# Posts tagged submissions

## 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. *

## 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. *

## Unveiling mysteries

with my Grenoble collaborators. Fresh submission.

**How many quasiparticles can be in a superconductor?**

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

*Experimentally and mysteriously, the concentration of quasiparticles in a gapped superconductor at low temperatures always by far exceeds its equilibrium value. We study the dynamics of localized quasiparticles in superconductors with a spatially fluctuating gap edge. The competition between phonon-induced quasiparticle recombination and generation by a weak non-equilibrium agent results in an upper bound for the concentration that explains the mystery.*

## Engineering topological materials

It’s been a while I’ve submitted something with experimentalists, yet it has happened, rather fast and unexpected. Volia!

**The ω-SQUIPT: phase-engineering of Josephson topological materials**

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

Abstract:

*Multi-terminal superconducting Josephson junctions based on the proximity effect offer the bright opportunity to tailor non trivial quantum states in nanoscale weak-links. These structures can realize exotic topologies in multidimensions as, for example, artificial topological superconductors able to support Majorana bound states, and pave the way to emerging quantum technologies and future quantum information schemes. Here, we report the first realization of a three-terminal Josephson interferometer based on a proximized nanosized weak-link. Our tunneling spectroscopy measurements reveal transitions between gapped (i.e., insulating) and gapless (i.e., conducting) states, those being controlled by the phase configuration of the three superconducting leads connected to the junction. We demonstrate the topological nature of these transitions: a gapless state necessarily occurs between two gapped states of different topological index, very much like the interface between two insulators of different topology is necessarily conducting. The topological numbers characterizing such gapped states are given by superconducting phase windings over the two loops forming the Josephson interferometer. Since these gapped states cannot be transformed to one another continuously withouth passing through a gapless condition, these are topologically protected. Our observation of the gapless state is pivotal for enabling phase engineering of more sophisticated artificial topological materials realizing Weyl points or the anomalous Josephson effect.
*

## Keldysh formalism for multiple parallel worlds

this paper with M. Ansari has appeared on arxiv today: see it here. This is our contribution to the forthcoming Special JETP issue dedicated to 85th anniversary of Prof. L. V. Keldysh.

**Abstract:**

*We present here a compact and self-contained review of recently developed Keldysh formalism for multiple parallel worlds. The formalism has been applied to consistent quantum evaluation of the flows of informational quantities, in particular, to evaluation of Renyi and Shannon entropy flows. We start with the formulation of standard and extended Keldysh technique in single world in a form convenient for our presentation. We explain the use of Keldysh contours encompassing multiple parallel worlds In the end, we shortly summarize the concrete results obtained with the method. *

## Paper to commemorate Markus Buttiker

who has passed away on Oct 4, 2013 in the age of 63. There will be a special issue of Physica E devoted to his memory.

From the conclusions:

*“In conclusion, we have provided a technical and comprehensive introduction to the Keldysh action formalism for a multi-terminal scatterer with special emphasis on superconducting leads. We have derived a very general and compact formula and have elaborated on simple important examples to demonstrate the variety of its applications.*

*I did this to commemorate Markus Buttiker, the pioneer of scattering approach to quantum transport, one of the fathers of this big, prosperous and fruitfully developing research field. I admire not only his research merits: throughout 25 years of our acquaintance I was appreciating much his daring to remain himself, to keep his own research style, research topics and idea sets in times where the close following of a quickly changing scientific fashion seemed to be a must. He was also a charming personality and a good friend.”*

The paper can be found here.

## Multi-terminal Josephson junctions as topological materials

if you ask me, is a splendid piece of research. I mentioned the submission earlier: now the preprint is available here.

**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 a straightforward realization of tunable topological materials in n−1 dimensions. 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 2e^2/(πℏ). *

## Exact correspondence

Me and Mohammad Ansari have submitted a paper that concludes a nice piece of research on Renyi entropies. We have found an exact relation, like fluctuation-dissipation theorem, that relates physical and unphysical quantities: you can guess the implications:))))

**Exact correspondence between Renyi entropy flows and physical flows**

Mohammad H. Ansari, Yuli V. Nazarov

*We present a universal relation between the flow of a Renyi entropy and the full counting statistics of energy transfers. We prove the exact relation for a flow to a system in thermal equilibrium that is weakly coupled to an arbitrary time-dependent and non-equilibrium system. The exact correspondence, given by this relation, provides a simple protocol to quantify the flows of Shannon and Renyi entropies from the measurements of energy transfer statistics. *

## Mutli-terminal Josephson junctions as topological materials

This is the title of the manuscript I have submitted on Tuesday with my Grenoble friends Julia Meyer, Roman Riwar and Manuel Houzet. Mmm, perhaps I exaggerate in excitation, but this looks the most significant piece of research I accomplished for last years. The preprint is not available yet, but I expect this to happen soon 🙂