arXiv subjects

M. Hein

Publications and source records attributed to M. Hein.

8 recordsLinked to original sources

arXiv2025

Collapse of the superconducting order parameter in Ising superconductors with Rashba spin-orbit coupling

Ising superconductors have attracted quite some attention recently, due to their resilience against magnetic fields way beyond the Pauli-paramagnetic limit. Their protection against external magnetic field relies on strong Ising spin-orbit coupling, which originates from in-plane inversion symmetry breaking. Due to the heavy atom nature of Ising SCs, a smaller but sizable Rashba SOC could be present through gating or interfacial effects. Here, we consider the effect of Rashba SOC in a two valley model of Ising superconductors with an attractive $s$-wave interaction. We show that Rashba SOC gives a critical magnetic field, above which the superconducting order parameter collapses at low temperatures. This effect, however, disappears at high temperatures. Our findings demonstrate that the low- and high temperature physics of Ising SCs is quantitatively and qualitatively different in our two-valley model, and may lead to new ways to determine the strength of the Rashba SOC in Ising SCs.

cond-mat.supr-con↗

arXiv2016

On the capillary self-focusing in a microfluidic system

A computational framework is developed to address capillary self-focusing in Step Emulsification. The microfluidic system consists of a single shallow and wide microchannel that merges into a deep reservoir. A continuum approach coupled with a volume of fluid method is used to model the capillary self-focusing effect. The original governing equations are reduced using the Hele-Shaw approximation. We show that the interface between the two fluids takes the shape of a neck narrowing in the flow direction just before entering the reservoir, in agreement with our experimental observations. Our computational model relies on the assumption that the pressure at the boundary, where the fluid exits into the reservoir, is the uniform pressure in the reservoir. We investigate this hypothesis by comparing the numerical results with experimental data. We conjecture that the pressure boundary condition becomes important when the width of the neck is comparable to the depth of the microchannel. A correction to the exit pressure boundary condition is then proposed, which is determined by comparison with experimental data. We also present the experimental observations and the numerical results of the transitions of breakup regimes.

physics.flu-dyn↗

arXiv2014

Capillary focusing close to a topographic step: Shape and instability of confined liquid filaments

Step-emulsification is a microfluidic technique for droplet generation which relies on the abrupt decrease of confinement of a liquid filament surrounded by a continuous phase. A striking feature of this geometry is the transition between two distinct droplet breakup regimes, the "step-regime" and "jet-regime", at a critical capillary number. In the step-regime, small and monodisperse droplets break off from the filament directly at a topographic step, while in the jet-regime a jet protrudes into the larger channel region and large plug-like droplets are produced. We characterize the breakup behavior as a function of the filament geometry and the capillary number and present experimental results on the shape and evolution of the filament for a wide range of capillary numbers in the jet-regime. We compare the experimental results with numerical simulations. Assumptions based on the smallness of the depth of the microfluidic channel allow to reduce the governing equations to the Hele-Shaw problem with surface tension. The full nonlinear equations are then solved numerically using a volume-of-fluid based algorithm. The computational framework also captures the transition between both regimes, offering a deeper understanding of the underlying breakup mechanism.

physics.flu-dyn↗

arXiv2006

Entanglement in Graph States and its Applications

Graph states form a rich class of entangled states that exhibit important aspects of multi-partite entanglement. At the same time, they can be described by a number of parameters that grows only moderately with the system size. They have a variety of applications in quantum information theory, most prominently as algorithmic resources in the context of the one-way quantum computer, but also in other fields such as quantum error correction and multi-partite quantum communication, as well as in the study of foundational issues such as non-locality and decoherence. In this review, we give a tutorial introduction into the theory of graph states. We introduce various equivalent ways how to define graph states, and discuss the basic notions and properties of these states. The focus of this review is on their entanglement properties. These include aspects of non-locality, bi-partite and multi-partite entanglement and its classification in terms of the Schmidt measure, the distillability properties of mixed entangled states close to a pure graph state, as well as the robustness of their entanglement under decoherence. We review some of the known applications of graph states, as well as proposals for their experimental implementation.

