Momentum Quantum Research Articles

Fractional Chern insulator edges and layer-resolved lattice contacts

Fractional Chern insulators (FCIs) realized in fractional quantum Hall systems subject to a periodic potential are topological phases of matter for which space group symmetries play an important role. In particular, lattice dislocations in an FCI can host topology-altering non-Abelian topological defects, known as genons. Genons are of particular interest for their potential application to topological quantum computing. In this work, we study FCI edges and how they can be used to detect genons. We find that translation symmetry can impose a quantized momentum difference between the edge electrons of a partially-filled Chern band. We propose {\it layer-resolved lattice contacts}, which utilize this momentum difference to selectively contact a particular FCI edge electron. The relative current between FCI edge electrons can then be used to detect the presence of genons in the bulk FCI. Recent experiments have demonstrated graphene is a viable platform to study FCI physics. We describe how the lattice contacts proposed here could be implemented in graphene subject to an artificial lattice, thereby outlining a path forward for experimental dectection of non-Abelian topological defects.

Numerical simulation the influence of bubbles on the structure and friction of turbulent gas–liquid flow in vertical pipe

The paper the results of a computational study of the local structure of the ascending gas-liquid flow in a vertical pipe are presented. The mathematical model is based on the use of two-fluid Eulerian approach taking into account the inverse influence of bubbles on averaged characteristics and turbulence of carrying phase. The equations conservation of mass and momentum quantity of motion in the form of Navier-Stokes equations averaged over Reynolds for each phase are written down. For turbulent stresses the relations under the assumption of the Boussinesq hypothesis are written. Turbulent viscosity for the carrier liquid phase is determined using a two-parameter turbulence model modified for two-phase media. Investigation is performed of the impact made by the variation of the degree of dispersion of the gas phase, volumetric flow ratio of gas and velocity of the liquid phase on the local structure and skin friction in two-phase flow.

Giant Valley Coherence at Room Temperature in 3R WS 2 with Broken Inversion Symmetry

Breaking the space-time symmetries in materials can markedly influence their electronic and optical properties. In 3R-stacked transition metal dichalcogenides, the explicitly broken inversion symmetry enables valley-contrasting Berry curvature and quantization of electronic angular momentum, providing an unprecedented platform for valleytronics. Here, we study the valley coherence of 3R WS2 large single-crystal with thicknesses ranging from monolayer to octalayer at room temperature. Our measurements demonstrate that both A and B excitons possess robust and thickness-independent valley coherence. The valley coherence of direct A (B) excitons can reach 0.742 (0.653) with excitation conditions on resonance with it. Such giant and thickness-independent valley coherence of large single-crystal 3R WS2 at room temperature would provide a firm foundation for quantum manipulation of the valley degree of freedom and practical application of valleytronics.

Dynamical localization in nonideal kicked rotors

We discuss a general useful theoretical framework to study dynamical localization in ultracold atomic systems confined in periodically shaken optical lattices. Our theory allows to understand some limitations of the usual approach concerning prototypical $\ensuremath{\delta}$-kicked systems, as well as to explain the experimental results for which finite-time effects cannot be neglected. Specifically, we predict that the strength of dynamical localization reaches a maximum as a function of the width of the pulsatile modulation, whenever its amplitude and period satisfy a given relationship. Additionally, we describe a quite simple scenario for the quantum suppression of classical diffusion, which is confirmed by extensive numerical simulations: The activation of Heisenberg's uncertainty principle giving rise to a drastic reduction of the quantum momentum dispersion if, and only if, the classical dynamics is sufficiently chaotic.

Electron Effective Mass and Momentum Relaxation Time in One-Sided δ-Doped PHEMT AlGaAs/InGaAs/GaAs Quantum Wells with High Electron Density

Using the Shubnikov–de Haas effect, the dependences of electron effective mass m* and transport and quantum momentum relaxation times in Al0.25Ga0.75As/In0.2Ga0.8As/GaAs pseudomorphic quantum wells with one-sided silicon δ-doping on the electron density in the range of (1.1–2.6) × 1012 cm–2 have been established. Nonparabolicity coefficient m* in the linear approximation was found to be 0.133m0/eV. Both the transport and quantum momentum relaxation times depend nonmonotonically on Hall electron density nH, which is related to the competition between growth mechanisms of the Fermi momentum and the increasing contribution of large-angle scattering with increasing donor concentration.

