Long-time limit behavior of the solution to an atom＇s master equation

We study the long-time limit behavior of the solution to an atom＇s master equation. For the first time we derive that the probability of the atom being in the α-th （α = j ＋ 1 -jz, j is the angular momentum quantum number, jz is the z-component of angular momentum） state is {（1 - K/G）/[1 - （K/G）2j＋1]}（K/G）^α-1 as t → ＋∞, which coincides with the fact that when K/G 〉 1, the larger the a is, the larger the probability of the atom being in the α-th state （the lower excited state） is. We also consider the case for some possible generaizations of the atomic master equation.     

On long-time limit behavior of the solution of atom's master equation

We study long-time limit behavior of the solution of atom's master equation, for the first time we derive that the probability of the atom being in the α-th (α =j+1-j_z, j is the angular momentum quantum number, j_z is the z-component of angular momentum) state is {(1-K/G)/[1-(K/G)^2j+1]}(K/G)^α-1 as t→+∞, which coincides with the fact that when K/G > 1, the larger the α is, the larger probability of the atom being in the α-th state (the lower excited state). We also consider the case for some possible generalizations of the atomic master equation.     

EPR Entangled States for Bipartite Kinematics and New Bosonic Representation of SU（2） Algebra

We find that the Einstein-Podolsky-Rosen (EPR) entangled state representation descr/bing bipartite kinematics is closely related to a new Bose operator realization of SU(2) Lie algebra. By virtue of the new realization some ttamiltonian eigenfunction equation can be directly converted to the generalized confluent equation in the EPR entangled state representation and its solution is obtainable. This thus provides a new approach for studying dynamics of angular momentum systems.     

1984年CUSPEA试题(二)(英文)

B1. Consider a hydrogen atom, and assume that the proton, instead of being a point, is auniformly charged sphere of radius R <相似文献   

A Lower Bound on the Entanglement in the Jaynes-Cummings Model

The entanglement between an atom and field is investigated by using the 3aynes-Cummings model. The initial atomic state is supposed in a mixed state and the field is in a squeezed state. The lower bound on the entanglement quantified by concurrence is calculated. It is found that the entanglement with the atom being initially in a mixed state can be larger than that with the atom being initially in a pure state. The entanglement is not a monotone function of the squeezing parameter r of the field and it achieves the maximum for certain r and then decreases with further increase of r.     

THE AMPLITUDE-N-TH POWERED SQUEEZING OF AN ELECTROMAGNETIC FIELD IN THE MULTIPHOTON JAYNES-CUMMINGS MODEL INTERACTING WITH THE SUPERPOSITION STATE

We have studied the properties of the amplitude-N-th powered squeezing of an elec-tromagnetic field in the k-photon Jaynes-Cummings model of an atom initially being in the ground state and coupling with the superposition state. The results show that, under the condition of n≥k, where n is the photon number of the superposition state, the field exhibits not only the amplitude-N = n-th powered squeezing but also the amplitude-N = (n/2)-th powered squeezing for even n. The variations of the amplitude-N-th powered squeezing of the field with the powers N and k are discussed.     

Radiative Energy Shifts of an Atom Coupled to the Derivative of a Scalar Field near a Reflecting Boundary

We study the radiative energy level shifts of a two-level atom in dipole coupling to the derivative of a massless scalar quantum field in a spacetime with a perfectly reflecting boundary, and calculate the contributions of vacuum fluctuations and radiation reaction to the level shift. It is found that the energy level shift of the excited state is an oscillating function of the atom＇s distance from the boundary and it can either be positive or negative, while that of the ground state is always positive. The most remarkable feature is that the energy level shift of the ground state behaves like 1/z^4 when the atom＇s distance from the boundary, z, is very large as compared to the transition wavelength of the atom, while it behaves like 1/z^3 when z is very small     

Inversion of an Atomic Wave Packet in a Circularly Polarized Electromagnetic Wave

We study behavior of an atomic wave packet in a circularly polarized electromagnetic wave,and particularly calculate the atomic inversion of the wave packet.A general method of calculation is presented.The results are interesting.For example,if the wave packet is very narrow or /and the interaction is very strong,no matter the atom is initially in its ground state or excited state,the atomic inversion approaches zero as time approaches infinity.If the atom is initially in its ground state and excited state with the probability 1/2 respectively,and if the momentum density is an even function,then the atomic inversion equals zero at any time.     

