Hornberger group - Welcome

Welcome to our website

We are exploring the complex dynamics of open nanoscale quantum systems, partly in collaboration with leading experimentalists.

Current projects focus on the study of coherence and entanglement phenomena in nanomechanical systems and molecular matter waves, and on the microscopic mechanisms that effect their quantum-to-classical transition.

May 15, 2024

Postdoc wanted

We have a postdoctoral position available on quantum interference with large molecules and nanoparticles, matter wave decoherence, and precision sensing. [More info..]

November 2, 2023

Quantum theory of optical binding

The laser-induced interaction between microparticles, which seemingly violates Newton's third law, causes characteristic quantum signatures in their motion.


October 20, 2023

Rotational decoherence of an ion crystal

Quantum superpositions of different angular velocities of a calcium ion gyroscope degrade as predicted by decoherence theory. This was demonstrated in collaboration with experimental physicists at the University of California, Berkeley.


October 4, 2023

Non-Hermitian dynamics of nanoparticles

Nonreciprocal optical forces can break a PT-symmetry in the joint motion of nanoparticles, and effect a transition to stable limit cycles, as shown in collaboration with physicists from Vienna and Ulm.


August 1, 2023

Professor Benjamin Stickler

Habemus professorem! Benjamin Stickler was appointed Professor for Theoretical Physics at the University of Ulm.

Congrats Ben! So well deserved!

June 5, 2023

Lukas Martinetz, Ph.D.

Habemus etiam doctorem! Lukas Martinetz received a Ph.D. from the Faculty of Physics for his dissertation on Quantum electromechanics with levitated charged particles.

Congrats Lukas!

April 28, 2023

Birthe Schrinski, Ph.D.

Habemus doctoram! Birthe Schrinski received a Ph.D. from the Faculty of Physics for her dissertation on Rotational Quantum Superposition Tests.

Congrats Birthe!

Directly measured Wigner functions of an acoustic mode in sapphire

September 15, 2022

Sapphire in a macroscopic quantum state

A sapphire crystal can be prepared in a highly macroscopic quantum state, as demonstrated in collaboration with experimenters at ETH Zurich.

Physical Review Letters 130, 133604 (2023)

This work is featured in Physics.

November 2, 2022

Massive entanglement

Two charged nanoparticles can be placed in an entangled state by feeding back a quantum-limited measurement signal, enabling high-precision force measurements.

Physical Review Letters 129, 193602 (2022)

(Credit: Equinox Graphics Ltd.)

August 26, 2022

Optically induced non-reciprocal interactions between nanoparticles

Particles trapped by phase-coherent optical tweezers can exert forces on each other that appear to violate Newton's third law, as demonstrated in collaboration with experimenters at the University of Vienna.

Science 377, 987 (2022)

This work is featured in Nature, Science and Physics World.

A nanoparticle delocalized in position and orientation nearby a dielectric

August 24, 2022

Surface-induced decoherence of charged particles

Macroscopic quantum electrodynamics predicts the loss of quantum coherence in particle motion due to nearby thermal surfaces.

PRX Quantum 3, 030327 (2022)


August 10, 2022

Benjamin Stickler in the Heisenberg program

The German Research Foundation included Benjamin Stickler in its prestigious Heisenberg program.

Congrats Ben!

A colloqium lecture on "How ants move large objects collectively" concluded the habilitation.

Juni 29, 2022

PD Benjamin Sticker

Benjamin Stickler has been appointed as a Privatdozent by the University of Duisburg-Essen.

Congrats Ben!

Febryary 28, 2022

Recognition as Outstanding Referee

Klaus Hornberger has been designated as Outstanding Referee by the American Physical Society.

Febryary 2, 2022

Interferometric control of nanorotor alignment

A quantum interference effect allows steering freely flying objects from fully aligned to completely antialigned using a weak laser pulse.

