Decay and recurrence of non-Gaussian correlations in a quantum many-body system
Thomas Schweigler, Marek Gluza, Mohammadamin Tajik, Spyros Sotiriadis, Federica Cataldini, Si-Cong Ji, Frederik S. Møller, João Sabino, Bernhard Rauer, Jens Eis… 展开作者
Thomas Schweigler, Marek Gluza, Mohammadamin Tajik, Spyros Sotiriadis, Federica Cataldini, Si-Cong Ji, Frederik S. Møller, João Sabino, Bernhard Rauer, Jens Eisert, Jörg Schmiedmayer
Gaussian models provide an excellent effective description of many quantum many-body systems ranging from condensed matter systems all the way to neutron stars. Gaussian states are common at equilibrium when the interactions are weak. Recently it was proposed that they can also emerge dynamically from a non-Gaussian initial state evolving under non-interacting dynamics. In this work, we present the experimental observation of such a dynamical emergence of Gaussian correlations in a quantum many-body system. This non-equilibrium evolution is triggered by abruptly switching off the effective interaction between the observed collective degrees of freedom, while leaving the interactions between the microscopic constituents unchanged. Starting from highly non-Gaussian correlations, consistent with the sine-Gordon model, we observe a Gaussian state to emerge over time as revealed by the decay of the fourth and sixth order connected correlations in the quantum field. A description of this dynamics requires a novel mechanism for the emergence of Gaussian correlations, which is relevant for a wide class of quantum many-body systems. In our closed system with non-interacting effective degrees of freedom, we do not expect full thermalization. This memory of the initial state is confirmed by observing recurrences of non-Gaussian correlations.
Even though the evolution of an isolated quantum system is unitary, the complexity of interacting many-body systems prevents the observation of recurrences of quantum states for all but the smallest systems. For large systems one can not access the full complexity of the quantum states and the requirements to observe a recurrence in experiments reduces to being close to the initial state with respect to the employed observable. Selecting an observable connected to the collective excitations in one-dimensional superfluids, we demonstrate recurrences of coherence and long range order in an inter…
Decoherence with recurrences appear in the dynamics of the one-body density matrix of an $F = 1$ spinor Bose-Einstein condensate, initially prepared in coherent states, in the presence of an external uniform magnetic field and within the single mode approximation. The phenomenon emerges as a many-body effect of the interplay of the quadratic Zeeman effect, that breaks the rotational symmetry, and the spin-spin interactions. By performing full quantum diagonalizations very accurate time evolution of large condensates are analyzed, leading to heuristic analytic expressions for the time dependenc…
Recurrence time is evaluated for some initial quantum states in the one-dimensional Bose gas with repulsive short-range interactions. In the relatively strong and weak coupling cases some different types of initial states show almost complete recurrence and the estimates of recurrence time are proportional to some powers of the system size at least in some range of the system size. They are much longer than in the case of free particles such as 100 times. In the free-bosonic and free-fermionic regimes we evaluate the recurrence time rigorously, which is proportional to the square of the system…
We analyze quantum dynamics of strongly interacting, kinetically constrained many-body systems. Motivated by recent experiments demonstrating surprising long-lived, periodic revivals after quantum quenches in Rydberg atom arrays, we introduce a manifold of locally entangled spin states, representable by low-bond dimension matrix product states, and derive equations of motions for them using the time-dependent variational principle. We find that they feature isolated, unstable periodic orbits, which capture the recurrences and represent nonergodic dynamical trajectories. Our results provide a t…
Quantum mechanical few-body systems in reduced dimensionalities can exhibit many interesting properties such as scale-invariance and universality. Analytical descriptions are often available for integer dimensionality, however, numerical approaches are necessary for addressing dimensional transitions. The Fully-Correlated Gaussian method provides a variational description of the few-body real-space wavefunction. By placing the particles in a harmonic trap, the system can be described at various degrees of anisotropy by squeezing the confinement. Through this approach, configurations of two and…
Through an exact method we numerically solve the time evolution of the density profile for an initially localized state in the one-dimensional bosons with repulsive short-range interactions. We show that a localized state with a density notch is constructed by superposing one-hole excitations. The initial density profile overlaps the plot of the squared amplitude of a dark soliton in the weak coupling regime. We observe the localized state collapsing into a flat profile in equilibrium for a large number of particles such as N=1000. The relaxation time increases as the coupling constant decreas…
We develop an innovative numerical technique to describe few-body systems. Correlated Gaussian basis functions are used to expand the channel functions in the hyperspherical representation. The method is proven to be robust and efficient compared to other numerical techniques. The method is applied to few-body systems with short range interactions, including several examples for three- and four-body systems. Specifically, for the two-component, four-fermion system, we extract the coefficients that characterize its behavior at unitarity.
