Interaction-induced Localization Research Articles

Stable interaction-induced Anderson-like localization embedded in standing waves

We uncover the interaction-induced stable self-localization of few bosons in finite-size disorder-free superlattices. In these nonthermalized multi-particle states, one of the particles forms a superposition of multiple standing waves, so that it provides a quasi-random potential to localize the other particles. We derive effective Hamiltonians for self-localized states and find their energy level spacings obeying the Poisson statistics. The spatial distribution of the localized particles decays exponentially, which is refered to Anderson-like localization (ALL). Surprisingly, we find that the correlated self-localization can be solely induced by interaction in the well-studied Bose–Hubbard models, which has been overlooked for a long time. We propose a dynamical scheme to detect self-localization, where long-time quantum walks of a single particle form a superposition of multiple standing waves for trapping the subsequently loaded particles. Our work provides an experimentally feasible way to realize stable ALL in translation-invariant disorder-free few-body systems.

Hilbert space fragmentation and interaction-induced localization in the extended Fermi-Hubbard model

We study Hilbert space fragmentation in the extended Fermi-Hubbard model with nearest and next-nearest-neighbor interactions. Using a generalized spin/mover picture and saddle point methods, we derive lower bounds for the scaling of the number of frozen states and for the size of the largest block preserved under the dynamics. We find fragmentation for strong nearest- and next-nearest-neighbor repulsions as well as for the combined case. Our results suggest that the involvement of next-nearest-neighbor repulsions leads to an increased tendency for localization. We then model the dynamics for larger systems using Markov simulations to test these findings and unveil in which interaction regimes the dynamics becomes spatially localized. In particular, we show that for strong nearest- and next-nearest-neighbor interactions random initial states will localize provided that the density of initial movers is sufficiently low.

Hilbert Space Shattering and Disorder-Free Localization in Polar Lattice Gases.

Emerging dynamical constraints resulting from intersite interactions severely limit particle mobility in polar lattice gases. Whereas in absence of disorder hard-core Hubbard models with only strong nearest-neighbor interactions present Hilbert space fragmentation but no many-body localization for typical states, the 1/r^{3} tail of the dipolar interaction results in Hilbert space shattering, as well as in a dramatically slowed down dynamics and eventual disorder-free localization. Our results show that the study of the intriguing interplay between disorder- and interaction-induced many-body localization is within reach of future experiments with magnetic atoms and polar molecules.

Topological excitations and bound photon pairs in a superconducting quantum metamaterial

Recent discoveries in topological physics hold a promise for disorder-robust quantum systems and technologies. Topological states provide the crucial ingredient of such systems featuring increased robustness to disorder and imperfections. Here, we use an array of superconducting qubits to engineer a one-dimensional topologically nontrivial quantum metamaterial. By performing microwave spectroscopy of the fabricated array, we experimentally observe the spectrum of elementary excitations. We find not only the single-photon topological states but also the bands of exotic bound photon pairs arising due to the inherent anharmonicity of qubits. Furthermore, we detect the signatures of the two-photon bound edge-localized state which hints towards interaction-induced localization in our system. Our work demonstrates an experimental implementation of the topological model with attractive photon-photon interaction in a quantum metamaterial.

Density profile of a semi-infinite one-dimensional Bose gas and bound states of the impurity

We study the effect of the boundary on a system of weakly interacting bosons in one dimension. It strongly influences the boson density which is completely suppressed at the boundary position. Away from it, the density is depleted over the distances on the order of the healing length at the mean-field level. Quantum fluctuations modify the density profile considerably. The local density approaches the average one as an inverse square of the distance from the boundary. We calculate an analytic expression for the density profile at arbitrary separations from the boundary. We then consider the problem of localization of a foreign quantum particle (impurity) in the potential created by the inhomogeneous boson density. At the mean-field level, we find exact results for the energy spectrum of the bound states, the corresponding wave functions, and the condition for interaction-induced localization. The quantum contribution to the boson density gives rise to small corrections of the bound state energy levels. However, it is fundamentally important for the existence of a long-range Casimir-like interaction between the impurity and the boundary.

Photon-Mediated Localization in Two-Level Qubit Arrays.

We predict the existence of a novel interaction-induced spatial localization in a periodic array of qubits coupled to a waveguide. This localization can be described as a quantum analogue of a self-induced optical lattice between two indistinguishable photons, where one photon creates a standing wave that traps the other photon. The localization is caused by the interplay between on-site repulsion due to the photon blockade and the waveguide-mediated long-range coupling between the qubits.

Topological Quantum Walks in Momentum Space with a Bose-Einstein Condensate.

We report the experimental implementation of discrete-time topological quantum walks of a Bose-Einstein condensate in momentum space. Introducing stroboscopic driving sequences to the generation of a momentum lattice, we show that the dynamics of atoms along the lattice is effectively governed by a periodically driven Su-Schrieffer-Heeger model, which is equivalent to a discrete-time topological quantum walk. We directly measure the underlying topological invariants through time-averaged mean chiral displacements, which are consistent with our experimental observation of topological phase transitions. We then observe interaction-induced localization in the quantum-walk dynamics, where atoms tend to populate a single momentum-lattice site under interactions that are nonlocal in momentum space. Our experiment opens up the avenue of investigating discrete-time topological quantum walks using cold atoms, where the many-body environment and tunable interactions offer exciting new possibilities.

