Involved institute: Theoretical Physics (from 2018)
Public type of publication: Articles ref. in Journals
"Online First" included

Worldline master formulas for the dressed electron propagator, part 1: Off-shell amplitudes

Ahmadiniaz, N.; Guzman, V. M. B.; Bastianelli, F.; Corradini, O.; Edwards, J. P.; Schubert, C.

In the firrst-quantised worldline approach to quantum field theory, a long-standing problem has been to extend this formalism to amplitudes involving open fermion lines while maintaining the efficiency of the well-tested closed-loop case. In the present series of papers, we develop a suitable formalism for the case of quantum electrodynamics (QED) in vacuum (part one and two) and in a constant external electromagnetic field (part three), based on second-order fermions and the symbol map. We derive this formalism from standard field theory, but also give an alternative derivation intrinsic to the worldline theory. In this first part, we use it to obtain a Bern-Kosower type master formula for the fermion propagator, dressed with N photons in configuration as well as in momentum space.

Keywords: Worlline formalism; QED; Scattering Amplitudes; Gauge Symmetry


Trapped-ion toolkit for studies of quantum harmonic oscillators under extreme conditions

Wittemer, M.; Schröder, J.-P.; Hakelberg, F.; Kiefer, P.; Fey, C.; Schützhold, R.; Warring, U.; Schaetz, T.

Many phenomena described in relativistic quantum field theory are inaccessible to direct observations, but analogue processes studied under well-defined laboratory conditions can present an alternative perspective. Recently, we demonstrated an analogy of particle creation using an intrinsically robust motional mode of two trapped atomic ions. Here, we substantially extend our classical control techniques by implementing machine-learning strategies in our platform and, consequently, increase the accessible parameter regime. As a proof of methodology, we present experimental results of multiple quenches and parametric modulation of an unprotected motional mode of a single ion, demonstrating the increased level of real-time control. In combination with previous results, we enable future experiments that may yield entanglement generation using a process in analogy to Hawking radiation. This article is part of a discussion meeting issue 'The next generation of analogue gravity experiments'.

Keywords: Trapped Ions; Qubits; Ion Traps (Instrumentation)

Heisenberg limit for detecting vacuum birefringence

Ahmadiniaz, N.; Cowan, T.; Sauerbrey, R.; Schramm, U.; Schlenvoigt, H.-P.; Schützhold, R.

Quantum electrodynamics predicts the vacuum to behave as a nonlinear medium, including effects such as birefringence. However, for experimentally available field strengths, this vacuum polarizability is extremely small and thus very hard to measure. In analogy to the Heisenberg limit in quantum metrology, we study the minimum requirements for such a detection in a given strong field (the pump field). Using a laser pulse as the probe field, we find that its energy must exceed a certain threshold depending on the interaction time. However, a detection at that threshold, i.e., the Heisenberg limit, requires highly nonlinear measurement schemes--while for ordinary linear-optics schemes, the required energy (Poisson or shot noise limit) is much larger. Finally, we discuss several currently considered experimental scenarios from this point of view.

Keywords: Quantum Electrodynamics; Vacuum birefringence; Heisenberg limit


Quantum radiation in dielectric media with dispersion and dissipation

Lang, S.; Schützhold, R.; Unruh, W.

By a generalization of the Hopfield model, we construct a microscopic Lagrangian describing a dielectric medium with dispersion and dissipation. This facilitates a well-defined and unambiguous ab initio treatment of quantum electrodynamics in such media, even in time-dependent backgrounds. As an example, we calculate the number of photons created by switching on and off dissipation in dependence on the temporal switching function. This effect may be stronger than quantum radiation produced by variations of the refractive index Δn(t) since the latter are typically very small and yield photon numbers of order (Δn)². As another difference, we find that the partner particles of the created medium photons are not other medium photons but excitations of the environment field causing the dissipation (which is switched on and off).

