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Register a new userEquilibration via Gaussification in fermionic lattice systems
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In this work, we present a result on the non-equilibrium dynamics causing equilibration and Gaussification of quadratic non-interacting fermionic Hamiltonians. Specifically, based on two basic assumptions - clustering of correlations in the initial state and the Hamiltonian exhibiting delocalizing transport - we prove that non-Gaussian initial states become locally indistinguishable from fermionic Gaussian states after a short and well controlled time. This relaxation dynamics is governed by a power-law independent of the system size. Our argument is general enough to allow for pure and mixed initial states, including thermal and ground states of interacting Hamiltonians on and large classes of lattices as well as certain spin systems. The argument gives rise to rigorously proven instances of a convergence to a generalized Gibbs ensemble. Our results allow to develop an intuition of equilibration that is expected to be more generally valid and relates to current experiments of cold atoms in optical lattices.
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The time evolution of a finite fermion system towards statistical equilibrium is investigated using analytical solutions of a nonlinear partial differential equation that had been derived earlier from the Boltzmann collision term. The solutions of this fermionic diffusion equation are rederived in closed form, evaluated exactly for simplified initial conditions, and applied to hadron systems at low energies in the MeV-range, as well as to quark systems at relativistic energies in the TeV-range where antiparticle production is abundant. Conservation laws for particle number including created antiparticles, and for the energy are discussed.
We demonstrate fluorescence microscopy of individual fermionic potassium atoms in a 527-nm-period optical lattice. Using electromagnetically induced transparency (EIT) cooling on the 770.1-nm D$_1$ transition of $^{40}$K, we find that atoms remain at individual sites of a 0.3-mK-deep lattice, with a $1/e$ pinning lifetime of $67(9),rm{s}$, while scattering $sim 10^3$ photons per second. The plane to be imaged is isolated using microwave spectroscopy in a magnetic field gradient, and can be chosen at any depth within the three-dimensional lattice. With a similar protocol, we also demonstrate patterned selection within a single lattice plane. High resolution images are acquired using a microscope objective with 0.8 numerical aperture, from which we determine the occupation of lattice sites in the imaging plane with 94(2)% fidelity per atom. Imaging with single-atom sensitivity and addressing with single-site accuracy are key steps towards the search for unconventional superfluidity of fermions in optical lattices, the initialization and characterization of transport and non-equilibrium dynamics, and the observation of magnetic domains.
We show that the Kapitza stabilization can occur in the context of nonlinear quantum fields. Through this phenomenon, an amplitude-modulated lattice can stabilize a Bose-Einstein condensate with repulsive interactions and prevent the spreading for long times. We present a classical and quantum analysis in the framework of Gross-Pitaevskii equation, specifying the parameter region where stabilization occurs. Effects of nonlinearity lead to a significant increase of the stability domain compared with the classical case. Our proposal can be experimentally implemented with current cold atom settings.
We investigate generalized thermalization in an isolated free Fermionic chain evolving from an out of equilibrium initial state through a sudden quench. We consider the quench where a Fermionic chain is broken into two disjoint chains. We focus on the evolution of the local observables namely, occupation number, information sharing and out-of-time-order correlations after the quench and study the relaxation of the observable, leading to generalized Gibbs ensemble for the system in the thermodynamic limit. We obtain the light cone formed by the evolution of the observables along the Fermionic lattice chain due to the sudden quench which abides by the Lieb-Robinson bound in quantum systems. We also analytically study a simpler model which captures the essential features of the system. Our analysis strongly suggest that the internal interactions within the system do not remain of much importance once the quench is sufficiently strong.
The presence of non-local and long-range interactions in quantum systems induces several peculiar features in their equilibrium and out-of-equilibrium behavior. In current experimental platforms control parameters such as interaction range, temperature, density and dimension can be changed. The existence of universal scaling regimes, where diverse physical systems and observables display quantitative agreement, generates a common framework, where the efforts of different research communities can be -- in some cases rigorously -- connected. Still, the application of this general framework to particular experimental realisations requires the identification of the regimes where the universality phenomenon is expected to appear. In the present review we summarise the recent investigations of many-body quantum systems with long-range interactions, which are currently realised in Rydberg atom arrays, dipolar systems, trapped ion setups and cold atoms in cavity experiments. Our main aim is to present and identify the common and (mostly) universal features induced by long-range interactions in the behaviour of quantum many-body systems. We will discuss both the case of very strong non-local couplings, i.e. the non-additive regime, and the one in which energy is extensive, but nevertheless low-energy, long wavelength properties are altered with respect to the short-range limit. Cases of competition with other local effects in the above mentioned setups are also reviewed.
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