In this article, we study an exponential decay for the gas of bosons with strong repulsive delta interactions from a double-well potential. We consider an exactly solvable model comprising an infinite wall and two Dirac delta barriers. We explore its features both within the exact method and with the resonance expansion approach. The study reveals the effect of the splitting barrier on the decay rate in dependence on the number of particles. Among other things, we find that the effect of the splitting barrier on the decay rate is most pronounced in systems with odd particle numbers. During exponential decay, the spatial correlations in an internal region are well captured by the "radiating state".
We present a proposal for the realization of entanglement Hamiltonians in one-dimensional critical spin systems with strongly interacting cold atoms. Our approach is based on the notion that the entanglement spectrum of such systems can be realized with a physical Hamiltonian containing a set of position-dependent couplings. We focus on reproducing the universal ratios of the entanglement spectrum for systems in two different geometries: a harmonic trap, which corresponds to a partition embedded in an infinite system, and a linear potential, which reproduces the properties of a half-partition …
Standard analytical construction of the many-body wave function of interacting particles in one dimension, beyond mean-field theory, is based on the Jastrow approach. The many-body interacting ground state is build up from the ground state of the non-interacting system and the product of solutions of the corresponding interacting two-body problem. However, this is possible only if the center-of-mass motion is decoupled from the mutual interactions. In our work, based on the general constraints given by contact nature of the atom-atom interactions, we present an alternative approach to the stan…
Motivated by recent advance in orbitally tuned Feshbach resonance experiments, we analyze the ground-state phase diagram and related low-energy excitation spectra of a d-wave interacting Bose gas. A two-channel model with d-wave symmetric interactions and background s-wave interactions is adopted to characterize the gas. The ground state is found to show three interesting phases: atomic, molecular, and atomic-molecular superfluidity. Remarkably differently from what was previously known in the p-wave case, the atomic superfluid is found to be momentum-independent in the present d-wave case. Bo…
We theoretically investigate the collisional heating of a cold atom system subjected to time-periodic forces. We show within the Floquet framework that this heating rate due to two-body collisions has a general semiclassical expression $\mathcal{P}\propto ρσv_{\rm col} E_0$, depending on the kinetic energy $E_0$ associated with the shaking, particle number density $ρ$, elastic collision cross section $σ$, and an effective collisional velocity $v_{\rm col}$ determined by the dominant energy scale in the system. We further show that the collisional heating is suppressed by Pauli blocking in cold…
In a recent work, Murmann {\it et. al.} [Phys. Rev. Lett. {\bf114}, 080402 (2015)] have experimentally prepared and manipulated a double-well optical potential containing a pair of Fermi atoms as a possible building block of Hubbard model. Here, we carry out a detailed theoretical study on the properties of both fermionic and bosonic two-site Hubbard models with a pair of interacting atoms in a trap with a double-well structure along z-axis and a 2D harmonic confinement along the transverse directions. We consider fermions as of two-component type and bosons as of spinless as well as of two sp…
We present a mapping between the Edwards model of disorder describing the motion of a single particle subject to randomly-positioned static scatterers and the Bose polaron problem of a light quantum impurity interacting with a Bose-Einstein condensate (BEC) of heavy atoms. The mapping offers an experimental setting to investigate the physics of Anderson localization where, by exploiting the quantum nature of the BEC, the time evolution of the quantum impurity emulates the disorder-averaged dynamics of the Edwards model. Valid in any space dimension, the mapping can be extended to include inter…
We study thermoelectric currents of neutral, fermionic atoms flowing through a mesoscopic channel connecting a hot and a cold reservoir across the superfluid transition. The thermoelectric response results from a competition between density-driven diffusion from the cold to the hot reservoir and the channel favoring transport of energetic particles from hot to cold. We control the relative strength of both contributions to the thermoelectric response using an external optical potential in a nearly non-interacting and a strongly-interacting system. Without interactions, the magnitude of the par…
We study ensembles of fermionic cold-atom quantum wires with tunable transverse mode population and single-wire resolution. From in situ density profiles, we determine the temperature of the atomic wires in the weakly interacting limit and reconstruct the underlying potential landscape. By varying atom number and temperature, we control the occupation of the transverse modes and study the 1D-3D crossover. In the 1D limit, we observe an increase of the reduced temperature $T/T_{F}$ at nearly constant entropy per particle $S/N k_{B}$. The ability to probe individual atomic wires in situ paves th…
We study numerically the problem of dynamical thermalization of interacting cold fermionic atoms placed in an isolated Sinai-oscillator trap. This system is characterized by a quantum chaos regime for one-particle dynamics. We show that for a many-body system of cold atoms the interactions, with a strength above a certain quantum chaos border given by the Aberg criterion, lead to the Fermi-Dirac distribution and relaxation of many-body initial states to the thermalized state in absence of any contact with a thermostate. We discuss the properties of this dynamical thermalization and its links w…
The superfluid insulator transition of ultra-cold bosons in disordered 1d traps
我们导出了一个有效的量子约瑟夫森阵列模型，用于弱相互作用的一维凝聚体，该凝聚体被无序势分裂成弱耦合的水坑。从第一性原理得到的耦合常数的分布表明，无序势中的弱相互作用玻色子经历由强随机不动点控制的超流绝缘体转变[Phys. Rev. Lett. 93，150402（2004）]。我们计算重整化群流的具体实现的无序势，以方便有限尺寸标度的实验结果，并允许比较的行为所规定的强随机性不动点。通过对平均场结果的修正，得到了系统的相图。
The $N$-flavor interacting Su-Schrieffer-Heeger (i-SSH) model realizable in cold-atoms in an optical lattice is studied. We clarify the relationship between the i-SSH model and the Chiral-Gross-Neveu-Wilson (CGNW) model. Following the previous study of the CGNW model in the high-energy physics community, the groundstate phases of the i-SSH model are investigated and interpreted from the view of the phases of the CGNW model. The interaction effect on the i-SSH model, belonging to the topological BDI class, is grasped by following the view of the dynamical breakdown of chiral symmetry in the CGN…
Cold atomic gases of interacting bosons subject to rapid rotation and confined in anharmonic traps can theoretically exhibit analogues of the fractional quantum Hall effect for electrons in strong magnetic fields. In this setting the Coriolis force due to the rotation mimics the Lorentz force on charged particles but artificial gauge fields can also be obtained by coupling the internal structure of the atoms to light fields. The chapter discusses mathematical aspects of transitions to different strongly correlated phases that appear when the parameters of a model Hamiltonian are varied.
