Adiabatic and isothermal elastic constants for highly anharmonic crystals

The mass operator of the phonon Green function for a highly anharmonic crystal in the ladder approximation is derived. In order to calculate the mass operator in the collision-dominated regime it is necessary to solve the Boltzmann-like equations. These solutions allow us to find the thermal conductivity coefficient and to prove that the thermodynamic relation between adiabatic and isothermal elastic constants is satisfied.     

Electron transport through a quantum dot in the presence of electron-photon and electron-phonon coupling

In this study, electron transport through a mesoscopic quantum dot system (QD-system) in the presence of electron-photon (el-pt) and electron-phonon (el-ph) interactions is discussed. The role of both of these interactions is to induce additional steps in the current, and sideband peaks in the differential conductance. By calculating the current and differential conductance of a QD-system in the presence of el-pt or el-ph coupling, we have shown that photon or phonon steps and sideband peaks are induced in the current and differential conductance whenever the applied voltage resonates with their frequency. Furthermore, additional side band peaks are induced in the differential conductance when el-pt and el-ph interactions are simultaneously included in the QD. These extra sideband peaks (ESBPs) are induced when the applied voltage and the photon frequency are in close proximity with the phonon frequency. To investigate the relationship that exists between the photon and phonon frequency in inducing ESBPs in the differential conduction, we have discussed zero applied voltage differential conductance. Under such conditions, ESBP is induced only when the photon frequency resonates with the phonon frequency. With increasing el-ph coupling amplitude, more ESBPs are induced in the differential conductance.     

多原子半无限晶体中表面极化子的内部激发态

研究多原子半无限晶体中电子与表面光学(SO)声子耦合强,而与体纵光学(LO)声子耦合弱的极化子的激发态性质.采用线性组合算符和幺正变换方法导出与SO声子耦合强而与LO声子耦合弱情形下极化子的基态能量、第一内部激发态能量和激发能量.结果表明,多原子半无限晶体中与SO声子耦合强,而与LO声子耦合弱的极化子的基态能量、第一内部激发态能量不仅包含不同支LO声子和不同支SO声子与电子耦合的能量,而且也包含不同支SO声子之间相互作用贡献的附加能量.激发能量与体纵光学声子无关.     

Uncertainty relation for photons

The uncertainty relation for the photons in three dimensions that overcomes the difficulties caused by the nonexistence of the photon position operator is derived in quantum electrodynamics. The photon energy density plays the role of the probability density in configuration space. It is shown that the measure of the spatial extension based on the energy distribution in space leads to an inequality that is a natural counterpart of the standard Heisenberg relation. The equation satisfied by the photon wave function in momentum space which saturates the uncertainty relations has the form of the Schr?dinger equation in coordinate space in the presence of electric and magnetic charges.     

The cranked harmonic oscillator in coordinate space

The spectroscopic factor is considered for two-nucleon transfer reactions involving the excitation of quadrupole one-phonon states. Special attention is payed to the number of particles conservation condition in the dynamically distorted average potential of the deforming nucleus. It is required that the mean square of the time-derivtive of the particle number operator is zero in the collective phonon state. The condition is satisfied by a specially chosen residual interaction terms.     

Quantum Mechanical Model Calculations of Phonon Polaritons in Two-Dimensional Crystals

The properties of the simplest phonon-polaritons exist in a two-dimensional diatomic ionic or polar dielectric are investigated by the quantum field theory methods. We considered the two-dimensional crystal as a simple model of a thin slab, an interface or a heterojunction. The Hamiltonian operator describing the interaction between a photon and the phonon mode of the two-dimensional medium is calculated. Anharmonic effects are neglected. The dispersion curves of the phonon-polaritons and the k‖-dependence of the electric field strength in each polaAton branch are calculated and presented for various cases in a graphical form. It is shown that these properties have close relations with the distributidn of the electromagnetic field in the z direction.     

Theoretical investigation of hot electron cooling process in GaAs/AlAs cylindrical quantum wire under the influence of an intense electromagnetic wave

Hot electrons cooling by phonons in GaAs/AlAs cylindrical quantum wire (CQW), under the influence of an intense electromagnetic wave (EMW), is studied theoretically. Analytic expression for the electron cooling power (CP) is derived from the quantum transport equation for phonons, using the Hamiltonian of interacting electron–optical phonon system. Both photon absorption and emission processes are considered. Numerical results show that the CP reaches maximum when the energy difference between electronic subbands equals the energy of an optical phonon plus the photon energy. Under the influence of the EMW, the negative CP is observed showing that electrons gain energy from phonon and photon instead of losing their energy. Also, the CP increases with increasing the EMW amplitude. Our results theoretically clarify the mechanism of the electron cooling process by phonons in the GaAs/AlAs CQW under the EMW, which is of significance for designing and fabricating high-speed nanoelectronic devices based on this material.     

