# Research

## Press releases

- 05.12.2019: Fusion by strong lasers
- 12.12.2018: Mini-detectors for the Gigantic?
- 22.10.2018: Simulating the Big Bang in a laboratory setting
- 18.05.2018: Theoretische Physik: Neue Gruppe am HZDR

## Strong Fields

Abstract:

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.

Abstract:

We study electron-positron pair creation from the Dirac vacuum induced by a strong and slowly varying electric field (Schwinger effect) which is superimposed by a weak and rapidly changing electromagnetic field (dynamical pair creation). In the subcritical regime where both mechanisms separately are strongly suppressed, their combined impact yields a pair creation rate which is dramatically enhanced. Intuitively speaking, the strong electric field lowers the threshold for dynamical particle creation—or, alternatively, the fast electromagnetic field generates additional seeds for the Schwinger mechanism. These findings could be relevant for planned ultrahigh-intensity lasers.

Abstract:

The semiclassical approximation of the worldline path integral is a powerful tool to study nonperturbative 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.

- Dynamically assisted Sauter-Schwinger effect in inhomogeneous electric fields (J. High Energ. Phys. (2016) 2016: 164)
- Prefactor in the dynamically assisted Sauter-Schwinger effect (Phys. Rev. D 94, 085015, 2016)
- Doubly assisted Sauter-Schwinger effect (Phys. Rev. D 94, 065035, 2016)
- Pulse shape dependence in the dynamically assisted Sauter-Schwinger effect (Phys. Rev. D 92, 085009, 2015)
- Catalysis of Schwinger vacuum pair production (Phys. Rev. D 80, 111301(R), 2009)

## Graphene

Abstract:

We study electronic transport in graphene under the influence of a transversal magnetic field B(r)=B(x)ez with the asymptotics B(x→±∞)=±B0, which could be realized via a folded graphene sheet in a constant magnetic field, for example. By solving the effective Dirac equation, we find robust modes with a finite energy gap which propagate along the fold—where particles and holes move in opposite directions. Exciting these particle-hole pairs with incident (optical or infrared) photons would then generate a nearly perfect charge separation and thus a strong magnetophotoelectric or magnetothermoelectric effect—even at room temperature.

Abstract:

We study the optical response of a suspended, monolayer graphene field-effect transistor structure in magnetic fields of up to 9 T (quantum Hall regime). With an illumination power of only 3 μW, we measure a photocurrent of up to 400 nA (without an applied bias) corresponding to a photo-responsivity of 0.13 A W^{−1}, which we believe to be one of the highest values ever measured in single-layer graphene. We discuss possible mechanisms for generating this strong photo-response (17 electron–hole pairs per 100 incident photons). Based on our experimental findings, we believe that the most likely scenario is a ballistic two-stage process including carrier multiplication via Auger-type inelastic Coulomb scattering at the graphene edge.

**Strongly Correlated Systems**

Abstract:

Motivated by the recent interest in nonequilibrium 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 timescales strongly depend on the type of excitations (particles or holes or both) that are initially present.

Abstract:

We study a quantum quench in the Bose-Hubbard model where the tunneling rate J is suddenly switched from zero to a finite value in the Mott regime. In order to solve the many-body quantum dynamics far from equilibrium, we consider the reduced density matrices for a finite number of lattice sites and split them up into on-site density operators, i.e., the mean field, plus two-point and three-point correlations etc. Neglecting three-point and higher correlations, we are able to numerically simulate the time-evolution of the on-site density matrices and the two-point quantumcorrelations (e.g., their effective light-cone structure) for a comparably large number ~1000 of lattice sites.

Abstract:

The hierarchy of correlations is an analytical approximation method which allows us to study non-equilibrium phenomena in strongly interacting quantum many-body systems on lattices in higher dimensions (with the underlying idea being somewhat similar to dynamical mean-field theory). So far, this method was restricted to equal-time correlators such as 〈A_{μ}(t)B_{ν}(t)〉. Using the method of complete induction, we generalize this method to double-time correlators such as 〈A_{μ}(t)B_{ν}(t')〉, which allows us to study effective light cones and Green functions and to incorporate finite initial temperatures. As an application, we study the non-equilibrium dynamics after quantum quenches of the Bose-Hubbard model in the Mott insulator phase.

Abstract:

We study the Bose-Hubbard and Fermi-Hubbard models in the (formal) limit of large coordination numbers Z≫1. Via an expansion into powers of 1/Z, we establish a hierarchy of correlations which facilitates an approximate analytical derivation of the time evolution of the reduced density matrices for one and two sites, etc. With this method, we study the quantum dynamics (starting in the ground state) after a quantum quench, i.e., after suddenly switching the tunneling rate J from zero to a finite value, which is still in the Mott regime. We find that the reduced density matrices approach a (quasi)equilibrium state after some time. For one lattice site, this state can be described by a thermal state (within the accuracy of our approximation). However, the (quasi)equilibrium state of the reduced density matrices for two sites including the correlations can not be described by a thermal state. Thus, real thermalization (if it occurs) should take a much longer time. This behavior has already been observed in other scenarios and is sometimes called “prethermalization”. Finally, we compare our results to numerical simulations for finite lattices in one and two dimensions and find qualitative agreement.

