**Fokker-Planck formalism approach to Kibble-Zurek scaling laws and nonequilibrium dynamics** – R. Puebla, R. Nigmatullin, T. E. Mehlstäubler, and M. B. Plenio, *Physical Review B, 95, 134104* (2017) | ArXiv

DOI:https://doi.org/10.1103/PhysRevB.95.134104

**The gist of it**

A system undergoing a symmetry-breaking second-order phase transition is characterized by the emergence of singular behavior in distinct quantities at a critical value of an external parameter. However, while equilibrium or static properties of these phase transitions are well understood, features of the dynamics when traversing a phase transition at a finite rate are less clear and are object of current research. This includes the study of defect formation, how equilibrium singularities leave their imprint on the resulting nonequilibrium dynamics or how such dynamics are affected by finite size systems, among other aspects. In this context, the celebrated Kibble-Zurek mechanism merits special mention as it successfully predicts the scaling behavior of the formed defects as a function of the rate at which the second-order phase transition is traversed.

In this work we explore the aforementioned scenario in two different models, namely, a one-dimensional Ginzburg-Landau model and a linear to zigzag phase transition in an ion Coulomb crystal. We analyze the nonequilibrium dynamics resulting when traversing at finite rate the second-order phase transition by means of a Fokker-Planck formalism. This formalism allows us to obtain the probabilistic state of the system in a deterministic manner, and therefore, it aims to solve the nonequilibrium dynamics problem at the ensemble rather than at the individual realization level, as is the case in the Langevin approach. Furthermore, we show that the nonequilibrium results are well reproduced when nonlinear terms in both models are neglected, as for example the Kibble-Zurek scaling laws that dictate the dependence of spatial correlations on the quench rate. The developed framework is computationally efficient and enables the prediction of finite-size scaling functions. Additionally, it might be useful to investigate scaling laws of other important quantities in stochastic thermodynamics such as entropy production and work done.

**Delayed entanglement echo for individual control of a large number of nuclear spins ** – Z.-Y. Wang, J. Casanova and M. B. Plenio, *Nature Communications, 8, 14660* (2017) | ArXiv

licensed under CC BY 4.0

**The gist of it**

Quantum technologies require reliable quantum control on individual elements of microscopic quantum systems. But for potential massive quantum resources such as hundreds of long-lived nuclear spins near the electron of single nitrogen-vacancy (NV) centers in diamond, individual detection and manipulation are challenging. In this work, we solve the difficulties and problems ahead by using a delayed entanglement operation. With our protocol one can detect, address and control nuclear spins around an electron spin unambiguously and individually in a broad frequency band. Hybrid quantum systems can be naturally incorporated to our scheme for improved performance. Our work would allow large-scale quantum information processing and quantum simulation on nuclear spin qubits, as well as atomic-scale imaging for biomolecules. There are also applications of our method in traditional fields of nuclear magnetic resonance (NMR) and electron-nuclear double resonance (ENDOR), for example, in analysis of chemical shifts and materials.

**Open Systems with Error Bounds: Spin-Boson Model with Spectral Density Variations ** – F. Mascherpa, A. Smirne, S. F. Huelga and M. B. Plenio, *Physical Review Letters, 118, 100401* (2017) | ArXiv

DOI: https://doi.org/10.1103/PhysRevLett.118.100401

**The gist of it**

Open quantum systems in harmonic environments are often modeled theoretically and simulated numerically in terms of the spectral density of the bath, which details how strongly the central system couples to each of the environmental modes as a function of the mode frequency. The spectral density is not usually known exactly; in this paper, we investigate the sensitivity of operator expectation values to variations and errors in it, and derive upper bounds on the error affecting the predictions as a function of the spectral deviation considered.

**Quantum Machine Learning over Infinite Dimensions ** – H.-K. Lau, R. Pooser, G. Siopsis and C. Weedbrook

*Physical Review Letters, 118, 080501* (2017) | ArXiv

DOI: https://doi.org/10.1103/PhysRevLett.118.080501

**The gist of it**

Machine learning is a data-manipulation techniques that has been increasingly important in e.g. finance and national security. Recently, it is discovered that quantum computer can reduce the resource requirement of machine learning. Nevertheless, current quantum machine learning algorithms store information as qubits, which can be implemented on only discrete-variable type of quantum systems. In this work, we generalize quantum machine learning algorithm to continuous-variable type of quantum system, which could be found in various physical platforms and could store more information in each degree of freedom. Specifically, we developed a continuous-variable version of exponential-swap operation. We showed how exponential-swap can be applied to various machine learning tasks, which include Matrix inversion, Principal component analysis, and Vector distance computation. We also discussed potential optical implementation of the operations.

This work has recently attracted some public attention. For a popular science report, please visit https://phys.org/news/2017-03-physicists-quantum-machine-infinite-dimensions.html

**Probing the Dynamics of a Superradiant Quantum Phase Transition with a Single Trapped Ion ** – R. Puebla, M.-J. Hwang, J. Casanova and M. B. Plenio,

*Physical Review Letters, 118, 073001* (2017) | ArXiv

DOI:https://doi.org/10.1103/PhysRevLett.118.073001

**The gist of it**

Phase transitions typically take place in the limit of infinitely many particles, the so-called thermodynamic limit. A recent theoretical finding has shown, however, that a quantum phase transition can occur even in finite-component systems of coupled bosons and spins in the limit of extremely large coupling strength and large detuning (see Phys. Rev. Lett. 115, 180404 (2015)). In this work, we demonstrate for the first time that such an extreme parameter regime can be indeed achieved using a single trapped ion with currently available technology and that it is possible to probe the universal properties of the nonequilibrium dynamics of the phase transition. Our work demonstrates that the trapped ion system can serve as an ideal platform to explore the physics of a phase transition both in and out of equilibrium without the daunting task of scaling up the number of ions.

