Weak Interaction Regime Research Articles

Atom-Photon Spin-Exchange Collisions Mediated by Rydberg Dressing

We show that a single photon propagating through a Rydberg-dressed atomic ensemble can exchange its spin state with a single atom. Such a spin-exchange collision exhibits both dissipative and coherent features, depending on the interaction strength. For strong interaction, the collision dissipatively drives the system into an entangled dark state of the photon with an atom. In the weak interaction regime, the scattering coherently flips the spin of a single photon in the multiphoton input pulse, demonstrating a generic single-photon subtracting process. An analytical treatment of this process reveals a universal trade-off between efficiency and purity of the extracted photon, which applies to a wide class of single-photon subtractors. We show that such a trade-off can be optimized by adjusting the scattering rate under a novel phase-matching condition.

Mean field theory of weakly-interacting Rydberg polaritons in the EIT system based on the nearest-neighbor distribution.

The combination of high optical nonlinearity in the electromagnetically induced transparency (EIT) effect and strong electric dipole-dipole interaction (DDI) among the Rydberg-state atoms can lead to important applications in quantum information processing and many-body physics. One can utilize the Rydberg-EIT system in the strongly-interacting regime to mediate photon-photon interaction or qubit-qubit operation. One can also employ the Rydberg-EIT system in the weakly-interacting regime to study the Bose-Einstein condensation of Rydberg polaritons. Most of the present theoretical models dealt with the strongly-interacting cases. Here, we consider the weakly-interacting regime and develop a mean field model based on the nearest-neighbor distribution. Using the mean field model, we further derive the analytical formulas for the attenuation coefficient and phase shift of the output probe field. The predictions from the formulas are consistent with the experimental data in the weakly-interacting regime, verifying the validity of our model. As the DDI-induced phase shift and attenuation can be seen as the consequences of elastic and inelastic collisions among particles, this work provides a very useful tool for conceiving ideas relevant to the EIT system of weakly-interacting Rydberg polaritons and for evaluating experimental feasibility.

Berry phase for a Bose gas on a one-dimensional ring

We study a system of strongly interacting one-dimensional (1D) bosons on a ring pierced by a synthetic magnetic flux tube. By the Fermi-Bose mapping, this system is related to the system of spin-polarized non-interacting electrons confined on a ring and pierced by a solenoid (magnetic flux tube). On the ring there is an external localized delta-function potential barrier $V(\phi)=g \delta(\phi-\phi_0)$. We study the Berry phase associated to the adiabatic motion of delta-function barrier around the ring as a function of the strength of the potential $g$ and the number of particles $N$. The behavior of the Berry phase can be explained via quantum mechanical reflection and tunneling through the moving barrier which pushes the particles around the ring. The barrier produces a cusp in the density to which one can associate a missing charge $\Delta q$ (missing density) for the case of electrons (bosons, respectively). We show that the Berry phase (i.e., the Aharonov-Bohm phase) cannot be identified with the quantity $\Delta q/\hbar \oint \mathbf{A}\cdot d\mathbf{l}$. This means that the missing charge cannot be identified as a (quasi)hole. We point out to the connection of this result and recent studies of synthetic anyons in noninteracting systems. In addition, for bosons we study the weakly-interacting regime, which is related to the strongly interacting electrons via Fermi-Bose duality in 1D systems.

Bose-Einstein condensate immersed in a Fermi sea: Theory of static and dynamic behavior across phase separation

We theoretically study the static and dynamic behavior of a BEC immersed in a large Fermi sea of ultracold atoms under conditions of tunable interspecies interaction. The degenerate Bose-Fermi mixture is kept in an elongated trap, typical for a single-beam optical dipole trap. We focus on the case of repulsive Bose-Fermi interaction and develop mean-field models to simulate the system over a wide range of repulsion strength. We further get analytical solutions in the regimes of phase separation and weak interaction. We obtain static density profiles and the frequency of the radial breathing mode, which is an elementary dynamic phenomenon of the mixture. Our results unveil the structure of the Bose-Fermi interface and describe the origin of the frequency shift of the breathing mode when the components become phase-separated at strong repulsion. We show that the mediated interaction between bosons induced by the Fermi sea can be understood as an adiabatic second-order mean-field effect, which is valid also beyond the weak-interaction regime for relevant experimental conditions. These results are consistent with our recent observations in a mixture of $^{41}$K and $^6$Li.

