Non-interacting Regime Research Articles

Coexistence of antiferromagnetism and unconventional superconductivity in a quasi-one-dimensional flat-band system: Creutz lattice

We study the coexistence of antiferromagnetism and unconventional superconductivity on the Creutz lattice which shows strictly flat bands in the noninteracting regime. The famous renormalized mean-field theory is used to deal with strong electron–electron repulsive Hubbard interaction in the effective low-energy t–J model, the superfluid weight of the unconventional superconducting state has been calculated via the linear response theory. An unconventional superconducting state with both spin-singlet and staggered spin-triplet pairs emerges beyond a critical antiferromagnetic coupling interaction, while antiferromagnetism accompanies this state. The superconducting state with only spin-singlet pairs is dominant with paramagnetic phase. The A phase is analogous to the pseudogap phase, which shows that electrons go to form pairs but do not cause a supercurrent. We also show the superfluid behavior of the unconventional superconducting state and its critical temperature. It is proven directly that the flat band can effectively raise the critical temperature of superconductivity. It is implementable to simulate and control strongly-correlated electrons’ behavior on the Creutz lattice in the ultracold atoms experiment or other artificial structures. Our results may help the understanding of the interplay between unconventional superconductivity and magnetism.

Wigner-molecularization-enabled dynamic nuclear polarization

Multielectron semiconductor quantum dots (QDs) provide a novel platform to study the Coulomb interaction-driven, spatially localized electron states of Wigner molecules (WMs). Although Wigner-molecularization has been confirmed by real-space imaging and coherent spectroscopy, the open system dynamics of the strongly correlated states with the environment are not yet well understood. Here, we demonstrate efficient control of spin transfer between an artificial three-electron WM and the nuclear environment in a GaAs double QD. A Landau–Zener sweep-based polarization sequence and low-lying anticrossings of spin multiplet states enabled by Wigner-molecularization are utilized. Combined with coherent control of spin states, we achieve control of magnitude, polarity, and site dependence of the nuclear field. We demonstrate that the same level of control cannot be achieved in the non-interacting regime. Thus, we confirm the spin structure of a WM, paving the way for active control of correlated electron states for application in mesoscopic environment engineering.

Entanglement of stationary states in the presence of unstable quasiparticles

The effect of unstable quasiparticles in the out-of-equilibrium dynamics of certain integrable systems has been the subject of several recent studies. In this paper we focus on the stationary value of the entanglement entropy density, its growth rate, and related functions, after a quantum quench. We consider several quenches, each of which is characterised by a corresponding squeezed coherent state. In the quench action approach, the coherent state amplitudes K(θ) become input data that fully characterise the large-time stationary state, thus also the corresponding Yang-Yang entropy. We find that, as function of the mass of the unstable particle, the entropy growth rate has a global minimum signalling the depletion of entropy that accompanies a slowdown of stable quasiparticles at the threshold for the formation of an unstable excitation. We also observe a separation of scales governed by the interplay between the mass of the unstable particle and the quench parameter, separating a non-interacting regime described by free fermions from an interacting regime where the unstable particle is present. This separation of scales leads to a double-plateau structure of many functions, where the relative height of the plateaux is related to the ratio of central charges of the UV fixed points associated with the two regimes, in full agreement with conformal field theory predictions. The properties of several other functions of the entropy and its growth rate are also studied in detail, both for fixed quench parameter and varying unstable particle mass and viceversa.

Effect of specific surface area on the rheological properties of graphene nanoplatelet/poly(ethylene oxide) composites

The rheological properties of poly(ethylene oxide) containing graphene nanoplatelets (GNPs) having different specific surface areas (SSAs) are studied using steady shear and small amplitude oscillatory shear experiments. A series of GNPs having SSAs ranging from 175 ± 5 to 430 ± 13 m2/g was prepared using a thermomechanical exfoliation process. The complex viscosity, moduli, and yield stress of the composites increase with SSA, whereas electrical and rheological percolation threshold concentrations decrease, suggesting that higher SSAs promote filler network formation. Modeling of small amplitude oscillatory shear data using a two-phase model confirms that hydrodynamic effects dominate at low concentrations below 8 wt. %, where the particles are noninteracting. At higher concentrations, the response is dominated by filler-phase contributions. We demonstrate that the two-phase model parameters can be used to track the exfoliation of graphite into GNPs. Fitting of rheological percolation curves using Utracki and Lyngaae–Jørgensen models at low concentrations (noninteracting regime) resulted in aspect ratios between 19 and 76. At high concentrations (interacting particles), the aspect ratios determined by the Krieger–Daugherty model ranged between 5 and 24 due to aggregation. The highest aspect ratios (defined as the ratio of major dimension to minor dimension) were associated with GNPs that had the highest SSA of 430 m2/g. Strain sweeps revealed that the critical strain for the onset of nonlinear viscoelasticity scaled with SSA above the percolation threshold. The scaling relationships of the critical strain and storage modulus with volume fraction were used to infer the fractal dimensions of filler networks.

