# Posted in October 2016

## Quantum measurements made predictable

This is the first submission by Albert.

See it here.

**Probability distributions of continuous measurement results for conditioned quantum evolution**

A. Franquet, Yuli V. Nazarov

(Submitted on 24 Aug 2016)

ABSTRACT: *We address the statistics of continuous weak linear measurement on a few-state quantum system that is subject to a conditioned quantum evolution. For a conditioned evolution, both the initial and final states of the system are fixed: the latter is achieved by the post-selection in the end of the evolution. The statistics may drastically differ from the non-conditioned case, and the interference between initial and final states can be observed in the probability distributions of measurement outcomes as well as in the average values exceeding the conventional range of non-conditioned averages. We develop a proper formalism to compute the distributions of measurement outcomes, evaluate and discuss the distributions in experimentally relevant setups. We demonstrate the manifestations of the interference between initial and final states in various regimes. We consider analytically simple examples of non-trivial probability distributions. We reveal peaks (or dips) at half-quantized values of the measurement outputs. We discuss in detail the case of zero overlap between initial and final states demonstrating anomalously big average outputs and sudden jump in time-integrated output. We present and discuss the numerical evaluation of the probability distribution aiming at extend- ing the analytic results and describing a realistic experimental situation of a qubit in the regime of resonant fluorescence. *

## New submission: one device, 3 distinct topologies :)

This is possible: see it on cond-mat

**Order, disorder and tunable gaps in the spectrum of Andreev bound states in a multi-terminal superconducting device**

*Tomohiro Yokoyama, Johannes Reutlinger, Wolfgang Belzig, Yuli V. Nazarov*

(Submitted on 18 Sep 2016)

ABSTRACT: *We consider the spectrum of Andreev bound states (ABSs) in an exemplary 4-terminal superconducting structure where 4 chaotic cavities are connected by QPCs to the terminals and to each other forming a ring. Such a tunable device can be realized in 2DEG-superconductor structures.
We concentrate on the limit of a short structure and large conductance of the QPCs where a quasi-continuous spectrum is formed. The energies can be tuned by the superconducting phases. We observe the opening and closing of gaps in the spectrum. This concerns the usual proximity gap that separates the levels from zero energy as well as less usual “smile” gaps that split the levels of the spectrum.
We demonstrate a remarkable crossover in the overall spectrum that occurs upon changing the ratio of conductance of the inner and outer QPCs. At big values of the ratio, the levels exhibit a generic behavior expected for the spectrum of a disordered system manifesting level repulsion and “Brownian motion” upon changing the phases. At small values of the ratio, the levels are squeezed into narrow bunches separated by wide smile gaps. Each bunch consists of almost degenerate ABSs.
We study in detail the properties of the spectrum in the limit of a small ratio, paying special attention to the crossings of bunches. We distinguish two types of crossings: i. with a regular phase dependence of the levels and ii. crossings where the Brownian motion of the levels leads to an apparently irregular phase-dependence. We work out a perturbation theory to explain the observations.
The unusual properties of the spectrum originate from unobvious topological effects. Topology of the first kind is related to the winding of the semiclassical Green’s function. It is responsible for the proximity gaps. Topology of the second kind comes about the discreteness of the number of modes and is responsible for the smile gaps. *

## Nature Nanotechnology: how to engineer topology

The engineering efforts reported in March made their way to Nature Nanotechnology on Sep. 12,

**The ω-SQUIPT as a tool to phase-engineer Josephson topological materials**

* E. Strambini, S. D’Ambrosio, F. Vischi, F. S. Bergeret, Yu. V. Nazarov & F. Giazotto*

Nature Nanotechnology (2016) doi:10.1038/nnano.2016.157

Full text can be accessed via this link

## PRL quasiparticles

The attempt to unveil quasiparticle mysteries has been finally published in PRL

**Theoretical Model to Explain Excess of Quasiparticles in Superconductors**

*Anton Bespalov, Manuel Houzet, Julia S. Meyer, and Yuli V. Nazarov*

Phys. Rev. Lett. 117, 117002 – Published 9 September 2016

ABSTRACT: Experimentally, the concentration of quasiparticles in gapped superconductors always largely exceeds the equilibrium one at low temperatures. Since these quasiparticles are detrimental for many applications, it is important to understand theoretically the origin of the excess. We demonstrate in detail that the dynamics of quasiparticles localized at spatial fluctuations of the gap edge becomes exponentially slow. This gives rise to the observed excess in the presence of a vanishingly weak non-equilibrium agent.