S. Stenholm, K. -A. Suominen
We summarize the theoretical description of wave packets on molecular energy levels. We review the various quantum mechanical effects which can be studied and the models that can be verified on this system. This justifies our claim that the wave packet constitutes a universal quantum object.
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Based on the statistical concept of the median, we propose a quantum uncertainty relation between semi-interquartile ranges of the position and momentum distributions of arbitrary quantum states. The relation is universal, unlike that based on the mean and standard deviation, as the latter may become non-existent or ineffective in certain cases. We show that the median-based one is not saturated for Gaussian distributions in position. Instead, the Cauchy-Lorentz distributions in position turn out to be the one with the minimal uncertainty, among the states inspected, implying that the minimum-…
We investigate the time evolution of wave packets in systems with a mixed phase space where regular islands and chaotic motion coexist. For wave packets started in the chaotic sea on average the weight on a quantized torus of the regular island increases due to dynamical tunneling. This flooding weight initially increases linearly and saturates to a value which varies from torus to torus. We demonstrate for the asymptotic flooding weight universal scaling with an effective tunneling coupling for quantum maps and the mushroom billiard. This universality is reproduced by a suitable random matrix…
We present a universal physical picture for describing storage and retrieval of photon wave packets in a Lambda-type atomic medium. This physical picture encompasses a variety of different approaches to pulse storage ranging from adiabatic reduction of the photon group velocity and pulse-propagation control via off-resonant Raman fields to photon-echo based techniques. Furthermore, we derive an optimal control strategy for storage and retrieval of a photon wave packet of any given shape. All these approaches, when optimized, yield identical maximum efficiencies, which only depend on the optica…
According to the classical special theory of relativity any nonstationary system moving with velocity $v$ must evolve (e.g., decay) $1/γ$ times slower than the system at rest, $γ=(1-v^2)^{-1/2}$ (the Einstein retardation ER). Quantum mechanics allows one to calculate the evolution of both systems separately and to compare them thus verifying ER. It is shown here that ER is not valid for a simple system: the spreading packet of the free spinless particle. Earlier it was shown that ER does not hold for some other systems. So one may state that ER is not a universal kinematic law in quantum mecha…
The problem of wave packet tunneling from a parabolic potential well through a barrier represented by a power potential is considered in the case when the barrier height is much greater than the oscillator ground state energy, and the difference between the average energy of the packet and the nearest oscillator eigenvalue is sufficiently small. The universal Poisson distribution of the partial tunneling rates from the oscillator energy levels is discovered. The explicit expressions for the tunneling rates of different types of packets (coherent, squeezed, even/odd, thermal, etc.) are given in…
The paper is devoted to a numerical study of the problem of interaction of the wave packet with potential structures moving with constant acceleration. In all the cases considered the result of the interaction is a change in the velocity spectrum. In the first approximation the magnitude of the shift in the spectrum is determined by the product of acceleration by group delay time. Also, as the direction of acceleration reverses the effect changes its sign. The results are completely consistent with the idea of universality of the Effect of Acceleration which consists in a change in the frequen…
We present a scheme for universal quantum computing using XY Heisenberg spin chains. Information is encoded into packets propagating down these chains, and they interact with each other to perform universal quantum computation. A circuit using g gate blocks on m qubits can be encoded into chains of length $O(g^{3+δ} m^{3+δ})$ for all $δ>0$ with vanishingly small error.
Time evolution of wave packets built from the eigenstates of the Dirac equation for a hydrogenic system is considered. We investigate the space and spin motion of wave packets which, in the non-relativistic limit, are stationary states with a probability density distributed uniformly along the classical, elliptical orbit (elliptic WP). We show that the precession of such a WP, due to relativistic corrections to the energy eigenvalues, is strongly correlated with the spin motion. We show also that the motion is universal for all hydrogenic systems with an arbitrary value of the atomic number Z.
