Low-energy Collective Modes Research Articles

Spectroscopy of edge and bulk collective modes in fractional Chern insulators

The exploration of atomic fractional quantum Hall (FQH) states is now within reach in optical-lattice experiments. While ground-state signatures have been observed in a system realizing the Hofstadter-Bose-Hubbard model in a box [Léonard , ], how to access hallmark low-energy collective modes remains a central open question in this context. We introduce a spectroscopic scheme based on two interfering Laguerre-Gaussian beams, which transfer a controlled angular momentum and energy to the system. The edge and bulk responses to the probe are detected through local density measurements by tracking the transfer of atoms between the bulk and the edge of the FQH droplet. This detection scheme is shown to simultaneously reveal two specific signatures of FQH states: their chiral edge branch and their bulk magnetoroton mode. We numerically benchmark our method by considering few bosons in the ν=1/2 Laughlin ground state of the Hofstadter-Bose-Hubbard model, and demonstrate that these signatures are already detectable in realistic systems of two bosons, provided that the box potential is sufficiently large compared to the droplet. Our paper paves the way for the detection of fractional statistics in cold atoms through edge signatures. Published by the American Physical Society 2024

Effects of Quantum Fluctuations on the Low-Energy Collective Modes of Two-Dimensional Superfluid Fermi Gases from the BCS to the Bose Limit.

We investigate the effects of quantum fluctuations on the low-energy collective modes of two-dimensional (2D) s-wave Fermi superfluids from the BCS to the Bose limit. We compare our results to recent Bragg scattering experiments in 2D box potentials, with very good agreement. We show that quantum fluctuations in the phase and modulus of the pairing order parameter are absolutely necessary to give physically acceptable chemical potential and dispersion relation of the low-energy collective mode throughout the BCS to Bose evolution. Furthermore, we demonstrate that the dispersion of the collective modes change from concave to convex as interactions are tuned from the BCS to the Bose regime, and never crosses the two-particle continuum, because arbitrarily small attractive interactions produce bound states in two dimensions.

Collective density fluctuations of strange metals with critical Fermi surfaces

Recent spectroscopic measurements in a number of strongly correlated metals that exhibit non-Fermi liquid like properties have observed evidence of anomalous frequency and momentum-dependent charge-density fluctuations. Specifically, in the strange metallic regime of the cuprate superconductors, there is a featureless particle-hole continuum exhibiting unusual power-laws, and experiments suggest that the plasmon mode decays into this continuum in a manner that is distinct from the expectations of conventional Fermi liquid theory. Inspired by these new experimental developments, we address the nature of low-energy collective modes and the particle-hole continua for different "solvable" lattice models of non-Fermi liquids that host a critical Fermi surface -- a sharp electronic Fermi surface without any low-energy electronic quasiparticles. We scrutinize theoretically the possible existence of a long-lived zero-sound mode, which is renormalized to the plasma frequency in the presence of long-ranged coulomb interactions, and its decay into the continuum over a wide range of frequencies and momenta. Quite remarkably, some of the models analyzed here can account for certain aspects of the universal experimental observations, that clearly lie beyond the purview of standard Fermi liquid theory.

Strong increase in ultrasound attenuation below Tc in Sr2RuO4 : Possible evidence for domains

Recent experiments suggest that the superconducting order parameter of Sr$_2$RuO$_4$ has two components. A two-component order parameter has multiple degrees of freedom in the superconducting state that can result in low-energy collective modes or the formation of domain walls -- a possibility that would explain a number of experimental observations including the smallness of the time reversal symmetry breaking signal at T$_\mathrm{c}$ and telegraph noise in critical current experiments. We perform ultrasound attenuation measurements across the superconducting transition of Sr$_2$RuO$_4$ using resonant ultrasound spectroscopy (RUS). We find that the attenuation for compressional sound increases by a factor of seven immediately below T$_\mathrm{c}$, in sharp contrast with what is found in both conventional ($s$-wave) and high-T$_\mathrm{c}$ ($d$-wave) superconductors. We find our observations to be most consistent with the presence of domain walls between different configurations of the superconducting state. The fact that we observe an increase in sound attenuation for compressional strains, and not for shear strains, suggests an inhomogeneous superconducting state formed of two distinct, accidentally-degenerate superconducting order parameters that are not related to each other by symmetry. Whatever the mechanism, a factor of seven increase in sound attenuation is a singular characteristic with which any potential theory of the superconductivity in Sr$_2$RuO$_4$ must be reconciled.