Topological phase diagrams of the frustrated Ising ferromagnet

The emergence of complex modulated structures in the magnetization pattern of thin films is a well-established experimental phenomenology caused by the frustrating effects of competing interactions. Using a coarse-grained version of the Ising ferromagnet with dipolar interactions, we develop a method that uses the information from the microscopic Hamiltonian to predict the specific topological phases present in the temperature-external magnetic field phase diagram. This is done by the combination of mean-field variational calculations and the renormalization group equations from the classical theory of two-dimensional melting. In this framework, we are able to distinguish when the orientational and translational symmetries are broken, discriminating between the ordered and disordered states of the system for all temperatures and fields. We observe that the reentrance developed by the $H$-$T$ phase diagrams in the regime of weak dipolar interactions is directly related with the appearance of anomalous topological transitions. These results motivate the realization of new experiments on magnetic thin films in order to explore the topological properties of the magnetic textures, allowing to identify new exotic phases in these materials.

Molecular Approach for Engineering Interfacial Interactions in Magnetic/Topological Insulator Heterostructures

Controlling interfacial interactions in magnetic/topological insulator heterostructures is a major challenge for the emergence of novel spin-dependent electronic phenomena. As for any rational design of heterostructures that rely on proximity effects, one should ideally retain the overall properties of each component while tuning interactions at the interface. However, in most inorganic interfaces, interactions are too strong, consequently perturbing, and even quenching, both the magnetic moment and the topological surface states at each side of the interface. Here, we show that these properties can be preserved using ligand chemistry to tune the interaction of magnetic ions with the surface states. By depositing Co-based porphyrin and phthalocyanine monolayers on the surface of Bi2Te3 thin films, robust interfaces are formed that preserve undoped topological surface states as well as the pristine magnetic moment of the divalent Co ions. The selected ligands allow us to tune the interfacial hybridization within this weak interaction regime. These results, which are in stark contrast with the observed suppression of the surface state at the first quintuple layer of Bi2Se3 induced by the interaction with Co phthalocyanines, demonstrate the capability of planar metal-organic molecules to span interactions from the strong to the weak limit.

Coadsorption of Counterionic Colloids at Fluid Interfaces: A Coarse-Grained Simulation Study of Gibbs Monolayers.

Monolayers of oppositely charged colloids form versatile self-organizing substrates, with a recognized potential to tailor functional interfaces. In this study, a coarse-grained Monte Carlo simulation approach is laid out to assess the structural properties of Gibbs monolayers, in which one of the counterionic species is partially soluble. It is shown that the composition of this type of monolayer varies in a nontrivial way with surface coverage, as a result of a subtle competition between steric and attractive forces. In the regime of weak electrostatic interactions, the monolayer is depleted of soluble colloids as the surface coverage is increased. At sufficiently strong interactions, the incorporation of soluble colloids is favored at high surface coverage, leading to a re-entrant-type behavior in the expansion/compression isotherms. Strong electrostatic interactions also favor the clustering of the colloids, leading to a range of aggregated configurations, qualitatively resembling those obtained in previous experimental studies. At sufficiently high surface coverage, the clusters collapse into a gel-like percolated mesoscopic structure and eventually into a square crystal lattice configuration. Such interfacial structures are in good agreement with the ones observed in the few experimental investigations available for these systems, showing that the simple methodology introduced in this study provides a valuable predictive framework to anticipate the landscape of interfacial structures that may be produced with oppositely charged colloids, through the modulation of pair interactions and thermodynamical conditions.

Imaginary replica analysis of loopy regular random graphs

We present an analytical approach for describing spectrally constrained maximum entropy ensembles of finitely connected regular loopy graphs, valid in the regime of weak loop-loop interactions. We derive an expression for the leading two orders of the expected eigenvalue spectrum, through the use of infinitely many replica indices taking imaginary values. We apply the method to models in which the spectral constraint reduces to a soft constraint on the number of triangles, which exhibit ‘shattering’ transitions to phases with extensively many disconnected cliques, to models with controlled numbers of triangles and squares, and to models where the spectral constraint reduces to a count of the number of adjacency matrix eigenvalues in a given interval. Our predictions are supported by MCMC simulations based on edge swaps with nontrivial acceptance probabilities.

