Publication Highlights
### Colloquium: Atomic quantum gases in periodically driven optical lattices

André Eckardt, Rev. Mod. Phys. 89, 011004 (2017)

Time-periodic forcing in the form of coherent radiation is a standard tool for the coherent manipulation of small quantum systems like single atoms. In the last years, periodic driving has more and more also been considered as a means for the coherent control of many-body systems. In particular, experiments with ultracold quantum gases in optical lattices subjected to periodic driving in the lower kilohertz regime have attracted much attention. Milestones include the observation of dynamic localization, the dynamic control of the quantum phase transition between a bosonic superfluid and a Mott insulator, as well as the dynamic creation of strong artificial magnetic fields and topological band structures. This Colloquium reviews these recent experiments and their theoretical description. Moreover, fundamental properties of periodically driven many-body systems are discussed within the framework of Floquet theory, including heating, relaxation dynamics, anomalous topological edge states, and the response to slow parameter variations.

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Time-periodic forcing in the form of coherent radiation is a standard tool for the coherent manipulation of small quantum systems like single atoms. In the last years, periodic driving has more and more also been considered as a means for the coherent control of many-body systems. In particular, experiments with ultracold quantum gases in optical lattices subjected to periodic driving in the lower kilohertz regime have attracted much attention. Milestones include the observation of dynamic localization, the dynamic control of the quantum phase transition between a bosonic superfluid and a Mott insulator, as well as the dynamic creation of strong artificial magnetic fields and topological band structures. This Colloquium reviews these recent experiments and their theoretical description. Moreover, fundamental properties of periodically driven many-body systems are discussed within the framework of Floquet theory, including heating, relaxation dynamics, anomalous topological edge states, and the response to slow parameter variations.

Publication Highlights
### Growth and Division of Active Droplets Provides a Model for Protocells

D. Zwicker, R. Seyboldt, C. A. Weber, A. A. Hyman and F. Jülicher, Nature Physics (2016)

We show that liquid droplets that are driven away from thermodynamic equilibrium by chemical reactions can undergo cycles of growth and division reminiscent of living cells. We propose such active droplets as simple models for prebiotic protocells. Our work shows that protocells could have been able to propagate and divide without having established membranes.

See also coverage in Chemistry World and two articles in Quanta Magazine: article 1 and article 2.

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We show that liquid droplets that are driven away from thermodynamic equilibrium by chemical reactions can undergo cycles of growth and division reminiscent of living cells. We propose such active droplets as simple models for prebiotic protocells. Our work shows that protocells could have been able to propagate and divide without having established membranes.

See also coverage in Chemistry World and two articles in Quanta Magazine: article 1 and article 2.

Publication Highlights
### U(1) Wilson lattice gauge theories in digital quantum simulators

Christine Muschik, Markus Heyl, et al., arXiv:1612.08653

Lattice gauge theories describe fundamental phenomena in nature, but calculating their real-time dynamics on classical computers appears to be notoriously difficult. Digital quantum simulation has been proposed as a general strategy to solve such computationally hard problems on a programmable quantum device instead of using conventional computers. Recently, an experiment has demonstrated for the first time a digital quantum simulation of a lattice gauge theory on a small-scale quantum computer made of trapped ions. This work has been selected by the magazine Physics World as one of the top ten breakthroughs in physics in 2016. Now, a detailed theoretical analysis of the experimentally used scheme has been published which studies in detail the scheme's performance, robustness against various error sources, and scalability.

See also coverage in Physics World and the experimental work .

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Lattice gauge theories describe fundamental phenomena in nature, but calculating their real-time dynamics on classical computers appears to be notoriously difficult. Digital quantum simulation has been proposed as a general strategy to solve such computationally hard problems on a programmable quantum device instead of using conventional computers. Recently, an experiment has demonstrated for the first time a digital quantum simulation of a lattice gauge theory on a small-scale quantum computer made of trapped ions. This work has been selected by the magazine Physics World as one of the top ten breakthroughs in physics in 2016. Now, a detailed theoretical analysis of the experimentally used scheme has been published which studies in detail the scheme's performance, robustness against various error sources, and scalability.