Extremely low-energy collective modes in a quasi-one-dimensional topological system

We have investigated the quasiparticle dynamics and collective excitations in the quasi-one-dimensional material ZrTe5 using ultrafast optical pump-probe spectroscopy. Our time-domain results reveal two coherent oscillations having extremely low energies of ħω1 ∼0.33 meV (0.08 THz) and ħω2 ∼1.9 meV (0.45 THz), which are softened as the temperature approaches two different critical temperatures (∼54 K and ∼135 K). We attribute these two collective excitations to the amplitude mode of photoinduced dynamic charge density waves in ZrTe5 with tremendously small nesting wave vectors. Furthermore, a peculiar quasiparticle decay process associated with the ħω2 mode with a timescale of ∼1–2 ps is found below the transition temperature T* (∼135 K). Our findings provide pivotal information for studying the fluctuating order parameters and their associated quasiparticle dynamics in various low-dimensional topological systems and other materials.

Lattice collective modes from a continuum model of magic-angle twisted bilayer graphene

We show that the insulating states of magic-angle twisted bilayer graphene support a series of collective modes corresponding to local particle-hole excitations on triangular lattice sites. Our theory is based on a continuum model of the magic angle flat bands. When the system is insulating at moir\'e band filling $\nu=-3$, our calculations show that the ground state supports seven low-energy modes that lie well below the charge gap throughout the moir\'e Brillouin zone, one of which couples strongly to THz photons. The low-energy collective modes are faithfully described by a model with a local $SU(8)$ degree of freedom in each moir\'e unit cell that we identify as the direct product of spin, valley, and an orbital pseudospin. Apart from spin and valley-wave modes, the collective mode spectrum includes a low-energy intra-flavor exciton mode associated with transitions between flat valence and conduction band orbitals.

Dynamical structure factor of a fermionic supersolid on an optical lattice

Interfacing unbiased quantum Monte Carlo simulations with state-of-art analytic continuation techniques, we obtain exact numerical results for dynamical density and spin correlations in the attractive Hubbard model, describing a spin-balanced two-dimensional cold Fermi gas on an optical lattice. We focus on half-filling, where on average one fermion occupies each lattice site, and the system displays an intriguing supersolid phase: a superfluid with a checkerboard density modulation. The coexistence of $U(1)$ broken symmetry and the density modulations makes this regime very challenging and interesting for the calculation of dynamical properties. We compare our unbiased results with state-of-the-art Generalized Random Phase Approximation calculations: both approaches agree on a well-defined low-energy Nambu-Goldstone collective mode in the density correlations, while the higher energy structures appear to differ significantly. We also observe an interesting high-energy spin mode. We argue that our results provide a robust benchmark for Generalized Random Phase Approximation techniques, which are widely considered to be the method of choice for dynamical correlations in Fermi gases. Also, our calculations yield new physical insight in the high-energy behavior of the dynamical structure factor of the attractive Hubbard model, which is a well known prototype lattice model for superconductors and is a fertile field to target the observation of collective modes in strongly correlated systems.

Narrow-band and tunable intense terahertz pulses for mode-selective coherent phonon excitation

We generate frequency-tunable narrow-band intense fields in the terahertz (THz) range by optical rectification of a temporally modulated near-infrared laser pumping a nonlinear organic crystal. Carrier-frequency tunability between 0.5 and 6.5 THz is achieved by changing the modulation period of the laser pump. This tunable narrow-band THz source allows the selective coherent excitation of adjacent vibrational modes, which are demonstrated for two phonons with a frequency offset of 0.8 THz in single-crystal SrCu2(BO3)2. Our compact and scalable source enables an effective approach for the advanced manipulation of low-energy collective modes in condensed matter and has the potential to reveal the coupling of specific lattice vibrations with other degrees of freedom.

