A time-dependent density functional theory investigation of plasmon resonances of linear Au atomic chains

We report theoretical studies on the plasmon resonances in linear Au atomic chains by using ab initio time-dependent density functional theory. The dipole responses are investigated each as a function of chain length. They converge into a single resonance in the longitudinal mode but split into two transverse modes. As the chain length increases, the longitudinal plasmon mode is redshifted in energy while the transverse modes shift in the opposite direction (blueshifts). In addition, the energy gap between the two transverse modes reduces with chain length increasing. We find that there are unique characteristics, different from those of other metallic chains. These characteristics are crucial to atomic-scale engineering of single-molecule sensing, optical spectroscopy, and so on.     

Quantum state transfer and time-dependent disorder in quantum chains

One of the most basic tasks required for Quantum Information Technology is the ability to connect different components of a Quantum Computer by quantum wires that obey the superposition principle. Since superpositions can be very sensitive to noise this turns out to be already quite difficult. Recently, it was suggested to use chains of permanently coupled spin-1/2 particles (quantum chains) for this purpose. They have the advantage that no external control along the wire is required during the transport of information, which makes it possible to isolate the wire from sources of noise. We first give an introduction to basic quantum state transfer and review existing advanced schemes by other authors. We then show a new result that demonstrates the stability of the scheme [1] against disorder that is approximately constant during one application of the channel, but time-dependent with respect to multiple applications.     

End and central plasmon resonances in linear atomic chains

The existence and nature of end and central plasmon resonances in a linear atomic chain, the 1D analog to surface and bulk plasmons in 2D metals, has been predicted by ab initio time-dependent density functional theory. Length dependence of the absorption spectra shows the emergence and development of collectivity of these resonances. It converges to a single resonance in the longitudinal mode, and two transverse resonances, which are localized at the ends and center of the atom chains. These collective modes bridge the gaps, in concept and scale, between the collective excitation of atomic physics and nanoplasmonics. It also outlines a route to atomic-scale engineering of collective excitations.     

Classical impurities and boundary Majorana zero modes in quantum chains

We study the response of classical impurities in quantum Ising chains. The Z₂${\mathbb{Z}}_2$ degeneracy they entail renders the existence of two decoupled Majorana modes at zero energy, an exact property of a finite system at arbitrary values of its bulk parameters. We trace the evolution of these modes across the transition from the disordered phase to the ordered one and analyze the concomitant qualitative changes of local magnetic properties of an isolated impurity. In the disordered phase, the two ground states differ only close to the impurity, and they are related by the action of an explicitly constructed quasi-local operator. In this phase the local transverse spin susceptibility follows a Curie law. The critical response of a boundary impurity is logarithmically divergent and maps to the two-channel Kondo problem, while it saturates for critical bulk impurities, as well as in the ordered phase. The results for the Ising chain translate to the related problem of a resonant level coupled to a 1d p-wave superconductor or a Peierls chain, whereby the magnetic order is mapped to topological order. We find that the topological phase always exhibits a continuous impurity response to local fields as a result of the level repulsion of local levels from the boundary Majorana zero mode. In contrast, the disordered phase generically features a discontinuous magnetization or charging response. This difference constitutes a general thermodynamic fingerprint of topological order in phases with a bulk gap.     

Classical and quantum mechanical aspects of time-dependent Hartree-Fock trajectories

In terms of a quantum mechanical representation based on Slater determinants, classical and quantum mechanical aspects of TDHF trajectories are investigated. The invariant integration measure of the determinantal representation is obtained in a general closed form. Phase space structures of the TDHF equation and its solutions are discussed on this basis. The formal classical structures provide a way of finding a semiclassical expression for the quantum mechanical propagator, into which the superposition principle among TDHF trajectories is incorporated. General properties of the semiclassical propagator such as the time translation/reversal symmetry, unitarity, etc., are studied. Two simple hamiltonian systems are employed as examples which exhibit analytical solutions for the propagator. To illustrate the effects of superposition of TDHF paths, a system of interacting two-level nuclei is numerically studied and a comparison with the exact result is made.     