Generation of single entangled photon-phonon pairs via an atom-photon-phonon interaction

Quantum blockade and entanglement play important roles in quantum information and quantum communication as quantum blockade is an effective mechanism to generate single photons (phonons) and entanglement is a crucial resource for quantum information processing. In this work, we propose a method to generate single entangled photon-phonon pairs in a hybrid optomechanical system. We show that photon blockade, phonon blockade, and photon-phonon correlation and entanglement can be observed via the atom-photon-phonon (tripartite) interaction, under the resonant atomic driving. The correlated and entangled single photons and single phonons, i.e., single entangled photon-phonon pairs, can be generated in both the weak and strong tripartite interaction regimes. Our results may have important applications in the development of highly complex quantum networks.

Efficiently solving the dynamics of many-body localized systems at strong disorder

We introduce a method to efficiently study the dynamical properties of many-body localized systems in the regime of strong disorder and weak interactions. Our method reproduces qualitatively and quantitatively the real-time evolution with a polynomial effort in system size and independent of the desired time scales. We use our method to study quantum information propagation, correlation functions, and temporal fluctuations in one- and two-dimensional MBL systems. Moreover, we outline strategies for a further systematic improvement of the accuracy and we point out relations of our method to recent attempts to simulate the real-time dynamics of quantum many-body systems in classical or artificial neural networks.

Quantitative analysis of p -wave three-body losses via a cascade process

We describe the three-body loss coefficient of identical fermions with $p$-wave interactions using a set of rate equations in which three-body recombination happens via an indirect process. Our theoretical treatment explains experimental results just above the universal scaling law regime of weak interactions. Furthermore, we theoretically extend and experimentally verify the rate equation model for the case of atoms trapped in two dimensions. Moreover, we find that the three-body loss coefficient in a two-dimensional trap is proportional to $A_{p}^{3}$ in the weakly interacting regime, where $A_{p}$ is the scattering area. Our results are useful in understanding three-body physics with $p$-wave interactions.

Chiral topological superconductivity arising from the interplay of geometric phase and electron correlation

In modern theory of solids, many-electron correlations can give rise to superconductivity, while the Berry or geometric phase is responsible for non-trivial topology. So far, these two physical ingredients have been taken into account only in a simple additive manner. Here, we carry out a systematic study of the interplay between geometric phase and electron correlation as well as their combined effects on topological and superconducting properties. Based on first-principles studies of Pb3Bi/Ge(111) as a prototypical system, we develop a generic two-dimensional effective formalism that respects hexagonal symmetry with Rashba spin–orbit coupling, displays a van Hove singularity and includes geometric phase-decorated electron correlations. Our functional renormalization group analysis shows that superconductivity dominates the competing orders in the weak interaction regime, with two consequences. First, the renormalized geometric phase flows to three stable fixed points, favouring chiral (px ± ipy)-wave and f-wave superconducting states. Second, the corresponding superconductivity can be substantially enhanced. We construct the phase diagram of the topological quantum states, and identify hole-doped Pb3Bi/Ge(111) as an appealing platform for realizing chiral topological superconductivity in two-dimensional systems that are highly desirable for detecting and braiding Majorana fermions. Renormalization group calculations incorporate band structure and interaction effects on an equal footing. Applying this methodology to Ge-doped Pb3Bi shows that this material is a chiral topological superconductor and hosts Majorana fermions.