Effects of Efimov states on quench dynamics in a three-boson trapped system

We investigate the effects of Efimov states on the postquench dynamics of a system of three identical bosons with contact interactions in a spherically symmetric three-dimensional harmonic trap. The quench we consider is in the $s$-wave contact interaction, and we focus on quenches from the noninteracting to strongly interacting regimes and vice versa. The calculations use the hyperspherical solutions of the three-body problem and enable us to evaluate the semianalytical results of the Ramsey and particle separation, postquench. In the case where the interactions are quenched from the noninteracting to strongly interacting regime we find convergent aperiodic solutions for both the Ramsey signal and the particle separation. In contrast, for quenches from the strongly interacting regime to the noninteracting regime both the Ramsey signal and particle separation are periodic functions. However, in this case we find that the solutions for the particle separation diverge, indicating that in such a system large oscillations may be observable.

Number-conserving solution for dynamical quantum backreaction in a Bose-Einstein condensate

We provide a number-conserving approach to the backreaction problem of small quantum fluctuations onto a classical background for the exactly soluble dynamical evolution of a Bose-Einstein condensate, experimentally realizable in the ultracold gas laboratory. A force density exerted on the gas particles which is of quantum origin is uniquely identified as the deviation from the classical Eulerian force density. The backreaction equations are then explored for the specific example of a finite size uniform density condensate initially at rest. By assuming that the condensate starts from a non-interacting regime, and in its ground state, we fix a well-defined initial vacuum condition, which is driven out-of-equilibrium by instantaneously turning on the interactions. The assumption of this initial vacuum accounts for the ambiguity in choosing a vacuum state for interacting condensates, which is due to phase diffusion and the ensuing condensate collapse. As a major finding, we reveal that the time evolution of the condensate cloud leads to condensate density corrections that cannot in general be disentangled from the quantum depletion in measurements probing the power spectrum of the total density. Furthermore, while the condensate is initially at rest, quantum fluctuations give rise to a nontrivial condensate flux, from which we demonstrate that the quantum force density attenuates the classical Eulerian force. Finally, the knowledge of the particle density as a function of time for a condensate at rest determines, to order $N^0$, where $N$ is the total number of particles, the quantum force density, thus offering a viable route for obtaining experimentally accessible quantum backreaction effects.

Segregation forces in dense granular flows: closing the gap between single intruders and mixtures

Using simulations and a virtual-spring-based approach, we measure the segregation force, $F_{seg},$ in size-bidisperse sphere mixtures over a range of concentrations, particle-size ratios and shear rates to develop a semiempirical model for $F_{seg}$ that extends its applicability from the well-studied non-interacting intruders regime to finite-concentration mixtures where cooperative phenomena occur. The model predicts the concentration below which the single-intruder assumption applies and provides an accurate description of the pressure partitioning between species.

Atom-optically synthetic gauge fields for a noninteracting Bose gas

Synthetic gauge fields in synthetic dimensions are now of great interest. This concept provides a convenient manner for exploring topological phases of matter. Here, we report on the first experimental realization of an atom-optically synthetic gauge field based on the synthetic momentum-state lattice of a Bose gas of 133Cs atoms, where magnetically controlled Feshbach resonance is used to tune the interacting lattice into noninteracting regime. Specifically, we engineer a noninteracting one-dimensional lattice into a two-leg ladder with tunable synthetic gauge fields. We observe the flux-dependent populations of atoms and measure the gauge field-induced chiral currents in the two legs. We also show that an inhomogeneous gauge field could control the atomic transport in the ladder. Our results lay the groundwork for using a clean noninteracting synthetic momentum-state lattice to study the gauge field-induced topological physics.