Collective Quantum Memory Activated by a Driven Central Spin.

Coupling a qubit coherently to an ensemble is the basis for collective quantum memories. A single driven electron in a quantum dot can deterministically excite low-energy collective modes of a nuclear spin ensemble in the presence of lattice strain. We propose to gate a quantum state transfer between this central electron and these low-energy excitations-spin waves-in the presence of a strong magnetic field, where the nuclear coherence time is long. We develop a microscopic theory capable of calculating the exact time evolution of the strained electron-nuclear system. With this, we evaluate the operation of quantum state storage and show that fidelities up to 90% can be reached with a modest nuclear polarization of only 50%. These findings demonstrate that strain-enabled nuclear spin waves are a highly suitable candidate for quantum memory.

Low-energy collective electronic excitations inLiC6,SrC6, andBaC6

We present a first-principles study of the electronic band structure and low-energy dielectric response properties of a representative group of graphite intercalated compounds---${\mathrm{LiC}}_{6},{\mathrm{SrC}}_{6}$, and ${\mathrm{BaC}}_{6}$. Our results obtained from time-dependent density functional theory calculations reveal the presence of different plasmons in these compounds at energies below 12 eV. The presence of these collective electronic excitations is discussed in terms of intra- and interband transitions. In addition to the bulk plasmon, we find the $\ensuremath{\pi}$- and intraband plasmons. However, their properties vary greatly from one material to another. In ${\mathrm{LiC}}_{6}$ and ${\mathrm{BaC}}_{6}$, the $\ensuremath{\pi}$ plasmon is a two-dimensional excitation, whereas in ${\mathrm{SrC}}_{6}$ it has a three-dimensional character. As for the intraband plasmon, it is observed in all momentum-transfer symmetry directions, with rather strong anisotropy in the energy position between momentum transfers in the basal carbon plane and perpendicular to it. Also, we discuss the appearance in ${\mathrm{SrC}}_{6}$ and ${\mathrm{BaC}}_{6}$ of a low-energy collective electronic mode with the characteristic soundlike dispersion in terms of the energy bands crossing the Fermi level with different group velocities. We find a correlation between the appearance of such low-energy electronic modes and the occupation of the graphite interlayer band.

Collective modes for helical edge states interacting with quantum light

We investigate the light-matter interaction between the edge state of a 2D topological insulator and quantum electromagnetic field. The interaction originates from the Zeeman term between the spin of the edge electrons and the magnetic field, and also through the Peierls substition. The continuous U(1) symmetry of the system in the absence of the vector potential reduces into discrete time reversal symmetry in the presence of the vector potential. Due to light-matter interaction, a superradiant ground state emerges with spontaneously broken time reversal symmetry, accompanied by a net photocurrent along the edge, generated by the vector potential of the quantum light. The spectral function of the photon field reveals polariton continuum excitations above a threshold energy, corresponding to a Higgs mode and another low energy collective mode due to the phase fluctuations of the ground state. This collective mode is a zero energy Goldstone mode that arises from the broken continuous U(1) symmetry in the absence of the vector potential, and acquires finite a gap in the presence of the vector potential. The optical conductivity of the edge electrons is calculated using the random phase approximation by taking the fluctuation of the order parameter into account. It contains the collective modes as a Drude peak with renormalized effective mass, which moves to finite frequencies as the symmetry of the system is lowered by the inclusion of the vector potential.

Collective mode in the SU(2) theory of cuprates

Recent advances in momentum-resolved electron energy-loss spectroscopy (MEELS) and resonant inelastic X-ray scattering (RIXS) now allow one to access the charge response function with unprecedented versatility and accuracy. This allows for the study of excitations which were inaccessible recently, such as low-energy and finite momentum collective modes. The SU(2) theory of the cuprates is based on a composite order parameter with SU(2) symmetry fluctuating between superconductivity and charge order. The phase where it fluctuates is a candidate for the pseudogap phase of the cuprates. This theory has a signature, enabling its strict experimental test, which is the fluctuation between these two orders, corresponding to a charge 2 spin 0 mode at the charge ordering wave-vector. Here we derive the influence of this SU(2) collective mode on the charge susceptibility in both strong and weak coupling limits, and discuss its relation to MEELS, RIXS and Raman experiments. We find two peaks in the charge susceptibility at finite energy, whose middle is the charge ordering wave-vector, and discuss their evolution in the phase diagram.