Phonon-assisted normal incidence intersubband absorption in semiconductor quantum wells

In the presence of a normally incident mid-IR pulsed laser field, phonon-assisted photon absorption by both intrasubband and intersubband phonon scattering of conduction electrons in GaAs/AlGaAs quantum wells are predicted. The novel non-resonant and non-linear intersubband absorption is found by including the photon-induced phonon scattering process in a Boltzmann equation for phonon energies smaller than the energy separation between two electron subbands in the quantum well. The predicted phonon-assisted photon absorption by intersubband transitions of electrons from the first to the second subband is a unique feature in quantum-well systems and is expected to have a significant effect on the electron populations in both subbands.     

Thermal resistance of GaAs/AlAs superlattices used in modern light-emitting diodes

Superlattices are used in modern light-emitting diodes to modify intentionally electron, phonon and/or photon transport within their volumes, which leads to their expected performance characteristics. In particular, superlattices may have a dramatic impact on device thermal properties. Superlattice thermal resistance is anisotropic and usually distinctly higher than its values in constituent bulk materials, which results from phonon reflections and/or phonon scatterings at numerous layer interfaces. In the present paper, thermal resistance of a typical superlattice of layer thicknesses neither much higher nor much lower than the phonon free path is discussed. Besides, as an important example, thermal resistance of the typical GaAs/AlAs superlattice is determined theoretically and compared with its measured values known from literature.     

The theory of phonon relaxation in He(II) at low temperatures

We have investigated analytically relaxation processes in the phonon system in helium(II) at sufficiently low temperatures where rotons are not exited. In accordance with the recent experimental data, the phonon velocity dispersion is supposed to be positive, though small. Two different relaxation processes exist in the phonon system in this case: (i) the fast longitudinal relaxation establishing equilibrium phonon distribution along each direction in the momentum space with the temperature and the drift velocity depending on the direction; (ii) the slow transverse relaxation setting up equilibrium between different directions.Using the energy and momentum conservation and general principles of the irreversible thermodynamics we have derived the expression for the transverse relaxation operator. It appears to be a differential operator of the fourth order and depends on a function of the “phonon temperature” Θ that cannot be determined from the general consideration. We have calculated this function for the case of three-phonon collisions.Physical properties of the transverse relaxation operator are discussed and the corresponding boundary conditions are formulated. Several typical physical problems, both linear and nonlinear, which can be formulated in terms of the transverse relaxation operator, are enumerated. With the help of the diagram method the contribution of multiphonon collisions both in the longitudional and in the transverse relaxation is evaluated.     

极化子效应对核壳量子点中光学克尔效应的影响

在有效质量近似下利用量子力学的密度矩阵理论,采用无限深势阱模型解三维薛定谔方程得到电子的本征能量和波函数.从理论上计算了考虑极化子效应后,在导带子带间跃迁时ZnS/CdSe柱型核壳结构量子点光学克尔效应的三阶极化率.通过数值计算,分析了电子-LO声子和电子-IO声子相互作用对ZnS/CdSe柱型核壳结构量子点光学克尔效应的三阶极化率的影响.结果表明：极化子效应对光学克尔效应的三阶极化率 有很大影响,并且影响的大小与量子点的尺寸大小有关.       

Phase-modulated Autler–Townes splitting in a giant-atom system within waveguide QED

The nonlocal emitter-waveguide coupling, which gives birth to the so called giant atom, represents a new paradigm in the field of quantum optics and waveguide QED. We investigate the single-photon scattering in a one-dimensional waveguide on a two-level or three-level giant atom. Thanks to the natural interference induced by the back and forth photon transmitted/reflected between the atom-waveguide coupling points, the photon transmission can be dynamically controlled by the periodic phase modulation via adjusting the size of the giant atom. For the two-level giant-atom setup, we demonstrate the energy shift which is dependent on the atomic size. For the driven three-level giant-atom setup, it is of great interest that, the Autler–Townes splitting is dramatically modulated by the giant atom, in which the width of the transmission valleys (reflection range) is tunable in terms of the atomic size. Our investigation will be beneficial to the photon or phonon control in quantum network based on mesoscopical or even macroscopical quantum nodes involving the giant atom.     

