Publications

 

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

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

Oertel, J.ORC; 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.

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Boltzmann relaxation dynamics in the strongly interacting Fermi-Hubbard model

Queißer, F.ORC; 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.

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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

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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.

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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.

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Entangling continuous variables with a qubit array

Navez, P.; Sowa, A.ORC; 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.

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Reducible contributions to quantum electrodynamics in external fields

Ahmadiniaz, N.ORC; 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.

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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

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Analog of cosmological particle creation in electromagnetic waveguides

Lang, S.ORC; 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).

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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.

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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.

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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.

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