Hydrogen Bonding versus Entropy: Revealing the Underlying Thermodynamics of the Hybrid Organic–Inorganic Perovskite [CH3NH3]PbBr3

The enormous research efforts dedicated to hybrid organic–inorganic perovskites have led to a deep understanding of these materials; however, the role of entropy and its ramifications for the properties of the materials have been only sparsely explored. In this study, we quantify the phase transition mechanism in the hybrid organic–inorganic perovskite [CH3NH3]PbBr3 by studying low-energy collective phonon modes using a combination of inelastic neutron scattering and ab initio lattice dynamics. We demonstrate that a delicate interplay among hydrogen bonding interactions, lattice vibrational entropy, and configurational disorder determines the thermodynamics and results in the rich phase evolution of [CH3NH3]PbBr3 as a function of temperature. Our results have important implications for the manipulation of macroscopic properties and provide a blueprint for future studies that will focus on unravelling phase transition mechanisms in hybrid perovskites and related materials such as dense and porous coordinat...

Ramifications of topology and thermal fluctuations in quasi-2D condensates

We explore the topological transformation of quasi-2D Bose–Einstein condensates of dilute atomic gases, and changes in the collective modes as the confining potential is modified from rotationally symmetric multiply connected to multiply connected with broken rotational symmetry and ultimately to a simply connected geometry. In particular, we show that the condensate density, and the non-condensate density arising from the quantum fluctuations, follow the transition in the geometry of the confining potential. The non-condensate density arising from the thermal fluctuations, in contrast, remain multiply connected when the thermal energy exceeds the maximum value in the basin of the confining potential. Otherwise, both the condensate and non-condensate densities become simply connected. The topology of the non-condensate densities is determined by the thermal energy, the repulsive interaction energy between atoms, and the trapping potential energy. In particular, the origin of the difference lies in the structure of the low-energy collective modes, which we examine using the Hartree–Fock–Bogoliubov formalism. We then use the Hartree–Fock–Bogoliubov theory with the Popov approximation to investigate the density and the momentum distribution associated with the thermal fluctuations.

Terahertz Spectra Revealing the Collective Excitation Mode in Charge‐Density‐Wave Single Crystal LuFe 2 O 4

A low-energy collective excitation mode in charge-ordered multiferroic LuFe2O4 is reported via terahertz time-domain spectroscopy. Upon cooling from 300 to 40 K, the central resonance frequency showed a pronounced hardening from 0.85 to 1.15 THz. In analogy to the well-known low-energy optical properties of LuFe2O4, this emerging resonance was attributed to the charge–density–wave (CDW) collective excitations. By using the Drude–Lorentz model fitting, the CDW collective mode becomes increasingly damped with the increasing temperature. Furthermore, the kinks of the CDW collective mode at the magnetic transition temperature are analyzed, which indicate the coupling of spin order with electric polarization.

Recent experimental results in sub- and near-barrier heavy-ion fusion reactions

Recent advances obtained in the field of near and sub-barrier heavy-ion fusion reactions are reviewed. Emphasis is given to the results obtained in the last decade, and focus will be mainly on the experimental work performed concerning the influence of transfer channels on fusion cross sections and the hindrance phenomenon far below the barrier. Indeed, early data of sub-barrier fusion taught us that cross sections may strongly depend on the low-energy collective modes of the colliding nuclei, and, possibly, on couplings to transfer channels. The coupled-channels (CC) model has been quite successful in the interpretation of the experimental evidences. Fusion barrier distributions often yield the fingerprint of the relevant coupled channels. Recent results obtained by using radioactive beams are reported. At deep sub-barrier energies, the slope of the excitation function in a semi-logarithmic plot keeps increasing in many cases and standard CC calculations over-predict the cross sections. This was named a hindrance phenomenon, and its physical origin is still a matter of debate. Recent theoretical developments suggest that this effect, at least partially, may be a consequence of the Pauli exclusion principle. The hindrance may have far-reaching consequences in astrophysics where fusion of light systems determines stellar evolution during the carbon and oxygen burning stages, and yields important information for exotic reactions that take place in the inner crust of accreting neutron stars.

