Strong Interaction Regime Research Articles

Micromagnetic Simulations of Vortex Resonances in Coupled Nanodisks

The high-frequency response of two magnetostatically coupled nanodisks supporting a vortex state within a stack has been investigated by means of 3-D dynamic micromagnetic simulations performed in the frequency domain. These spectra reveal one or two resonance lines according to the vortex polarizations and chiralities. These sub-gigahertz resonance modes are associated with vortex core modes. The magnetostatic coupling controlled by the interdisk distance affects both the structure of the vortex core modes and their associated resonance frequencies. In the regime of strong magnetostatic interaction, coupled vortex core modes are analyzed in terms of the relative phase relation between the vortex core motions. Lastly, the characteristics of the dynamic susceptibility spectra are also strongly dependent on the relative disk thicknesses. It results that these dynamic magnetic couplings play a major role in the high-frequency response of layered magnetic nanostructures and should be taken into account in the design of new spintronic or microwave devices based on vortex dynamics.

Structure and consequences of vortex-core states inp-wave superfluids

It is now well established that in two-dimensional chiral p-wave paired superfluids, the vortices carry zero-energy modes which obey non-abelian exchange statistics and can potentially be used for topological quantum computation. In such superfluids there may also exist other excitations below the bulk gap inside the cores of vortices. We study the properties of these subgap states, and argue that their presence affects the topological protection of the zero modes. In conventional superconductors where the chemical potential is of the order of the Fermi energy of a non-interacting Fermi gas, there is a large number of subgap states and the mini-gap towards the lowest of these states is a small fraction of the Fermi energy. It is therefore difficult to cool the system to below the mini-gap and at experimentally available temperatures, transitions between the subgap states, including the zero modes, will occur and can alter the quantum states of the zero-modes. We show that compound qubits involving the zero-modes and the parity of the occupation number of the subgap states on each vortex are still well defined. However, practical schemes taking into account all subgap states would nonetheless be difficult to achieve. We propose to avoid this difficulty by working in the regime of small chemical potential mu, near the transition to a strongly paired phase, where the number of subgap states is reduced. We develop the theory to describe this regime of strong pairing interactions and we show how the subgap states are ultimately absorbed into the bulk gap. Since the bulk gap vanishes as mu -> 0 there is an optimum value mu_c which maximises the combined gap. We propose cold atomic gases as candidate systems where the regime of strong interactions can be explored, and explicitly evaluate mu_c in a Feshbach resonant K-40 gas.

Atom-pair tunnelling-induced quantum phase transition and scaling behaviour of fidelity susceptibility in the extended boson Josephson-junction model

In this paper we theoretically investigate the nonlinear tunnelling of two weakly linked Bose–Einstein condensates in a double-well trap in a strong interaction regime with the two-body interaction extended to neighbouring lattice sites. As a consequence the boson Josephson-junction tunnelling depends on the atom–atom interaction and the total atom number as well. A crucial atom-pair tunnelling term, obtained directly from the extension, results in significant energy spectrum corrections and an abrupt change of the ground state viewed as quantum phase transition. An atom-number oscillation state with a tunable relative phase between two Bose–Einstein condensates predicted for the first time is seen to be a degenerate ground state in an interaction region. The quantum phase transitions between degenerate and non-degenerate ground states driven by the atom-pair tunnelling are analysed. We show the scaling behaviours and the critical exponents of fidelity susceptibility, which can classify the universality.

Ab Initio Study of the VUV-Induced Multistate Photodynamics of Formaldehyde

Although formaldehyde, H₂CO, has been extensively studied there are still several issues not-well understood, specially regarding its dynamics in the VUV energy range, mainly due to the amount of nonadiabatic effects governing its dynamics. Most of the theoretical work on this molecule has focused on vertical excitation energies of Rydberg and valence states. In contrast to photodissociation processes involving the lowest-lying electronic states below 4.0 eV, there is little known about the photodynamics of the high-lying electronic states of formaldehyde (7-10 eV). One question of particular interest is why the (π, π*) electronic state is invisible experimentally even though it corresponds to a strongly dipole-allowed transition. In this work we present a coupled multisurface 2D photodynamics study of formaldehyde along the CO stretching and the symmetric HCH bending motion, using a quantum time-dependent approach. Potential energy curves along all the vibrational normal modes of formaldehyde have been computed using equation-of-motion coupled cluster including single and double excitations with a quadruply augmented basis set. In the case of the CO stretching coordinate, state-averaged complete active space self-consistent field followed by multireference configuration interaction was used for large values of this coordinate. 2D (for the CO stretching coordinate and the HCH angle) and 3D (including the out-of-plane distortion) potential energy surfaces have been computed for several Rydberg and valence states. Several conical intersections (crossings between potential energy surfaces of the same multiplicity) have been characterized and analyzed and a 2D 5 × 5 diabatic model Hamiltonian has been constructed. Based on this Hamiltonian, electronic absorption spectra, adiabatic and diabatic electronic populations and vibrational densities have been obtained and analyzed. The experimental VUV absorption spectrum in the 7-10 eV energy range is well reproduced, including the vibrational structure and the high irregularity in the regime of strong interaction between the (π, π*) electronic state and neighboring Rydberg states.

