Measuring Loschmidt echo via Floquet engineering in superconducting circuits

The Loschmidt echo is a useful diagnostic for the perfection of quantum time-reversal process and the sensitivity of quantum evolution to small perturbations. The main challenge for measuring the Loschmidt echo is the time reversal of a quantum evolution. In this work, we demonstrate the measurement of the Loschmidt echo in a superconducting 10-qubit system using Floquet engineering and discuss the imperfection of an initial Bell-state recovery arising from the next-nearest-neighbor (NNN) coupling present in the qubit device. Our results show that the Loschmidt echo is very sensitive to small perturbations during quantum-state evolution, in contrast to the quantities like qubit population that is often considered in the time-reversal experiment. These properties may be employed for the investigation of multiqubit system concerning many-body decoherence and entanglement, etc., especially when devices with reduced or vanishing NNN coupling are used.     

基于分数阶傅立叶变换的线性调频回波参数估计

本文提出了一种适用于宽带线性调频回波的分数阶傅立叶变换参数估计方法。它通过寻找合适的信号代替发射信号做模版,使得模版信号与接收信号的模糊函数匹配度高,峰值尖锐,失真率低。再利用分数阶傅立叶变换与模糊函数的关系,使用两次分数阶域的峰值搜索代替原有的一次二维搜索降低计算量。仿真实验结果表明,本文提出的方法在精确估计宽带回波的时延和频移的同时降低了计算复杂度。     

基于LabVIEW激光引信回波模拟装置设计

激光引信回波模拟装置是激光引信测试设备的重要组成部分。介绍了激光引信回波模拟装置的组成,设计了用于该装置的硬件电路和软件控制系统。硬件电路采用单片机完成控制指令的接收和控制信号的产生,使用串行扩展芯片GM8125将单片机AT89S52的串行口扩展成5个,满足了激光引信回波模拟装置串口资源要求。软件控制系统基于LabVlFⅣ设计,主要包括串口通信程序和控制指令的产生程序,控制指令经串口通信传送给硬件电路。实验结果表明,该装置满足激光引信测试设备的要求。     

Electromagnetically induced transparency and evolution of a two-level system under chaotic field of arbitrary intensity

The electromagnetically induced transparency (EIT) with a (near-)resonant chaotic (amplitude-phase fluctuating, Gaussian-Markovian) coupling field is studied theoretically. The Fourier transform of the steady-state EIT spectrum, which determines a nonstationary probe absorption, is also considered. This quantity equals the average diagonal element of the (reduced) evolution operator of the coupled transition (the evolution function). The exact solution in the form of a continued fraction is obtained and used to perform numerical calculations. Moreover, a number of approximate analytical results are obtained, which, together with the results of previous publications, describe the EIT and the evolution function in all possible regimes. In particular, in the constructive-interference case the EIT increases with the coupling-field bandwidth ν at sufficiently small ν. For a strong field, the maximum of the transparency as a function of ν is less than that for a monochromatic field of the same average intensity. In contrast, for a weak field, there is a range of ν values, where the field fluctuations do not affect the EIT. The latter result is shown to hold for a broad class of stochastic fields. Received 31 December 2000 and Received in final form 14 May 2001     

Mathematical Models for Unstable Quantum Systems and Gamow States

We review some results in the theory of non-relativistic quantum unstable systems. We account for the most important definitions of quantum resonances that we identify with unstable quantum systems. Then, we recall the properties and construction of Gamow states as vectors in some extensions of Hilbert spaces, called Rigged Hilbert Spaces. Gamow states account for the purely exponential decaying part of a resonance; the experimental exponential decay for long periods of time physically characterizes a resonance. We briefly discuss one of the most usual models for resonances: the Friedrichs model. Using an algebraic formalism for states and observables, we show that Gamow states cannot be pure states or mixtures from a standard view point. We discuss some additional properties of Gamow states, such as the possibility of obtaining mean values of certain observables on Gamow states. A modification of the time evolution law for the linear space spanned by Gamow shows that some non-commuting observables on this space become commuting for large values of time. We apply Gamow states for a possible explanation of the Loschmidt echo.     

Propagation of shape-preserving optical pulses in inhomogeneously broadened multi-level systems

We study stable propagation of multiple shape-preserving optical pulses in an inhomogeneously broadened multi-level atomic medium. By analytically solving the Maxwell-Schr?dinger equations governing the evolution of N coupled optical fields and atomic amplitudes we show that N pulsed optical waves coupling to (N+1)-levels can be automatically matched with the same soliton waveform and identical yet very slow propagation velocity. Several sets of coupled soliton solutions for two different (N+1)-level models are given and their stability is studied by using a numerical simulation.     

随机电报过程引起的光失相的计算

本文计算了红宝石中Al核自旋跳变引起的R₁[⁴A₂(S=-3/2)→²E(S=-1/2)]回波衰减。用随机电报过程描述每个Al核自旋(i)跳变引起Cr共振频率的起伏Δi,这个过程对光子回波衰减的贡献〈E_i(t₂₁)〉可以用解析式表示。首先计算核自旋(i)跳变的总速率Wi及它引起的Δi,求出〈E_i(t₂₁)〉。设对Cr光失相起主要贡献的每个Al核自旋跳变近似是独立的,所以总的回波强度是所有Al引起的〈E_i(t)₂₁〉的乘积。计算得到非指数的回波衰减,以I=I₀exp〔-(4t/t_m)^x〕拟合,x=2.56,t_m=50.6μs,与实验及计算机模拟的结果一致.     

Influence of Reversible and Irreversible Relaxation on the Single-Pulse Echo Signal

An analytical expression for a signal of the single-pulse echo generated in nonresonant pulse excitation of an inhomogeneously broadened two-level quantum system has been obtained, with the reversible and irreversible relaxation taken into account. It is shown that the rate of decay of the single-pulse echo is determined by the rate of reversible and irreversible transverse relaxation. It has been established that the contribution of the reversible and irreversible relaxations to decay of the single-pulse echo depends on the ratio between the detuning of the pulse-carrying frequency from resonance to the Rabi frequency. The difference between the times of transverse irreversible relaxation measured in manganese ferrite MnFe₂O₄ by the methods of single and two-pulse echo of nuclear magnetic resonance has been explained within the framework of the theoretical expressions obtained.