See also coverage in Physics World and the experimental work .

Publication Highlights
### Superdiffusive Dispersals Impart the Geometry of Underlying Random Walks

V. Zaburdaev, I. Fouxon, S. Denisov, and E. Barkai, Phys. Rev. Lett. **117**, 270601

It is recognized now that a variety of real-life phenomena ranging from diffusion of cold atoms to the motion of humans exhibit dispersal faster than normal diffusion. Lévy walks is a model that excelled in describing such superdiffusive behaviors albeit in one dimension. Here we show that, in contrast to standard random walks, the microscopic geometry of planar superdiffusive Lévy walks is imprinted in the asymptotic distribution of the walkers. The geometry of the underlying walk can be inferred from trajectories of the walkers by calculating the analogue of the Pearson coefficient.

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It is recognized now that a variety of real-life phenomena ranging from diffusion of cold atoms to the motion of humans exhibit dispersal faster than normal diffusion. Lévy walks is a model that excelled in describing such superdiffusive behaviors albeit in one dimension. Here we show that, in contrast to standard random walks, the microscopic geometry of planar superdiffusive Lévy walks is imprinted in the asymptotic distribution of the walkers. The geometry of the underlying walk can be inferred from trajectories of the walkers by calculating the analogue of the Pearson coefficient.

Publication Highlights
### Load Response of the Flagellar Beat

Gary S. Klindt, Christian Ruloff, Christian Wagner, and Benjamin M. Friedrich, Phys. Rev. Lett. **117**, 258101 (2016)

Cilia and flagella exhibit regular bending waves that perform mechanical work on the surrounding fluid, to propel cellular swimmers and pump fluids inside organisms. Here, we quantify a force-velocity relationship of the beating flagellum, by exposing flagellated Chlamydomonas cells to controlled microfluidic flows. A simple theory of flagellar limit-cycle oscillations, calibrated by measurements in the absence of flow, reproduces this relationship quantitatively. We derive a link between the energy efficiency of the flagellar beat and its ability to synchronize to oscillatory flows.

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Cilia and flagella exhibit regular bending waves that perform mechanical work on the surrounding fluid, to propel cellular swimmers and pump fluids inside organisms. Here, we quantify a force-velocity relationship of the beating flagellum, by exposing flagellated Chlamydomonas cells to controlled microfluidic flows. A simple theory of flagellar limit-cycle oscillations, calibrated by measurements in the absence of flow, reproduces this relationship quantitatively. We derive a link between the energy efficiency of the flagellar beat and its ability to synchronize to oscillatory flows.

Publication Highlights
### Fermionic response from fractionalization in an insulating two-dimensional magnet

J. Nasu, J. Knolle, D. L. Kovrizhin, Y. Motome and R. Moessner Nature Physics (2016)

Conventionally ordered magnets possess bosonic elementary excitations, called magnons. By contrast, no magnetic insulators in more than one dimension are known whose excitations are not bosons but fermions. Theoretically, some quantum spin liquids (QSLs)—new topological phases that can occur when quantum fluctuations preclude an ordered state—are known to exhibit Majorana fermions as quasiparticles arising from fractionalization of spins. Alas, despite much searching, their experimental observation remains elusive. Here, we show that fermionic excitations are remarkably directly evident in experimental Raman scattering data across a broad energy and temperature range in the two-dimensional material α-RuCl3. This shows the importance of magnetic materials as hosts of Majorana fermions. In turn, this first systematic evaluation of the dynamics of a QSL at finite temperature emphasizes the role of excited states for detecting such exotic properties associated with otherwise hard-to-identify topological QSLs.

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Conventionally ordered magnets possess bosonic elementary excitations, called magnons. By contrast, no magnetic insulators in more than one dimension are known whose excitations are not bosons but fermions. Theoretically, some quantum spin liquids (QSLs)—new topological phases that can occur when quantum fluctuations preclude an ordered state—are known to exhibit Majorana fermions as quasiparticles arising from fractionalization of spins. Alas, despite much searching, their experimental observation remains elusive. Here, we show that fermionic excitations are remarkably directly evident in experimental Raman scattering data across a broad energy and temperature range in the two-dimensional material α-RuCl3. This shows the importance of magnetic materials as hosts of Majorana fermions. In turn, this first systematic evaluation of the dynamics of a QSL at finite temperature emphasizes the role of excited states for detecting such exotic properties associated with otherwise hard-to-identify topological QSLs.