Dynamics of Pair Correlations in the Attractive Lieb-Liniger Gas

We investigate the dynamics of a one-dimensional Bose gas after a quench from the Tonks-Girardeau regime to the regime of strong attractive interactions applying analytical techniques and numerical simulations. After the quench the system is found to be predominantly in an excited gaslike state, the so-called super-Tonks gas, however with a small coherent admixture of two-particle bound states. Despite its small amplitude, the latter leads to a pronounced oscillation of the local density correlation with a frequency corresponding to the binding energy of the pair. Contributions from bound states with larger particle numbers are found to be negligible.

Spectral Properties near the Mott Transition in the One-Dimensional Hubbard Model

The single-particle spectral properties near the Mott transition in the one-dimensional Hubbard model are investigated by using the dynamical density-matrix renormalization group method and the Bethe ansatz. The pseudogap, hole-pocket behavior, spectral-weight transfer, and upper Hubbard band are explained in terms of spinons, holons, antiholons, and doublons. The Mott transition is characterized by the emergence of a gapless mode whose dispersion relation extends up to the order of hopping t (spin exchange J) in the weak (strong) interaction regime caused by infinitesimal doping.

Propagation of perturbations in the three-dimensional boundary layer on a delta wing in the viscid-inviscid interaction regime

The propagation of perturbations in the three-dimensional boundary layer on a planar delta wing in a hypersonic gas stream is investigated in the strong viscid-inviscid interaction regime. A characteristic associated with the induced pressure is found and an integral relation determining the velocity of its propagation is obtained. The directional diagrams of the propagation velocity of the characteristic surface in the boundary layer are determined for a series of constitutive parameters. This makes it possible to calculate the perturbation propagation velocities in the boundary layer when the velocity profiles in the longitudinal and transverse directions are known.

Erratum: Metastable quantum phase transitions in a periodic one-dimensional Bose gas. II. Many-body theory [Phys. Rev. A81, 023625 (2010)

We show that quantum solitons in the Lieb-Liniger Hamiltonian are precisely the yrast states. We identify such solutions clearly with Lieb's type II excitations from weak to strong interactions, clarifying a long-standing question of the physical meaning of this excitation branch. We demonstrate that the metastable quantum phase transition previously found in mean field analysis of the weakly-interacting Lieb-Liniger Hamiltonian [Phys. Rev. A {\bf 79}, 063616 (2009)] extends into the medium- to strongly-interacting regime of a periodic one-dimensional Bose gas. Our methods are exact diagonalization, finite-size Bethe ansatz, and the boson-fermion mapping in the Tonks-Girardeau limit.

Repulsive bound-atom pairs in an optical lattice with two-body interaction of nearest neighbors

Repulsively interacting particles in a periodic potential can form bound composite objects with long lifetimes, as has been observed experimentally [Winkler et al., Nature (London) 441, 853 (2006)]. In this paper, a complete two-particle solution of one-dimensional periodical potential was derived in a strong interaction regime, where the on-site approximation of a two-body interaction in the Bose-Hubbard model (BHM) is extended to include the interaction of nearest neighbors, which results in atom-pair hopping. The energy spectrum of the bound pair is drastically reshaped due to the pair-hopping term, and complex eigenenergy corresponding to metastable states is also found that has not been discovered in the usual BHM. When the absolute value of a center-of-mass quasimomentum wave vector is greater than a critical value ($|K|>{K}_{c}$), two bound-pair solutions are found. Furthermore, the spatial and momentum distributions of the bound pair displays a crossover from dark to bright soliton-like solutions in the extended BHM. Our results reduce to that of the usual BHM in the weak interaction case.

Isomeric and hybrid isomeric-vibrational states of Wigner molecules

An accurate configuration-interaction method employing a numerical mean-field basis set is used to study the excitation spectrum of Wigner molecules, including isomeric excitations, in small parabolic quantum dots. We find that at intermediate electron densities $({r}_{s}\ensuremath{\sim}8{a}_{0}^{\ensuremath{\ast}}--20{a}_{0}^{\ensuremath{\ast}})$, in the regime of strong interaction and partial Wigner localization, there are inversions of the usual Born-Oppenheimer ordering of isomeric and vibrational excitations, yielding low-lying isomeric excitations. Quantum-mechanical hybridization of different isomers can occur near an avoided crossing of a vibrational and an isomeric excitation. These findings suggest the possibility of observing isomers and hybrid isomeric-vibrational states experimentally.