Off-shell Ward identities for N-gluon amplitudes

Ahmadiniaz, N.; Schubert, C.

Off-shell Ward identities in non-abelian gauge theory continue to be a subject of active research, since they are, in general, inhomogeneous and their form depends on the chosen gauge-fixing procedure. For the three-gluon and four-gluon vertices, it is known that a relatively simple form of the Ward identity can be achieved using the pinch technique or, equivalently, the background-field method with quantum Feynman gauge. The latter is also the gauge-fixing underlying the string-inspired formalism, and here we use this formalism to derive the corresponding form of the Ward identity for the one-loop N - gluon amplitudes.


Pair production in temporally and spatially oscillating fields

Aleksandrov, I. A.; Kohlfürst, C.

Electron-positron pair production for inhomogeneous electric and magnetic fields oscillating in space and time is investigated. By employing accurate numerical methods (Furry-picture quantization and quantum kinetic theory), final particle momentum spectra are calculated and analyzed in terms of effective models. Furthermore, criteria for the applicability of approximate methods are derived and discussed. In this context, special focus is placed on the local density approximation, where fields are assumed to be locally homogeneous in space. Eventually, we apply our findings to the multiphoton regime. Special emphasis is on the importance of linear momentum conservation and the effect of its absence in momentum spectra within approximations based on local homogeneity of the fields.

On the effect of time-dependent inhomogeneous magnetic fields on the particle momentum spectrum in electron-positron pair production

Kohlfürst, C.

Electron-positron pair production in spatially and temporally inhomogeneous electric and magnetic fields is studied within the Dirac-Heisenberg-Wigner formalism (quantum kinetic theory) through computing the corresponding Wigner functions. The focus is on discussing the particle momentum spectrum regarding signatures of Schwinger and multiphoton pair production. Special emphasis is put on studying the impact of a strong dynamical magnetic field on the particle distribution functions. As the equal-time Wigner approach is formulated in terms of partial integro-differential equations an entire section of the manuscript is dedicated to present numerical solution techniques applicable to Wigner function approaches in general.

WKB approach to pair creation in spacetime-dependent fields: The case of a spacetime-dependent mass

Oertel, J.; Schützhold, R.

Besides tunneling in static potential landscapes, for example, the Wentzel-Kramers-Brillouin (WKB) approach is a powerful nonperturbative approximation tool to study particle creation due to time-dependent background fields, such as cosmological particle production or the Sauter-Schwinger effect, i.e., electron-positron pair creation in a strong electric field. However, our understanding of particle creation processes in background fields depending on both space and time is rather incomplete. In order to venture into this direction, we propose a generalization of the WKB method to truly spacetime-dependent fields and apply it to the case of a spacetime-dependent mass.

Boltzmann relaxation dynamics in the strongly interacting Fermi-Hubbard model

Queißer, F.; Schützhold, R.

Via the hierarchy of correlations, we study the Mott insulator phase of the Fermi-Hubbard model in the limit of strong interactions and derive a quantum Boltzmann equation describing its relaxation dynamics. In stark contrast to the weakly interacting case, we find that the scattering cross sections strongly depend on the momenta of the colliding quasi-particles and holes. Therefore, the relaxation towards equilibrium crucially depends on the spectrum of excitations. For example, for particle-hole excitations directly at the minimum of the (direct) Mott gap, the scattering cross sections vanish such that these excitations can have a very long life-time.

Phonon Pair Creation by Inflating Quantum Fluctuations in an Ion Trap

Schützhold, R.; Wittemer, M.; Hakelberg, F.; Kiefer, P.; Schröder, J.-P.; Warring, U.; Schaetz, T.; Fey, C.

Quantum theory predicts intriguing dynamics during drastic changes of external conditions. We switch the trapping field of two ions sufficiently fast to tear apart quantum fluctuations, i.e., create pairs of phonons and, thereby, squeeze the ions’ motional state. This process can be interpreted as an experimental analog to cosmological particle creation and is accompanied by the formation of spatial entanglement. Hence, our platform allows one to study the causal connections of squeezing, pair creation, and entanglement and might permit one to cross-fertilize between concepts in cosmology and applications of quantum information processing.

