Quantum simulation of lattice gauge theories on superconducting circuits: Quantum phase transition and quench dynamics

Recently,quantum simulation of low-dimensional lattice gauge theories(LGTs)has attracted many interests,which may improve our understanding of strongly correlated quantum many-body systems.Here,we propose an implementation to approximate Z;LGT on superconducting quantum circuits,where the effective theory is a mixture of a LGT and a gauge-broken term.By using matrix product state based methods,both the ground state properties and quench dynamics are systematically investigated.With an increase of the transverse(electric)field,the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase.In the ordered phase,an approximate Gauss law of the Z;LGT emerges in the ground state.Moreover,to shed light on the experiments,we also study the quench dynamics,where there is a dynamical signature of the spontaneous translational symmetry breaking.The spreading of the single particle of matter degree is diffusive under the weak transverse field,while it is ballistic with small velocity for the strong field.Furthermore,due to the emergent Gauss law under the strong transverse field,the matter degree can also exhibit confinement dynamics which leads to a strong suppression of the nearest-neighbor hopping.Our results pave the way for simulating the LGT on superconducting circuits,including the quantum phase transition and quench dynamics.     

Quantum efficiency and the photonic control of molecular fluorescence in the solid state

We investigate the role of quantum efficiency in determining the extent to which the local photonic environment may alter the spontaneous emission rate of organic dye molecules with broad luminescence spectra. Comparison of theory with experimental results shows that the quantum efficiency is a key determining factor in such control, low quantum efficiencies leading to poor control. These results help establish a firm basis for characterising near-fields in nano-optics and controlling fluorescing species. Received: 31 May 2002 / Revised version: 27 June 2002 / Published online: 25 October 2002 RID="*" ID="*"Corresponding author. Fax: +44-1392/264-111, E-mail: S. Astilean@exeter.ac.uk     

Aspects on Applications of IR Reflectivity- and Raman Scattering-Experiments on Polaritons in Solid State Chemistry and Biophysics

The coupled phonon-photon state called “polariton” is an elementary excitation which exists at all temperatures in single crystalline materials with well defined translational symmetries. In the view of this aspect polaritons turn out to be more important for the dynamics of crystal lattices in general than e.g. magnons or plasmons which normally can be excited only in certain low temperature ranges. The present article summarizes experimental results which all might be applied as analytical methods. An improved method for the determination of fundamental mode frequencies is described. Polariton interactions with localized modes, and second order phonons and the relation to the ferroelectric phase transition mechanism is reviewed. Furthermore experiments concerning parametric light scattering, the TM-reflection technique, the ATR-method, and nonlinear optical experiments are summarized. We finally discuss the question of mechanical-electromagnetic energy conversion and some tentative future aspects.     

Quantum computation with vibrationally excited polyatomic molecules: effects of rotation,level structure,and field gradients

Accurate rotation–vibration energy levels and transition dipoles of the molecule thiophosgene are used to model the execution of quantum gates with shaped laser pulses. Qubits are encoded in 2 ⁿ vibrational computing states on the ground electronic surface of the molecule. Computations are carried out by cycling amplitude between these computing states and a gateway state with a shaped laser pulse. The shaped pulse that performs the computation is represented by a physical model of a 128–1024 channel pulse shaper. Pulse shapes are optimized with a standard genetic algorithm, yielding experimentally realizable computing pulses. The robustness of optimization is studied as a function of the vibrational states selected, rotational level structure, additional vibrational levels not assigned to the computation, and compensation for laser power variation across a molecular ensemble.     

Friction tensor for a pair of Brownian particles: Spurious finite-size effects and molecular dynamics estimates

In this work, we show thatin any finite system, the binary friction tensor for two Brownian particlescannot be directly estimated from an evaluation of the microscopic Green-Kubo formula, involving the time integral of force-force autocorrelation functions. This pitfall is associated with a subtle inversion of the thermodynamic and long-time limits and leads to spurious results for the estimates of the friction matrix based on molecular dynamics simulations. Starting from a careful analysis of the coupled Langevin equations for two interacting Brownian particles, we derive a method to circumvent these effects and extract the binary friction tensor from the correlation function matrix of the instantaneous forces exerted by the bath particles on the fixed Brownian particles, and from the relaxation of the total momentum of the bath in afinite system. The general methodology is applied to the case of two hard or soft Brownian spheres in a bath of light particles. Numerical estimates of the relevant correlation functions and of the resulting self and mutual components of the matrix of friction tensors are obtained by molecular dynamics simulations for various spacings between the Brownian particles. This paper is dedicated to B. Jancovici on the occassion of his 65th birthday.     

