Unifying uncertainties for rotorlike quantum systems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F24%3A73625768" target="_blank" >RIV/61989592:15310/24:73625768 - isvavai.cz</a>

Výsledek na webu

<a href="https://journals.aps.org/pra/pdf/10.1103/PhysRevA.110.032208" target="_blank" >https://journals.aps.org/pra/pdf/10.1103/PhysRevA.110.032208</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1103/PhysRevA.110.032208" target="_blank" >10.1103/PhysRevA.110.032208</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Unifying uncertainties for rotorlike quantum systems

Popis výsledku v původním jazyce

The quantum rotor represents, after the harmonic oscillator, the next obvious quantum system to study the complementary pair of variables: the angular momentum and the unitary shift operator in angular momentum. Proper quantification of uncertainties and the incompatibility of these two operators are thus essential for applications of rotorlike quantum systems. While angular momentum uncertainty is characterized by variance, several uncertainty measures have been proposed for the shift operator, with dispersion the simplest example. We establish a hierarchy of those measures and corresponding uncertainty relations which are all perfectly or almost perfectly saturated by a tomographically complete set of von Mises states. Building on the interpretation of dispersion as the moment of inertia of the unit ring we then show that the other measures also possess the same mechanical interpretation. This unifying perspective allows us to express all measures as a particular instance of a single generic angular uncertainty measure. The importance of these measures is then highlighted by applying the simplest two of them to derive optimal simultaneous measurements of the angular momentum and the shift operator. Finally, we argue that the model of quantum rotor extends beyond its mechanical meaning with promising applications in the fields of singular optics, superconductive circuits with a Josephson junction, or optimal pulse shaping in the time-frequency domain. Our findings lay the groundwork for quantum-information and metrological applications of the quantum rotor and point to its interdisciplinary nature.

Název v anglickém jazyce

Unifying uncertainties for rotorlike quantum systems

Popis výsledku anglicky

The quantum rotor represents, after the harmonic oscillator, the next obvious quantum system to study the complementary pair of variables: the angular momentum and the unitary shift operator in angular momentum. Proper quantification of uncertainties and the incompatibility of these two operators are thus essential for applications of rotorlike quantum systems. While angular momentum uncertainty is characterized by variance, several uncertainty measures have been proposed for the shift operator, with dispersion the simplest example. We establish a hierarchy of those measures and corresponding uncertainty relations which are all perfectly or almost perfectly saturated by a tomographically complete set of von Mises states. Building on the interpretation of dispersion as the moment of inertia of the unit ring we then show that the other measures also possess the same mechanical interpretation. This unifying perspective allows us to express all measures as a particular instance of a single generic angular uncertainty measure. The importance of these measures is then highlighted by applying the simplest two of them to derive optimal simultaneous measurements of the angular momentum and the shift operator. Finally, we argue that the model of quantum rotor extends beyond its mechanical meaning with promising applications in the fields of singular optics, superconductive circuits with a Josephson junction, or optimal pulse shaping in the time-frequency domain. Our findings lay the groundwork for quantum-information and metrological applications of the quantum rotor and point to its interdisciplinary nature.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10306 - Optics (including laser optics and quantum optics)

Projekt

—

Návaznosti

R - Projekt Ramcoveho programu EK

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

PHYSICAL REVIEW A

ISSN

2469-9926

e-ISSN

2469-9934

Svazek periodika

110

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

15

Strana od-do

"033254-1"-"033254-15"

Kód UT WoS článku

001361592700012

EID výsledku v databázi Scopus

2-s2.0-85203866114