We have performed soft-X-ray angle resolved photoemission for metallic V$_2$O$_3$. Combining a micro focus beam (40 x 65 ${mu}$m$^2$) and micro positioning techniques with a long working distance microscope, we have succeeded in observing band disper
sions from tiny cleavage surfaces with typical size of the several tens of ${mu}$m. The photoemission spectra show a clear position dependence reflecting the morphology of the cleaved sample surface. By selecting high quality flat regions on the sample surface, we have succeeded in band mapping using both photon-energy and polar-angle dependences, opening the door to three-dimensional ARPES for typical three dimensional correlated materials where large cleavage planes are rarely obtained.
The expected return time to the original state is a key concept characterizing systems obeying both classical or quantum dynamics. We consider iterated open quantum dynamical systems in finite dimensional Hilbert spaces, a broad class of systems that
includes classical Markov chains and unitary discrete time quantum walks on networks. Starting from a pure state, the time evolution is induced by repeated applications of a general quantum channel, in each timestep followed by a measurement to detect whether the system has returned to the original state. We prove that if the superoperator is unital in the relevant Hilbert space (the part of the Hilbert space explored by the system), then the expectation value of the return time is an integer, equal to the dimension of this relevant Hilbert space. We illustrate our results on partially coherent quantum walks on finite graphs. Our work connects the previously known quantization of the expected return time for bistochastic Markov chains and for unitary quantum walks, and shows that these are special cases of a more general statement. The expected return time is thus a quantitative measure of the size of the part of the Hilbert space available to the system when the dynamics is started from a certain state.
We analyze a special class of 1-D quantum walks (QWs) realized using optical multi-ports. We assume non-perfect multi-ports showing errors in the connectivity, i.e. with a small probability the multi- ports can connect not to their nearest neighbor b
ut to another multi-port at a fixed distance - we call this a jump. We study two cases of QW with jumps where multiple displacements can emerge at one timestep. The first case assumes time-correlated jumps (static disorder). In the second case, we choose the positions of jumps randomly in time (dynamic disorder). The probability distributions of position of the QW walker in both instances differ significantly: dynamic disorder leads to a Gaussian-like distribution, while for static disorder we find two distinct behaviors depending on the parity of jump size. In the case of even-sized jumps, the distribution exhibits a three-peak profile around the position of the initial excitation, whereas the probability distribution in the odd case follows a Laplace-like discrete distribution modulated by additional (exponential) peaks for long times. Finally, our numerical results indicate that by an appropriate mapping an universal functional behavior of the variance of the long-time probability distribution can be revealed with respect to the scaled average of jump size.
The dynamics of an ensemble of identically prepared two-qubit systems is investigated which is subjected to the iteratively applied measurements and conditional selection of a typical entanglement purification protocol. It is shown that the resulting
measurement-induced non-linear dynamics of the two-qubit state exhibits strong sensitivity to initial conditions and also true chaos. For a special class of initially prepared two-qubit states two types of islands characterize the asymptotic limit. They correspond to a separable and a maximally entangled two-qubit state, respectively, and their boundaries form fractal-like structures. In the presence of incoherent noise an additional stable asymptotic cycle appears.
Time-resolved photoelectron spectroscopy (trPES) can directly detect transient electronic structure, thus bringing out its promising potential to clarify nonequilibrium processes arising in condensed matters. Here we report the result of core-level (
CL) trPES on 1T-TaS2, realized by developing a high-intensity 60 eV laser obtained by high-order harmonic (HH) generation. Ta4f CL-trPES offers the transient amplitude of the charge-density-wave (CDW), via the site-selective and real-time observation of Ta electrons. The present result indicates an ultrafast photoinduced melting and recovery of CDW amplitude, followed by a peculiar long-life oscillation (i.e. collective amplitudon excitation) accompanying the transfer of 0.01 electrons among adjacent Ta atoms. CL-trPES offers a broad range of opportunities for investigating the ultrafast atom-specific electron dynamics in photo-related phenomena of interest.
Recurrence of a random walk is described by the Polya number. For quantum walks, recurrence is understood as the return of the walker to the origin, rather than the full-revival of its quantum state. Localization for two dimensional quantum walks is
known to exist in the sense of non-vanishing probability distribution in the asymptotic limit. We show on the example of the 2-D Grover walk that one can exploit the effect of localization to construct stationary solutions. Moreover, we find full-revivals of a quantum state with a period of two steps. We prove that there cannot be longer cycles for a four-state quantum walk. Stationary states and revivals result from interference which has no counterpart in classical random walks.
We propose a definition for the Polya number of continuous-time quantum walks to characterize their recurrence properties. The definition involves a series of measurements on the system, each carried out on a different member from an ensemble in orde
r to minimize the disturbance caused by it. We examine various graphs, including the ring, the line, higher dimensional integer lattices and a number of other graphs and calculate their Polya number. For the timing of the measurements a Poisson process as well as regular timing are discussed. We find that the speed of decay for the probability at the origin is the key for recurrence.