Existence of excitonic insulator phase in the extended Falicov-Kimball model: SO(2)-invariant slave-boson approach

We re-examine the three-dimensional spinless Falicov-Kimball model with dispersive $f$ electrons at half-filling, addressing the dispute about the formation of an excitonic condensate, which is closely related to the problem of electronic ferroelectricity. To this end, we work out a slave-boson functional integral representation of the suchlike extended Falicov-Kimball model that preserves the $SO(2)\otimes U(1)^{\otimes 2}$ invariance of the action. We find a spontaneous pairing of $c$ electrons with $f$ holes, building an excitonic insulator state at low temperatures, also for the case of initially non-degenerate orbitals. This is in contrast to recent predictions of scalar slave-boson mean-field theory but corroborates previous Hartree-Fock and RPA results. Our more precise treatment of correlation effects, however, leads to a substantial reduction of the critical temperature. The different behavior of the partial densities of states in the weak and strong inter-orbital Coulomb interaction regimes supports a BCS-BEC transition scenario.

Non local theory of excitations applied to the Hubbard model

We propose a nonlocal theory of single-particle excitations. It is based on an off-diagonal effective medium and the projection operator method for treating the retarded Green function. The theory determines the nonlocal effective medium matrix elements by requiring that they are consistent with those of the self-energy of the Green function. This arrows for a description of long-range intersite correlations with high resolution in momentum space. Numerical study for the half-filled Hubbard model on the simple cubic lattice demonstrates that the theory is applicable to the strong correlation regime as well as the intermediate regime of Coulomb interaction strength. Furthermore the results show that nonlocal excitations cause sub-bands in the strong Coulomb interaction regime due to strong antiferromagnetic correlations, decrease the quasi-particle peak on the Fermi level with increasing Coulomb interaction, and shift the critical Coulomb interaction UC2 for the divergence of effective mass towards higher energies at least by a factor of two as compared with that in the single-site approximation.

Full Self-Consistent Projection Operator Approach to Nonlocal Excitations in Solids

A self-consistent projection operator method for single-particle excitations is developed. It describes the nonlocal correlations on the basis of a projection technique to the retarded Green function and the off-diagonal effective medium. The theory takes into account long-range intersite correlations making use of an incremental cluster expansion in the medium. A generalized self-consistent coherent potential is derived. It yields the momentum-dependent excitation spectra with high resolution. Numerical studies for the Hubbard model on a simple cubic lattice at half filling show that the theory is applicable in a wide range of Coulomb interaction strength. In particular, it is found that the long-range antiferromagnetic correlations in the strong interaction regime cause shadow bands in the low-energy region and sub-peaks of the Mott-Hubbard bands.

Bose-Hubbard model on a star lattice

We analyze the Bose-Hubbard model of hardcore bosons with nearest-neighbor hopping and repulsive interactions on a star lattice using both quantum Monte Carlo simulation and dual vortex theory. We obtain the phase diagram of this model as a function of the chemical potential and the relative strength of hopping and interaction. In the strong-interaction regime, we find that the Mott phases of the model at 1/2 and 1/3 fillings, in contrast to their counterparts on square, triangular, and kagome lattices, are either translationally invariant resonant valence bond (RVB) phases with no density-wave order or have coexisting density-wave and RVB orders. We also find that upon increasing the relative strength of hopping and interaction, the translationally invariant Mott states undergo direct second-order superfluid-insulator quantum phase transitions. We compute the critical exponents for these transitions and argue using the dual vortex picture that the transitions, when approached through the tip of the Mott lobe, belong to the inverted XY universality class.

Effective mass approach for a Bose-Einstein condensate in an optical lattice

We study the stationary and propagating solutions for a Bose-Einstein condensate (BEC) in a periodic optical potential with an additional confining optical or magnetic potential. Using an effective mass approximation we express the condensate wave function in terms of slowly-varying envelopes modulating the Bloch modes of the optical lattice. In the limit of a weak nonlinearity, we derive a nonlinear Schrodinger equation for propagation of the envelope function which does not contain the rapid oscillation of the lattice. We then consider the ground state solutions in detail in the regime of weak, moderate and strong nonlinear interactions. We describe the form of solution which is appropriate in each regime, and place careful limits on the validity of each type of solution. Finally we extend the study to the propagating dynamics of a spinor atomic BEC in an optical lattice and some interesting phenomena are revealed.

