Liouvillian spectral collapse in the Scully-Lamb laser model

Phase transitions of thermal systems and the laser threshold were first connected more than forty years ago. Despite the nonequilibrium nature of the laser, the Landau theory of thermal phase transitions, applied directly to the Scully-Lamb laser model (SLLM), indicates that the laser threshold is a second-order phase transition, associated with a U(1) spontaneous symmetry breaking (SSB). To capture the genuine nonequilibrium phase transition of the SLLM (i.e., a single-mode laser without a saturable absorber), here we employ a quantum theory of dissipative phase transitions. Our results confirm that the U(1) SSB can occur at the lasing threshold but, in contrast to the Landau theory and semiclassical approximation, they signal that the SLLM "fundamental" transition is a different phenomenon, which we call Liouvillian spectral collapse; that is, the emergence of diabolic points of infinite degeneracy. By considering a generalized SLLM with additional dephasing, we witness a second-order phase transition, with a Liouvillian spectral collapse, but in the absence of symmetry breaking. Most surprisingly, the phase transition corresponds to the emergence of dynamical multistability even without SSB. Normally, bistability is suppressed by quantum fluctuations, while in this case, the very presence of quantum fluctuations enables bistability. This rather anomalous bistability, characterizing the truly dissipative and quantum origin of lasing, can be an experimental signature of our predictions, and we show that it is associated with an emergent dynamical hysteresis.

Etude par microscopie électronique à transmission à haute résolution de l'élargissement thermique des parois de domaines ferroélectriques dans un système de premier ordre

The macroscopic properties of ferroelectric materials depend directly on the domain configuration and the structure of the domain boundaries. For this reason, their study is of great scientific and technological interest. Several models have been developed to describe the properties of domain walls (structure, thickness, stress at the interface, mobility, …). However, few quantitative experimental observations of ferroelectric domain walls at an atomic scale have been reported, and even less results exist at higher temperatures. The ferroelectric domain-wall thickness is an important parameter whose behavior as a function of temperature is directly related to the order of the phase transition. In a second-order system, the temperature dependence of the domain-wall thickness follows a power law L ~ (Tc - T)-ω where ω is the critical exponent characterizing the divergence of L near the critical temperature Tc The predictions concerning the numerical value of are different depending on the theoretical model considered. Nevertheless, the majority of ferroelectric materials are known to undergo a first-order transition. In these systems the domain-wall thickness increases when the transition temperature is approached, but without diverging as for a second-order phase transition. The major objective of this work was to measure this broadening predicted by the theory for the first time at the approach of the phase transition temperature. We have shown that high resolution transmission electron microscopy is powerful technique for the study of ferroelectric domain walls not only at room temperature but also at higher temperatures. This method allows a direct and local observation of interfaces at an atomic scale which is a considerable advantage over diffraction techniques (X-ray, neutron, electron) and most of the other electron microscopy methods. However, the requirements of this method concerning the performance of the optical system of the microscope, the quality of the specimen and its stability in the column are very high, and today high resolution microscopy at high temperature remains a major challenge. The domain-wall thickness is obtained from the measurement of the crystal lattice distortion near the interface using two different numerical techniques of image analysis. The first method is based on the accurate determination of the center of bright peaks which appear on high resolution images for a judicious choice of the experimental parameters (delocalization and crystal thickness) and which represent the crystal lattice nodes. The second technique consists in selecting a circular region of the power spectrum around a reflection peak, centering the Fourier space on this reflection and performing the inverse Fourier transform. The information about the local displacement of atomic planes corresponding to the selected reflection is extracted form the phase component of the obtained complex image. Both techniques have been successfully applied to the measurement of the thickness of the 90° ferroelectric domain walls in PbTiO3 single crystals. This perovskite presents a first order phase transition at Tc = 492.2°C. which corresponds to the transformation of the crystal from the high-temperature paraelectric cubic phase to the low-temperature ferroelectric tetragonal phase. For the first time, the thermal broadening of domain walls has been measured quantitatively using HRTEM. The results are compared with the predictions made by phenomenological theories. We find that the domain wall thickness increases continuously from 0.7 nm at room temperature up to 5.5 nm near the transition temperature. Our results are consistent with those obtained by other authors at room temperature and those of a very recent study performed at higher temperatures using weak-beam microscopy. The measured domain-wall broadening is greater than the one predicted by a three-dimensional Ginzburg-Landau model where the polarization which is the primary order parameter is coupled to the elastic strain which plays the role of secondary order parameter. Our results are better described by a one-dimensional Ginzburg-Landau model without secondary order parameter. In this case the gradient coupling coefficient κ of the Ginzburg-Landau free energy is found to be 1.3 · 10-10 m3F-1. The methods developed for the measurement of the domain-wall thickness can by applied not only to other first-order ferroelectric crystals but also to ferroelectric systems presenting a second-order phase transition thus allowing the determination of the critical exponent ω. Characteristics only present in 2-D systems could also be detected by studying very thin specimens. Moreover, the same techniques can be adapted to the study of domain walls in purely ferroelastic materials.