Physical Review A 105 (2022) L021502 (Letter)

December 1, 2021

Benjamin Sticker becomes member of the NRW Academy of Sciences

As of January 1. 2022, Benjamin Stickler will become a member of the Young College of the North Rhine-Westphalia Academy for Sciences and Arts.

Congrats Ben!

July 8, 2021

Filip Kiałka, Ph.D.

Habemus doctorem! Filip Kiałka received a Ph.D. from the Universitiy of Duisburg-Essen and the Universitiy of Vienna for his bi-national dissertation Talbot-Lau Schemes and Bragg Diffraction: Theory and Applications in High-Mass Matter-Wave Interferometry.

Congrats, Filip!

June 29, 2021

Quantum rotations of nanoparticles

Our review article on quantum effects in the rotational dynamics of nanoparticles appeared in Nature Reviews Physics.

Nature Reviews Physics 3, 589 (2021)


April 23, 2021

Nanoparticles in the quantum ground state

An elliptically polarized laser beam tuned to an optical cavity can cool a nanoparticle to the quantum groundstate of its rotational and linear motion.

Physical Review Letters 126, 163603 (2021) 

The underlying theory, which can be found in Phys. Rev. A 103, 043514 (2021), was designated as an Editor's Suggestion.

December 11, 2020

Quantum electromechanics with charged nanoparticles

Nanoparticles levitating in a Paul trap can be prepared and observed in quantum superposition by interfacing the endcap electrodes with a Cooper-pair box.

npj Quantum Information 6,101 (2020)

How to achive the necessary all-electric cooling of the center-of-mass and rotation dynamics is presented in New J. Phys. 23, 093001 (2021).

July 16, 2020

A Beam Splitter for Large Organic Molecules

The demonstration of Bragg diffraction of organic molecules off a standing laser beam paves the way to molecular interferometers with large path separation.

Physical Review Letters 125, 033604 (2020)

This article is designated as an Editor's Suggestion by Physical Review Letters, and is featured in  Physics and in Chemistry World.

June 6, 2020

Dissertation Award for Björn Schrinski

Björn Schrinski was awarded the prize for the best PhD thesis from the Faculty of Physics. The award certificate was bestowed by the Rector of the University of Duisburg-Essen, Prof. Ulrich Radtke, at the Dies Academicus.

Congrats, Björn!


June 6, 2020

Thesis Award for Henning Rudolph

Henning Rudolph was awarded the prize for the best master thesis from the Faculty of Physics. The award certificate was bestowed by the Rector of the University of Duisburg-Essen, Prof. Ulrich Radtke, at the Dies Academicus.

Congrats, Henning!


May 6, 2020

Orbital angular momentum interference

A novel interference scheme for matter waves is based on the quanitzation of orbital anular momentum.

Physical Review Research 2, 022030 (2020)  (Rapid Communication)


February 29, 2020

Poster award for Björn Schrinski

Björn Schrinski received the Best Poster Award for his poster presentation on the International Conference on Quantum Optics 2020.

Congrats, Björn!


January 29, 2020

Entangling levitated nanoparticles

An entangeld quantum state of two nanoparticles can be realistically demonstrated by levitating them with optical tweezers in a laser cavity.

Physical Review A 101, 011804 (2020) (Rapid Communication)

October 25, 2019

Marduk Bolaños Puchet, Ph.D.

Habemus etiam doctorem! Marduk Bolaños received a Ph.D. from the Faculty of Physics for his dissertation on the Decoherence of non-relativistic bosonic quantum fields.

Congrats, Marduk!

September 24, 2019

Björn Schrinski, Ph.D.

Habemus doctorem! Björn Schrinski received a Ph.D. from the Faculty of Physics for his dissertation on Assessing the macroscopicity of quantum mechanical superposition tests via hypothesis falsification.

Congrats, Björn!

