Universality in driven open quantum matter

Abstract

Universality is a powerful concept, which enables making qualitative and quantitative predictions in systems with extensively many degrees of freedom. It finds realizations in almost all branches of physics, including in the realm of nonequilibrium systems. Our focus here is on its manifestations within a specific class of nonequilibrium stationary states: driven open quantum matter. Progress in this field is fueled by a number of uprising platforms ranging from light-driven quantum materials over synthetic quantum systems like cold atomic gases to the functional devices of the noisy intermediate scale quantum era. These systems share in common that, on the microscopic scale, they obey the laws of quantum mechanics, while detailed balance underlying thermodynamic equilibrium is broken due to the simultaneous presence of Hamiltonian unitary dynamics and nonunitary drive and dissipation. The challenge is then to connect this microscopic physics to macroscopic observables, and to identify universal collective phenomena that uniquely witness the breaking of equilibrium conditions, thus having no equilibrium counterparts. In the framework of a Lindblad-Keldysh field theory, we discuss on the one hand the principles delimiting thermodynamic equilibrium from driven open stationary states, and on the other hand show how unifying concepts such as symmetries, the purity of states, and scaling arguments are implemented. We then present instances of universal behavior structured into three classes: new realizations of paradigmatic nonequilibrium phenomena, including a survey of first experimental realizations; novel instances of nonequilibrium universality found in these systems made of quantum ingredients; and genuinely quantum phenomena out of equilibrium, including in fermionic systems. We also discuss perspectives for future research on driven open quantum matter.

Figures (16)

• Figure 1: Illustration of typical environmental and drive scales and the corresponding regimes of driven-dissipative many-body systems. (a) This review focusses on universal phenomena emerging in rapidly driven systems with Markovian dissipation. An excursion on universality in slowly driven systems, utilizing the Kibble-Zurek argument and the Floquet formalism, is presented in Sec. \ref{['sec:slowly-rapidly-driven-open-systems']}. Extensive reviews of (open) Floquet many-body systems are provided in Refs. Bukov2015Eckardt2017MoriReview2023. For Non-Markovian systems we refer to the reviews in Refs. deVegaReviewBreuerNonMarkovian. (b) Illustration of the emergence of the typical system and bath scales. (c) Scaling regimes of the environment-induced noise kernel with the quantum scaling limit and semiclassical Martin-Siggia-Rose-Janssen-de Dominicis (MSRJD) limit illustrated as particular cases.
• Figure 2: Top: Illustration of the sandpile model. Sand is piling up on a plate via slow deposition ($=$ drive). The sandpile reaches a critical slope at which friction and gravitation balance each other. Further deposition triggers scale invariant avalanches, which deplete at the boundaries ($=$ dissipation). Bottom: Illustration of excitation spreading in a Rydberg gas in the facilitation regime. Excited atoms (red) act as seeds which facilitate the excitation of neighboring atoms that traverse the facilitation shell (gray circles). This leads to spreading of excitations. Ionization or loss of excited atoms yields a depletion of the atom density proportional to the number of excited atoms.
• Figure 3: Self-organized criticality in a gas of ultracold Rydberg atoms. (a) Driving an inhomogeneously trapped gas with an off-resonant laser induces the facilitated spreading of excitations (blue dots). (b) Evolution of the density of atoms $n$ ($\equiv n(t, \mathbf{x})$) and the excitation density $\phi$ ($\equiv \phi(t, \mathbf{x})$) from facilitation, loss and atomic motion. The initial supercritical state $n(t=0,\mathbf{x}) > n_c$ evolves through three stages: (i) fast growth of excitations; (ii-a) self-organization into a critical density due to loss of particles; (ii-b) regrowth of the density in the center due to atomic motion from the flanks toward the center; (iii) the critical point is stabilized on transient time scales. (c) Upper panels: two-dimensional experimental absorption images. Lower panels: reconstructed atom densities along a 1D slice with $y = z = 0$. The flat-top coincides with the critical density. Figure adapted from Ref. KlockeHydro.
• Figure 4: Exciton-polariton dispersion relation and pumping schemes. The coherent coupling of photons and excitons leads to the formation of two bands that are called lower and upper polaritons. Incoherent pumping: Excitations which are injected at high energies undergo relaxation through complex scattering processes and eventually condense at the bottom of the lower polariton branch. Coherent pumping: A laser is tuned close to the inflection point of the lower polariton dispersion relation. Pairs of coherently excited polaritons in the pump mode scatter parametrically into the signal and idler modes. In both pumping schemes, time-continuous pumping is required to compensate losses due to cavity leakage.
• Figure 5: A single vortex in the anisotropic cKPZ equation. Colors from blue to red encode $\theta \in [0, 2 \pi)$. (a) Weakly anisotropic (WA) regime with $\lambda_x/(2D) \approx 0.9$ and $\lambda_y/(2D) \approx 0.4$, leading to a pronounced spiral structure. (b) Strongly anisotropic (SA) regime with $\lambda_x/(2D) \approx 0.9$ and $\lambda_y/(2D) \approx -0.4$, where the radial dependence of the vortex far field is much weaker. (c) Fully anisotropic (FA) configuration with $\lambda_x/(2D) = - \lambda_y/(2D) \approx 0.7$. The vortex field does not depend on the radial coordinate. (d) The radial dependence of the vortex field along the dashed black lines in (a--c) is $\sim r$ for WA, $\sim \ln(r)$ for SA, and $\sim \mathrm{const.}$ for FA. Straight lines are fits to the numerical data. Figure adapted from Ref. Sieberer2018b.