Keywords: Inflation; Quantum Information with trapped Ions; Quantum simulation

Relaxation dynamics in a Hubbard dimer coupled to fermionic baths: phenomenological description and its microscopic foundation

Schützhold, R.; Kleinherbers, E.; Szpak, N.; König, J.

We study relaxation dynamics in a strongly-interacting two-site Fermi-Hubbard model that is induced by fermionic baths. To derive the proper form of the Lindblad operators that enter an effective description of the system-bath coupling in different temperature regimes, we employ a diagrammatic real-time technique for the reduced density matrix. An improvement on the commonly-used secular approximation, referred to as coherent approximation, is presented. We analyze the spectrum of relaxation rates and identify different time scales that are involved in the equilibration of the Hubbard dimer after a quantum quench.

Boltzmann relaxation dynamics of strongly interacting spinless fermions on a lattice

Queißer, F.; Schützhold, R.; Schreiber, S.; Kratzer, P.

Motivated by the recent interest in non-equilibrium phenomena in quantum many-body systems, we study strongly interacting fermions on a lattice by deriving and numerically solving quantum Boltzmann equations that describe their relaxation to thermodynamic equilibrium.The derivation is carried out by inspecting the hierarchy of correlations within the framework of the 1/Z-expansion. Applying the Markov approximation, we obtain the dynamic equations for the distribution functions. Interestingly, we find that in the strong-coupling limit, collisions between particles and holes dominate over particle-particle and hole-hole collisions -- in stark contrast to weakly interacting systems. As a consequence, our numerical simulations show that the relaxation time scales strongly depend on the type of excitations (particles or holes or both) that are initially present.

Environment induced pre-thermalization in the Mott-Hubbard model

Queißer, F.; Schützhold, R.

Via the hierarchy of correlations, we study the strongly interacting Fermi-Hubbard model in the Mott insulator state and couple it to a Markovian environment which constantly monitors the particle numbers \hat n_\mu^\uparrow and \hat n_\mu^\downarrow for each lattice site \mu. As expected, the environment induces an imaginary part \gamma (i.e., decay rate) of the quasi-particle frequencies \omega_{\mathbf{k}}\to\omega_{\mathbf{k}}-i\gamma and tends to diminish the correlations between lattice sites. Surprisingly, the environment does also steer the state of the system on intermediate time scales \mathcal{O}(1/\gamma) to a pre-thermalized state very similar to a quantum quench (i.e., suddenly switching on the hopping rate J). Full thermalization occurs via local on-site heating and takes much longer.

Dynamically assisted nuclear fusion

Queißer, F.; Schützhold, R.

We consider deuterium-tritium fusion as a generic example for general fusion reactions. For initial kinetic energies in the keV regime, the reaction rate is exponentially suppressed due to the Coulomb barrier between the nuclei, which is overcome by tunneling. Here, we study whether the tunneling probability could be enhanced by an additional electromagnetic field, such as an x-ray free electron laser (XFEL). We find that the XFEL frequencies and field strengths required for this dynamical assistance mechanism should come within reach of present-day or near-future technology.

Entangling continuous variables with a qubit array

Navez, P.; Sowa, A.; Zagoskin, A.

We show that an array of qubits embedded in a waveguide can emit entangled pairs of microwave photon beams. The quadratures obtained from the homodyne detection of these outputs beams form a pair of correlated continuous variables similar to the Einstein-Podolsky-Rosen experiment. The photon pairs are produced by the decay of plasmonlike collective excitations in the qubit array. The maximum intensity of the resulting beams is bounded by only the number of emitters. We calculate the excitation decay rate both into a continuum of the photon state and into a one-mode cavity. We also determine the frequency of Rabi-like oscillations resulting from a detuning.