Unraveling the Structure of Ultracold Mesoscopic Collinear Molecular Ions.

We present an in-depth many-body investigation of the so-called mesoscopic molecular ions that can buildup when an ion is immersed into an atomic Bose-Einstein condensate in one dimension. To this end, we employ the multilayer multiconfiguration time-dependent Hartree method for mixtures of ultracold bosonic species for solving the underlying many-body Schrödinger equation. This enables us to unravel the actual structure of such massive charged molecules from a microscopic perspective. Laying out their phase diagram with respect to atom number and interatomic interaction strength, we determine the maximal number of atoms bound to the ion and reveal spatial densities and molecular properties. Interestingly, we observe a strong interaction-induced localization, especially for the ion, that we explain by the generation of a large effective mass, similarly to ions in liquid Helium. Finally, we predict the dynamical response of the ion to small perturbations. Our results provide clear evidence for the importance of quantum correlations, as we demonstrate by benchmarking them with wave function ansatz classes employed in the literature.

Interaction-induced localization of mobile impurities in ultracold systems

The impurities, introduced intentionally or accidentally into certain materials, can significantly modify their characteristics or reveal their intrinsic physical properties, and thus play an important role in solid-state physics. Different from those static impurities in a solid, the impurities realized in cold atomic systems are naturally mobile. Here we propose an effective theory for treating some unique behaviors exhibited by ultracold mobile impurities. Our theory reveals the interaction-induced transition between the extended and localized impurity states, and also explains the essential features obtained from several previous models in a unified way. Based on our theory, we predict many intriguing phenomena in ultracold systems associated with the extended and localized impurities, including the formation of the impurity-molecules and impurity-lattices. We hope this investigation can open up a new avenue for the future studies on ultracold mobile impurities.

Interaction-Induced Localization of Fermionic Mobile Impurities in a Larkin-Ovchinnikov Superfluid

We theoretically investigate the interplay between the fermionic mobile impurity atoms and a Larkin-Ovchinnikov (LO) superfluid in a two dimensional optical lattice. We find that the impurity atoms get localized and can form pairs when the interaction between the impurity atoms and the LO superfluid is strong enough. These features are due to the phenomena of self-localization whose underlying mechanism is revealed by an effective model. The impurity atoms with finite concentrations can drive the transition from a two-dimensional, checkerboardlike LO state to a quasi-one-dimensional, stripelike one. Experimental preparations to observe these features are also discussed.

Localization in an inhomogeneous quantum wire

We study interaction-induced localization of electrons in an inhomogeneous quasi-one-dimensional system--a wire with two regions, one at low density and the other high. Quantum Monte Carlo techniques are used to treat the strong Coulomb interactions in the low density region, where localization of electrons occurs. The nature of the transition from high to low density depends on the density gradient--if it is steep, a barrier develops between the two regions, causing Coulomb blockade effects. Ferromagnetic spin polarization does not appear for any parameters studied. The picture emerging here is in good agreement with measurements of tunneling between two wires.

Interaction-induced strong localization in quantum dots

We argue that Coulomb blockade phenomena are a useful probe of the crossover to strong correlation in quantum dots. Through calculations at low density using variational and diffusion quantum Monte Carlo (up to ${r}_{s}\ensuremath{\sim}55$), we find that the addition energy shows a clear progression from features associated with shell structure to those caused by commensurability of a Wigner crystal. This crossover (which occurs near ${r}_{s}\ensuremath{\sim}20$ for spin-polarized electrons) is, then, a signature of interaction-driven localization. As the addition energy is directly measurable in Coulomb blockade conductance experiments, this provides a direct probe of localization in the low density electron gas.

Interaction-Induced Localization of Anomalously Diffracting Nonlinear Waves

We study experimentally the interactions between normal solitons and tilted beams in glass waveguide arrays. We find that as a tilted beam, traversing away from a normally propagating soliton, coincides with the self-defocusing regime of the array, it can be refocused and routed back into any of the intermediate sites due to the interaction, as a function of the initial phase difference. Numerically, distinct parameter regimes exhibiting this behavior of the interaction are identified.

Interaction-induced localization of an impurity in a trapped Bose-Einstein condensate

We study the ground state properties of a trapped Bose condensate with a neutral impurity. By varying the strength of the attractive atom-impurity interactions the degree of localization of the impurity at the trap center can be controlled. As the impurity becomes more strongly localized the peak condensate density, which can be monitored experimentally, grows markedly. For strong enough attraction, the impurity can make the condensate unstable by strongly deforming the atom density in the neighborhood of the impurity. This "collapse" can possibly be investigated in bosenova-type experiments.

Antiresonance and interaction-induced localization in spin and qubit chains with defects

We study a spin chain with an anisotropic XXZ coupling in an external field. Such a chain models several proposed types of a quantum computer. The chain contains a defect with a different on-site energy. The interaction between excitations is shown to lead to two-excitation states localized next to the defect. In a resonant situation scattering of excitations on each other might cause decay of an excitation localized on the defect. We find that destructive quantum interference suppresses this decay. Numerical results confirm the analytical predictions.