quant-ph↗

arXiv2005

Multi-party entanglement in graph states

Graph states are multi-particle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions. They are many-body spin states of distributed quantum systems that play a significant role in quantum error correction, multi-party quantum communication, and quantum computation within the framework of the one-way quantum computer. We characterize and quantify the genuine multi-particle entanglement of such graph states in terms of the Schmidt measure, to which we provide upper and lower bounds in graph theoretical terms. Several examples and classes of graphs will be discussed, where these bounds coincide. These examples include trees, cluster states of different dimension, graphs that occur in quantum error correction, such as the concatenated [7,1,3]-CSS code, and a graph associated with the quantum Fourier transform in the one-way computer. We also present general transformation rules for graphs when local Pauli measurements are applied, and give criteria for the equivalence of two graphs up to local unitary transformations, employing the stabilizer formalism. For graphs of up to seven vertices we provide complete characterization modulo local unitary transformations and graph isomorphies.

quant-ph↗

arXiv2005

Standard forms of noisy quantum operations via depolarization

We consider noisy, non-local unitary operations or interactions, i.e. the corresponding evolutions are described by completely positive maps or master equations of Lindblad form. We show that by random local operations the completely positive maps can be depolarized to a standard form with a reduced number of parameters describing the noise process in such a way that the noiseless (unitary) part of the evolution is not altered. A further reduction of the parameters, in many cases even to a single one (i.e. global white noise), is possible by tailoring the decoherence process and increasing the amount of noise. We generalize these results to the dynamical case where the ideal unitary operation is given by some interaction Hamiltonian. The resulting standard forms may be used to compute lower bounds on channel capacities, to simplify quantum process tomography or to derive error thresholds for entanglement purification and quantum computation.

quant-ph↗

arXiv2005

Entanglement in spin chains and lattices with long-range Ising-type interactions

We consider N initially disentangled spins, embedded in a ring or d-dimensional lattice of arbitrary geometry, which interact via some long--range Ising--type interaction. We investigate relations between entanglement properties of the resulting states and the distance dependence of the interaction in the limit N to infinity. We provide a sufficient condition when bipartite entanglement between blocks of L neighboring spins and the remaining system saturates, and determine S_L analytically for special configurations. We find an unbounded increase of S_L as well as diverging correlation and entanglement length under certain circumstances. For arbitrarily large N, we can efficiently calculate all quantities associated with reduced density operators of up to ten particles.

quant-ph↗

arXiv2004

Entanglement properties of multipartite entangled states under the influence of decoherence

We investigate entanglement properties of multipartite states under the influence of decoherence. We show that the lifetime of (distillable) entanglement for GHZ-type superposition states decreases with the size of the system, while for a class of other states -namely all graph states with constant degree- the lifetime is independent of the system size. We show that these results are largely independent of the specific decoherence model and are in particular valid for all models which deal with individual couplings of particles to independent environments, described by some quantum optical master equation of Lindblad form. For GHZ states, we derive analytic expressions for the lifetime of distillable entanglement and determine when the state becomes fully separable. For all graph states, we derive lower and upper bounds on the lifetime of entanglement. To this aim, we establish a method to calculate the spectrum of the partial transposition for all mixed states which are diagonal in a graph state basis. We also consider entanglement between different groups of particles and determine the corresponding lifetimes as well as the change of the kind of entanglement with time. This enables us to investigate the behavior of entanglement under re-scaling and in the limit of large (infinite) number of particles. Finally we investigate the lifetime of encoded quantum superposition states and show that one can define an effective time in the encoded system which can be orders of magnitude smaller than the physical time. This provides an alternative view on quantum error correction and examples of states whose lifetime of entanglement (between groups of particles) in fact increases with the size of the system.

quant-ph↗