Publication Highlights
### Phase Structure of Driven Quantum Systems

Vedika Khemani, Achilleas Lazarides, Roderich Moessner, and S.L. Sondhi Phys. Rev. Lett. **116**, 250401 (2016)

Clean and interacting periodically driven systems are believed to exhibit a single, trivial “infinite-temperature” Floquet-ergodic phase. In contrast, here we show that their disordered Floquet many-body localized counterparts can exhibit distinct ordered phases delineated by sharp transitions. Some of these are analogs of equilibrium states with broken symmetries and topological order, while others—genuinely new to the Floquet problem—are characterized by order and nontrivial periodic dynamics. We illustrate these ideas in driven spin chains with Ising symmetry.

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Clean and interacting periodically driven systems are believed to exhibit a single, trivial “infinite-temperature” Floquet-ergodic phase. In contrast, here we show that their disordered Floquet many-body localized counterparts can exhibit distinct ordered phases delineated by sharp transitions. Some of these are analogs of equilibrium states with broken symmetries and topological order, while others—genuinely new to the Floquet problem—are characterized by order and nontrivial periodic dynamics. We illustrate these ideas in driven spin chains with Ising symmetry.

Publication Highlights
### Similarity of Symbol Frequency Distributions with Heavy Tails

Martin Gerlach, Francesc Font-Clos, and Eduardo G. Altmann, Phys. Rev. X **6**, 021009 (2016)

Quantifying the similarity between symbolic sequences is a traditional problem in information theory which requires comparing the frequencies of symbols in different sequences. In numerous modern applications, ranging from DNA over music to texts, the distribution of symbol frequencies is characterized by heavy-tailed distributions (e.g., Zipf’s law). The large number of low-frequency symbols in these distributions poses major difficulties to the estimation of the similarity between sequences; e.g., they hinder an accurate finite-size estimation of entropies. Here, we show analytically how the systematic (bias) and statistical (fluctuations) errors in these estimations depend on the sample size N and on the exponent γ of the heavy-tailed distribution. Our results are valid for the Shannon entropy (α=1), its corresponding similarity measures (e.g., the Jensen-Shanon divergence), and also for measures based on the generalized entropy of order α. For small α’s, including α=1, the errors decay slower than the 1/N decay observed in short-tailed distributions. For α larger than a critical value α*=1+1/γ <= 2, the 1/N decay is recovered. We show the practical significance of our results by quantifying the evolution of the English language over the last two centuries using a complete α spectrum of measures. We find that frequent words change more slowly than less frequent words and that α=2 provides the most robust measure to quantify language change.

See also coverage in Physics Today and Physics.

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Quantifying the similarity between symbolic sequences is a traditional problem in information theory which requires comparing the frequencies of symbols in different sequences. In numerous modern applications, ranging from DNA over music to texts, the distribution of symbol frequencies is characterized by heavy-tailed distributions (e.g., Zipf’s law). The large number of low-frequency symbols in these distributions poses major difficulties to the estimation of the similarity between sequences; e.g., they hinder an accurate finite-size estimation of entropies. Here, we show analytically how the systematic (bias) and statistical (fluctuations) errors in these estimations depend on the sample size N and on the exponent γ of the heavy-tailed distribution. Our results are valid for the Shannon entropy (α=1), its corresponding similarity measures (e.g., the Jensen-Shanon divergence), and also for measures based on the generalized entropy of order α. For small α’s, including α=1, the errors decay slower than the 1/N decay observed in short-tailed distributions. For α larger than a critical value α*=1+1/γ <= 2, the 1/N decay is recovered. We show the practical significance of our results by quantifying the evolution of the English language over the last two centuries using a complete α spectrum of measures. We find that frequent words change more slowly than less frequent words and that α=2 provides the most robust measure to quantify language change.