September 16, 2019

Schrödinger's cat put on the scale

We establish an objective scheme to determine the degree of macroscopicity reached in quantum mechanical superposition tests, i.e. the size of an experimentally realized Schrödinger's cat. Based on the Bayesian falsification of macrorealistic modifications, it uses the raw data of an experiment, taking into account all measurement uncertainties.

Physical Review A 100, 032111 (2019)

Applying the measure to advanced matter-wave experiments with Bose-Einstein-condensed atoms and large molecules shows that these reach the highest macroscpicities:

Physical Review Research 2, 033034 (2020)



29 Jul - 1 Aug 2019

Workshop on Levitated Optomechanics

A WE-Heraeus seminar on Levitated Optomechanics was held at Physikzentrum Bad Honnef, Germany on 29 Jul - 1 Aug 2019 (organized by K. Hornberger, J. Millen, and M. Arndt).

The seminar brought together leading scientists and young researchers working on the control of nanoparticles suspended in vacuum by optical or electric forces. The most recent advances were discussed of cooling untethered nano-mechanical systems into the quantum regime and of observing their rotranslational motion in the quantum-classical borderlands, as well as the perspectives of harnessing their coherent quantum dynamics for fundamental experiments and technological applications.

Workshop program



June 27, 2019

Decoherence of quantum fields

We present a generic description of the quantum-to-classical transition of non-relativistic bosonic fields.

Physical Review A 99, 060103 (2019) (Rapid Communication)



May 1, 2019

Marie Curie Fellowship for Benjamin Stickler

Benjamin A. Stickler secured a Marie Sklodowska-Curie European Fellowship from the European Union, to work for one year at Imperial College London in the group of Myungshik Kim.

Congrats, Ben!

November 20, 2018

Coherence of molecular superrotors

Decoherence theory explains the surprising stability of the alignment of rapidly rotating molecules, in excellent quantitative agreement with the experimental observation.

Physical Review Letters 121, 243402 (2018)


October 29, 2018

Orientational quantum superpositions of nanoscale rotors

In a recent preprint, we propose an experimentally viable scheme to probe orientational quantum revivals with nanoscale particles, an interference effect of the rotational degrees of freedom testifying a superposition of all orientations. This opens the door to tests of rotational quantum physics with submicron objects and to quantum gyroscopic torque sensors.

New Journal of Physics 20, 122001 (2018) (Fast Track Communication)


September 17, 2018

Conformer-selection by matter-wave interference

In almost all larger molecules, the spatial arrangement of the atoms can show up in different geometries, even with all binding links equal. We show that such conformers can be selected from a mixture using a matter-wave interferometer.

Physical Review Letters 121, 173002 (2018

July 3, 2018

Best Talk Award for Björn Schrinski

At the Bayesian Young Statisticians Meeting (BAYSM 2018) in Warwick (UK) Björn Schrinski gave a lecture entitled "Towards Bayesian hypothesis testing of macrorealistic modifications of quantum mechanics", and he duly received a Best Talk Award for his presentation.

Congrats, Björn!

June 15, 2018

Rotational friction and diffusion of quantum rotors

We present the general quantum description of friction, diffusion, decoherence, and thermalization in the rotational motion of rigid bodies. In the semiclassical limit, one obtains the classical Fokker-Planck equation for the rotational dynamics of a top.

Physical Review Letters 121, 040401 (2018)


June 15, 2018

Thesis Award for Lukas Martinetz

Lukas Martinetz was awarded the prize for the best master thesis from the Faculty of Physics. The award certificate was presented by the Rector of the University of Duisburg-Essen, Prof. Ulrich Radtke, during the Dies Academicus ceremony.

Congrats, Lukas!


May 11, 2018

Gas-induced friction and diffusion of classical rigid rotors

The impact of a rarefid gas on the coupled rotational and translational motion of arbitrarily shaped particles can be predicted microscopically from the Boltzmann equation, yielding the associated friction and diffusion tensors.