极化子效应对ZnS/CdSe核壳量子点光吸收系数的影响

在有效质量近似下,利用量子力学密度矩阵理论,从理论上研究了考虑极化子效应后核壳量子点中线性、三阶非线性以及总的光吸收系数在不同条件下随入射光能量变化的关系。通过数值计算,分析了电子-LO声子和电子-IO声子相互作用对ZnS/CdSe柱型核壳结构量子点光吸收系数的影响。结果表明,极化子效应对光吸收系数有很大影响,不同声子模式对光吸收系数影响大小不同。考虑电子-LO声子后,光吸收系数被大大提高。另外,入射光强和弛豫时间对系统的吸收系数也有很大影响。     

Investigation of various operation modes of a miniature superconducting detector of microwave radiation

Nonequilibrium electron and phonon distribution functions have been calculated for a metallic absorber of a promising miniature superconducting detector irradiated by microwave radiation. The response of this detector has been calculated, and it has been shown that this detector can operate in either the photon counter mode or bolometric mode in dependence on the degree of nonequilibrium of the phonon subsystem.     

光声互作用模型中的Pancharatnam相位

通过解析求解简单极化激元模型的Pancharatnam相位, 研究了温度、耦合强度、声子与光子频率差、平均光子数等对其演化的影响. 结果表明,Pancharatnam相位随时间振荡,且振荡频率和振荡波形随时间变化,这种变化随着温度升高和耦合强度、声子与光子频率差增加而加大. 系统Pancharatnam相位随时间的演化在平均光子数较小时表现比较有规律,但随着平均光子数的增加,它趋于混沌化. 关键词： 极化激元 Pancharatnam 相位 Mach-Zehnder干涉仪 相干态     

Wigner functions for two arbitrary operators and spectrum perturbation

We have concentrated on the Wigner function for the photon number and a quadrature operator, which we find to differ from zero outside the spectrum of the photon number operator. We have provided an illustration with a coherent state.     

Entanglement dynamics for a solid polariton system at zero and finite temperatures

The dynamics of the entanglement for a solid polariton system is investigated. The polariton system is a photon-phonon complex and its time-dependent characteristic function in the Wigner representation for the system is obtained analytically. It is found that when the photon field is initially prepared in the squeezed vacuum state, and the phonon in the thermal state, the polariton system can evolve into a two-mode Gaussian mixed state. The entanglement between photon and phonon turns out to be apparently dependent on the squeezing parameter and exhibits a critical behavior with respect to the temperature.     

Phoxonic crystals and cavity optomechanics

Phoxonic crystals are dual phononic/photonic crystals exhibiting simultaneously band gaps for both types of excitations. Therefore, they have the ability to confine phonons and photons in the same cavity and in turn allow the enhancement of their interaction. In this paper, we review some of our theoretical works on cavity optomechanical interactions in different types of phoxonic crystals, including two-dimensional, slab, and nanobeam structures. Two mechanisms are behind the phonon–photon interaction, namely the photoelastic and the moving interface effects. Coupling rates of a few MHz are obtained with high-frequency phonons of a few GHz. Finally, we give some preliminary results about the optomechanical interaction when a metallic nanoparticle is introduced into the cavity, giving rise to coupled photon–plasmon modes or, in the case of very small particles, to an enhancement of the electric field at the position of the particle.     

High-Speed Quantum Transducer with a Single-Photon Emitter in a 2D Resonator

Quantum transducers can transfer quantum information between different systems. Microwave–optical photon conversion is important for future quantum networks to interconnect remote superconducting quantum computers with optical fibers. Here, a high-speed quantum transducer based on a single-photon emitter in an atomically thin membrane resonator, that can couple single microwave photons to single optical photons, is proposed. The 2D resonator is a freestanding van der Waals heterostructure (which may consist of hexagonal boron nitride, graphene, or other 2D materials) that hosts a quantum emitter. The mechanical vibration (phonon) of the 2D resonator interacts with optical photons by shifting the optical transition frequency of the single-photon emitter with strain or the Stark effect. The mechanical vibration couples to microwave photons by shifting the resonant frequency of an LC circuit that includes the membrane. Thanks to the small mass of the 2D resonator, both the single-photon optomechanical coupling strength and the electromechanical coupling strength can reach the strong coupling regime. This provides a way for high-speed quantum state transfer between a microwave photon, a phonon, and an optical photon.