Dynamic magnetic susceptibility of a ferrofluid: The influence of interparticle interactions and ac field amplitude.

Based on numerical results of dynamic susceptibility, a simple theory of the dynamic response of a ferrofluid to an ac magnetic field is obtained that includes both the effects of interparticle dipole-dipole interactions and the dependence on field amplitude. Interparticle interactions are incorporated in the theory using the so-called modified mean-field approach. The new theory has the following important characteristics: in the noninteracting regime at a weak ac field, it gives the correct single-particle Debye theory results; it expands the applicability of known theories valid for high concentrations [Ivanov, Zverev, and Kantorovich, Soft Matter 12, 3507 (2016)10.1039/C5SM02679B] or large values of ac field amplitudes [Yoshida and Enpuku, Jpn. J. Appl. Phys. 48, 127002 (2009)10.1143/JJAP.48.127002], in accordance with their applicability. The susceptibility spectra are analyzed in detail. It is demonstrated that interparticle dipole-dipole interactions and an increase in field amplitude have an opposite effect on the dynamic response of ferrofluids, so that at certain field amplitudes, relaxation processes in the system of interacting particles are determined by the characteristic relaxation times for an ideal paramagnetic gas. The new theory correctly predicts the dynamic susceptibility and characteristic relaxation times of a ferrofluid at high ac field amplitudes as long as the Langevin susceptibility χ_{L}≲1, which is a complex characteristic of ferrofluid density and the intensity of interparticle dipole-dipole interactions.

Jeans mass-radius relation of self-gravitating Bose-Einstein condensates and typical parameters of the dark matter particle

We study the Jeans mass-radius relation of Bose-Einstein condensate dark matter in Newtonian gravity. We show at a general level that it is similar to the mass-radius relation of Bose-Einstein condensate dark matter halos [P.H. Chavanis, Phys. Rev. D {\bf 84}, 043531 (2011)]. Bosons with a repulsive self-interaction generically evolve from the Thomas-Fermi regime to the noninteracting regime as the Universe expands. In the Thomas-Fermi regime, the Jeans radius remains approximately constant while the Jeans mass decreases. In the noninteracting regime, the Jeans radius increases while the Jeans mass decreases. Bosons with an attractive self-interaction generically evolve from the nongravitational regime to the noninteracting regime as the Universe expands. In the nongravitational regime, the Jeans radius and the Jeans mass increase. In the noninteracting regime, the Jeans radius increases while the Jeans mass decreases. The transition occurs at a maximum Jeans mass which is similar to the maximum mass of Bose-Einstein condensate dark matter halos with an attractive self-interaction. We use the mass-radius relation of dark matter halos and the observational evidence of a ``minimum halo'' (with typical radius $R\sim 1\, {\rm kpc}$ and typical mass $M\sim 10^8\, M_{\odot}$) to constrain the mass $m$ and the scattering length $a_s$ of the dark matter particle.

A first comparison of Kinetic Field Theory with Eulerian Standard Perturbation Theory

We present a detailed comparison of the newly developed particle-based Kinetic Field Theory framework for cosmic large-scale structure formation with the established formalism of Eulerian Standard Perturbation Theory. We highlight the qualitative differences of both approaches by a comparative analysis of the respective equations of motion and implementation of initial conditions. A natural starting point for a first quantitative comparison is given by the non-interacting regime of free-streaming kinematics. Our results suggest that Kinetic Field Theory contains a complete resummation of Standard Perturbation Theory in this regime. We further show that the exact free-streaming solution of Kinetic Field Theory cannot be recovered in any finite order of Standard Perturbation Theory. Kinetic Field Theory should therefore provide a better starting point for perturbative treatments of non-linear structure formation.

Many-Body Physics in Small Systems: Observing the Onset and Saturation of Correlation in Linear Atomic Chains.