Nonlocal statistical field theory of dipolar particles forming chain-like clusters

We present a nonlocal statistical field theory of a diluted solution of dipolar particles which are capable of forming chain-like clusters in accordance with the ’head-to-tail’ mechanism. As in our previous study [Yu.A. Budkov 2018 J. Phys.: Condens. Matter 30 344001], we model dipolar particles as dimers comprised of oppositely charged point-like groups, separated by fluctuating distance. For the special case of the Yukawa-type distribution function of distance between the charged groups of dipolar particles we obtain an analytical expression for the electrostatic free energy of solution within the random phase approximation. We show that an increase in the association constant leads to a decrease in the absolute value of the electrostatic free energy of solution, preventing its phase separation which is in agreement with the former computer simulations and theoretical results. We obtain a non-linear integro-differential equation for the self-consistent field potential created by the fixed external charges in a solution medium, taking into account the association of dipolar particles. As a consequence of the derived self-consistent field equation, in regime of weak electrostatic interactions, we obtain an analytical expression for the electrostatic potential of the point-like test ion, surrounded by the chain-like clusters of the dipolar particles. We show that in the mean-field approximation the association does not change the bulk dielectric permittivity of the solution, but increases the solvation radius of the point-like charge, relative to the theory of non-associating dipolar particles.

Disturbance Propagation in Boundary Layers under the Conditions of Weak Hypersonic Interaction

Disturbance propagation in laminar boundary layers is investigated at large freestream velocities. An integral relation determining the disturbance propagation velocity in the weak hypersonic interaction regime is obtained for the first time.

Microscopic Linear Response Theory of Spin Relaxation and Relativistic Transport Phenomena in Graphene

We present a unified theoretical framework for the study of spin dynamics and relativistic transport phenomena in disordered two-dimensional Dirac systems with pseudospin-spin coupling. The formalism is applied to the paradigmatic case of graphene with uniform Bychkov-Rashba interaction and shown to capture spin relaxation processes and associated charge-to-spin interconversion phenomena in response to generic external perturbations, including spin density fluctuations and electric fields. A controlled diagrammatic evaluation of the generalized spin susceptibility in the diffusive regime of weak spin-orbit interaction allows us to show that the spin and momentum lifetimes satisfy the standard Dyakonov-Perel relation for both weak (Gaussian) and resonant (unitary) nonmagnetic disorder. Finally, we demonstrate that the spin relaxation rate can be derived in the zero-frequency limit by exploiting the SU(2) covariant conservation laws for the spin observables. Our results set the stage for a fully quantum-mechanical description of spin relaxation in both pristine graphene samples with weak spin-orbit fields and in graphene heterostructures with enhanced spin-orbital effects currently attracting much attention.

Self-energy functional theory with symmetry breaking for disordered lattice bosons

We extend the self-energy functional theory to the case of interacting lattice bosons in the presence of symmetry breaking and quenched disorder. The self-energy functional we derive depends only on the self-energies of the disorder-averaged propagators, allowing for the construction of general non-perturbative approximations. Using a simple single-site reference system with only three variational parameters, we are able to reproduce numerically exact quantum Monte Carlo (QMC) results on local observables of the Bose–Hubbard model with box disorder with high accuracy. At strong interactions, the phase boundaries are reproduced qualitatively but shifted with respect to the ones observed with QMC due to the extremely low condensate fraction in the superfluid phase. Deep in the strongly-disordered weakly-interacting regime, the simple reference system employed is insufficient and no stationary solutions can be found within its restricted variational subspace. By systematically analyzing thermodynamical observables and the spectral function, we find that the strongly interacting Bose glass is characterized by different regimes, depending on which local occupations are activated as a function of the disorder strength. We find that the particles delocalize into isolated superfluid lakes over a strongly localized background around maximally-occupied sites whenever these sites are particularly rare. Our results indicate that the transition from the Bose glass to the superfluid phase around unit filling at strong interactions is driven by the percolation of superfluid lakes which form around doubly occupied sites.

Investigating the Effects of the Interaction Intensity in a Weak Measurement

Measurements are crucial in quantum mechanics, for fundamental research as well as for applicative fields like quantum metrology, quantum-enhanced measurements and other quantum technologies. In the recent years, weak-interaction-based protocols like Weak Measurements and Protective Measurements have been experimentally realized, showing peculiar features leading to surprising advantages in several different applications. In this work we analyze the validity range for such measurement protocols, that is, how the interaction strength affects the weak value extraction, by measuring different polarization weak values on heralded single photons. We show that, even in the weak interaction regime, the coupling intensity limits the range of weak values achievable, setting a threshold on the signal amplification effect exploited in many weak measurement based experiments.