EPFL2000

Electric field effect on superconductivity in $La_{2-x}$$Sr_{x}$$CuO_{4}$

Ivan Bozovic, Guy Joseph Günter Dubuis, Davor Pavuna

We demonstrate a method to tune the carrier concentration of a high temperature superconductor over a wide range, using an applied electric field. Thin film devices were made in an electrical double layer transistor configuration utilizing an ionic liquid. In this way, the surface carrier density in La2-xSrxCuO4 films can be varied between 0.01 and 0.14 carriers per Cu atom with a resulting change in critical temperature of 25 K (70% of the maximum critical temperature in this compound). This allows one to study a large segment of the cuprate phase diagram without altering the level of disorder. We used this method [A. T. Bollinger et al., Nature 472, 458–460 (2011)] to study the quantum critical point at the superconductor to insulator phase transition on the underdoped side of superconducting dome, and concluded that this transition is driven by quantum phase fluctuations and Cooper pair delocalization.

American Institute of Physics2012

Engineering and characterizing nonclassical states of light in quantum optical networks

Kilian Robert Seibold

The exploration of open quantum many-body systems -systems of microscopic size exhibiting quantum coherence and interacting with their surrounding- has emerged as a key research area over the last years. The recent advances in controlling and preserving quantum coherence at the level of a single particle, developed in a wide variety of physical platforms, have been a major driving force in this field. The driven dissipative nature is a common characteristic of a wide class of modern experimental platforms in quantum science and technology, such as photonic systems, ultracold atoms, optomechanical systems, or superconducting circuits. The interplay between the coherent quantum dynamics and dissipation in open quantum systems leads to a wide range of novel out-of-equilibrium behaviours. Among them, the emergence in these systems of dynamical phases with novel broken symmetries, topological phases and the occurrence of dissipative phase transitions are of particular interest. This thesis aims at establishing a theoretical framework to engineer, characterize and control nonclassical states of light in photonic quantum optical networks in different regimes. The emphasis is put on its implementation, in particular with respect to integration and scalability in photonic platforms. In this thesis, we tackle some interesting aspects arising in the study of the dynamics of driven dissipative coupled nonlinear optical resonators. In that context, we consider the dynamics of two coupled nonlinear photonic cavities in the presence of inhomogeneous coherent driving and local dissipations using the Lindblad master equation formalism.We show that this simple open quantum many-body system can be subject to dynamical instabilities. In particular, our analysis shows that this system presents highly nonclassical properties and its dynamics exhibits dissipative Kerr solitons (DKSs), characterized by the robustness of its specific temporal or spatial waveform during propagation.In a second step, our intuition gained from this system composed of only few degrees of freedom is expanded to the study of systems of bigger size. In particular, we study DKSs originating from the parametric gain in Kerr microresonators. While DKSs are usually described using a classical mean-field approach, our work proposes a quantum-mechanical model formulated in terms of the truncated Wigner formalism. This analysis is motivated by the fact that technological implementations push towards the realization of DKSs in miniaturized integrated systems. These are operating at low power, a regime where quantum effects are expected to be relevant. Using the tools provided by the theory of open quantum systems, we propose a detailed investigation of the impact of quantum fluctuations on the spectral and dynamical properties of DKSs. We show that the quantum fluctuations arising from losses engender a finite lifetime to the soliton, and demonstrate that DKSs correspond to a specific class of dissipative time crystals.

EPFL2022

Etude par microscopie électronique à transmission à haute résolution de l'élargissement thermique des parois de domaines ferroélectriques dans un système de premier ordre

EPFL2000

Engineering and characterizing nonclassical states of light in quantum optical networks

Kilian Robert Seibold

EPFL2022