The exact study of small systems can guide us toward relevant measures for extracting information about many-body physics as we move to larger and more complex systems capable of quantum information processing or quantum analog simulation. We use exact diagonalization to study many electrons in short 1-D atom chains represented by long-range extended Hubbard-like models. We introduce a novel measure, the Single-Particle Excitation Content (SPEC) of an eigenstate and show that the dependence of SPEC on eigenstate number reveals the nature of the ground state (ordered phases), and the onset and saturation of correlation between the electrons as Coulomb interaction strength increases. We use this SPEC behavior to identify five regimes as interaction is increased: a non-interacting single-particle regime, a regime of perturbative Coulomb interaction in which the SPEC is a nearly universal function of eigenstate number, the onset and saturation of correlation, a regime of fully correlated states in which hopping is a perturbation and SPEC is a different universal function of state number, and the regime of no hopping. In particular, the behavior of the SPEC shows that when electron-electron correlation plays a minor role, all of the lowest energy eigenstates are made up primarily of single-particle excitations of the ground state, and as the Coulomb interaction increases, the lowest energy eigenstates increasingly contain many-particle excitations. In addition, the SPEC highlights a fundamental, distinct difference between a non-interacting system and one with minute, very weak interactions. While SPEC is a quantity that can be calculated for small exactly diagonalizable systems, it guides our intuition for larger systems, suggesting the nature of excitations and their distribution in the spectrum. Thus, this function, like correlation functions or order parameters, provides us with a window of intuition about the behavior of a physical system.

Learning the best nanoscale heat engines through evolving network topology

The quest to identify the best heat engine has been at the center of science and technology. Considerable studies have so far revealed the potentials of nanoscale thermal machines to yield an enhanced thermodynamic efficiency in noninteracting regimes. However, the full benefit of many-body interactions is yet to be investigated; identifying the optimal interaction is a hard problem due to combinatorial explosion of the search space, which makes brute-force searches infeasible. We tackle this problem with developing a framework for reinforcement learning of network topology in interacting thermal systems. We find that the maximum possible values of the figure of merit and the power factor can be significantly enhanced by electron-electron interactions under nondegenerate single-electron levels with which, in the absence of interactions, the thermoelectric performance is quite low in general. This allows for an alternative strategy to design the best heat engines by optimizing interactions instead of single-electron levels. The versatility of the developed framework allows one to identify full potential of a broad range of nanoscale systems in terms of multiple objectives.

Entanglement and fermionization of two distinguishable fermions in a strict and non strict one-dimensional space

The fermionization regime and entanglement correlations of two distinguishable harmonically confined fermions interacting via a zero-range potential is addressed. We present two alternative representations of the ground state that we associate with two different types of one-dimensional spaces. These spaces, in turn, induce different correlations between particles and thus require a suitable definition of entanglement. We find that the entanglement of the ground state is strongly conditioned by those one-dimensional space features. We also find that in the strongly attractive regime the relative ground state is a highly localized state leading to maximum entanglement. Our analysis shows that in the strongly repulsive regime the ground state changes smoothly from a superposition of Slater-like states to a finite superposition of Slaters, this lack of accessible states yields to Pauli blocking as a strong signature of fermionization. Our results indicate that entangled states could be obtained in current experiments by reaching the non-interacting regime from the interacting regime. Entangled states could also be obtained when a state is brought from the interacting regime into the strongly repulsive regime by changing the scattering length near the confinement-induced resonance (CIR). Finally, we show that the first excited state obtained in the absence of interactions and the third excited fermionized state are maximally entangled.

Excitonic insulator phase and condensate dynamics in a topological one-dimensional model

We employ mean-field approximation to investigate the interplay between the nontrivial band topology and the formation of excitonic insulator (EI) in a one-dimensional chain of atomic $s-p$ orbitals in the presence of repulsive inter-orbital Coulomb interaction. We find that our model, in a non-interacting regime, admits topological and trivial insulator phases, whereas, in strong Coulomb interaction limit, the chiral symmetry is broken and the system undergoes a topological-excitonic insulator phase transition. The latter phase transition stems from an orbital pseudomagnetization and band inversion around $k=0$. Our findings show that contrary to the topological insulator phase, electron-hole bound states do not form exciton condensate in the trivial band insulator phase due to lack of band inversion. Interestingly, the EI phase in low $s-p$ hybridization limit hosts a Bardeen-Cooper-Schrieffer (BCS)/Bose-Einstein condensation (BEC) crossover. Irradiated by a pump pulse, our findings reveal that the oscillations of exciton states strongly depend on the frequency of the laser pulse. We further explore the signatures of dynamics of the exciton condensate in optical measurements.

