Quantum measurement of single electron state by a quantum point contact

Closely related to the quantum information processing in solid states, we study the quantum measurement of single electron state by a mesoscopic charge-sensitive detector, namely the quantum point contact (QPC). We find that the conventional Lindblad-type master equation is not appropriate for describing the underlying measurement dynamics. The treatment developed in this work properly accounts for the energy-exchange between the detector and the measured system, and its role on the detailed-balance relation. A valid description for the QPC measurement dynamics is provided which may have impact on the study of quantum measurement and quantum feedback control in solid states.

Quantum measurement of an electron in a disordered potential: Delocalization versus measurement voltages

Quantum point contact (QPC), one of the typical mesoscopic transport devices, has been suggested to be an efficient detector for quantum measurement. In the context of two-state charge qubit, our previous studies showed that the QPC's measurement back-action cannot be described by the conventional Lindblad quantum master equation. In this work, we study the measurement problem of a multistate system, say, an electron in disordered potential, subject to the quantum measurement of the mesoscopic detector QPC. The effect of measurement back-action and the detector's readout current are analyzed, where particular attention is focused on some new features and the underlying physics associated with the measurement-induced delocalization versus the measurement voltages.

Solid-state qubit measurement with single electron transistors

In this paper we consider the continuous weak measurement of a solid-state qubit by single electron transistors (SET). For single-dot SET, we find that in nonlinear response regime the signal-to-noise ratio can violate the universal upper bound imposed quantum mechanically on any linear response detectors. We understand the violation by means of the cross-correlation of the detector currents. For double-dot SET, we discuss its robustness against wider range of temperatures, quantum efficiency, and the relevant open issues unresolved.

Quantum Measurement of Single Electron State by a Mesoscopic Detector

A realistic measurement setup for a system such system measured by a mesoscopie detector,is theoretically as a charged two-state （qubit） or multi-state quantum studied. To properly describe the measurement-induced back-action,a detailed-balance preserved quantum master equation treatment is developed. The established framework is applicable for arbitrary voltages and temperatures.

Neutron and proton diffusion in fusion reactions for the synthesis of superheavy nuclei

The restriction of the one dimensional (1D) master equation (ME) with the mass number of the projectile-like fragment as a variable is studied, and a two-dimensional (2D) master equation with the neutron and proton numbers as independent variables is set up, and solved numerically. Our study showed that the 2D ME can describe the fusion process well in all projectile-target combinations. Therefore the possible channels to synthesize super-heavy nuclei can be studied correctly in wider possibilities. The available condition for employing 1D ME is pointed out.

Formation of superheavy nuclei in cold fusion reactions

Within the concept of the dinuclear system (DNS), a dynamical model is proposed for describing the formation of superheavy nuclei in complete fusion reactions by incorporating the coupling of the relative motion to the nucleon transfer process. The capture of two heavy colliding nuclei, the formation of the compound nucleus, and the de-excitation process are calculated by using an empirical coupled channel model, solving a master equation numerically and applying statistical theory, respectively. Evaporation residue excitation functions in cold fusion reactions are investigated systematically and compared with available experimental data. Maximal production cross sections of superheavy nuclei in cold fusion reactions with stable neutron-rich projectiles are obtained. Isotopic trends in the production of the superheavy elements Z=110, 112, 114, 116, 118, and 120 are analyzed systematically. Optimal combinations and the corresponding excitation energies are proposed.

Study of the mechanism for synthesizing superheavy nuclei based on dinuclear system

Based on the concept of dinuclear system, considering the strong competition between fusion and quasiffision processes, by solving the master equation numerically to calculate the fusion probability of superheavy nuclei, we have estimated the excitation functions for the reactions Ti-50, Fe-58 + Pb-208, Bi-209, and the experimental data are basically reproduced. For different incident energies and different angular momentum, the effects on fusion and survival probability and the contribution to evaporation residue cross section have been given. These results help to further understand the mechanism for, synthesizing superheavy nuclei.

Isotopic dependence of production cross sections of superheavy nuclei in hot fusion reactions

The dinuclear system model has been further developed by introducing the barrier distribution function method in the process of heavy-ion capture and fusion to synthesize superheavy nuclei. The capture of two colliding nuclei, formation and de-excitation process of compound nucleus are decribed by using empirical coupled channel model, solving master equation numerically and statistical evaporation model, respectively. Within the framework of the dinuclear system model, the fusion-evaporation excitation functions of the systems Ca-48(Am-243, 3n-5n) (288-286)115 and Ca-48(Cm-248, 3n-5n)(293-291)116 are calculated, which are used for synthesizing new superheavy nuclei at Dubna in recent years. Isotopic dependence of production cross sections with double magic nucleus Ca-48 bombarding actinide targets U, Np, Pu, Am, Cm to synthesize superheavy nuclei with charged numbers Z=112-116 is analyzed systematically. Based on these analysis, the optimal projectile-target combination and the optimal excitation energy are proposed. It is shown that shell correction energy and neutron separation energy will play an important role on the isotopic dependence of production cross sections of superheavy nuclei.

