Self—Trapping State and Atomic Tunnelling Current of an Atomic Bose—Einstein Condensate Interacting with a Laser Field in a Double—Well Potential

We present a theoretical treatment of dynamics of an atomic Bose-Einstein condensation interacting with a single-mode quantized travelling-wave laser field in a double-well potential.When the atom-field system is initially in a coherent state,expressions for the energy exchange between atoms and photons are derived.It is revealed that atoms in the two wells can be in a self-trapping state when the tunnelling frequency satisfies two specific conditions,in which the resonant and far off-resonant cases are included.It is found that there is an alternating current with two different sinusoidal oscillations between the two wells,but no dc characteristic of the atomic tunnelling current occurs.It should be emphasized that when without the laser field,both the population difference and the atomic tunnelling current are only a single oscillation.But they will respectively become a superposition of two oscillations with different oscillatory frequencies in the presence of the laser field.For the two oscillations of the population difference,one always has an increment in the oscillatory frequency,the other can have an increment or a decrease under different cases.These conclusions are also suitable to those of the atomic tunnelling current.As a possible application,by measurement of the atomic tunnelling current between the two wells,the number of Bose-condensed atoms can be evaluated.By poperly selecting the laser field,the expected atomic tunnelling current can be obtained too.     

薛定谔猫态光场与二能级原子相互作用系统的量子特性

在非旋波近似下,通过采用相干态正交化展开的方法,研究了薛定谔猫态光场与二能级原子相互作用系统中,原子的布局数和光场的反聚束效应,并与旋波近似下的结果进行了对比.在旋波近似与非旋波近似下,讨论了初始光场强度、相干态间的相位角以及失谐量对原子布局数和光场反聚束效应的影响;在非旋波近似下,讨论了强弱耦合情况下光场的反聚束效应.研究结果表明:旋波近似与非旋波近似下,原子的布局数随着初始光场强度的不同,表现出不同的特性;当初始光场强度较小时,旋波近似与非旋波近似下,原子的布局数表现出相同的特性;随着初始光场强度的增大,旋波近似下,原子的布局数将表现出坍塌现象.耦合强度较大时,光场的聚束与反聚束效应在非旋波近似与旋波近似下有较大的区别;非旋波近似下,随着初始光场强度的增大,光场一直处于聚束效应状态;而旋波近似下,光场的聚束效应与反聚束效应交替出现.     

Influence of External Magnetic Fields on Tunneling of Spin-1 Bose Condensate

In this letter, we have studied the influence of the external magnetic fields on tunneling of the spin-1 Bose condensate. We find that the population transfer between spin-0 and spin-±1 exhibits the step structure under the external cosinusoidal magnetic field and a combination of static and cosinusoidal one, respectively. Compared with the longitudinal component of the external magnetic field, the smaller the transverse component of the magnetic field is, the larger the time scale of exhibiting the step structure does. The tunneling current may exhibit periodically oscillation behavior when the ratio of the transverse component of the magnetic field is smaller than that of the longitudinal component, otherwise it exhibits a damply oscillating behavior. This means that the dynamical spin localization can be adjusted by the external magnetic fields.     

Effects of traps on dynamics of two coupled Bose-Einstein condensates

Effects of the traps are investigated on the dynamics of two coupled Bose-Einstein condensates, and the atom population transfer between the two condensates is discussed. It is found that the traps and the initial condition determine the switching and self-trapping effects on the atom population imbalance. There are the critical potential amplitude and the critical potential width, by which the oscillation manner of the population transferring ratio can be analyzed as time changes.     

Quantum Correlation of Many Atoms in Spinor Bose-Einstein Condensates

In this letter, we have studied sub-Poissonian distributions and quantum correlation of atoms in spinor Bose-Einstein condensates. It is found that there exists the sub-Poissonian distributions for spin-1 and spin-(-1) components, respectively. There may exist the violation of the Cauchy-Schwartz inequality. For the same atomic numbers, the regions that include violation of the Cauchy-Schwartz inequality will shift rightwards with the increment of the Rabi frequency, whereas for the same Rabi frequency, the regions will shift leftwards with the increment of the atomic numbers.     

Bloch oscillation and Landau\ben Zener tunnelling in a modulated optical lattice in a photovoltaic photorefractive crystal

We theoretically study the beam dynamical behaviour in a modulated optical lattice with a quadratic potential in a photovoltaic photorefractive crystal.We find that two different Bloch oscillation patterns appear for the excitation of both broad and narrow light beams.One kind of optical Landau–Zener tunnelling also appears upon the Bloch oscillation and can be controlled by adjusting the parameter of the optical lattice.Unlike the case of linear potential,the energy radiation due to Landau–Zener tunnelling can be confined in modulated lattices of this kind.For high input intensity levels,the Landau–Zener tunnelling is suppressed by the photovoltaic photorefractive nonlinearity and a symmetry breaking of beam propagation from the modulational instability appears.     