**Metastability in the driven-dissipative Rabi model** – A. Le Boité, M.-J. Hwang and M. B. Plenio,

*Physical Review A, 95, 023829* (2017) | ArXiv

DOI:https://doi.org/10.1103/PhysRevA.95.023829

**The gist of it**

Experiments in cavity quantum electrodynamics (cavity QED), involving a strong interaction between an atom and a cavity photonic mode, have proved to be very powerful for testing our understanding of the quantum world. In this context, a common way to probe the quantum nature of the interaction between light and matter is to drive the system with a classical light field (such as a laser), and record the statistics of the photons emitted from the cavity. The number of photons in a coherent light field like a laser follows a Poissonian distribution. A sub-Poissonian statistics, which shows less fluctuations in the number of photons, is however a genuine quantum effect and an important evidence of effective photon-photon interactions induced by the atom-cavity coupling.

From a theoretical point of view, the interaction between a two-level atom and a single cavity mode is well captured by the quantum Rabi model. A driven-dissipative version of this model, including the external driving field and the inevitable leakage of photons out of the cavity, is thus well suited to describe the cavity QED experiments mentioned above. Until now, most of the studies have focused on the steady-state of the system, reached when the external driving exactly compensate the different losses mechanisms. In this paper, we go beyond the study of steady-state properties and explore the transient dynamics of the driven-dissipative Rabi model.

In particular, we show that, as the atom-cavity coupling strength becomes larger than the cavity frequency, a new time scale emerges. This time scale, much larger than the natural relaxation time of the atom and the cavity, leads to long-lived metastable states susceptible to being observed experimentally. By systematically investigating the set of possible metastable states, we find that their properties can differ drastically from those of the steady state and relate these properties to the energy spectrum of the Rabi Hamiltonian.

**Relations between dissipated work in non-equilibrium process and the family of Rényi divergences** – B.-B. Wei and M. B. Plenio,

*New Journal of Physics, 19, 0023002* (2017) | ArXiv

licensed under CC BY 3.0

**The gist of it**

While the statistical mechanics of thermodynamical system in equilibrium is well understood and taught at undergraduate level, a similar theory for systems that are far off equilibrium has not been established yet. What is, for example, the work done when a system is pushed far away from equilibrium? Even such a seemingly, simple question that has a straightforward answer in equilibrium statistical mechanics is difficult to assess far away from equilibrium. This is a question that we consider in our work. More specifically, we link the dissipated work done on a system driven arbitrarily far from equilibrium to a concept from quantum information science, namely the family of Rényi divergences between initial and final state along the forward and reversed dynamics.

**Universal continuous-variable quantum computation without cooling** – H.-K. Lau and M. B. Plenio, *Physical Review A, 95, 022303* (2017) | ArXiv

DOI:https://doi.org/10.1103/PhysRevA.95.022303

**The gist of it**

When we do quantum computation, the computer is usually initiated in a known state, i.e., pure state. If the quantum computer is composed of harmonic oscillators, i.e., continuous-variable quantum computer, it is usually initialised by ground-state cooling, which is unfortunately not an easy process for many quantum systems. In this work, we show that, surprisingly, quantum computation is possible even if we do not completely know the quantum state, i.e., mixed state, so ground-state cooling is not necessary. We explicitly propose a two-qumode parity encoding that each qubit is represented by two mixed-state harmonic oscillators, and outline how the quantum logic gates can be implemented. We show that in some situation, our scheme allows quantum computation at which ground-state cooling is challenging. Our scheme can also tolerate a wider range of error, and reduce the fundamental initialisation energy, than any pure-state scheme.

**Signatures of spatially correlated noise and non-secular effects in two-dimensional electronic spectroscopy** – J. Lim, D. J. Ing, J. Rosskopf, J. Jeske, J. H. Cole, S. F. Huelga and M. B. Plenio,

J. Chem. Phys. 146, 024109 (2017)|ArXiv

**The gist of it**

Several competing theoretical models have been proposed to explain long-lived quantum coherences in photosynthetic complexes observed by using two-dimensional (2D) electronic spectroscopy. These models consider different vibrational structures, such as correlated fluctuations in dephasing noise and disorder induced by delocalised phonon modes coupled to several pigments, and vibronic features in phonon spectral densities induced by underdamped vibrational modes. Vibronic models have been tested both experimentally and theoretically for many biological and artificial systems, as shown in Nature Comm. 6, 7755 (2015) by our group. However, correlated fluctuation models have received little attention in the context of 2DES simulations, even though recent 2D experiments suggested the presence of correlated fluctuations in some biological and engineered molecular systems. In this work, we theoretically investigate how correlations in the noise affect 2D optical responses with the aim to identify the signatures of correlated fluctuations in 2D electronic spectra.