Possible universal dynamics of a many-body system far from thermal equilibrium are explored. A focus is set on meta-stable non-thermal states exhibiting critical properties such as self-similarity and independence of the details of how the respective state has been reached. It is proposed that universal dynamics far from equilibrium can be tuned to exhibit a dynamical phase transition where these critical properties change qualitatively. This is demonstrated for the case of a superfluid two-component Bose gas exhibiting different types of long-lived but non-thermal critical order. Scaling exponents controlled by the ratio of experimentally tuneable coupling parameters offer themselves as natural smoking guns. The results shed light on the wealth of universal phenomena expected to exist in the far-from-equilibrium realm.
We shift the paradigm of feedback control from the control of quantum states to the control of phase transitions in quantum systems. We show that feedback allows tuning the universality class of phase transitions via modifying its critical exponent. We expand our previous treatment [D. A. Ivanov, T. Yu. Ivanova, S. F. Caballero-Benitez, and I. B. Mekhov, Phys. Rev. Lett. 124, 010603 (2020)] of Dicke model and go beyond the approximation of adiabatically eliminated light field. Both linearized and nonlinear models of spin ensembles are considered. The tunability of quantum fluctuations near the…
The dynamics of quantum systems far from equilibrium represents one of the most challenging problems in theoretical many-body physics. While the evolution is in general intractable in all its details, relevant observables can become insensitive to microscopic system parameters and initial conditions. This is the basis of the phenomenon of universality. Far from equilibrium, universality is identified through the scaling of the spatiotemporal evolution of the system, captured by universal exponents and functions. Theoretically, this has been studied in examples as different as the reheating pro…
Understanding and classifying nonequilibrium many-body phenomena, analogous to the classification of equilibrium states of matter into universality classes, is an outstanding problem in physics. Any many-body system, from stellar matter to financial markets, can be out of equilibrium in a myriad of ways; since many are also difficult to experiment on, it is a major goal to establish universal principles that apply to different phenomena and physical systems. At the heart of the classification of equilibrium states is the universality seen in the self-similar spatial scaling of systems close to…
We study a one-dimensional lattice model subject to non-Hermitian quasiperiodic potentials. Firstly, we strictly demonstrate that there exists an interesting dual mapping relation between $|a|<1$ and $|a|>1$ with regard to the potential tuning parameter $a$. The localization property of $|a|<1$ can be directly mapping to that of $|a|>1$, the analytical expression of the mobility edge of $|a|>1$ is therefore obtained through spectral properties of $|a|<1$. More impressive, we prove rigorously that even if the phase $θ\neq 0$ in quasiperiodic potentials, the model becomes non-$\mathcal{PT}$ symm…
We provide experimental evidence of universal dynamics far from equilibrium during the relaxation of an isolated one-dimensional Bose gas. Following a rapid cooling quench, the system exhibits universal scaling in time and space, associated with the approach of a non-thermal fixed point. The time evolution within the scaling period is described by a single universal function and scaling exponent, independent of the specifics of the initial state. Our results provide a quantum simulation in a regime, where to date no theoretical predictions are available. This constitutes a crucial step in the …
We consider a system of three helium-4 atoms, which is so far the simplest realistic three-body system exhibiting the Efimov effect, in order to analyse deviations from the universal Efimov three-body spectrum. We first calculate the bound states using a realistic two-body potential, and then analyse how they can be reproduced by simple effective models beyond Efimov's universal theory. We find that the non-universal variations of the first two states can be well reproduced by models parametrized with only three quantities: the scattering length and effective range of the original potential, a…
In these notes we discuss recent developments in the field of non-equilibrium quantum dynamics. Specifically, we consider nearly coherent Bose gases brought far out of equilibrium and study their behaviour in view of connections between universal properties, (quasi-)topological field configurations and turbulent dynamics. We demonstrate that the isolated Bose gas, on its way back to thermal equilibrium, can approach metastable non-equilibrium configurations and spend a long time in their vicinity. In such configurations, which have been termed non-thermal fixed points, the system shows univers…
Unifying Finite-Temperature Dynamical and Excited-State Quantum Phase Transitions
Instituto de Estructura de la Materia, IEM-CSIC（物质结构研究所，西班牙国家科学研究委员会）；Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Complutense de Madrid（马德里康普顿斯大学复杂系统跨学科小组）；Departamento de Estructura de la Materia, Física Térmica y Electrónica, Universidad Complutense de Madrid（马德里康普顿斯大学物质结构、热学和电子学系）；Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München（慕尼黑大学物理系与阿诺德·索末菲理论物理中心）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Dahlem Center for Complex Quantum Systems, Freie Universität Berlin（柏林自由大学达勒姆复杂量子系统中心）
We show that ideal Bose-Einstein condensation (BEC) in $d = 3$ dimensions is a non-classical critical second order phase transition with exponents $α= -1$, $β= 1$, $γ= 1$, $δ= 2$, $η= 1$ and $ν= 1$, obeying all the scaling equalities. These results are found with no approximations or assumptions. The previous exponents are a critical universality class on its own, different from the so-far accepted notion that BEC belongs to the Spherical Model universality class.
Efimov physics is a universal phenomenon arising in quantum three-body systems. For systems with resonant two-body interactions, Efimov predicted an infinite series of three-body bound states with geometric scaling symmetry. These Efimov states were first observed in cold Cs atoms and have since been reported in a variety of atomic systems. While theories predict non-universal behavior for narrow Feshbach resonances, experiments on Efimov resonances are so far consistent with predictions based on universal theories. Here we directly compare the Efimov spectra in a $^6$Li-$^{133}$Cs mixture nea…
It is now possible to study experimentally the combined effect of disorder and interactions in cold atom physics. Motivated by these developments we investigate the dynamics around the metal-insulator transition (MIT) in a one-dimensional (1D) Fermi gas with short-range interactions in a quasiperiodic potential by the time-dependent density-matrix renormalization group (tDMRG) technique. By tuning disorder and interactions we study the MIT from the weakly to the strongly interacting limit. The MIT is not universal as time evolution, well described by a process of anomalous diffusion, depends q…
Universal chiral Luttinger liquid behavior has been predicted for fractional quantum Hall edge states, but so far has not been observed experimentally in semiconductor-based two-dimensional electron gases. One likely cause of this absence of universality is the generic occurrence of edge reconstruction in such systems, which is the result of a competition between confinement potential and Coulomb repulsion. We show that due to a completely different mechanism of confinement, edge reconstruction can be avoided in graphene, which allows for the observation of the predicted universality.