Field theoretical derivation of L\xfcscher\u2019s formula and calculation of finite volume form factors

We initiate a systematic method to calculate both the finite volume energy levels and form factors from the momentum space finite volume two-point function. By expanding the two point function in the volume we extracted the leading exponential volume correction both to the energy of a moving particle state and to the simplest non-diagonal form factor. The form factor corrections are given in terms of a regularized infinite volume 3-particle form factor and terms related to the Lüsher correction of the momentum quantization. We tested these results against second order Lagrangian and Hamiltonian perturbation theory in the sinh-Gordon theory and we obtained perfect agreement.

Quantum phase transition with dissipative frustration

We study the quantum phase transition of the one-dimensional phase model in the presence of dissipative frustration, provided by an interaction of the system with the environment through two non-commuting operators. Such a model can be realized in Josephson junction chains with shunt resistances and resistances between the chain and the ground. Using a self-consistent harmonic approximation, we determine the phase diagram at zero temperature which exhibits a quantum phase transition between an ordered phase, corresponding to the superconducting state, and a disordered phase, corresponding to the insulating state with localized superconducting charge. Interestingly, we find that the critical line separating the two phases has a non monotonic behavior as a function of the dissipative coupling strength. This result is a consequence of the frustration between (i) one dissipative coupling that quenches the quantum phase fluctuations favoring the ordered phase and (ii) one that quenches the quantum momentum (charge) fluctuations leading to a vanishing phase coherence. Moreover, within the self-consistent harmonic approximation, we analyze the dissipation induced crossover between a first and second order phase transition, showing that quantum frustration increases the range in which the phase transition is second order. The non monotonic behavior is reflected also in the purity of the system that quantifies the degree of correlation between the system and the environment, and in the logarithmic negativity as entanglement measure that encodes the internal quantum correlations in the chain.

Work production of quantum rotor engines

We study the mechanical performance of quantum rotor heat engines in terms of common notions of work using two prototypical models: a mill driven by the heat flow from a hot to a cold mode, and a piston driven by the alternate heating and cooling of a single working mode. We evaluate the extractable work in terms of ergotropy, the kinetic energy associated to net directed rotation, as well as the intrinsic work based on the exerted torque under autonomous operation, and we compare them to the energy output for the case of an external dissipative load and for externally driven engine cycles. Our results connect work definitions from both physical and information-theoretical perspectives. In particular, we find that apart from signatures of angular momentum quantization, the ergotropy is consistent with the intuitive notion of work in the form of net directed motion. It also agrees with the energy output to an external load or agent under optimal conditions. This sets forth a consistent thermodynamical description of rotating quantum motors, flywheels, and clocks.

A modified Stern-Gerlach experiment using a quantum two-state magnetic field

The Stern-Gerlach experiment has played an important role in our understanding of quantum behavior. We propose and analyze a modified version of this experiment where the magnetic field of the detector is in a quantum superposition, which may be experimentally realized using a superconducting flux qubit. We show that if incident spin-$1/2$ particles couple with the two-state magnetic field, a discrete target distribution results that resembles the distribution in the classical Stern-Gerlach experiment. As an application of the general result, we compute the distribution for a square waveform of the incident fermion. This experimental setup allows us to establish: (1) the quantization of the intrinsic angular momentum of a spin-$1/2$ particle, and (2) a correlation between EPR pairs leading to nonlocality, without necessarily collapsing the particle's spin wavefunction.

