Exploring dynamical phase transitions and prethermalization with quantum noise of excitations

Abstract

Dynamical phase transitions can occur in isolated quantum systems that are brought out of equilibrium by sudden parameter changes. We discuss the characterization of such dynamical phase transitions based on the statistics of produced excitations. We consider both the O(N) model in the large N limit and a spin model with long range interactions and show that the dynamical criticality of their prethermal steady-states manifests most dramatically not in the average number of excitations but in their higher moments. We argue that the growth of defect fluctuations carries unique signatures of the dynamical criticality, irrespective of the precise details of the model. Our theoretical results should be relevant to quantum quench experiments with ultracold bosonic atoms in optical lattices.

Quantum gas microscopy with spin, atom-number, and multilayer readout

“…For one-and two-dimensional systems, our techniques can yield complete number statistics and provide spectra of high-order density-density correlations and distribution functions. Such observables can be used to directly characterize quantum phases, for example the Tonks-Girardeau gas through its local and nonlocal pair correlations [14] or the dynamics of quantum phase transitions through counting statistics of excitations [15].…”

Linear ramps of the mass in the O(N) model: Dynamical transition and quantum noise of excitations

“…We find that ν * = 1/(d − 2) for 2 < d < 4, and ν * = 1/2 for d ≥ 4, which is the upper critical dimension. The fact that these critical exponents are similar to those of a thermal transition at equilibrium suggest that the two might be analogous 38,42 . Indeed, one could imagine that fixing r f 0 in the equilibrium ordered phase and increasing r i 0 from r f 0 to higher values amounts to increase the energy density injected by the quench into the system.…”

“…Focusing now on the dynamics, it has been shown numerically 37,38,41,42 that this model can undergo a dynamical phase transition after a sudden quench in the bare mass, i.e., suddenly changing its value from r 0,i to r 0,f ( we focus here on the case of a quench starting from the ground state in the paramagnetic phase). The time dependent effective mass (satisfying Eq.…”

“…Notice however that, despite the analogies, the distribution of quasi-particles after a quench in the N → +∞ limit is not thermal. Moreover, the difference between the two cases becomes apparent if one studies the statistics of excitations produced close to a dynamical transition, since, unlike the equilibrium case, in the dynamical one the fluctuations in the number of excitations are very sensitive to how close one is to a dynamical critical point 38 .…”

“…Most importantly, recent literature has shown that such quasistationary states may display dynamical critical behaviour. Originally studied for sudden changes of parameters (quenches) in the Hubbard model [31][32][33] such criticality was later observed in several systems at the mean-field level 34,35 and in field theories [36][37][38][39] . While the characterization of these dynamical transitions and their peculiarity as compared to thermal transition is a topic of recent research, it has been recently shown that a simple protocol measuring the statistics of excitations produced in a sudden quench can single out their non-equilibrium nature 38 .…”