Study of mass distributions of quasifission products based on dinuclear system

In the concept of dinuclear system, the quasifission rate from Kramers formula has been incorporated in the master equation in order to study the competition between fusion and qusifission. Mass yields of quasifission products of the three reactions Ca-48 + Pu-244, Ca-48 + U-238 and Fe-58 + Th-232 have been calculated, and the experimental data are reproduced very well, which is a critical test for the existing fusion model. Also we have shown the time evolution of the mass distributions of quasifission products, which provides valuable information of the process of competition between fusion and quasifission.

The influence of nuclear orientation in fusion dynamics

Fusion barriers have been calculated for different orientations of the axial symmetry axis of deformed projectile-and target-nucleus. Using the concept of dinuclear system, considering the strong competition between fusion and quasifission processes, by solving the master equation numerically to calculate the fusion probability of superheavy nuclei, we have estimated the dependence of the fusion probabilities for Ge-76 + Pb-208 and Ca-48 + Pu-244 on the orientation angles of the symmetry axis of projectile-and target-nucleus, which shows that belly-belly is the most favorable orientation for synthesizing superheavy nuclei.

Particle transfer and fusion cross-section for super-heavy nuclei in dinuclear system

Within the dinuclear system (DNS) conception, instead of solving the Fokker-Planck equation (FPE) analytically, the master equation is solved numerically to calculate the fusion probability of super-heavy nuclei, so that the harmonic oscillator approximation to the potential energy of the DNS is avoided. The relative motion concerning the energy, the angular momentum and the fragment deformation relaxations is explicitly treated to couple with the diffusion process. The nucleon transition probabilities, which are derived microscopically, are related with the energy dissipation of the relative motion. Thus they are time dependent. Comparing with the analytical solution of FPE at the equilibrium, our time-dependent results preserve more dynamical effects. The calculated evaporation residue cross-sections for one-neutron emission channel of Pb-based reactions are basically in agreement with the known experimental data within one order of magnitude.

Production cross sections of superheavy nuclei based on dinuclear system model

The barrier distribution function method is introduced in the dinuclear system model in the calculation of the transmission probability, which is the first stage in the synthesis of superheavy nuclei. Dynamical deformation and averaging collision orientations are considered in the calculation of the fusion probability by solving master equation numerically. Survival probability with respect to xn evaporation channel (x = 1-5) in the de-excitation process of the thermal compound nucleus is calculated, in which the level density of the Fermi-gas model is used. Production cross sections of a series of superheavy nuclei formed in the reactions taken magic and deformed nuclei as target in Ca-48 induced reactions are studied systematically. The calculated results are in good agreement with available experimental data. Isotopic dependence of the production cross sections in the reactions Ca-48 + Pu is analyzed.

Production of Superheavy Nuclei in Massive fusion reactions

A master equation is constructed to treat the nucleon transfer process in heavy ion fusion reactions to form superheavy nucleus. The relative motion concerning the energy, the angular momentum and the fragment deformation relaxations is explicitly treated to couple with the diffusion process. The nucleon transition probabilities, which are derived microscopically, are thus time dependent. The calculated evaporation residue cross-sections for both cold and hot fusion are in good agreement with the known experimental data.

Competing fusion and quasifission reaction mechanisms in the production of superheavy nuclei

Within the framework of a dinuclear system model, a new master equation is constructed and solved, which includes the relative distance of nuclei as a new dynamical variable in addition to the mass asymmetry variable so that the nucleon transfer, which leads to fusion and the evolution of the relative distance, which leads to quasifission (QF) are treated simultaneously in a consistent way. The QF mass yields and evaporation residual cross sections to produce superheavy nuclei are systematically investigated under this framework. The results fit the experimental data well. It is shown that the Kramers formula gives results of QF, which agree with those by our diffusion treatment, only if the QF barrier is high enough. Otherwise some large discrepancies occur.

超重核合成机制—包含中子、质子跃迁的二维主方程

用双核模型研究超重核的合成机制，最主要的部分是由双核系统演化到复合核的熔合机制研究。双核模型认为超重复合核的形成是由弹核的核子全部转移到靶核所致。核子分中子和质子，在以前的研究中，描述熔合过程的主方程是一维的，以类弹核的质量数 为变量，与此对应的驱动势也是一维的。对确定的 ，其同位旋的确定是由较低的势能面确定的，这样确定的同位旋与反应系统的同位旋很接近。但是我们的研究发现，对入射道同位旋与复合系统同位旋相差较大的情况，入射道在双核系统势能面比较高的位置，有时甚至在最高位置，这时核子转移的同位旋路径比较复杂，以致一维主方程的描述给出错误的结果。为此，建立了以类弹碎片中子数 和质子数 为变量的二维主方程，并建立了二维主方程的分步差分的解法，完成了解二维主方程的程序编写。并对一些典型的弹核、靶核同位旋与复合系统同位旋相差较大的系统进行了研究。对这些反应道的研究表明，无论1D主方程对这些反应道的蒸发剩余截面的研究给出了过高、或过低的估计，2D主方程都能给出与实验值一致地结果。二维主方程适用于所有的弹靶组合入射道。对确定的超重核目标，可以较准确的对各种弹靶组合的合成几率给出预言，特别是研究合成超重核的同位素依赖性，因而极大增加了预言合成预期超重岛区域超重核的弹靶组合的选择性。本工作还检验了一维主方程的适用条件：入射点必须在比较接近二维驱动势谷底时才适用，这时一维主方程预言的蒸发剩余截面的结果与二维主方程的结果很接近