Evaluating the effects of loading parameters on single-crystal slip in tantalum using molecular mechanics

This study is aimed at developing a physics-based crystal plasticity finite element model for body-centred cubic (BCC) metals, through the introduction of atomic-level deformation information from molecular dynamics (MD) investigations of dislocation motion at the onset of plastic flow. In this study, three critical variables governing crystal plasticity mediated by dislocation motion are considered. MD simulations are first performed across a range of finite temperatures up to 600K to quantify the temperature dependence of critical stress required for slip initiation. An important feature of slip in BCC metals is that it is not solely dependent on the Schmid law measure of resolved shear stress, commonly employed in crystal plasticity models. The configuration of a screw dislocation and its subsequent motion is studied under different load orientations to quantify these non-Schmid effects. Finally, the influence of strain rates on thermal activation is studied by inducing higher stresses during activation at higher applied strain rates. Functional dependence of the critical resolved shear stress on temperature, loading orientation and strain rate is determined from the MD simulation results. The functional forms are derived from the thermal activation mechanisms that govern the plastic behaviour and quantification of relevant deformation variables. The resulting physics-based rate-dependent crystal plasticity model is implemented in a crystal plasticity finite element code. Uniaxial simulations reveal orientation-dependent tension–compression asymmetry of yield that more accurately represents single-crystal experimental results than standard models.     

Hydrogen, sulphur and chlorine coadsorption on Pd(111): a theoretical study of poisoning and promotion

First principles calculations for the coadsorption of hydrogen with sulphur and chlorine on Pd(111) are presented. Individually, both sulphur and chlorine poison hydrogen adsorption, sulphur being the more efficient poison. The observed sulphur poisoning is a structural effect. The adsorption energy decreases and the diffusion barrier increases for hydrogen atoms in the vicinity of sulphur adatoms. A sulphur coverage of 0.33 ML is sufficient to completely poison hydrogen adsorption on Pd(111). The presence of chlorine adatoms on the sulphur-poisoned surface is found to stabilise localised hydrogen adsorption. The possible promotional effects of chlorine on sulphur-poisoned catalysts are discussed.     

Ethylene, sulphur, and chlorine coadsorption on Pd(111): a theoretical study of poisoning and promotion

First principles calculations for the coadsorption of C₂H₄ with S and Cl on Pd(111) are presented. Sulphur poisons adsorption, decreasing the strength of the ethylene–surface interaction. While low coverages of chlorine alone do not appear to affect ethylene adsorption on the otherwise clean palladium surface, chlorine does act as a promoter on the sulphur poisoned surface, increasing the strength of the ethylene–surface interaction. The promotional effect is attributed to changes in the dative bonding of the molecule and the surface and cannot be explained solely in terms of changes in the metal workfunction.     

Role of oxygen functional groups for structure and dynamics of interfacial water on low rank coal surface: a molecular dynamics simulation

Molecular dynamics simulations were employed to study the effects of oxygen functional groups for structure and dynamics properties of interfacial water molecules on the subbituminous coal surface. Because of complex composition and structure, the graphite surface modified by hydroxyl, carboxyl and carbonyl groups was used to represent the surface model of subbituminous coal according to XPS results, and the composing proportion for hydroxyl, carbonyl and carboxyl is 25:3:5. The hydration energy with ?386.28 kJ/mol means that the adsorption process between water and coal surface is spontaneous. Density profiles for oxygen atoms and hydrogen atoms indicate that the coal surface properties affect the structural and dynamic characteristics of the interfacial water molecules. The interfacial water exhibits much more ordering than bulk water. The results of radial distribution functions, mean square displacement and local self-diffusion coefficient for water molecule related to three oxygen moieties confirmed that the water molecules prefer to absorb with carboxylic groups, and adsorption of water molecules at the hydroxyl and carbonyl is similar.     

