R. V. Ramos, S. D. G. Martinz
In this work we show an analytical result for the scattering in a particular type of double quantum well triple barrier structure and numerical results, via the Numerov method, for bound states of a double quantum well triple barrier inside of a infinite quantum well. For the last, we consider both, constant and position dependent mass.
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We present a theoretical proposal of a tunable charge qubit, hosted in triple quantum dots. The manipulation is solely performed by changing the heights of the two potential barriers between the three dots, while the energy of all three dots are fixed. We have found that when the relative height of the two barriers are changed, the direction of the axis of rotation in performing single-qubit gates can be varied. On the other hand, the corresponding rotation speed can be tuned by raising or lowering the two barriers at the same time. Our proposal therefore allows for tunability of both the rota…
Transient tunneling effects in triple barrier systems are investigated by considering a time-dependent solution to the Schrödinger equation with a cutoff wave initial condition. We derive a two-level formula for incidence energies $E$ near the first resonance doublet of the system. Based on that expression we find that the probability density along the internal region of the potential, is governed by three oscillation frequencies: one of them refers to the well known Bohr frequency, given in terms of the first and second resonance energies of the doublet, and the two others, represent a coupli…
Collective charge measurement in quantum dot chains: controlling barrier occupation and tunneling current
本文研究了三量子点系统中的非平衡输运，通过量子点接触对所有三个量子点进行全局测量，发现这种测量方式对输运的影响不同于单点测量，并通过工程化相位失真显著提高了势垒占据和隧道电流，在强测量极限下，稳态与底层哈密顿量参数无关，合适的测量配置可使势垒占据接近1/2，识别出最优测量配置以最大化稳态电流，并展示简单中心点读出方案可实现近最优性能。
Approximate analytical bound state solutions of the radial Schrödinger equation are studied for a two-term diatomic molecular potential in terms of the hypergeometric functions for the cases where $q\geq1$ and $q=0$. The energy eigenvalues and the corresponding normalized wave functions of the Manning-Rosen potential, the 'standard' Hulthén potential and the generalized Morse potential are briefly studied as special cases. It is observed that our analytical results are the same with the ones obtained before.
The full set of resonant states in double and triple quantum well/barrier structures is investigated. This includes bound, anti-bound and normal resonant states which are all eigensolutions of Schrodinger's equation with generalized outgoing wave boundary conditions. The transformation of resonant states and their transitions between different subgroups as well as the role of each subgroup in observables, such as the quantum transmission, is analyzed. The quantum well potentials are modeled by Dirac delta functions; therefore, as part of this study, the well-known problem of bound states in de…
By using a usual instanton method we obtain the energy splitting due to quantum tunneling through the triple well barrier. It is shown that the term related to the midpoint of the energy splitting in propagator is quite different from that of double well case, in that it is proportional to the algebraic average of the frequencies of the left and central wells.
We analytically compute the time evolution of an initial infinite plane wave in the presence of a 1-dimensional square quantum barrier. This calculation generalizes the analysis of the shutter problem and sets the basis for the calculation of the transmission of general wave packets, aiming to work out the explicit contribution of the resonant (Gamow) states. The method relies mainly on the analytical properties of the Green function. The role of separate boundary conditions on the Green function and on the evolution equation is highlighted. As in previous works on related problems, only the d…
We investigate quantum tunneling of two repulsive bosons in a triple-well potential subject to a high-frequency driving field. By means of the multiple-time-scale asymptotic analysis, we evidence a far-resonant strongly-interacting regime in which the selected coherent destruction of tunneling can occur between the paired states and unpaired states, and the dominant tunneling of the paired states is a second order process. Two Floquet quasienergy bands of the both kinds of states are given analytically, where a fine structure up to the second order corrections is displayed. The analytical resu…
We investigate the optimal approximation to triple incompatible quantum measurements within the framework of statistical distance and joint measurability. According to the lower bound of the uncertainty inequality presented in [Physical Review A 99, 312107 (2019)], we give the analytical expressions of the optimal jointly measurable approximation to two kinds of triple incompatible unbiased qubit measurements. We also obtain the corresponding states which give the minimal approximation errors in measuring process. The results give rise to plausible experimental verifications of such statistica…
Analytical simulations of the resonant transmission of electrons in a closed nanocircuit for terahertz applications where a tunneling junction is shunted by a metallic nanowire
本文基于洛斯阿拉莫斯国家实验室的太赫兹谐波产生研究，提出由铍灯丝旁路的闭合量子纳米电路解析模型，通过求解薛定谔方程并构建四阶复矩阵方程，分析了矩形、三角形和delta函数等势垒参数对电子共振透射的影响。
The time evolution of plane waves in the presence of a 1-dimensional square quantum barrier is considered. Comparison is made between the cases of an infinite and a cut-off (shutter) initial plane wave. The difference is relevant when the results are applied to the analysis of the tunnelling regime. This work is focused on the analytical calculation of the time-evolved solution and highlights the contribution of the resonant (Gamow) states. PACS numbers: 11.10.Ef, 11.10.Lm, 04.60
The flux-flux correlation function formalism is a standard and widely used approach for the computation of reaction rates. In this paper we introduce a method to compute the classical and quantum flux-flux correlation functions for anharmonic barriers essentially analytically through the use of the classical and quantum normal forms. In the quantum case we show that the quantum normal form reduces the computation of the flux-flux correlation function to that of an effective one dimensional anharmonic barrier. The example of the computation of the quantum flux-flux correlation function for a fo…
We show that quantum Bateman's system which arises in the quantization of a damped harmonic oscillator is equivalent to a quantum problem with 2D parabolic potential barrier known also as 2D inverted isotropic oscillator. It turns out that this system displays the family of complex eigenvalues corresponding to the poles of analytical continuation of the resolvent operator to the complex energy plane. It is shown that this representation is more suitable than the hyperbolic one used recently by Blasone and Jizba.
We propose an analytical study of relativistic tunneling through opaque barriers. We obtain a closed formula for the phase time. This formula is in excellent agreement with the numerical simulations and corrects the standard formula obtained by the stationary phase method. An important result is found when the upper limit of the incoming energy distribution coincides with the upper limit of the tunneling zone. In this case, the phase time is proportional to the barrier width.
Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom
本文通过三个良好qLDPC码的同调积、Freedman-Hastings码到流形映射及三重杯积，构造出实现横向CCZ门且距离达Ω(N^{2/3})的量子码，突破√N距离障碍，可单次免蒸馏制备Θ(N^{1/3})个逻辑CCZ魔法态，并启发发现具有幂律Z₂收缩自由度的奇异流形族。
We study both classical and quantum algorithms to solve a hard optimization problem, namely 3-XORSAT on 3-regular random graphs. By introducing a new quasi-greedy algorithm that is not allowed to jump over large energy barriers, we show that the problem hardness is mainly due to entropic barriers. We study, both analytically and numerically, several optimization algorithms, finding that entropic barriers affect in a similar way classical local algorithms and quantum annealing. For the adiabatic algorithm, the difficulty we identify is distinct from that of tunnelling under large barriers, but …
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