constant fields and plane-wave backgrounds, as well as nonlinear Compton scattering in constant fields.

hep-th↗

arXiv2023

Master formulas for photon amplitudes in a combined constant and plane-wave background field

The worldline formalism has previously been used for deriving compact master formulas for the QED $N$ - photon amplitudes in vacuum, in a constant field and in a plane-wave field. Here we carry this program one step further by deriving master formulas for the scalar and spinor QED $N$-photon amplitudes in the background of the "parallel" special case of a combined constant and plane-wave field.

hep-th↗

arXiv2023

Group invariants for Feynman diagrams

It is well-known that the symmetry group of a Feynman diagram can give important information on possible strategies for its evaluation, and the mathematical objects that will be involved. Motivated by ongoing work on multi-loop multi-photon amplitudes in quantum electrodynamics, here I will discuss the usefulness of introducing a polynomial basis of invariants of the symmetry group of a diagram in Feynman-Schwinger parameter space.

math.RT↗

arXiv2022

STE-QUEST -- Space Time Explorer and QUantum Equivalence principle Space Test: The 2022 medium-class mission concept

Space-borne quantum technologies, particularly those based on atom interferometry, are heralding a new era of strategic and robust space exploration. The unique conditions of space, characterized by low noise and low gravity environments, open up diverse possibilities for applications ranging from precise time and frequency transfer to Earth Observation and the search of new Physics. In this paper, we summarise the M-class mission proposal in response to the 2022 call in ESA's science program: Space-Time Explorer and Quantum Equivalence Principle Space Test (STE-QUEST). It consists in a satellite mission featuring a dual-species atom interferometer operating over extended durations. This mission aims to tackle three of the most fundamental questions in Physics: (i) testing the universality of free fall with an accuracy better than one part in $10^{-17}$, (ii) exploring various forms of Ultra-Light Dark Matter, and (iii) scrutinizing the foundations of Quantum Mechanics.

physics.space-ph↗

arXiv2022

Understanding the gravitational and magnetic environment of a very long baseline atom interferometer

By utilizing the quadratic dependency of the interferometry phase on time, the Hannover Very Long Baseline Atom Interferometer facility (VLBAI) aims for sub nm/s$^2$ gravity measurement sensitivity. With its 10 m vertical baseline, VLBAI offers promising prospects in testing fundamental physics at the interface between quantum mechanics and general relativity. Here we discuss the challenges imposed on controlling VLBAI's magnetic and gravitational environment and report on their effect on the device's accuracy. Within the inner 8 m of the magnetic shield, residual magnetic field gradients expect to cause a bias acceleration of only 6$\times$10$^{-14}$ m/s$^2$ while we evaluate the bias shift due to the facility's non-linear gravity gradient to 2.6 nm/s$^2$. The model allows the VLBAI facility to be a reference to other mobile devices for calibration purposes with an uncertainty below the 10 nm/s$^2$ level.

physics.atom-ph↗

arXiv2022

Large-momentum-transfer atom interferometers with $μ$rad-accuracy using Bragg diffraction

Large-momentum-transfer~(LMT) atom interferometers using elastic Bragg scattering on light waves are among the most precise quantum sensors to date. To advance their accuracy from the mrad to the $μ$rad regime, it is necessary to understand the rich phenomenology of the Bragg interferometer, which differs significantly from that of a standard two-mode interferometer. We develop an analytic model for the interferometer signal and demonstrate its accuracy using comprehensive numerical simulations. Our analytic treatment allows the determination of the atomic projection noise limit of an LMT Bragg interferometer, and provides the means to saturate this limit. It affords accurate knowledge of the systematic phase errors as well as their suppression by two orders of magnitude down to a few $μ\mathrm{rad}$ using appropriate light pulse parameters.

physics.atom-ph↗