Detecting molecular vibrational modes of side chains and endpoints in nanoscale proteins with graphene plasmon

Monitoring the chemical and structural changes in protein side chains and endpoints by infrared(IR)spectroscopy is important for studying the chemical reaction and physical adsorption process of proteins.However, the detection of side chains and endpoints in nanoscale proteins is still challenging due to its weak IR response. Here, by designing a double layered graphene plasmon sensor on MgF_2/Si substrate in the IR fingerprint region, we detect the vibrational modes in side chains and endpoints(1397 cm~(-1) and 1458 cm~(-1)) of monolayer protein. The sensor could be applied on biochemistry to investigate the physical and chemical reaction of biomolecules.     

Dynamics of coupled vibration modes in a quantum non-linear mechanical resonator

We investigate the behaviour of two non-linearly coupled flexural modes of a doubly clamped suspended beam (nanomechanical resonator). One of the modes is externally driven. We demonstrate that classically, the behavior of the non-driven mode is reminiscent of that of a parametrically driven linear oscillator: it exhibits a threshold behavior, with the amplitude of this mode below the threshold being exactly zero. Quantum-mechanically, we were able to access the dynamics of this mode below the classical parametric threshold. We show that whereas the mean displacement of this mode is still zero, the mean squared displacement is finite and at the threshold corresponds to the occupation number of 1/2. This finite displacement of the non-driven mode can serve as an experimentally verifiable quantum signature of quantum motion.     

Loss of nonclassical properties of quantum states in linear phase-insensitive processes with arbitrary time-dependent parameters

Conditions of disappearance of different “nonclassical” properties (usual and high-order squeezing, sub-Poissonian statistics, negativity of s-parametrized quasidistributions) are derived for a quantum oscillator, whose evolution is governed by the standard master equation of quantum optics with arbitrary time-dependent coefficients.     

Excitation of radial collective modes in a quantum dot: Beyond linear response

The recent results on the linear breathing mode of the excitation spectrum of a quantum dot obtained by McDonald et. al [Phys. Rev. Lett. 111 , 256801 (2013)] are extended to the nonlinear regime. To accomplish this and analyze the results the response of five different models of two interacting electrons in a quantum dot to an external short lived radial excitation that is strong enough to excite the system well beyond the linear response regime is compared. The models considered describe the Coulomb interaction between the electrons in different ways ranging from mean‐field approaches to configuration interaction (CI) models, where the two‐electron Hamiltonian is diagonalized in a large truncated Fock space. The radially symmetric excitation is selected in order to severely put to test the different approaches to describe the interaction and correlations of an electron system in a nonequilibrium state. As can be expected for the case of only two electrons none of the mean‐field models can in full details reproduce the results obtained by the CI model. Nonetheless, some linear and nonlinear characteristics are reproduced reasonably well. All the models show activation of an increasing number of collective modes as the strength of the excitation is increased. By varying slightly the confinement potential of the dot it was observed how sensitive the properties of the excitation spectrum are to the Coulomb interaction and its correlation effects. In order to approach closer the question of nonlinearity one of the mean‐field models has been solved directly in a nonlinear fashion without resorting to iterations.     

Spin chains viewed as the fermionic parts of supersymmetric quantum mechanical models

This paper shows that (anisotropic) spin chains of XY type arise by matrix representation of the fermionic terms of hamiltonians of quantum systems whose supersymmetry involves in general no more than a single hermitian supercharge. It provides some background relevant to this type of supersymmetry and makes applications to such chains including those which admit quantum groups as invariance algebras.     

Unified quantum mechanical picture for confined spinons in dimerized and frustrated spin chains

A quantum mechanical picture is presented to describe the behavior of confined spinons in a variety of S =1/2 chains. The confinement is due to dimerization and frustration and it manifests itself as a nonlinear potential , centered at chain ends () or produced by modulation kinks (b > 1). The calculation extends to weak or zero frustration some previous ideas valid for spinons in strongly frustrated spin chains. The local magnetization patterns of the confined spinons are calculated. A (minimum) enhancement of the local moments of about 11/3 over a single S =1/2 is found. Estimates for excitation energies and binding lengths are obtained. Received: 8 May 1998 / Revised and Accepted: 12 August 1998     

Reprint of : Dynamics of coupled vibration modes in a quantum non-linear mechanical resonator

We investigate the behaviour of two non-linearly coupled flexural modes of a doubly clamped suspended beam (nanomechanical resonator). One of the modes is externally driven. We demonstrate that classically, the behavior of the non-driven mode is reminiscent of that of a parametrically driven linear oscillator: it exhibits a threshold behavior, with the amplitude of this mode below the threshold being exactly zero. Quantum-mechanically, we were able to access the dynamics of this mode below the classical parametric threshold. We show that whereas the mean displacement of this mode is still zero, the mean squared displacement is finite and at the threshold corresponds to the occupation number of 1/2. This finite displacement of the non-driven mode can serve as an experimentally verifiable quantum signature of quantum motion.     