Physical Review E 97, 052112 (2018)

This article was designated as an Editor's Suggestion by Physical Review E.

December 7, 2017

Quantum Angular Momentum Diffusion of Nanoparticles

The rotational quantum dynamics of an arbitrarily shaped nanoparticle exhibits angular momentum diffusion due to the interaction with environmental gases and background fields.

New Journal of Physics 19, 122001 (2017) [Fast Track Communication]


This article was designated as Highlight 2017 by New Journal of Physics.

November 22, 2017

A nanoscale clock with precise dials

Suitably modulated laser beams imprint the precision of an electronic clock onto the intrinsically chaotic angular motion of a levitated nanoscale dial.

Nature Communications 8, 1670 (2017)

March 13, 2017

Optical Control of Levitated Nanorods

The ro-translational motion of silicon nanorods can be detected and manipulated by laser light in an optical cavity.

Optica 4, 356-360 (2017)
Nano Letters 15, 5604 (2015)

November 4, 2016

Kai Walter, Ph.D.

Habemus doctorem! Kai Walter received a Ph.D. from the Faculty of Physics for his dissertation on Coherence and Decoherence in High-mass Matter-wave Interferometry.

Congrats, Kai!


Read his dissertation

October 14, 2016

Rotranslational Cavity Cooling of Dielectric Rods and Disks

Nonspherical nanoparticles can be cooled to the quantum regime of their center-of-mass and rotational motion.

Physical Review A 94, 033818 (2016)

October 10, 2016

Lutz Sörgel, Ph.D.

Habemus doctorem! Lutz Sörgel received a Ph.D. from the Faculty of Physics for his dissertation on Pointer state dynamics of dissipative quantum systems.

Congrats, Lutz!

Read his dissertation

September 10, 2016

Björn Schrinski Receives Poster Award

Björn Schrinski presented his poster entitled Interference of Bose-Einstein Condensates under the Influence of Decoherence at the Conference Frontiers in Matter Wave Optics (FOMF2016) in Arcachon, France, and he received a poster award for his contribution.

Congrats, Björn!

July 4, 2016

Attending Bill Phillips' Master Class

Benjamin Stickler attended this year's Lindau Nobel Laureate Meeting at Lake Constance, and presented his research results in Bill Phillips' master class. Benjamin was also one of the few young researchers selected to present their work on a poster for all participants.

Congrats, Benjamin!

June 11, 2015

Coherent photoabsorption in a molecule interferometer

The absorption of individual photons by large molecules gives rise to surprising coherence effects which can be observed in a matter wave interferometer.

Nature Communications 6, 7336 (2015)

Physical Review A 94, 033818 (2016)

December 4, 2014

Stefan Nimmrichter receives Award of Excellence 2014

Stefan Nimmrichter was granted the Award of Excellence by the Federal Minister for Science, Research, and Commerce of the Republic of Austria.

Congrats Stefan!

More about the dissertation

September 2, 2014

Near-field interferometry of a free-falling nanoparticle from a point-like source

Our proposal for a near-field interference scheme for 106 amu silicon particles based on the single-source Talbot effect appeared in Nature Communications. It would allow testing the quantum superposition principle at unrivaled scales.

Nature Communications 5, 4788 (2014)

August 6, 2014

Felix Lucas, Ph.D.

Habemus doctorem! Felix Lucas received a Ph.D. from the Faculty of Physics for his dissertation on Adaptive Resummation of Markovian Quantum Dynamics.

Congrats, Felix!

August 5, 2014

Incoherent Control of the Retinal Isomerization

The back-action of quantum measurements can provide a handle for controling relatively complex quantum systems. This is demonstrated by means of an important bio-chemical reaction, the photo-induced isomerization of retinal in the protein rhodopsin.

Phys. Rev. Lett. 113, 058301 (2014)


Optomechanical sensing of spontaneous wave-function collapse

Hypothetical modifications of the Schrödinger equation, which serve to destroy superpositions on macroscopic scales, can be sensed by monitoring a test mass. Surprisingly, this mass should not be much greater than a few picogramms.

