Topological edge states arise in parity-time ($\mathcal{PT}$)-symmetric

non-unitary quantum dynamics but have so far only been discussed in the

$\mathcal{PT}$-symmetry-unbroken regime. Here we report the experimental

detection of robust topological edge states in one-dimensional photonic quantum

walks with spontaneously broken $\mathcal{PT}$ symmetry, thus establishing the

existence of topological phenomena therein. We theoretically prove and

experimentally confirm that the global Berry phase in non-unitary quantum-walk

# All

We assess the energy cost of shortcuts to adiabatic expansions or

compressions of a harmonic oscillator, the power strokes of a quantum Otto

engine. Difficulties to identify the cost stem from the interplay between

different parts of the total system (the primary system -the particle-, and the

control system) and definitions of work (exclusive and inclusive). While

attention is usually paid to the inclusive work of the primary system, we

identify the energy cost as the exclusive work of the total system, which, for

We show how the universal low-energy properties of Weyl semimetals with

spatially varying time-reversal (TR) or inversion (I) symmetry breaking are

described in terms of chiral fermions experiencing curved-\emph{spacetime}

geometry and synthetic gauge fields. By employing Clifford representations and

Schrieffer-Wolff transformations, we present a systematic derivation of an

effective curved-space Weyl theory with rich geometric and gauge structure. To

The Hodgkin-Huxley model describes the conduction of the nervous impulse

through the axon, whose membrane's electric response can be described employing

multiple connected electric circuits containing capacitors, voltage sources,

and conductances. These conductances depend on previous depolarizing membrane

voltages, which can be identified with a memory resistive element called

memristor. Inspired by the recent quantization of the memristor, a simplified

Hodgkin-Huxley model including a single ion channel has been studied in the

Let S be a set of states of a physical system and p(s) be the probability of

the occurrence of an event when the system is in state s. A function p from S

to [0,1] is called a numerical event or alternatively an S-probability. If a

set P:={p(s)|s in S} is ordered by the order of real functions such that

certain plausible requirements are fulfilled, P becomes an orthomodular poset

in which properties can be described by the addition and comparison of

functions. P is then called an algebra of S-probabilities or algebra of

We introduce a simple model system to study synchronization theoretically in

quantum oscillators that are not just in limit-cycle states, but rather display

a more complex bistable dynamics. Our oscillator model is purely dissipative,

with a two-photon gain balanced by single- and three-photon loss processes.

When the gain rate is low, loss processes dominate and the oscillator has a

very low photon occupation number. In contrast, for large gain rates, the

Quantum computers will allow calculations beyond existing classical

computers. However, current technology is still too noisy and imperfect to

construct a universal digital quantum computer with quantum error correction.

Inspired by the evolution of classical computation, an alternative paradigm

merging the flexibility of digital quantum computation with the robustness of

analog quantum simulation has emerged. This universal paradigm is known as

digital-analog quantum computing. Here, we introduce an efficient

We consider the logarithmic negativity and related quantities of time

evolution operators. We study free fermion, compact boson, and holographic

conformal field theories (CFTs) as well as numerical simulations of random

unitary circuits and integrable and chaotic spin chains. The holographic

behavior strongly deviates from known non-holographic CFT results and displays

clear signatures of maximal scrambling. Intriguingly, the random unitary

circuits display nearly identical behavior to the holographic channels.

Floquet engineering or coherent time periodic driving of quantum systems has

been successfully used to synthesize Hamiltonians with novel properties. In

ultracold atomic systems, this has led to experimental realizations of

artificial gauge fields, topological band structures, and observation of

dynamical localization, to name just a few. Here we present a Floquet-based

framework to stroboscopically engineer Hamiltonians with spatial features and

periodicity below the diffraction limit of light used to create them by

We propose and discuss a method to engineer stroboscopically arbitrary

one-dimensional optical potentials with subwavelength resolution. Our approach

is based on subwavelength optical potential barriers for atoms in the dark

state in an optical \Lambda system, which we use as a stroboscopic drawing tool

by controlling their amplitude and position by changing the amplitude and the

phase of the control Rabi frequency in the \Lambda system. We demonstrate the