甲基橙-银胶体系pH和氯离子效应的光谱研究

研究了甲基橙-银胶体系的光吸收和光致发光信号随pH值和加入氯离子的变化规律.实验发现随着pH值的增加, 分子的荧光发射峰与银胶的光吸收峰的重叠增大, 引起体系中能量转移效率的增加, 即428 nm分子荧光峰的淬灭和560 nm聚集体的特征光致发光峰增强现象的加剧.另外, 不同pH值下氯离子的加入都会使染料分子更加密集的吸附在胶体银颗粒表面, 形成分子吸附更加紧密的聚集体, 造成体系中受表面吸附分子影响的光致发光峰获得了极大的增强.同时, 因聚集体表面吸附层染料分子对入射光的大量吸收, 导致到达内核银表面的入射光强度减弱, 致使体系能量转移通道在一定程度上受阻, 表现为428 nm荧光峰的淬灭幅度减小.参照分子聚集体的形成理论, 接合体系光谱的变化, 从pH值的改变和Cl^-的加入对分子结构及加剧聚集体的形成等方面的影响来解释发光和光吸收的显著变化.     

Ferromagnetism in the Hubbard model: instability of the Nagaoka state on the triangular,honeycomb and kagome lattices

In order to analyse the lattice dependence of ferromagnetism in the two-dimensional Hubbard model we investigate the instability of the fully polarised ferromagnetic ground state (Nagaoka state) on the triangular, honeycomb and kagome lattices. We mainly focus on the local instability, applying single spin flip variational wave functions which include majority spin correlation effects. The question of global instability and phase separation is addressed in the framework of Hartree-Fock theory. We find a strong tendency towards Nagaoka ferromagnetism on the non-bipartite lattices (triangular, kagome) for more than half filling. For the triangular lattice we find the Nagaoka state to be unstable above a critical density of n = 1.887 at U = ∞, thereby significantly improving former variational results. For the kagome lattice the region where ferromagnetism prevails in the phase diagram widely exceeds the flat band regime. Our results even allow the stability of the Nagaoka state in a small region below half filling. In the case of the bipartite honeycomb lattice several disconnected regions are left for a possible Nagaoka ground state.     

Coherent transport in linear arrays of quantum dots: The effects of period doubling and of quasi-periodicity

We evaluate the phase-coherent transport of electrons along linear structures of varying length, which are made from two types of potential wells set in either a periodic or a Fibonacci quasi-periodic sequence. The array is described by a tight-binding Hamiltonian and is reduced to an effective dimer by means of a decimation-renormalization method, extended to allow for connection to external metallic leads, and the transmission coefficient is evaluated in a T-matrix-scattering approach. Parallel behaviors are found for the energy dependence of the density of electron states and of the transmittivity of the array. In particular, we explicitly show that on increasing its length the periodic array undergoes a metal–insulator transition near single occupancy per dot, whereas prominent pseudo-gaps emerge away from the band center in the Fibonacci-ordered array.     

An analytic algebraic approach to study the influence of molecular alignment and orientation on multiphoton excitation in intense laser fields

The influence of molecular alignment and orientation on multiphoton vibrational excitation of diatomic molecules H₂, HD, and D₂ is studied by an analytical algebraic approach. The explicit expressions of the time-evolution operator and the excitation probability are given. The long-time average absorbed energy spectra and the time-dependent absorbed energy are obtained. Results show that the impact of molecular orientation on the multiphoton resonant excitation is decided by the molecular type and molecular anharmonicity. This is valuable for controlling the vibrational excitation of molecules, which is relevant to the whole field of molecular physics and physical chemistry. Furthermore, good agreement with numerical simulation is achieved.     

Study of the effects of Cr ions on Yb in Cr,Yb:YAG crystal

The absorption and fluorescence spectra of Cr,Yb:YAG crystal were measured. There are two absorption bands at 940 nm and 968 nm although the absorption coefficient is lower than that of the absorption peak of Yb:YAG superimposed in Cr:YAG absorption peak. The emission peak intensity is 4 times lower than that of Yb:YAG, which may be caused by the existence of the ground state absorption of Cr⁴⁺ which quenches the Yb³⁺ emission intensity. Although the emission peak of Cr,Yb:YAG is lower than that of Yb:YAG, there is an advantage of this crystal which combines the saturable absorber and gain medium into one and can be a self-Q switching laser crystal if Cr,Yb:YAG crystal is pumped with high energy power.     