Optimal control for manipulating vibrational wave packets through polarizability interactions induced by non-resonant laser pulses
本文基于最优控制理论研究利用非共振激光脉冲诱导的极化率相互作用操控分子振动波包，针对I2的B态系统考察了选择性布居转移、波包整形和波包形变抑制三类目标，发现最优解为与振动动力学协同利用量子干涉的NR脉冲序列。
Large-scale quantum networks with thousands of nodes require scalable network protocols and physical hardware to realize. In this work, we introduce packet switching as a new paradigm for quantum data transmission in both future and near-term quantum networks. We propose a classical-quantum data frame structure and explore methods of frame generation and processing. Further, we present conceptual designs for a quantum reconfigurable optical add-drop multiplexer to realize the proposed transmission scheme. Packet switching allows for a universal design for a next generation Internet where class…
Wave Packet Sizes in Quantum Mechanical Scatterings: New Perspective
本文针对量子力学散射中依赖环境与实验条件的波包尺寸，结合束缚态与传播波包的尺寸决定因素，开展系统分析，为相关研究提供新视角。
A non-dispersing wave packet has been attracting much interest from various scientific and technological viewpoints. However, most quantum systems are accompanied by anharmonicity, so that retardation of quantum wave-packet dispersion is limited to very few examples only under specific conditions and targets. Here we demonstrate a conceptually new and universal method to retard or advance the dispersion of a quantum wave packet through 'programmable time shift' induced by a strong non-resonant femtosecond laser pulse. A numerical simulation has verified that a train of such retardation pulses …
How much time does a tunneling wave packet spent in traversing a barrier? Quantum mechanical calculations result in zero time inside a barrier . In the nineties analogous tunneling experiments with microwaves were carried out. The results agreed with quantum mechanical calculations. Electron tunneling time is hard to measure being extremely short and parasitic effects due to the electric charge of electrons may be dominant. However, quite recently the atomic ionization tunneling time has been measured. Experimental data of photonic, phononic, and electronic tunneling time is available now and …
The article discusses the properties of time evolution of wave packets in a few systems. Dynamics of wave packet motion for Rydberg atoms with the hierarchy of collapses and revivals is briefly reviewed. The main part of the paper focuses on the new mechanism of quantum reccurrences in wave packet dynamics. This mechanism can occur (in principle) in any physical system with strong enough spin-orbit interaction. We discuss here the SPIN_ORBIT PENDULUM effect that consists in different motions of subpackets possessing different spin fields and results in oscillations of a fraction of average ang…
The Hubbard model may be the simplest model of particles interacting on a lattice, but simulation of its dynamics remains beyond the reach of current numerical methods. In this article, we show that general quantum computations can be encoded into the physics of wave packets propagating through a planar graph, with scattering interactions governed by the fermionic Hubbard model. Therefore, simulating the model on planar graphs is as hard as simulating quantum computation. We give two different arguments, demonstrating that the simulation is difficult both for wave packets prepared as excitatio…
Kardar-Parisi-Zhang and glassy properties in 2D Anderson localization: eigenstates and wave packets
本文通过KPZ框架揭示二维安德森局域化中波动的普遍性及玻璃性质，展示本征态与波包的标度行为。
We discover numerically that a moving wave packet in a quantum chaotic billiard will always evolve into a quantum state, whose density probability distribution is exponential. This exponential distribution is found to be universal for quantum chaotic systems with rigorous proof. In contrast, for the corresponding classical system, the distribution is Gaussian. We find that the quantum exponential distribution can smoothly change to the classical Gaussian distribution with coarse graining.