Reducible contributions to quantum electrodynamics in external fields

Ahmadiniaz, N.; Edwards, J. P.; Ilderton, A.

We consider one-particle reducible (1PR) contributions to QED and scalar QED processes in external fields, at one-loop and two-loop order. We investigate three cases in detail: constant crossed fields, constant magnetic fields, and plane waves. We find that 1PR tadpole contributions in plane waves and constant crossed fields are non-zero, but contribute only divergences to be renormalised away. In constant magnetic fields, on the other hand, tadpole contributions give physical corrections to processes at one-loop and beyond. Our calculations are exact in the external fields and we give strong and weak field expansions in the magnetic case.

Compton-like scattering of a scalar particle with N photons and one graviton

Ahmadiniaz, N.; Balli, F. M.; Corradini, O.; Dávila, J. M.; Schubert, C.

Tree-level scattering amplitudes for a scalar particle coupled to an arbitrary number N of photons and a single graviton are computed. We employ the worldline formalism as the main tool to compute the irreducible part of the amplitude, where all the photons and the graviton are directly attached to the scalar line, then derive a tree replacement rule to construct the reducible parts of the amplitude which involve irreducible pure N-photon two-scalar amplitudes where one photon line emits the graviton. We test our construction by verifying the on-shell gauge and diffeomorphism Ward identities, at arbitrary N.

Keywords: Scattering amplitudes; gravitons; Ward identities

Analog of cosmological particle creation in electromagnetic waveguides

Lang, S.; Schützhold, R.

We consider an electromagnetic waveguide with a time-dependent propagation speed v(t) as an analog for cosmological particle creation. In contrast to most previous studies which focus on the number of particles produced, we calculate the corresponding two-point correlation function. For a small steplike variation delta v(t), this correlator displays characteristic signatures of particle pair creation. As another potential advantage, this observable is of first order in the perturbation delta v(t), whereas the particle number is second order in delta v(t) and thus more strongly suppressed for small delta v(t).

Ion-trap analog of particle creation in cosmology

Fey, C.; Schätz, T.; Schützhold, R.

We consider the transversal modes of ions in a linear radio-frequency trap where we control the time-dependent axial confinement to show that we can excite quanta of motion via a two-mode squeezing process. This effect is analogous to phenomena predicted to occur in the early universe, in general out of reach for experimental investigation. As a substantial advantage of this proposal in comparison to previous ones we propose to exploit the radial and axial modes simultaneously to permit experimental access of these effects based on state-of-the-art technology. In addition, we propose to create and explore entanglement between the two ions.


Discrete worldline instantons

Schneider, C.; Torgrimsson, G.; Schützhold, R.

The semiclassical approximation of the worldline path integral is a powerful tool to study non-perturbative electron-positron pair creation in spacetime-dependent background fields. Finding solutions of the classical equations of motion, i.e., worldline instantons, is possible analytically only in special cases, and a numerical treatment is nontrivial as well. We introduce a completely general numerical approach based on an approximate evaluation of the discretized path integral that easily and robustly gives the full semiclassical pair production rate in nontrivial multidimensional fields, and apply it to some example cases.


Interaction of a Bose-Einstein condensate with a gravitational wave

Schützhold, R.

Partly motivated by recent proposals for the detection of gravitational waves, we study their interaction with Bose-Einstein condensates. For homogeneous condensates at rest, the gravitational wave does not directly create phonons (to lowest order) but merely affects existing phonons or indirectly creates phonon pairs via quantum squeezing-an effect which has already been considered in the literature. For inhomogeneous condensate flows such as a vortex lattice, however, the impact of the gravitational wave can directly create phonons. This more direct interaction can be more efficient and could perhaps help bring such a detection mechanism for gravitational waves a step closer towards experimental realizability-even though there is still a long way to go. Finally, we argue that super-fluid helium might offer some advantages in this respect.