We develop a wavepacket approach to the diffraction of charged particles by a thin material target and we use the de Broglie-Bohm quantum trajectories to study various phenomena in this context. We find the form of the separator, i.e.the limit between the domains of prevalence of the ingoing and outgoing quantum flow. The structure of the quantum-mechanical currents in the neighborhood of the separator implies the formation of an array of \emph{quantum vortices} (nodal point - X point complexes). We show how the deformation of the separatior near Bragg angles explains the emergence of a diffraction pattern by the de Broglie - Bohm trajectories. We calculate the arrival time distributions for particles scattered at different angles. The predictions of the de Broglie - Bohm theory for $ΔT$ turn to be different from estimates of the same quantity using other theories on time observables like the sum-over-histories or the Kijowski approach. We propose an experimental setup aiming to test such predictions. Finally, we explore the semiclassical limit of short wavelength and short quantum coherence lengths, and demonstrate how, in this case, results with the de Broglie - Bohm trajectories are similar to the classical results of Rutherford scattering.
A nonreflecting wavepacket is constructed by the superposition of reflectionless eigenstates of sech2 potential. Free propagation and propagation in the presence of the above potential of such a wavepacket is considered using the concept of arrival time. Comparison is made with the free evolving Gaussian wavepacket. Mean arrival time at a detector behind the well is given as a function of mass for separate cases. A selection of Bohmian trajectories in the interacting case are computed and compared to the trajectories of a free particle guided by a Gaussian packet.
Some unexplored decoherence aspects within the Caldeira-Leggett master equation are analyzed and discussed. The decoherence process is controlled by the two environment parameters, the relaxation rate or friction and the temperature, leading to a gradual transition from the quantum to classical regime. Arrival time distributions, nonminimum-uncertainty-product or stretching Gaussian wave packets, identical particles and diffraction in time display interesting features during the decoherence process undergone by the time dependent interference patterns. We show that the presence of a constant f…
Diffraction in time of a particle confined in a box which its walls are removed suddenly at $t=0$ is studied. The solution of the time-dependent Schrödinger equation is discussed analytically and numerically for various initial wavefunctions. In each case Bohmian trajectories of the particles are computed and also the mean arrival time at a given location is studied as a function of the initial state.
I propose to resolve the controversy over the speed of collapse of quantum-mechanical wavefunctions by means of an experimental test with a modified symmetric Mach-Zehnder atom interferometer, with non-intersecting, parallel, widely separated final beams. According to the conventional collapse scenario, the coherent twin-peak atomic wavefunction in the beams of the interferometer suffers an instantaneous collapse, at infinite speed, when the atom is captured by one of the two detectors at the ends of the beams, but it remains coherent until that instant. In contrast, according to the Hellwig-K…
Time-Frequency Continuous-Variable Quantum Teleportation with Single Photons
Telecom Paris, Institut Polytechnique de Paris（巴黎电信学院，巴黎理工学院）；Centre for Nanosciences and Nanotechnology, CNRS, Université Paris-Saclay（纳米科学与工程中心，法国国家科学研究中心，巴黎萨克雷大学）
With the ability to directly obtain the Wigner function and density matrix of photon states, quantum tomography (QT) has had a significant impact on quantum optics, quantum computing and quantum information. By an appropriate sequence of measurements on the evolution of each degreeof freedom (DOF), the full quantum state of the observed photonic system can be determined. The first proposal to extend the application of QT to reconstruction of complete quantum states of matter wavepackets had generated enormous interest in ultrafast diffraction imaging and pump-probe spectroscopy of molecules. T…
The problem of Schrödinger propagation of a discontinuous wavefunction -diffraction in time- is studied under a new light. It is shown that the evolution map in phase space induces a set of affine transformations on discontinuous wavepackets, generating expansions similar to those of wavelet analysis. Such transformations are identified as the cause for the infinitesimal details in diffraction patterns. A simple case of an evolution map, such as SL(2) in a two-dimensional phase space, is shown to produce an infinite set of space-time trajectories of constant probability. The trajectories emerg…
Run-and-tumble particles, frequently considered today for modeling bacterial locomotion, naturally appear outside a biological context as well, e.g. for producing waves in the telegraph process. Here, we use a wave function to drive their propulsion and tumbling. Such quantum-active motion realizes a jittery motion of Dirac electrons (as in the famous Zitterbewegung): the Dirac electron is a run-and-tumble particle, where the tumbling is between chiralities. We visualize the trajectories in diffraction and double slit experiments for electrons. In particular, that yields the time-of-arrival st…
We propose a dynamical model for state symmetrization of two identical particles produced in spacelike-separated events by independent sources. We adopt the hypothesis that the pair of non-interacting particles can initially be described by a tensor product state since they are in principle distinguishable due to their spacelike separation. As the particles approach each other, a quantum jump takes place upon particle collision, which erases their distinguishability and projects the two-particle state onto an appropriately (anti)symmetrized state. The probability density of the collision times…
The tunneling time problem earlier studied in Phys. Rev. Lett 108 170402 (2012) using a non-relativistic time-of-arrival (TOA) operator predicted that tunneling time is instantaneous. This raises the question on whether instantaneous tunneling time is a consequence of using a non-relativistic theory. Here, we extend the analysis by proposing a formalism on the construction of relativistic TOA-operators for spin-0 particles in the presence of an interaction potential via quantization. We then construct the corresponding barrier traversal time operator and impose the condition that the barrier h…
Deterministically aperiodic sequences are an intermediary between periodic sequences and completely random sequences. Materials which are translationally periodic have Bloch-like extended states, while random media exhibit Anderson localisation. Materials constructed on the basis of deterministic aperiodic sequences such as Fibonacci, Thue-Morse, and Rudin-Shapiro exhibit different properties, which can be related to their spectrum. Here, by investigating the dynamics of discrete-time quantum walks using different aperiodic sequences of coin operations in position space and time we establish t…
Transient phenomena of phase modulated cut-off wavepackets are explored by deriving an exact general solution to Schrödinger's equation for finite range potentials involving arbitrary initial quantum states. We show that the dynamical features of the probability density are governed by a virtual \textit{self-induced two-level system} with energies $E_{+}$, and $E_{-}$, due to the phase modulation of the initial state. The asymptotic probability density exhibits Rabi-oscillations characterized by a frequency $Ω=(E_{+}-E_{-})/\hbar$, which are independent of the potential profile. It is also fou…
We put forward a model that describes a decaying and evanescent point source of non-interacting quantum waves in 1D. This point-source assumption allows for a simple description that captures the essential aspects of the dynamics of a wave traveling through a classically forbidden region without the need to specify the details of the inner region. The dynamics of the resulting wave is examined and several characteristic times are identified. One of them generalizes the tunneling time-scale introduced by Büttiker and Landauer and it characterizes the arrival of the maximum of the wave function.…
Time-frequency Talbot effect as Clifford operations on entangled time-frequency GKP states
Télécom Paris-LTCI, Institut Polytechnique de Paris（巴黎电信学院-LTCI，巴黎理工学院）；Université Côte d’Azur, CNRS, Institut de physique de Nice（蔚蓝海岸大学，法国国家科学研究中心，尼斯物理研究所）
In this review we deal with open (dissipative and stochastic) quantum systems within the Bohmian mechanics framework which has the advantage to provide a clear picture of quantum phenomena in terms of trajectories, originally in configuration space. The gradual decoherence process is studied from linear and nonlinear Schrödinger equations through Bohmian trajectories as well as by using the so-called quantum-classical transition differential equation through scaled trajectories. This transition is governed by a continuous parameter, the transition parameter, covering these two extreme open dyn…