We investigate orbital alignment dynamics within the valence shell of atoms in coherently excited $j=3/2,1/2$ fine-structure manifolds generated by short-pulse photodetachment of F$^-$, Cl$^-$ and Br$^-$ anions. Using Keldysh-type theory, we calculate the density matrix of the residual atoms generated by few-cycle pulses, whose elements determine the populations and coherence among the electronic states. Our calculations demonstrate that the degree of atomic coherence can be represented by a near universal function of the ratio between the pulse duration $\tildeτ_p$ and the beat period $τ_{j'j…
In this work we study the effects of collapse and revival as well as {\it Zitterbewegung} (ZB) phenomenon, for the relativistic electron wave packets, which are a superposition of the states with quantum numbers sharply peaked around some level $n_0$ of the order of few tens. The probability densities as well as average velocities of the packet center and the average spin components were calculated analytically and visualized. Our computations demonstrate that due to dephasing of the states for times larger than the cyclotron period the initial wave packet (which includes the states with the p…
When a quantum object -- a particle as we call it in a non-rigorous way -- is described by a multi-branched wave- function, with the corresponding wave-packets occupying separated regions of the time-space, a frequently asked question is whether the quantum object is actually contained in only one of these wave-packets. If the answer is positive, then the other wave-packets are called in literature empty waves. The wave-packet containing the object is called a full wave, and is the only one that would produce a recording in a detector. A question immediately arising is whether the empty waves …
Universal features of high-energy scattering of Laguerre-Gaussian states
研究携带轨道角动量的拉盖尔-高斯波包在非零碰撞参数下的高能散射，揭示由波包形状导致的横向动量依赖的普遍运动学特征。
Coherent spatial control of wave packet dynamics on quantum lattices
针对紧束缚量子晶格上的波包动力学，通过分析空间相干性的作用，揭示了随机噪声对波包扩散的影响规律，提出通过空间操作控制波包动力学的新机制。
Anomalous universal quantum transport in 2D asymptotic quasiperiodic system
提出渐近准周期二维系统，预测由AQP、弛豫和有限温度相互作用驱动的多重金属-绝缘体转变，统一波包动力学与体边缘输运的标度律，揭示反常普适量子输运机制。
Quantum diffusion is studied via dissipative Madelung hydrodynamics. Initially the wave packet spreads ballistically, than passes for an instant through normal diffusion and later tends asymptotically to a sub-diffusive law. It is shown that the apparent quantum diffusion coefficient is not a universal physical parameter since it depends on the initial wave packet preparation. The overdamped quantum diffusion of an electron in the field of a periodic potential is also investigated; in this case the wave packet spreads logarithmically in time. Thermo-quantum diffusion of heavier particles as hy…
Kardar-Parisi-Zhang Physics in the Density Fluctuations of Localized Two-Dimensional Wave Packets
本文研究了二维 Anderson 局域化波包密度对数涨落中的 KPZ 普适类特征，发现涨落具有 $1/3$ 代数标度指数和 Tracy-Widom 分布，并验证了局域化波包存在拉伸指数修正。
In this paper we will discuss how to localise a quantum wave-packet due to self-gravitating meso-scopic object by taking into account gravitational self-interaction in the Schrödinger equation beyond General Relativity. In particular, we will study soliton-like solutions in infinite derivative ghost free theories of gravity, which resolves the gravitational $1/r$ singularity in the potential. We will show a unique feature that the quantum spread of such a gravitational system is larger than that of the Newtonian gravity, therefore enabling us a window of opportunity to test classical and quant…
We experimentally study universal nonequilibrium dynamics of two-dimensional atomic Bose gases quenched from repulsive to attractive interactions. We observe the manifestation of modulational instability that, instead of causing collapse, fragments a large two-dimensional superfluid into multiple wave packets universally around a threshold atom number necessary for the formation of Townes solitons. We confirm that the density distributions of quench-induced solitary waves are in excellent agreement with the stationary Townes profiles. Furthermore, our density measurements in the space and time…
Anderson localization confines the wave function of a quantum particle in a one-dimensional random potential to a volume of the order of the localization length $ξ$. Nonlinear add-ons to the wave dynamics mimic many-body interactions on a mean field level, and result in escape from the Anderson cage and in unlimited subdiffusion of the interacting cloud. We address quantum corrections to that subdiffusion by (i) using the ultrafast unitary Floquet dynamics of discrete-time quantum walks, (ii) an interaction strength ramping to speed up the subdiffusion, and (iii) an action discretization of th…
We propose an approach that allows to systematically take into account gravity in quantum particle physics. It is based on quantum field theory and the general principle of relativity. These are used to build a model for quantum particles in curved spacetime. We compute by its means a deviation from a classical geodesic in the Earth's gravitational field. This shows that free fall depends on quantum-matter properties. Specifically, we find that the free-fall universality and the wave-packet spreading are mutually exclusive phenomena. We then estimate the Eötvös parameter for a pair of atoms fr…
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