Heisenberg's wave packet reconsidered

在量子网络中，通过频谱编码的单光子波包激发双能级原子的可行性

On the excitability of two-level atoms by spectrally encoded single-photon wave packets in quantum networks

研究通过频谱编码单光子波包在量子网络中提升双能级原子激发效率，揭示编码参数对激发性能的影响及设计规则。

Minimal length effect on the broadening of free wave-packets and its physical implications

We study the Generalized Uncertainty Principle (GUP) modified time evolution for the width of wave-packets for a scalar potential. Free particle case is solved exactly where the wave-packet broadening is modified by a coupling between the GUP parameter and higher order moments in the probability distribution in momentum space. We consider two popular forms of deformations widely used in the literature - one of which modifies the commutator with a quadratic term in momentum, while the other modifies it with terms both linear and quadratic in momentum. Unlike the standard case, satisfying Heisen…

A complete set of Lorentz-invariant wave packets and modified uncertainty relation

We define a set of fully Lorentz-invariant wave packets and show that it spans the corresponding one-particle Hilbert subspace, and hence the whole Fock space as well, with a manifestly Lorentz-invariant completeness relation (resolution of identity). The position-momentum uncertainty relation for this Lorentz-invariant wave packet deviates from the ordinary Heisenberg uncertainty principle, and reduces to it in the non-relativistic limit.

On the experimental verification of the uncertainty principle of position and momentum

Historically, Kennard was the first to choose the standard deviation as a quantitative measure of uncertainty, and neither he nor Heisenberg explicitly explained why this choice should be appropriate from the experimental physical point of view. If a particle is prepared by a single slit of spatial width $Δx$, it has been shown that a finite standard deviation $σ_p<\infty$ can only be ensured if the wave-function is zero at the edge of $Δx$, otherwise it does not exist [8]. Under this circumstances the corresponding sharp inequality is $σ_p Δx\geq π\hbar$. This bound will be reconsidered from …

Forced quantum inverted oscillator

New exact and asymptotic results for a quantum inverted oscillator, driven by the variable external force, are presented. To illustrate the advantages of our approach, we applied the obtained propagator to the descriptions of evolution the initial Gaussian wave packet under arbitrary time-dependent force or a δ-pulse action. The alternative problem of tunneling a particle through a parabolic barrier under the influence of a low-frequency harmonic force we solve in the quasistatic approximation. Going to the Heisenberg picture in the Caldeira-Leggett model, we describe the influence of a time-d…

Open timelike curves violate Heisenberg's uncertainty principle

Toy models for quantum evolution in the presence of closed timelike curves (CTCs) have gained attention in the recent literature due to the strange effects they predict. The circuits that give rise to these effects appear quite abstract and contrived, as they require non-trivial interactions between the future and past which lead to infinitely recursive equations. We consider the special case in which there is no interaction inside the CTC, referred to as an open timelike curve (OTC), for which the only local effect is to increase the time elapsed by a clock carried by the system. Remarkably, …

基于盒中粒子动量新概念的反弹波包、Ehrenfest 定理与不确定关系

Bouncing Wave Packets, Ehrenfest Theorem, and Uncertainty Relation based upon a new Concept for the Momentum of a Particle in a Box

针对盒中粒子动量算符非自伴导致 Ehrenfest 定理失效的问题，本文采用新型自伴动量算符，证明该定理对所有物理边界条件成立，并用反弹波包加以阐释，同时给出 HRS 不确定关系的简洁形式及物理解释。

惯性运动与匀加速运动的物质波量子叠加

A Matter-Wave Quantum Superposition of Inertial and Constant Acceleration Motions

本研究提出三种计算惯性与加速运动叠加态量子物质波非相对论动力学的方法，验证了经典不可观测的相对相位可通过干涉实验探测，揭示海森堡绘景的适用性及与相对论处理的一致性，为等效原理相关研究提供支撑。

Circumventing Heisenberg's uncertainty principle in atom interferometry tests of the equivalence principle

Atom interferometry tests of universality of free fall based on the differential measurement of two different atomic species provide a useful complement to those based on macroscopic masses. However, when striving for the highest possible sensitivities, gravity gradients pose a serious challenge. Indeed, the relative initial position and velocity for the two species need to be controlled with extremely high accuracy, which can be rather demanding in practice and whose verification may require rather long integration times. Furthermore, in highly sensitive configurations gravity gradients lead …

高斯形式：压缩相干态对海森堡误差不确定性关系的联合测量

Gaussian Formalism: Joint Measurement for Heisenberg's Uncertainty Relation for Errors by Squeezed Coherent States

本文提出高斯波包形式可实现位置与动量的联合测量，基于POVM在投影测量间平滑插值，首次获得LT误差与精化Lee误差，发现精化Lee不确定性关系提供与海森堡值一致的常数下界。

Generalised Uncertainty Relations from Finite-Accuracy Measurements

In this short note we show how the Generalised Uncertainty Principle (GUP) and the Extended Uncertainty Principle (EUP), two of the most common generalised uncertainty relations proposed in the quantum gravity literature, can be derived within the context of canonical quantum theory, without the need for modified commutation relations. A GUP-type relation naturally emerges when the standard position operator is replaced by an appropriate Positive Operator Valued Measure (POVM), representing a finite-accuracy measurement that localises the quantum wave packet to within a spatial region $σ_g > 0…