Quantum regime of a plasma-wave-pumped free-electron laser in the presence of an axial magnetic field

The quantum regime of a plasma-whistler-wave-pumped free-electron laser (FEL) in the presence of an axial-guide magnetic field is presented. By quantizing both the plasma whistler field and axial magnetic field, an N-particle three-dimensional Hamiltonian of quantum-FEL (QFEL) has been derived. Employing Heisenberg evolution equations and introducing a new collective operator which controls the vertical motion of electrons, a quantum dispersion relation of the plasma whistler wiggler has been obtained analytically. Numerical results indicate that, by increasing the intrinsic quantum momentum spread and/or increasing the axial magnetic field strength, the bunching and the radiation fields grow exponentially. In addition, a spiking behavior of the spectrum was observed with increasing cyclotron frequency which provides an enormous improvement in the coherence of QFEL radiation even in a limit close-to-classical regime, where an overlapping of these spikes is observed. Also, an upper limit of the intrinsic quantum momentum spread which depends on the value of the cyclotron frequency was found.

Displacement operators: the classical face of their quantum phase

In quantum mechanics, the operator representing the displacement of a system in position or momentum is always accompanied by a path-dependent phase factor. In particular, two non-parallel displacements in phase space do not compose together in a simple way, and the order of these displacements leads to different displacement composition phase factors. These phase factors are often attributed to the nonzero commutator between quantum position and momentum operators, but such a mathematical explanation might be unsatisfactory to students who are after more physical insight. We present a couple of simple demonstrations, using classical wave mechanics and classical particle mechanics, that provide some physical intuition for the phase associated with displacement operators.

Observing Wave/Particle Duality of Light Using Topological Charge

Wave particle duality, also called complementarity, is deeply rooted in the heart of quantum theory. It is fully exemplified in the famous Wheeler's delayed choice experiment where the choice of the wave nature (ability to interfere) or the particle like behavior (path distinguishability) is introduced a posteriori. We perform here a delayed choice experiment in a Mach-Zehnder interferometer, using a classical laser beam and twisted light in a given mode. We entangle the polarization and the twisted internal degrees of freedom, with the which-path-information external degree of freedom of the beam. The particle behavior of light arises from the quantization of the orbital angular momentum. It is demonstrated from torque and light power measurements within 10% accuracy. We then experimentally evidence that the particle or wave behavior of light can be chosen a posteriori, even after the light has left the interferometer, at the moment of the detection.

Quantum Mechanics and Special Relativity: The Origin of Momentum Operator

The free relativistic particle, by definition, has to move in an inertial reference frame with uniform velocity less than the speed of light. The corresponding movement of a material quantum particle describes a wave packet, composed of matter waves—solutions of the Schr?dinger equation. The maximum of packet, corresponding to the largest probability to find the particle, has to move with the same uniform velocity, defined by the initial condition. It has been shown that the traditional definition of the quantum momentum operator i.e. taking it to correspond to the special relativity theory, relativistic momentum, cannot produce precise description of a relativistic matter particle. Different definitions are investigated and one that solves this issue is found. Obtained original expression of relativistic kinetic energy operator creates new possibilities for relativistic quantum systems theory.

Эффективная масса и время релаксации импульса электронов в односторонне delta-легированных PHEMT квантовых ямах AlGaAs/InGaAs/GaAs с высокой электронной плотностью

AbstractUsing the Shubnikov–de Haas effect, the dependences of electron effective mass m * and transport and quantum momentum relaxation times in Al_0.25Ga_0.75As/In_0.2Ga_0.8As/GaAs pseudomorphic quantum wells with one-sided silicon δ-doping on the electron density in the range of (1.1–2.6) × 1012 cm^–2 have been established. Nonparabolicity coefficient m * in the linear approximation was found to be 0.133 m _0/eV. Both the transport and quantum momentum relaxation times depend nonmonotonically on Hall electron density nH, which is related to the competition between growth mechanisms of the Fermi momentum and the increasing contribution of large-angle scattering with increasing donor concentration.

A Local-Realistic Model of Quantum Mechanics Based on a Discrete Spacetime

This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on probabilities, in particular assuming a discrete spacetime under the form of a Euclidean lattice. Individual (spinless) particle trajectories are described as random walks. Transition probabilities are simple functions of a few quantities that are either randomly associated to the particles during their preparation, or stored in the lattice nodes they visit during the walk. QM predictions are retrieved as probability distributions of similarly-prepared ensembles of particles. The scenarios considered to assess the model comprise of free particle, constant external force, harmonic oscillator, particle in a box, the Delta potential, particle on a ring, particle on a sphere and include quantization of energy levels and angular momentum.