Dicke model for quantum Hall systems

In GaAs quantum Hall (QH) systems, electrons are coupled with nuclear spins through the hyperfine interaction, which is normally not strong enough to change the dynamics of electrons and nuclear spins. The dynamics of the QH systems, however, may drastically change when the nuclear spins interact with low-energy collective excitation modes of the electron spins. We theoretically investigate the nuclear-electron spin interaction in the QH systems as hybrid quantum systems driven by the hyperfine interaction. In particular, we study the interaction between the nuclear spins and the Nambu–Goldstone (NG) mode with the linear dispersion relation associated with the U(1) spin rotational symmetry breaking. We show that such an interaction is described as nuclear spins collectively coupled to the NG mode, and can be effectively described by the Dicke model. Based on the model we suggest that various collective spin phenomena realized in quantum optical systems can also emerge in the QH systems.

Transition and Damping of Collective Modes in a Trapped Fermi Gas between BCS and Unitary Limits near the Phase Transition.

We investigate the transition and damping of low-energy collective modes in a trapped unitary Fermi gas by solving the Boltzmann-Vlasov kinetic equation in a scaled form, which is combined with both the T-matrix fluctuation theory in normal phase and the mean-field theory in order phase. In order to connect the microscopic and kinetic descriptions of many-body Feshbach scattering, we adopt a phenomenological two-fluid physical approach, and derive the coupling constants in the order phase. By solving the Boltzmann-Vlasov steady-state equation in a variational form, we calculate two viscous relaxation rates with the collision probabilities of fermion’s scattering including fermions in the normal fluid and fermion pairs in the superfluid. Additionally, by considering the pairing and depairing of fermions, we get results of the frequency and damping of collective modes versus temperature and s-wave scattering length. Our theoretical results are in a remarkable agreement with the experimental data, particularly for the sharp transition between collisionless and hydrodynamic behaviour and strong damping between BCS and unitary limits near the phase transition. The sharp transition originates from the maximum of viscous relaxation rate caused by fermion-fermion pair collision at the phase transition point when the fermion depair, while the strong damping due to the fast varying of the frequency of collective modes from BCS limit to unitary limit.

High spatial resolution mapping of individual and collective localized surface plasmon resonance modes of silver nanoparticle aggregates: correlation to optical measurements.

Non-isolated nanoparticles show a plasmonic response that is governed by the localized surface plasmon resonance (LSPR) collective modes created by the nanoparticle aggregates. The individual and collective LSPR modes of silver nanoparticle aggregated by covalent binding by means of bifunctional molecular linkers are described in this study. Individual contributions to the collective modes are investigated at nanometer scale by means of energy-filtering transmission electron microscopy and compared to ultraviolet–visible spectroscopy. It is found that the aspect ratio and the shape of the clusters are the two main contributors to the low-energy collective modes.

Optical excitation of phase modes in strongly disordered superconductors

According to the Goldstone theorem the breaking of a continuous U(1) symmetry comes along with the existence of low-energy collective modes. In the context of superconductivity these excitations are related to the phase of the superconducting (SC) order parameter and for clean systems are optically inactive. Here we show that for strongly disordered superconductors phase modes acquire a dipole moment and appear as a subgap spectral feature in the optical conductivity. This finding is obtained with both a gauge-invariant random-phase approximation scheme based on a fermionic Bogoliubov-de Gennes state as well as with a prototypical bosonic model for disordered superconductors. In the strongly disordered regime, where the system displays an effective granularity of the SC properties, the optically active dipoles are linked to the isolated SC islands, offering a new perspective for realizing microwave optical devices.