Arbitrary quantum superposition state for three-level system using oscillating dark states

An method for adiabatic population transfer and the preparation of an arbitrary quantum superposition state using the oscillating dark states (ODS) in atomic system is presented. Quantum state of a three-level Λ configuration atomic system finally evolves into the same time-dependent state, and oscillates periodically between two ground levels under evolving adiabatic conditions when two pairs of classical detuning laser fields drive the system into the ODS forcedly, whatever the initial states of the system are. The decoherence of the ODS evolution is greatly suppressed and the oscillation is very stable, therefore adiabatic population transfer and the preparation of an arbitrary quantum superposition state of atomic system can be completed accurately and conveniently.     

Exploring ground states and excited states of spin-1 Bose–Einstein condensates by continuation methods

A pseudo-arclength continuation method (PACM) is employed to compute the ground state and excited state solutions of spin-1 Bose–Einstein condensates (BEC). The BEC is governed by the time-independent coupled Gross–Pitaevskii equations (GPE) under the conservations of the mass and magnetization. The coupling constants that characterize the spin-independent and spin-exchange interactions are chosen as the continuation parameters. The continuation curve starts from a ground state or an excited state with very small coupling parameters. The proposed numerical schemes allow us to investigate the effect of the coupling constants and study the bifurcation diagrams of the time-independent coupled GPE. Numerical results on the wave functions and their corresponding energies of spin-1 BEC with repulsive/attractive and ferromagnetic/antiferromagnetic interactions are presented. Furthermore, we reveal that the component separation and population transfer between the different hyperfine states can only occur in excited states due to the spin-exchange interactions.     

Atomic Tunneling Effect in Two-Component Bose-Einstein Condensates with a Coupling Drive

In this paper, we have studied the atomic population difference and the atomic tunneling current of twocomponent Bose-Einstein condensates with a coupling drive. It is found that when the two-component Bose-Einstein condensates are initially in the coherent states, the atomic population difference may exhibit the step structure, in which the numbers of the step increase with the decrease of the Rabi frequency and with the increment of the initial phase difference. The atomic population difference may exhibit collapses, and revivals, in which their periods are affected dramatically by the Rabi frequency and the initial phase difference. The atomic tunneling current may exhibit damping oscillation behaviors, and exist the step structure for the time range of 10-10 ～ 10-9 second.     

Momentum Transfer and Effect of Motion of Atomic Mass Centre on an Atom-Cavity System

For a special ∧-type atom with dark state, the problem of momentum transfer is discussed in detail. Effect of moving mass centre on atomic dynamics for various initial conditions is also studied. The numerical results show that the Doppler effect exercised by the motion of atomic mass centre can lead to the modified phenomenon of oscillation collapse and revival in the transition probability and the atomic population inversion.     

Loschmidt echo near a dynamical phase transition in a Bose-Einstein condensate

We show that the quantum Loschmidt echo can be employed to characterize the dynamical phase transition, from a tunnelling phase to a self-trapping phase, of a Bose-Einstein condensate in a double-well potential. The echo is found to have a relatively fast decay in the transition region, with a Gaussian decay in the self-trapping phase and a stretched exponential decay in the tunnelling phase.     

双模压缩真空场与Λ型三能级原子非共振作用

研究了双模压缩真空场与Λ型三能级原子非共振相互作用系统中,场模失谐量对原子布居概率和光场的双模互关联函数、二阶相干度的影响.结果表明：失谐量使原子Rabi振荡呈现周期性崩塌与复苏现象；当光场初始压缩因子r较小时,失谐量将削弱光子的反聚束效应；当r较大时,失谐量又将增强光场两模相关的稳定性.     

Phases of a polar spin-1 Bose gas in a magnetic field

The two Bose–Einstein condensed phases of a polar spin-1 gas at nonzero magnetizations and temperatures are investigated. The Hugenholtz–Pines theorem is generalized to this system. Crossover to a quantum phase transition is also studied. Results are discussed in a mean field approximation.     

Quantum Phase Transition and Ferromagnetic Spin Correlation in Parallel Double Quantum Dots

We investigate electronic transport through a parallel double quantum dot （DQD） system with strong on-site Coulomb interaction, as well as the interdot tunnelling. By applying numerical renormalization group method, the ground state of the system and the transmission probability at zero temperature are obtained. For a system of quantum dots with degenerate energy levels and small interdot tunnel coupling, the spin correlations between the DQDs is ferromagnetic, and the ground state of the system is a spin-1 triplet state. The linear conductance will reach the unitary limit （2e^2/h） due to the Kondo effect at low temperature. As the interdot tunnel coupling increases, there is a quantum phase transition from ferromagnetic to anti-ferromagnetic spin correlation in DQDs and the linear conductance is strongly suppressed.     