Role of the dressed and bound states on below-threshold harmonic generation of He atom

High-order harmonic generation below ionization threshold of He atom in the laser field is investigated by solving the three-dimensional time-dependent Schro¨dinger equation. An angular momentum-dependent model potential of He atom was used for getting the accurate energy levels of singlet states. The satellite-peak structures of the below-threshold harmonic generation(BTHG) of He are observed. We analyze the emission properties of the BTHG by employing a synchrosqueezing transform technique. We find that the satellite-peak structures have two types related to two kinds of transitions. One is the transition of the dressed states of the excited states, the other is the transition between the excited states and the ground state in the field-free case. Furthermore, our results show that the maximum Stark shift of the 2 p state is about 0.9 U_p(penderomotive energy), and that of the 4 p state is about 1.0 U_p. It indicates that the energy difference between some satellite-and main-peaks of the BTHG can be used to measure the maximum Stark shift of the excited states of He atom in the laser field.     

Coexisting Condensates of Weakly Interacting Bose Gas in a Harmonic Trap

We study particles in a vortex state driven to a core state with lower energy and zero angular momentum by the trap potential asymmetries. We find that at T=0 when the role of the thermal gas can be ignored, there will be coexisting condensates. We also calculate the fluctuation of the number difference and argue that in certa/n range of the parameters the state of the whole system is the macroscopic quantum serf-trapping in the Josephson tunnelling regime.     

Quantum—Confined Stark Effect of Vertically Stacked Self—Assembled Quantum Discs

We study the electronic energy levels and probability distribution of vertically stacked self-assembled InAs quantum discs system in the presence of a vertically applied electric field. This field is found to increase the splitting between the symmetric and antisymmetric levels for the same angular momentum. The field along the direction from one disc to another affects the electronic energy levels similarly as that in the opposite direction because the two discs are identical. It is obvious from our calculation that the probability of finding an electron in one disc becomes larger when the field points from this disc to the other one.     

Influence of multi-photon excitation on the atomic above-threshold ionization

Using the time-dependent pseudo-spectral scheme, we solve the time-dependent Schr ¨odinger equation of a hydrogenlike atom in a strong laser field in momentum space. The intensity-resolved photoelectron energy spectrum in abovethreshold ionization is obtained and further analyzed. We find that with the increase of the laser intensity, the abovethreshold ionization emission spectrum exhibits periodic resonance structure. By analyzing the population of atomic bound states, we find that it is the multi-photon excitation of bound state that leads to the occurrence of this phenomenon, which is in fairly good agreement with the experimental results.     

Rotational symmetry of classical orbits, arbitrary quantization of angular momentum and the role of the gauge field in two-dimensional space

We study quantum–classical correspondence in terms of the coherent wave functions of a charged particle in two- dimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level space of angular momentum being greater or less than is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily 2π-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The well-known quantum mechanical anyon model becomes a special case of the arbitrary quantization, where the classical orbits are 2π-periodic.     

Propagation properties of electromagnetic fields in elliptic dielectric hollow fibres and their applications

We numerically calculate and analyse the electromagnetic fields, optical intensity distributions, polarization states and orbital angular momentum of some elliptic hollow modes in an elliptic dielectric hollow fiber (EDHF) by using Mathieu functions, and also calculate the optical potential of the blue-detuned _eHE₁₁ mode evanescent-light wave for ⁸⁵Rb atoms, including the position-dependent van der Waals potential, and discuss briefly some potential applications of our EDHF in atom and molecule optics, etc. Our study shows that the vector electric field distributions of the odd modes in the cross section of the EDHF are the same as that of the even modes and with different boundary ellipses by rotating an angle of π/2, and the orbital angular momentum (OAM) of single HE (EH) mode is exactly equal to zero, while that of dual-mode in the EDHF is fractional in h, and has a sinusoidal oscillation as z varies. The EDHF can be used to produce various elliptic hollow beams, even to generate and study various atomic vortices with a fractional charge and its fractional quantum Hall effect in atomic Bose--Einstein condensate, and so on.     

Dipole Oscillation in a Bose–Fermi Superfluid Mixture of ~(41)K and ~6Li

We study the relation between the bosonic frequency shift of a dipole oscillation and the fermionic compressibility in a Bose-Fermi super fluid mixture. Our results show that the A transition occurs in such a system, which interprets the perplexing phenomenon observed in the recent experiment [arXiv:1705.04496]. In that experiment,the frequency shift of the bosonic gas was measured with different fermion-fermion s-wave scattering lengths af. The most striking feature of their measurement is that the frequency shift shows a puzzling non-monotonic behavior around 1/kFaf(?)-0.2 with k_F being the Fermi momentum. In the present work, the relation between the bosonic frequency shift and the compressibility of the Fermi gas is revealed by means of the equation of state of the super fluid mixture. Making use of the relation, we find that the compressibility of Fermi gas shows a ∧-like shape around 1/k_Faf(?)-0.2. We would like to stress that no free parameter is used in our calculation and our results can be further testified in a future experiment.     