Nonequilibrium steady states and resonant tunneling in time-periodically driven systems with interactions

Time-periodically driven systems are a versatile toolbox for realizing interesting effective Hamiltonians. Heating, caused by excitations to high-energy states, is a challenge for experiments. While most setups address the relatively weakly-interacting regime so far, it is of general interest to study heating in strongly correlated systems. Using Floquet dynamical mean-field theory, we study non-equilibrium steady states (NESS) in the Falicov-Kimball model, with time-periodically driven kinetic energy or interaction. We systematically investigate the nonequilibrium properties of the NESS. For a driven kinetic energy, we show that resonant tunneling, where the interaction is an integer multiple of the driving frequency, plays an important role in the heating. In the strongly correlated regime, we show that this can be well understood using Fermi\textquoteright s golden rule and the Schrieffer-Wolff transformation for a time-periodically driven system. We furthermore demonstrate that resonant tunneling can be used to control the population of Floquet states to achieve "photo-doping". For driven interactions introduced by an oscillating magnetic field near a Feshbach resonance widely adopted, we find that the double occupancy is strongly modulated. Our calculations apply to shaken ultracold atom systems, and to solid state systems in a spatially uniform but time-dependent electric field. They are also closely related to lattice modulation spectroscopy. Our calculations are helpful to understand the latest experiments on strongly correlated Floquet systems.

Dynamical recovery of SU(2) symmetry in the mass-quenched Hubbard model

We use non-equilibrium dynamical mean-field theory with iterative perturbation theory as an impurity solver to study the recovery of $SU(2)$ symmetry in real-time following a hopping integral parameter quench from a mass-imbalanced to a mass-balanced single-band Hubbard model at half-filling. A dynamical order parameter $\gamma(t)$ is defined to characterize the evolution of the system towards $SU(2)$ symmetry. By comparing the momentum dependent occupation from an equilibrium calculation (with the $SU(2)$ symmetric Hamiltonian after the quench at an effective temperature) with the data from our non-equilibrium calculation, we conclude that the $SU(2)$ symmetry recovered state is a thermalized state. Further evidence from the evolution of the density of states supports this conclusion. At the same time, we find the order parameter in the weak Coulomb interaction regime undergoes an approximate exponential decay. We numerically investigate the interplay of the relevant parameters (initial temperature, Coulomb interaction strength, initial mass-imbalance ratio) and their combined effect on the thermalization behavior. Finally, we study evolution of the order parameter as the hopping parameter is changed with either a linear ramp or a pulse. Our results can be useful in strategies to engineer the relaxation behavior of interacting, quantum many-particle systems.

Synergistic interactions promote behavior spreading and alter phase transitions on multiplex networks.

Synergistic interactions are ubiquitous in the real world. Recent studies have revealed that, for a single-layer network, synergy can enhance spreading and even induce an explosive contagion. There is at the present a growing interest in behavior spreading dynamics on multiplex networks. What is the role of synergistic interactions in behavior spreading in such networked systems? To address this question, we articulate a synergistic behavior spreading model on a double layer network, where the key manifestation of the synergistic interactions is that the adoption of one behavior by a node in one layer enhances its probability of adopting the behavior in the other layer. A general result is that synergistic interactions can greatly enhance the spreading of the behaviors in both layers. A remarkable phenomenon is that the interactions can alter the nature of the phase transition associated with behavior adoption or spreading dynamics. In particular, depending on the transmission rate of one behavior in a network layer, synergistic interactions can lead to a discontinuous (first-order) or a continuous (second-order) transition in the adoption scope of the other behavior with respect to its transmission rate. A surprising two-stage spreading process can arise: due to synergy, nodes having adopted one behavior in one layer adopt the other behavior in the other layer and then prompt the remaining nodes in this layer to quickly adopt the behavior. Analytically, we develop an edge-based compartmental theory and perform a bifurcation analysis to fully understand, in the weak synergistic interaction regime where the dynamical correlation between the network layers is negligible, the role of the interactions in promoting the social behavioral spreading dynamics in the whole system.