# Weblog Yuli Nazarov

## 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.

## FACULTY POSITION IN EXPERIMENTAL PHYSICS

The Faculty of Applied Sciences, Department of Quantum Nanoscience at Delft University of Technology invites applications for a tenure-track assistant professor position in Experimental Physics. Consideration of applications for an associate or full professor level position may be given to exceptionally well-qualified individuals.

Candidates must be able to demonstrate the ability to develop a highly successful independent research program and to participate effectively in the teaching of the applied physics curriculum at both the undergraduate and graduate levels. Research areas of interest include, for example, optics and photonics, nanostructure science and technology, novel sensing methods, condensed-matter

physics, and materials physics. Direct experience in nanoscience is not required of applicants, but candidates should think about how they could integrate their research into a theme of nanoscience or nanotechnology. Prospective candidates who wish to pursue interdisciplinary research efforts are strongly encouraged to apply. Current research in the Quantum Nanoscience Department is active

across many fields, including nanophotonics, quantum optomechanics, quantum optics, quantum transport, mesoscopic physics, and condensed matter physics.

The successful applicant can expect a highly competitive start-up package for her/his research program. Considerable institutional resources are available at TU Delft that can strengthen this research program and support interdisciplinary and collaborative research ventures. Candidates will be appointed on a tenure track basis with the prospect of a tenured position based on a successful evaluation after 5 years.

TU Delft is an equal opportunity employer and is committed to increase the diversity of its faculty.

**Information and application**

For more information about this position please contact the head of the Quantum Nanoscience Department Prof. Dr. K. Kuipers at afdeling-QN-tnw@tudelft.nl.

To apply, candidates should send the following information to the above email address:

(1) cover letter

(2) curriculum vitae

(3) publication list

(4) description of research interests and plans (1 page summary + 6 page max detailed statement)

(5) short teaching vision

(6) the names of three people who could be contacted for a letter of reference

Applications submitted by December 1, 2016 will receive full consideration.

## Supercurrents in chiral channels originate from upstream information transfer: a theoretical prediction

This is the title of (relatively) new arxiv submission, first with Xiao-Li Huang.

It can be found here.

**Abstract:**

*It has been thought that the long chiral edge channels cannot support any supercurrent between the superconducting electrodes. We show theoretically that the supercurrent can be mediated by a non-local interaction that facilitates a long-distance information transfer in the direction opposite to electron flow. We compute the supercurrent for several interaction models, including that of an external circuit. *

## Nature news and views

Quite unexpectedly, I’ve published something in Nature, specifically in News ans Views:

**Quantum physics: Destruction of discrete charge**

*Electric charge is quantized in units of the electron’s charge. An experiment explores the suppression of charge quantization caused by quantum fluctuations and supports a long-standing theory that explains this behaviour. See Letter p.58*

Yuli V. Nazarov

*Nature 536, 38–39 (03 August 2016) | doi:10.1038/536038a*

Full text can be seen here.

## PhD and post-doc openings

In the framework of ERC Advanced Grand *Higher-dimensional topological solids realized with multi-terminal superconducting junctions*

(HITSUPERJU) I would like to announce

- 2 Ph.D. positions, duration 4 years, it is possible to start from 1-8-2016 while the preferable starting date is 1-12-2016
- 1 post-doc position, duration 2 years, starting date spring 2017.

Here you can find a short description of the project.

To apply, please send

- your CV,
- motivation letter with the references to the project content,
- the names of three referees,
- importantly, the results of the TEST

to my e-mail address

While the test is more appropriate for Ph.D. candidates, aspiring postdocs are also requested to make it.

I look forward to fruitful collaboration!

## Survey AQM #1

Here are the results of the first survey of AQM course. It took place on Feb 26. There were 36 participants. Main numbers are as follows:

Mark lectures: 7.4 Mark PPS: 6.7 Overall mark: 7.3

*Better than last year. Still lack of PPS appreciation.*

Read more

## Nature Communications

Another publication with Grenoble friends. The preprint is available for almost a year, it had a complex history of submissions and interactions with referees Anyway, it feels like my best paper so far.

Title: **Multi-terminal Josephson junctions as topological matter **

Authors: Roman-Pascal Riwar, Manuel Houzet, Julia S. Meyer & Yuli V. Nazarov

Ref: Nature Communications 7, Article number: 11167, doi:10.1038/ncomms11167

Abstract:* Topological materials and their unusual transport properties are now at the focus of modern experimental and theoretical research. Their topological properties arise from the bandstructure determined by the atomic composition of a material and as such are difficult to tune and naturally restricted to ≤3 dimensions. Here we demonstrate that n-terminal Josephson junctions with conventional superconductors may provide novel realizations of topology in n−1 dimensions, which have similarities, but also marked differences with existing 2D or 3D topological materials. For n≥4, the Andreev subgap spectrum of the junction can accommodate Weyl singularities in the space of the n−1 independent superconducting phases, which play the role of bandstructure quasimomenta. The presence of these Weyl singularities enables topological transitions that are manifested experimentally as changes of the quantized transconductance between two voltage-biased leads, the quantization unit being 4e2/h, where e is the electric charge and h is the Planck constant.*