Sub-Angstrom oscillation amplitude non-contact atomic force microscopy for lateral force gradient measurement

We report the first results from novel sub-Angstrom oscillation amplitude non-contact atomic force microscopy developed for lateral force gradient measurements. Quantitative lateral force gradients between a tungsten tip and Si(1 1 1)-(7 × 7) surface can be measured using this microscope. Simultaneous lateral force gradient and scanning tunnelling microscope images of single and multi atomic steps are obtained. In our measurement, tunnel current is used as feedback. The lateral stiffness contrast has been observed to be 2.5 N/m at single atomic step, in contrast to 13 N/m at multi atomic step on Si(1 1 1) surface. We also carried out a series of lateral stiffness-distance spectroscopy. We observed lateral stiffness-distance curves exhibit sharp increase in the stiffness as the sample is approached towards the surface. We usually observed positive stiffness and sometimes going into slightly negative region.     

Phase separation in the trapped spinor gases with anisotropic spin-spin interaction

We investigate the effect of the anisotropic spin-spin interaction on the ground state density distribution of the one dimensional spin-1 bosonic gases within a modified Gross-Pitaevskii theory both in the weakly interaction regime and in the Tonks-Girardeau (TG) regime. We find that for ferromagnetic spinor gas the phase separation occurs even for weak anisotropy of the spin-spin interaction, which becomes more and more obvious and the component of m_F=0 diminishes as the anisotropy increases. However, no phase separation is found for anti-ferromagnetic spinor gas in both regimes.     

Nonlinear Landau--Zener Tunnelling with Two and Three-Body Interactions

We investigate the nonlinear Landau-Zener tunnelling of Bose-Einstein condensate （BEC） in an accelerating optical lattice with two- and three-body interactions between the particles. The influence of the three-body interaction on the eigenstates and the transition probability are discussed both anaJytically and numerically. The analytical eigenstates and the tunnelling probability are obtained, which are verified by numerical methods. It is shown that the eigenstates and the tunnelling probability are modified dramatically by three-body interaction.     

Coherent states and quantum oscillations of BEC-BCS systems

We show by using the mean-field approximation that the states of composite Fermi-Bose superfluids created in cold-atom traps via a Feshbach resonance at zero temperature are generalized SU(2)⊗SU(1,1) coherent states. In response to a sudden change of the interaction between fermionic atoms and bosonic molecules, a Cooper pair can exhibit collapse and revival quantum behaviors for an initial generalized coherent state of molecules, and Rabi oscillation for a vacuum molecular state. Occurrence of the collapse and revival phenomenon is thus the manifestation of the formation of the Bose-Einstein condensate.     

Mesoscopic samples: the superconducting condensate via the Gross-Pitaevskii scenario

Mesoscopic superconductors are routinely investigated with the Ginzburg-Landau equations, whereby the confinement is taken into account by imposing that the normal component of the superconducting current vanishes through the sample boundary. We argue that this approach gives misleading results when applied to micron- and submicron-sized devices, and we introduce modified Ginzburg-Landau equations that take the confinement potential into account on the level of the free energy functional. For devices much larger than the Ginzburg-Landau coherence length, both approaches agree, but deviations appear for samples of the scale of the coherence length. In the absence of a magnetic field, the modified Ginzburg-Landau equation for the order parameter reduces to the Gross-Pitaevskii equation.     

Study of Nonclassical Features and Quantum Dynamics in the Jaynes-Cummings Model

Some nonclassical features, including photon antibunching, atomic squeezing and quantum collapse-revival phenomenon, were numerically studied in thp vacuum field Jaynes-Cummings model (JCM). The influence of the initial atomic coherence on these features was discussed. It is shown that the squeezing can appear only if the atom is initiaJly prepared in the coherent state, and photon antibunching cHn occur if the atom is initially in the excited state or the coherent one. The effect of the virtual-photon field was studied in JCM without the rotating-wave approximation (ftWA). We have shown that even undh the condition in which RWA is considered to be valid, there are significant effects on the nonc1assical features due to the interference between the virtual-photon processes and the real-photon processes. Quantum dynamics of JCM without RWA was aJso studied. We showed that regular dynamical behavior is exhibited in the cases rather close to the integrable limits, and irregular dynamical behavior is presented in the cases far from the integrable limits; in addition, all the nondassical features disappear in the cases far from the integrable limits.