Effect of cusps in time-dependent quantum mechanics

Within nonrelativistic quantum mechanics, spatial cusps in initial wave functions can lead to nonanalytic behavior in time. We suggest a method for calculating the short-time behavior in such situations. For these cases, the density does not match its Taylor expansion in time, but the Runge-Gross proof of time-dependent density functional theory still holds, as it requires only the potential to be time analytic.     

Emergence of chaos in quantum systems far from the classical limit

The dynamical status of isolated quantum systems is unclear as conventional measures fail to detect chaos in such systems. However, when quantum systems are subjected to observation--as all experimental systems must be--their dynamics is no longer linear and, in the appropriate limit(s), the evolution of expectation values, conditioned on the observations, closely approaches the behavior of classical trajectories. Here we show, by analyzing a specific example, that microscopic continuously observed quantum systems, even far from any classical limit, can have a positive Lyapunov exponent, and thus be truly chaotic.     

Multiple quantum dynamics in linear chains and rings of nuclear spins in solids at low temperatures

Multiple quantum spin dynamics is studied using analytical and numerical methods for one-dimensional finite systems of nuclear spins 12 coupled by dipole-dipole interactions at low temperatures. Exact expressions for intensities of multiple quantum coherences at low temperatures were obtained in the approximation of the nearest neighbor interactions. The time growth of multiple quantum coherences was analyzed numerically when all the dipole-dipole interactions in one-dimensional systems consisting of 6/8 spins were taken into account. It is shown that the growth of multiple quantum coherences gets faster when the temperature decreases, and the intensities of multiple quantum coherences can be negative at low temperatures.     

Emergence of a 4D world from causal quantum gravity

Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over geometries in nonperturbative quantum gravity, with a positive cosmological constant. We present evidence that a macroscopic four-dimensional world emerges from this theory dynamically.     

Emergence and collapse of quantum mechanical superposition: Orthogonality of reversible dynamics and irreversible diffusion

Based on the modelling of quantum systems with the aid of (classical) non-equilibrium thermodynamics, both the emergence and the collapse of the superposition principle are understood within one and the same framework. Both are shown to depend in crucial ways on whether or not an average orthogonality is maintained between reversible Schrödinger dynamics and irreversible processes of diffusion. Moreover, the said orthogonality is already in full operation when dealing with a single free Gaussian wave packet. In an application, the quantum mechanical “decay of the wave packet” is shown to simply result from sub-quantum diffusion with a specific diffusivity varying in time due to a particle’s changing thermal environment. The exact quantum mechanical trajectory distributions and the velocity field of the Gaussian wave packet, as well as Born’s rule, are thus all derived solely from classical physics.     

Characteristics of coupled plasmon modes in asymmetric layered system

We used an asymmetric layered system functioning as a plasmon waveguide coupler to couple surface plasmon modes with gap plasmon modes. The planar system was analyzed by the transfer matrix method to design the optical dimensions of the system. We simulated the effective mode indexes and H-field distribution of the coupled modes, for different gap widths and refractive indexes. For the calculated modes the propagation lengths were calculated. Furthermore, a sample structure was fabricated and odd gap plasmon modes were excited with a coupling prism in an attenuated-total-reflection (ATR) configuration. The mode index measurement showed good agreement with the simulation data.     

Polarons in linear chains of fullerenes

Polaron states in linear chains of fullerenes are studied with the use of the generalized model of Su-Shrieffer-Heeger (SSH) for the intermolecular and intramolecular degrees of freedom. Electron charge distributions over the molecular surface and Jahn-Teller distortions of carbon atoms in C₆₀ are calculated self-consistently for linear C₆₀ polymer and C ₆₀ ⁻ polyanion chains. A polaron band narrowing is examined. It is shown that the polymerization of C₆₀ molecules in phase transitions may be caused by the cooperative Jahn-Teller effect. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 8, 521–525 (25 October 1996) Published in English in the original Russian Journal. Edited by Steve Torstveit.