Further references:

- Boltzmann relaxation dynamics in the strongly interacting Fermi-Hubbard model (Phys. Rev. A 100, 053617, 2019)
- Environment-induced prerelaxation in the Mott-Hubbard model (Phys. Rev. B 99, 155110, 2019)
- Quasi-particle approach for lattice Hamiltonians with large coordination numbers (Journal of Physics A: Mathematical and Theoretical, Volume 47, Number 22, 2014)
- Emergence of coherence in the Mott-insulator–superfluid quench of the Bose-Hubbard model (Phys. Rev. A 82, 063603, 2010)

## Quantum Information and Quantum devices

Abstract:

We propose a scheme for entangling two photons via the quantum Zeno effect, which describes the inhibition of quantum evolution by frequent measurements and is based on the difference between summing amplitudes and probabilities. For a given error probability P_{error}, our scheme requires that the one-photon loss rate ξ_{1γ} and the two-photon absorption rate ξ_{2γ} in some medium satisfy ξ_{1γ} /ξ_{2γ} = 2(P_{error}/π)^{2}, which is significantly improved compared to previous approaches. Again based on the quantum Zeno effect, as well as coherent excitations, we present a possibility to fulfill this requirement in an otherwise linear optics setup.

Abstract:

We propose a probabilistic quantum algorithm that decides whether a monochrome picture matches a given template (or one out of a set of templates). As a major advantage to classical pattern recognition, the algorithm requires just a few incident photons and is thus suitable for very sensitive pictures (similar to the Elitzur-Vaidman problem). Furthermore, for a 2^{n}×2^{m} image, O(n+m) qubits are sufficient. Using the quantum Fourier transform, it is possible to improve the fault tolerance of the quantum algorithm by filtering out small-scale noise in the picture. For example images with 512×512 pixels, we have numerically simulated the unitary operations in order to demonstrate the applicability of the algorithm and to analyze its fault tolerance.

Abstract:

We study the ground-state entanglement in the quantum Ising model with nearest neighbor ferromagnetic coupling J and find a sequential increase of entanglement depth d with growing J. This entanglement avalanche starts with two-point entanglement, as measured by the concurrence, and continues via the three-tangle and four-tangle, until finally, deep in the ferromagnetic phase for J=∞, arriving at a pure L-partite (GHZ type) entanglement of all L spins. Comparison with the two, three, and four-point correlations reveals a similar sequence and shows strong ties to the above entanglement measures for small J. However, we also find a partial inversion of the hierarchy, where the four-point correlation exceeds the three- and two-point correlations, well before the critical point is reached. Qualitatively similar behavior is also found for the Bose-Hubbard model, suggesting that this is a general feature of a quantum phase transition. This should be taken into account in the approximations starting from a mean-field limit.

- Distance Dependence of Entanglement Generation via a Bosonic Heat Bath (Phys. Rev. Lett. 102, 160501, 2009)
- Non-Markovian decoherence in the adiabatic quantum search algorithm (Phys. Rev. A 75, 062313, 2007)
- General error estimate for adiabatic quantum computing (Phys. Rev. A 73, 062307, 2006)
- Adiabatic quantum algorithms as quantum phase transitions: First versus second order (Phys. Rev. A 74, 060304(R), 2006)

## Quantum simulators

Abstract:

We propose a design for the construction of a laboratory system based on present-day technology which reproduces and thereby simulates the quantum dynamics of the O(3) nonlinear sigma model. Apart from its relevance in condensed-matter theory, this strongly interacting quantum field theory serves as an important toy model for quantum chromodynamics (QCD) since it reproduces many crucial properties of QCD. The proposed design is therefore a feasibility and proof-of-principle study for more general analogue quantum simulators.

Abstract:

We study the Mott phase of the Bose-Hubbard model on a tilted lattice. On the (Gutzwiller) mean-field level, the tilt has no effect – but quantum fluctuations entail particle-hole pair creation via tunneling. For small potential gradients (long-wavelength limit), we derive a quantitative analogy to the Sauter-Schwinger effect, i.e., electron-positron pair creation out of the vacuum by an electric field. For large tilts, we obtain resonant tunneling related to Bloch oscillations.

Further references:

- Quantum simulator for the Schwinger effect with atoms in bichromatic optical lattices (Phys. Rev. A 84, 050101(R), 2011)
- Quantum simulation of cosmic inflation in two-component Bose-Einstein condensates (Phys. Rev. A 70, 063615, 2004)

## Analogues, Unruh effect and Hawking radation

Abstract:

Via suitable condensed matter analogues and other laboratory systems, it might be possible to model the Penrose process (superradiant scattering), the Unruh effect, Hawking radiation, the Eardley instability, black-hole lasers, cosmological particle creation, the Gibbons-Hawking effect, and the Schwinger mechanism. Apart from an experimental verification of these yet unobserved phenomena, the study of these laboratory systems might shed light onto the underlying ideas and problems and should therefore be interesting from a (quantum) gravity point of view as well.

Further references:

- On slow light as a black hole analogue (Phys. Rev. D 68, 024008, 2003)
- Universality of the Hawking effect (Phys. Rev. D 71, 024028, 2005)
- Hawking Radiation in an Electromagnetic Waveguide? (Phys. Rev. Lett. 95, 031301, 2005)
- Analogue of Cosmological Particle Creation in an Ion Trap (Phys. Rev. Lett. 99, 201301, 2007)