Measurement-induced quantum criticality under continuous monitoring

We investigate entanglement phase transitions from volume-law to area-law entanglement in a quantum many-body state under continuous position measurement on the basis of the quantum trajectory approach. We find the signatures of the transitions as peak structures in the mutual information as a function of measurement strength, as previously reported for random unitary circuits with projective measurements. At the transition points, the entanglement entropy scales logarithmically and various physical quantities scale algebraically, implying emergent conformal criticality, for both integrable and nonintegrable one-dimensional interacting Hamiltonians; however, such transitions have been argued to be absent in noninteracting regimes in some previous studies. With the aid of $U(1)$ symmetry in our model, the measurement-induced criticality exhibits a spectral signature resembling a Tomonaga-Luttinger liquid theory from symmetry-resolved entanglement. These intriguing critical phenomena are unique to steady-state regimes of the conditional dynamics at the single-trajectory level, and are absent in the unconditional dynamics obeying the Lindblad master equation, in which the system ends up with the featureless, infinite-temperature mixed state. We also propose a possible experimental setup to test the predicted entanglement transition based on the subsystem particle-number fluctuations. This quantity should readily be measured by the current techniques of quantum gas microscopy and is in practice easier to obtain than the entanglement entropy itself.

Realization and Detection of Nonergodic Critical Phases in an Optical Raman Lattice.

The critical phases, being delocalized but nonergodic, are fundamental phases different from both the many-body localization and ergodic extended quantum phases, and have so far not been realized in experiment. Here we propose an incommensurate topological insulating model of AIII symmetry class to realize such critical phases through an optical Raman lattice scheme, which possesses a one-dimensional (1D) spin-orbit coupling and an incommensurate Zeeman potential. We show the existence of both noninteracting and many-body critical phases, which can coexist with the topological phase, and show that the critical-localization transition coincides with the topological phase boundary in noninteracting regime. The dynamical detection of the critical phases is proposed and studied in detail based on the available experimental techniques. Finally, we demonstrate how the proposed critical phases can be achieved within the current ultracold atom experiments. This work paves the way to observe the novel critical phases.

Two-body quench dynamics of harmonically trapped interacting particles

We consider the quantum evolution of a pair of interacting atoms in a three dimensional isotropic trap where the interaction strength is quenched from one value to another. Using exact solutions of the static problem we are able to evaluate time-dependent observables such as the overlap between initial and final states and the expectation value of the separation between the two atoms. In the case where the interaction is quenched from the non-interacting regime to the strongly interacting regime, or vice versa, we are able to obtain analytic results. Examining the overlap between the initial and final states we show that when the interaction is quenched from the non-interacting to strongly interacting regimes the early time dependence dynamics are consistent with theoretical work in the single impurity many-body limit. When the system is quenched from the strongly to non-interacting regime we predict large oscillations in the separation between the two atoms, which arises from a logarithmic divergence due to the zero-range nature of the interaction potential.

Stationary and dynamical properties of two harmonically trapped bosons in the crossover from two dimensions to one

We unravel the stationary properties and the interaction quench dynamics of two bosons, confined in a two-dimensional anisotropic harmonic trap. A transcendental equation is derived giving access to the energy spectrum and revealing the dependence of the energy gaps on the anisotropy parameter. The relation between the two and the one dimensional scattering lengths as well as the Tan contacts is established. The contact, capturing the two-body short range correlations, shows an increasing tendency for a larger anisotropy. Subsequently, the interaction quench dynamics from attractive to repulsive values and vice versa is investigated for various anisotropies. A closed analytical form of the expansion coefficients of the two-body wavefunction, during the time evolution is constructed. The response of the system is studied by means of the time-averaged fidelity, the spectra of the spatial extent of the cloud in each direction and the one-body density. It is found that as the anisotropy increases, the system becomes less perturbed independently of the interactions while for fixed anisotropy quenches towards the non-interacting regime perturb the system in the most efficient manner. Furthermore, we identify that in the tightly confined direction more frequencies are involved in the dynamics stemming from higher-lying excited states.

Interacting topological frequency converter

We show that an interacting two-spin model subjected to two circularly polarized drives enables a feasible realization of a correlated topological phase in synthetic dimensions. The topological observable is given by a quantized frequency conversion between the dynamical drives, which is why we coin it the interacting topological frequency converter (ITFC). The ITFC is characterized by the interplay of interaction and synthetic dimension. This gives rise to striking topological phenomena that have no counterpart in the noninteracting regime. By calculating the topological phase diagrams as a function of interaction strength, we predict an enhancement of frequency conversion as a direct manifestation of the correlated topological response of the ITFC.