Phys. Rev. Lett. 113, 020405 (2014)


April 29, 2014

Timo Fischer, Ph.D.

Habemus doctorem! Timo Fischer received a Ph.D. from the Faculty of Physics for his dissertation Decoherence of the Orientation State.

Congrats, Timo!

April 1, 2014

Testing the limits of quantum mechanical superpositions

A review article on tests of the quantum superposition principle in increasingly macroscopic systems appeared in Nature Physics.

Nature Phys. 10, 271-277 (2014)

This is part of a dedicated issue, a Nature Physics Insight, on the foundations of quantum mechanics.

January 15, 2014

Adaptive Resummation of Markovian Quantum Dynamics

Our method for deriving analytic approximations for the dynamics of open quantum systems appeared in Physical Review Letters.

Phys. Rev. Lett 110, 240401 (2013)

A more detailled article discusses the convergence properties and the numerical implementation of the resummation: Phys. Rev. A 89, 012112 (2014)

Dezember 30, 2013

Quantum mechanics in curved phase spaces

Our consistent extension of the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces appeared in Physical Review A.

Phys. Rev. A 88, 062117 (2013)

October 29, 2013

Stefan Nimmrichter, Ph.D.

Habemus doctorem! Stefan Nimmrichter received a Ph.D. from the University of Vienna for his dissertation on Macroscopic matter wave interferometry.

The work was awarded a Springer Thesis Prize,and it will be published as a Springer Thesis  — 'Recognizing Outstanding Ph.D. Research'.

Congrats, Stefan!

July 9, 2013

Nonlocal Young tests with Einstein-Podolsky-Rosen-correlated particle pairs

Nonlocal interference based on EPR-correlated particles allows one to detect entanglement and non-classical particle behavior using simple position measurements.

Phys. Rev. A 88, 013610 (2013)

June 7, 2013

Wigner function for the orientation state

Our extension of the Wigner-Weyl phase space representation to the rotation dynamics of solid quantum objects appeared in New Journal of Physics.

New J. Phys. 15, 06004 (2013)

April 18, 2013

Macroscopicity of mechanical quantum superposition states

Our proposal for an experimentally accessible, objective, and universal measure for the macroscopicity of superposition states in material quantum systems appeared in Physical Review Letters.

Phys. Rev. Lett. 110, 160403 (2013)

Feature articles on this work can be found in New Scientist (Quantum effects get a weirdness scale), in Physics World (How fat is Schrödinger’s cat?) and in Physics (Quantumness put on the scale). See also phys.org (Physicists propose measure of macroscopicity) und phsycs.com (Physicists introduce magnitude of macroscopicity).

May 12th - 17th, 2013

Summer school on tests of the quantum superposition principle

A summer school on Exploring the quantum superposition principle took place at the Physikzentrum Bad Honnef (near Bonn/Germany) on May 12th-17th, 2013. Further information is available at the school website.

Organizers: M. Arndt (U Vienna), K. Hornberger (U Duisburg-Essen)

Generous funding is provided by the Wilhem & Else Heraeus Foundation

February 7th, 2013

Kickoff meeting of NANOQUESTFIT collaboration

The kickoff meeting of the NANOQUESTFIT collaboration took place at Campus Duisburg, MG 465 on February 7th and 8th. A goal of this EU research project (ICT FET Open STREP) is to use matter wave interferometry of large molecules and clusters to probe the limits of the quantum superposition principle.

Further information can be found at the project website.

Feb 8, 2012

Quantum interference of clusters and molecules

Our review article on matter wave interferometry of complex organic molecules and inorganic clusters appeared in Reviews of Modern Physics.

Rev. Mod. Phys 84, 157 (2012)

It has been reviewed by Mark Buchanan in Nature Physics.