Quantum chaotic interacting $N$-particle systems are assumed to show fast and irreversible spreading of quantum information on short (Ehrenfest) time scales $\sim\!\log N$. Here we show that, near criticality, certain many-body systems exhibit fast initial scrambling, followed subsequently by oscillatory behavior between reentrant localization and delocalization of information in Hilbert space. We consider both integrable and nonintegrable quantum critical bosonic systems with attractive contact interaction that exhibit locally unstable dynamics in the corresponding many-body phase space of th…
The theoretical study of ultracold few-body systems is often done using an idealized 1D model with zero range interactions. Here we study these systems using a more realistic 3D model with finite range interactions. We place three-particles, two identical and one impurity, in an axial symmetric harmonic trap and solve the corresponding stationary Schrödinger equation using the correlated Gaussian method for different particle types, aspect ratios and interactions strength. We show that the idealized model is accurate for small and intermediate strength interactions at aspect ratios larger than…
In this work, we generalize a recursive enumerative formula for connected Feynman diagrams with two external legs. The Feynman diagrams are defined from a fermionic gas with a two-body interaction. The generalized recurrence is valid for connected Feynman diagrams with an arbitrary number of external legs and an arbitrary order. The recurrence formula terms are expressed in function of weak compositions of non-negative integers and partitions of positive integers in such a way that to each term of the recurrence correspond a partition and a weak composition. The foundation of this enumeration …
Within the hyperspherical framework, the solution of the time-independent Schroedinger equation for a n-particle system is divided into two steps, the solution of a Schroedinger like equation in the hyperangular degrees of freedom and the solution of a set of coupled Schroedinger like hyperradial equations. The solutions to the former provide effective potentials and coupling matrix elements that enter into the latter set of equations. This paper develops a theoretical framework to determine the effective potentials, as well as the associated coupling matrix elements, for few-body systems with…
We analyze the properties of particles trapped in three-dimensional potentials formed from superimposed Gaussian beams, fully taking into account effects of potential anharmonicity and non-separability. Although these effects are negligible in more conventional optical lattice experiments, they are essential for emerging ultracold atom developments. We focus in particular on two potentials utilized in current ultracold atom experiments: arrays of tightly focused optical tweezers and a one-dimensional optical lattice with transverse Gaussian confinement and highly excited transverse modes. Our …
A unified theory of strong coupling Bose polarons: From repulsive polarons to non-Gaussian many-body bound states
Ludwig-Maximilians-Universität München（慕尼黑大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Université Libre de Bruxelles（布鲁塞尔自由大学）
We investigate a system of $N$ spinless bosons confined in quasi-two-dimensional harmonic trap with repulsive two-body finite-range Gaussian interaction potential of large $s$-wave scattering length. Exact diagonalization of the Hamiltonian matrix is carried out to obtain the $N$-body ground state as well as low-lying excited states, using Davidson algorithm in beyond lowest-Landau-level approximation. We examine the finite-range effects of the interaction potential on the many-body ground state energy as also the degree of condensation of the Bose-condensed gas. The results obtained indicate …
Gaussian Expansion Method for few-body states in two-dimensional materials
Department of Physics, Graduate School of Science, Tohoku University（东北大学理学研究科物理系）；Instituto Tecnológico de Aeronáutica（航空技术学院）；Physics Center of Minho and Porto Universities (CF-UM-UP) and Department of Physics, University of Minho（米尼奥和波尔图大学物理中心（CF-UM-UP）及米尼奥大学物理系）；RIKEN Nishina Center for Accelerator-Based Science（理化学研究所西村加速器科学中心）