Standing Shocks in Viscous Accretion Flows around Black Holes

We study the problem of standing shocks in viscous accretion flows around black holes. We parameterize such a flow with two physical constants, namely the specific angular momentum accreted by the black hole j and the energy quantity K. By providing the global dependence of shock formation in the j - K parameter space, we show that a significant parameter region can ensure solutions with shocks of different types, namely Rankine-Hugoniot shocks, isothermal shocks, and more realistically, mixed shocks.     

Sub-Half-Wavelength Atom Localization via Coherent Control of Autler-Townes Spontaneous Spectrum

We show that it is possible to localize an atom in a half-wavelength region by relaxing the strict condition that the atom is prepared in a specific excited state as in the recently proposed scheme [Phys. Rev. A 65 （2002） 043819]. In particular, we consider a four-level atom, for which a weak exciting field transfers population from the ground state to the excited state and three control fields （one standing-wave field while two travelling-wave fields） couple the excited state and two auxiliary states. By tuning the exciting field and by varying the collective phase of the control fields, the atom is localized in one of the two half-wavelength regions with 50% detecting probability. The main advantage of the scheme is the experimental accessibility and controllability.     

Energy and rotation-dependent stereodynamics of H(~2S) + NH(a~1?) → H_2(X~1Σ_g~+) + N(~2D) reaction

Quasi-classical trajectory calculations are performed to study the stereodynamics of the H(~2S) + NH(a~1?) →H_2(X~1Σ_g~+) + N(~2D) reaction based on the first excited state NH_2(1~2A') potential energy surface reported by Li et al.[Li Y Q and Varandas A J C 2010 J. Phys. Chem. A 114 9644] for the first time. We observe the changes of differential cross-sections at different collision energies and different initial reagent rotational excitations. The influence of collision energy on the k–k' distribution can be attributed to a purely impulsive effect. Initial reagent rotational excitation transforms the reaction mechanism from insertion to abstraction. The effect of initial reagent rotational excitations on k–k' distribution can be explained by the rotational excitation enlarging the rotational rate of reagent NH in the entrance channel to reduce the probability of collision between incidence H atom and H atom of target molecular. We also investigate the changes of vector correlations and find that the rotational angular momentum vector j' of the product H_2 is not only aligned, but also oriented along the y axis. The alignment parameter, the disposal of total angular momentum and the reaction mechanism are all analyzed carefully to explain the polarization behavior of the product rotational angular moment.     

Above-threshold ionization of hydrogen atom in chirped laser fields

Above-threshold ionization(ATI) of a hydrogen atom exposed to chirped laser fields is investigated theoretically by solving the time-dependent Schr o¨dinger equation. By comparing the energy spectra, the two-dimensional momentum spectra, and the angular distributions of photoelectron for the laser pulses with different chirp rates, we show a very clear chirp dependence both in the multiphoton and tunneling ionization processes but no chirp dependence in the single-photon ionization. We find that the chirp dependence in the multiphoton ionization based ATI can be attributed to the excited bound states. In the single-photon and tunneling ionization regimes, the electron can be removed directly from the ground state and thus the excited states may not be very important. It indicates that the chirp dependence in the tunneling ionization based ATI processes is mainly due to the laser pulses with different chirp rates.     

Magnetism and piezoelectricity of hexagonal boron nitride with triangular vacancy

First-principle calculations reveal that the configuration system of hexagonal boron nitride(h-BN) monolayer with triangular vacancy can induce obvious magnetism, contrary to that of the nonmagnetic pristine boron nitride monolayer.Interestingly, the h-BN with boron atom vacancy(VB-BN) displays metallic behavior with a total magnetic moment being 0.46μ_B per cell, while the h-BN with nitrogen atom vacancy(VN-BN) presents a half-metallic characteristic with a total magnetic moment being 1.0μ_B per cell. Remarkably, piezoelectric stress coefficient e_(11) of the VN-BN is about 1.5 times larger than that of pristine h-BN. Furthermore, piezoelectric strain coefficient d_(11)(12.42 pm/V) of the VN-BN is 20 times larger than that of pristine h-BN and also one order of magnitude larger than the value for the h-MoS_2 monolayer, which is mainly due to the spin-down electronic state in the V_N-BN system. Our study demonstrates that the nitrogen atom vacancies can be an efficient route to tailoring the magnetic and piezoelectric properties of h-BN monolayer, which have promising performances for potential applications in nano-electromechanical systems(NEMS) and nanoscale electronics devices.