Quantum effects on the black hole shadow and deflection angle in the presence of plasma

In this study, the optical properties of a renormalization group improved (RGI) Schwarzschild black hole (BH) are investigated in a plasma medium. Beginning with the equations of motion in a plasma medium, we aim to present the modifications in the shadow radius of the RGI BH. To this end, we compute the deflection angle of light in the weak gravity regime for uniform and non-uniform plasma media. Importantly, owing to the plasma media, we discover that the equations of motion for light obtained from the radiating and infalling/rest gas have to be modified. This, in turn, changes and modifies the expression for the intensity observed far away from the BH. Finally, we obtain the shadow images for the RGI BH for different plasma models. Although quantum effects change the background geometry, such effects are minimal, and practically detecting these effects using the current technology based on supermassive BH shadows is impossible. The parameter Ω encodes the quantum effects, and in principle, one expects such quantum effects to play significant roles only for very small BHs. However, the effects of plasma media can play an important role in the optical appearance of BHs, as they affect and modify the equations of motion.     

Rovibrational matrix elements of the multipole moments and of the polarizability of the H2 molecule in the solid phase: Effect of intermolecular potential

Rovibrational matrix elements of the multiple moments Q _l up to rank 10 and of the linear polarizability of the H₂ molecule in the condensed phase have been computed taking into account the effect of the intermolecular potential. Comparison with gas phase matrix elements shows that the effect of solid state interactions is marginal.     

Effects of Poisson's ratio on the band gaps and defect states in two-dimensional vacuum/solid porous phononic crystals

The effects of the Poisson’s ratio of the solid host on the band gaps and point defect states of the mixed elastic wave modes in two-dimensional vacuum/solid porous PNCs are studied by numerical simulations. Four typical systems are considered. The four systems are, respectively, (I) the system with a square lattice and circular pores, (II) the system with a hexagonal lattice and circular pores, (III) the system with a square lattice and square pores and (IV) the system with a hexagonal lattice and regular-hexagonal pores. In the latter two systems, with respect to the outer boundaries of the Wigner-Seitz unit cell, the pores rotate 45° and 30°, respectively. Some observable effects of the Poisson’s ratio are found in the numerical results. Especially, the variations of the band gap boundaries with the Poisson’s ratio exhibit relatively consistent behaviors. With the increase of the Poisson’s ratio, the normalized frequency of a band gap boundary generally increases, except that in system (III) the normalized frequency of the upper boundary of the first band gap remains almost unchanged. Detailed interpretations on this phenomenon are given.     

Control of amplification without inversion in H2 and LiH molecules: Dependence on relative magnitude of probe and coherent field Rabi frequencies in three-level Λ system

Dependence of amplification without inversion (AWI) on the relative strength of probe and coherent field Rabi frequencies has been studied in H₂ and LiH molecules for three-level Λ configuration. We have derived exact analytical expressions for coherences and populations keeping all the orders of probe field Rabi frequency (G) and coherent field Rabi frequency. (Θ) in the steady state limit. Previously, first-order approximation (i.e. keeping only the first-order term in G) was used and hence AWI was studied for the condition Θ>>G. Here, by using the exact analytical expressions of coherences and populations, we have shown that AWI is maximum when Θ is within the same order of probe field Rabi frequency G irrespective of the choice of different ro-vibrational transitions in both the molecules. However, the shape of the gain profile and the maximum value of gain on the probe field and the absorption on coherent field depend on the choice of different ro-vibrational levels as the upper lasing levels. Effect of bidirectional pumping, homogeneous and inhomogeneous broadening on AWI process has been studied. By solving the density matrix equations numerically it has been shown that both the transient and the steady state AWI can be obtained and the numerical values of coherences and populations at large time are in very good agreement with exact analytical values in the steady state limit. It has been shown that in molecules AWI can be obtained on probe field of smaller wavelength than that of the coherent field which has not been observed in atoms so far.