Analytic Thermodynamics and Thermometry of Gaudin-Yang Fermi Gases

We study the thermodynamics of a one-dimensional attractive Fermi gas (the Gaudin-Yang model) with spin imbalance. The exact solution has been known from the thermodynamic Bethe ansatz for decades, but it involves an infinite number of coupled nonlinear integral equations whose physics is difficult to extract. Here the solution is analytically reduced to a simple, powerful set of four algebraic equations. The simplified equations become universal and exact in the experimental regime of strong interaction and relatively low temperature. Using the new formulation, we discuss the qualitative features of finite-temperature crossover and make quantitative predictions on the density profiles in traps. We propose a practical two-stage scheme to achieve accurate thermometry for a trapped spin-imbalanced Fermi gas.

Enhanced paraconductivity-like fluctuations in the radiofrequency spectra of ultracold Fermi atoms

Radiofrequency spectroscopy provides a microscopic probe of fermionic pairing in ultracold Fermi gases. Calculations now suggest that there is a one-to-one correspondence between the theory of these spectra and the theory of paraconductivity fluctuations in superconductors, that is, the effect of enhanced conductivity even before the system enters the superconducting state. In gases of ultracold Fermi atoms, the crossover from Bardeen–Cooper–Schrieffer superconductivity to Bose–Einstein condensation1,2,3 can be realized by continuously varying the attraction between fermions of different species4. In this context, radiofrequency spectroscopy5,6,7 provides a microscopic probe to infer the nature of fermionic pairing. In the regime of strong interaction, the pairing affects a wide temperature range, which includes the critical temperature Tc, in analogy to the pseudogap physics for high-temperature superconductors. Here, we establish a direct connection between the theory of radiofrequency spectra for ultracold fermions above Tc and the theory of paraconductivity fluctuations in superconductors. Our calculations compare favourably to available experimental radiofrequency spectra, and demonstrate that the role of fluctuations for ultracold fermions is considerably enhanced with respect to superconductors. In addition, we illustrate how to extract from the spectra an energy scale associated with pairing and relate it to a universal quantity recently introduced for Fermi gases8.

Effective Two-State Model and NOON States for Double-Well Bose-Einstein Condensates in Strong-Interaction Regime

The model of double-well Bose–Einstein condensates in the strong-interaction regime is shown to reduce adiabatically to an effective two-state model describing the Rabi oscillations between the two atomic Fock states |N, 0〉 and |0, N〉, and the NOON states of arbitrary ultracold atoms can therefore be generated periodically from the initial state of either one of the Fock states.

Short-distance expansion for the electromagnetic half-space Green's tensor: general results and an application to radiative lifetime computations

We obtain a short-distance expansion for the half-space, frequency domain electromagnetic Green's tensor. The small parameter of the theory is , where ω is the frequency, ϵ1 is the permittivity of the upper half-space, in which both the source and the point of observation are located, and which is assumed to be transparent, c is the speed of light in vacuum and is a characteristic length, defined as the distance from the point of observation to the reflected (with respect to the planar interface) position of the source. In the case when the lower half-space (the substrate) is characterized by a complex permittivity ϵ2, we compute the expansion to third order. For the case when the substrate is a transparent dielectric, we compute the imaginary part of the Green's tensor to seventh order. The analytical calculations are verified numerically. The practical utility of the obtained expansion is demonstrated by computing the radiative lifetime of two electromagnetically interacting molecules in the vicinity of a transparent dielectric substrate. The computation is performed in the strong interaction regime when the quasi-particle pole approximation is inapplicable. In this regime, the integral representation for the half-space Green's tensor is difficult to use while its electrostatic limiting expression is grossly inadequate. However, the analytical expansion derived in this paper can be used directly and efficiently. The results of this study are also relevant to nano-optics and near-field imaging, especially when tomographic image reconstruction is involved.

GW approach to Anderson model out of equilibrium: Coulomb blockade and false hysteresis in theI−Vcharacteristics

The Anderson model for a single impurity coupled to two leads is studied using the GW approximation in the strong electron-electron interaction regime as a function of the alignment of the impurity level relative to the chemical potentials in the leads. We employ a nonequilibrium Green's function technique to calculate the electron self-energy, the spin density, and the current as a function of bias across the junction. In addition we develop an expression for the change in the expectation value of the energy of the system that results when the impurity is coupled to the leads, including the role of Coulomb interactions through the electron self-energy in the region of the junction. The current-voltage characteristics calculated within the GW approximation exhibit Coulomb blockade. Depending on the gate voltage and applied bias, we find that there can be more than one steady-state solution for the system, which may give rise to a hysteresis in the $I\text{\ensuremath{-}}V$ characteristics. We show that the hysteresis is an artifact of the GW approximation and would not survive if quantum fluctuations beyond the GW approximation are included.