See also coverage in Physics Today and Physics.

Publication Highlights
### Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet

A. Banerjee, C. A. Bridges, J.-Q. Yan, A. A. Achel, L. Li, M. B. Stone, G. E. Granroth, M. D. Lumsden, Y. Yiu, J. Knolle, S. Bhattacharjee, D. L. Kovrizhin, R. Moessner, D. A. Tennant, D. G. Mandrus & S. E. Nagler, Nature Materials **15**, 733 (2016)

Quantum spin liquids (QSLs) are topological states of matter exhibiting remarkable properties such as the capacity to protect quantum information from decoherence. Whereas their featureless ground states have precluded their straightforward experimental identification, excited states are more revealing and particularly interesting owing to the emergence of fundamentally new excitations such as Majorana fermions. Ideal probes of these excitations are inelastic neutron scattering experiments. These we report here for a ruthenium-based material, α-RuCl3, continuing a major search (so far concentrated on iridium materials) for realizations of the celebrated Kitaev honeycomb topological QSL. Our measurements confirm the requisite strong spin–orbit coupling and low-temperature magnetic order matching predictions proximate to the QSL. We find stacking faults, inherent to the highly two-dimensional nature of the material, resolve an outstanding puzzle. Crucially, dynamical response measurements above interlayer energy scales are naturally accounted for in terms of deconfinement physics expected for QSLs. Comparing these with recent dynamical calculations involving gauge flux excitations and Majorana fermions of the pure Kitaev model, we propose the excitation spectrum of α-RuCl3 as a prime candidate for fractionalized Kitaev physics.

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Quantum spin liquids (QSLs) are topological states of matter exhibiting remarkable properties such as the capacity to protect quantum information from decoherence. Whereas their featureless ground states have precluded their straightforward experimental identification, excited states are more revealing and particularly interesting owing to the emergence of fundamentally new excitations such as Majorana fermions. Ideal probes of these excitations are inelastic neutron scattering experiments. These we report here for a ruthenium-based material, α-RuCl3, continuing a major search (so far concentrated on iridium materials) for realizations of the celebrated Kitaev honeycomb topological QSL. Our measurements confirm the requisite strong spin–orbit coupling and low-temperature magnetic order matching predictions proximate to the QSL. We find stacking faults, inherent to the highly two-dimensional nature of the material, resolve an outstanding puzzle. Crucially, dynamical response measurements above interlayer energy scales are naturally accounted for in terms of deconfinement physics expected for QSLs. Comparing these with recent dynamical calculations involving gauge flux excitations and Majorana fermions of the pure Kitaev model, we propose the excitation spectrum of α-RuCl3 as a prime candidate for fractionalized Kitaev physics.

Publication Highlights
### Decision Making in the Arrow of Time

E. Roldán, I. Neri, M. Dörpinghaus, H. Meyr and F. Jülicher
Phys. Rev. Lett. **115**, 250602 (2015)

We show that the steady-state entropy production rate of a stochastic process is inversely proportional to the minimal time needed to decide on the direction of the arrow of time. Here we apply Wald’s sequential probability ratio test to optimally decide on the direction of time’s arrow in stationary Markov processes. Furthermore, the steady-state entropy production rate can be estimated using mean first-passage times of suitable physical variables. We derive a first-passage time fluctuation theorem which implies that the decision time distributions for correct and wrong decisions are equal. Our results are illustrated by numerical simulations of two simple examples of nonequilibrium processes.

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We show that the steady-state entropy production rate of a stochastic process is inversely proportional to the minimal time needed to decide on the direction of the arrow of time. Here we apply Wald’s sequential probability ratio test to optimally decide on the direction of time’s arrow in stationary Markov processes. Furthermore, the steady-state entropy production rate can be estimated using mean first-passage times of suitable physical variables. We derive a first-passage time fluctuation theorem which implies that the decision time distributions for correct and wrong decisions are equal. Our results are illustrated by numerical simulations of two simple examples of nonequilibrium processes.