Coulomb Problem for Z > Zcr in Doped Graphene

The dynamics of charge carriers in doped graphene, i.e., graphene with a gap in the energy spectrum depending on the substrate, in the presence of a Coulomb impurity with charge Z is considered within the effective two-dimensional Dirac equation. The wave functions of carriers with conserved angular momentum J = M + 1/2 are determined for a Coulomb potential modified at small distances. This case, just as any two-dimensional physical system, admits both integer and half-integer quantization of the orbital angular momentum in plane, M = 0, ±1, ±2, …. For J = 0, ±1/2, ±1, critical values of the effective charge Zcr(J, n) are calculated for which a level with angular momentum J and radial quantum numbers n = 0 and n = 1 reaches the upper boundary of the valence band. For Z Zcr (J, n = 0), scattering phases are calculated as a function of hole energy for several values of supercriticality, as well as the positions e0 and widths γ of quasistationary states as a function of supercriticality. The values of e0* and width γ* are pointed out for which quasidiscrete levels may show up as Breit–Wigner resonances in the scattering of holes by a supercritical impurity. Since the phases are real, the partial scattering matrix is unitary, so that the radial Dirac equation is consistent even for Z > Zcr. In this single-particle approximation, there is no spontaneous creation of electron–hole pairs, and the impurity charge cannot be screened by this mechanism.

Hot carrier relaxation in three dimensional gapped Dirac semi-metals

We calculate the relaxation rate of hot carriers in a Cd3As2 semi-metal with a finite gap. The quantization of the transverse momentum gives rise to a minimum gap at the Dirac point. Additional chemical doping further increases the gap. A finite gap relaxes the selection rule and gives rise to a nonvanishing internode coupling via phonon scattering. The gap also enhances the intra-node scattering. It is shown that the relaxation rate is proportional to the square of the gap. By considering the decay of the electron distribution function, we find that the relaxation rate increases with the square of the gap and the electron temperature.

Quantum Oscillations of the Microwave Sensitivity of a Spin-Torque Diode in a Magnetic Nanobridge

The reduction of the area of the cross section of a spin-valve-like structure to a nanoscale is an important problem of modern spin electronics. However, the transverse quantization of electronic states in the spin valve, which forms a magnetic nanobridge at this scale, additionally affects not only the magnetoresistance but also the spin-transfer torques. In this work, features of the quantization of the magnetoresistance and spin-angular momentum associated with the spin transfer in a Co/Au/Co metallic nanobridge with metallic contacts have been theoretically analyzed. It has been shown that these features are manifested in oscillations of the microwave sensitivity of a spin-torque diode based on the spin-valve structure mentioned above.

The analysis of rovibrational motion equations of a diatomic molecule in the linear regime

ABSTRACTThe motion equations of diatomic molecules are here extended from the absolute vibrational case to a more general and real rotational and vibrational (rovibrational) case. The rovibrational Hamiltonian is heuristically formed by substituting the respective number and angular momentum operators for the vibrational and rotational quantum numbers in the energy eigenvalues of a diatomic molecule which was first introduced by Dunham. The motion equations of observable quantities such as the position and linear momentum are then determined by implementing the well-known Heisenberg relation in quantum mechanics. We face with the second-order imaginary differential equations for describing the temporal variations of the relative position and the linear momentum of two oscillating atoms, which are coupled in the x–y horizontal plane. The possible rovibrational oscillations are distinguished by the three quantum numbers n, l and m associated with the energy and angular momentum quantities. It is finally demonstrated that the simultaneous solutions of rovibrational equations satisfy the energy conservation during all quantised oscillations of a diatomic molecule in space.

Role of volume and surface spontaneous parametric down-conversion in the generation of photon pairs in layered media

A rigorous description of volume and surface spontaneous parametric down-conversion in 1D nonlinear layered structures is developed considering exact continuity relations for the fields' amplitudes at the boundaries. The nonlinear process is described by the quantum momentum operator that provides the Heisenberg equations which solution is continuous at the boundaries. The transfer-matrix formalism is applied. The volume and surface contributions are clearly identified. Numerical analysis of a structure composed of 20 alternating GaN/AlN layers is given as an example.