Introduction

Muga, J. G.; Mayato, R. Sala; Egusquiza, I. L.

doi:10.1007/978-3-540-73473-4_1

Cited by 104 publications

(181 citation statements)

References 144 publications

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“…This is exactly the time-of-arrival probability density obtained by several authors via different approaches [8,[30][31][32][33] and is in excellent agreement with numerical "quantum jump" time-of-flight simulations [18]. However, the models employed have faced problems even in the free particle case.…”

supporting

confidence: 87%

Space-time-symmetric extension of nonrelativistic quantum mechanics

Dias

Parisio

2017

Phys. Rev. A

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In quantum theory we refer to the probability of finding a particle between positions x and x + dx at the instant t, although we have no capacity of predicting exactly when the detection occurs. In this work, first we present an extended non-relativistic quantum formalism where space and time play equivalent roles. It leads to the probability of finding a particle between x and x + dx during [t,t + dt]. Then, we find a Schrödinger-like equation for a "mirror" wave function φ(t, x) associated with the probability of measuring the system between t and t + dt, given that detection occurs at x. In this framework, it is shown that energy measurements of a stationary state display a non-zero dispersion, and that energy-time uncertainty arises from first principles. We show that a central result on arrival time, obtained through approaches that resort to ad hoc assumptions, is a natural, built-in part of the formalism presented here. In Schrödinger quantum mechanics (QM) there is a clear asymmetry between time and space. Time is a continuous parameter that can be chosen with arbitrary precision and used to label the solution of the wave equation. In contrast, the position of a particle is seen as an operator, and therefore its value under a measurement is inherently probabilistic. It is common to hear that this asymmetry is due to the non-relativistic character of the Schrödinger equation (SE). Although partially correct, this argument is largely insufficient to justify all the disparity between space and time in the formalism of QM.A clear illustration is as follows. In a position measurement, ψ(x, t) = x|ψ(t) gives the probability amplitude of finding the particle within [x, x + dx], given that the time of detection is t. Would it not be equally reasonable, even in the non-relativistic domain, to ask about the probability of measuring the particle between x and x + dx, and t and t + dt? In this broader scenario, inquiring about the state of a particle at a given time t (as we often do), should make as much sense as asking about the state of that particle in a given position x (which we never do). In addition, if symmetry is to hold at this level, then there should exist a "mirror" wave function φ(t, x) = t|φ(x) , where x is a continuous parameter and t is the eigenvalue of an observable. If the location of particle becomes a physical reality only when a measurement is made, then it is a tenable position to expect that time should emerge in the same way. To earnestly consider these issues is the main goal of this manuscript.Time has been addressed in different contexts in QM . Common to several of these works is the attempt to remain within the borders of the standard theory. However, the solution to the arrival-time problem is considered by several authors to lay outside the framework of QM. It concerns the arrival of a particle in a spatially localized apparatus, where a time operator may be defined so that the relation [T ,Ĥ] = i is satisfied, and * corresponding author: eduardodias@df.ufpe.br † parisio@df.ufpe.br ...

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supporting

confidence: 87%

Space-time-symmetric extension of nonrelativistic quantum mechanics

Dias

Parisio

2017

Phys. Rev. A

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“…Even the possibility of superluminal speeds for the traversal through the barrier have been discussed, referred to as the Hartman effect (Hartman, 1962). Accounts of this debate can be found in a large number of reviews (see de Carvalho and Nussenzveig, 2002;Hauge and Støvneng, 1989;Landauer and Martin, 1994;Olkhovsky et al, 2004;Winful, 2006;Muga et al, 2007;Choi and Jordan, 2013). As a well-defined operator whose eigenvalue would correspond to the travel time through the classically forbidden region could not be identified, unconventional operational descriptions have been put forward, such as complex travel time based on a Feynman path integral formulation (Sokolovski et al, 1994) or contextual values replacing conventional eigenvalues of a self-adjoined operators for so-called weak measurements (Choi and Jordan, 2013).…”

Section: Attosecond Streaking Of Tunneling Time?mentioning

confidence: 99%

Attosecond chronoscopy of photoemission

2015

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Recent advances in the generation of well characterized sub-femtosecond laser pulses have opened up unpredicted opportunities for the real-time observation of ultrafast electronic dynamics in matter. Such attosecond chronoscopy allows a novel look at a wide range of fundamental photophysical and photochemical processes in the time domain, including Auger and autoionization processes, photoemission from atoms, molecules, and surfaces, complementing conventional energy-domain spectroscopy. Attosecond chronoscopy raises fundamental conceptual and theoretical questions as which novel information becomes accessible and which dynamical processes can be controlled and steered. These questions are currently a matter of lively debate which we address in this review. We will focus on one prototypical case, the chronoscopy of the photoelectric effect by attosecond streaking. Is photoionization instantaneous or is there a finite response time of the electronic wavefunction to the photoabsorption event? Answers to this question turn out to be far more complex and multi-faceted than initially thought. They touch upon fundamental issues of time and time delay as observables in quantum theory. We review recent progress of our understanding of time-resolved photoemission from atoms, molecules, and solids. We will highlight the unresolved and open questions and we point to future directions aiming at the observation and control of electronic motion in more complex nanoscale structures and in condensed matter.

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“…According to an argument due to Pauli [1], there is no self-adjoint time operator conjugate to a semibounded Hamiltonian (see however [2]), and this limitation has hindered the research on the theoretical understanding and description of time quantities measured in the laboratories. The trend is slowly changing though [3]. During the last two decades, many works have been devoted to find consistent theories, in terms of operators or otherwise, about characteristic times for tunneling, quantum jumps, decay, or arrival [4,3].…”

Section: Introductionmentioning

confidence: 99%

On atomic time-of-arrival measurements with a laser of finite beam width

Damborenea

Egusquiza

Hegerfeldt

et al. 2003

J. Phys. B: At. Mol. Opt. Phys.

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Abstract. A natural approach to measure the time of arrival of an atom at a spatial region is to illuminate this region with a laser and detect the first fluorescence photons produced by the excitation of the atom and subsequent decay. We investigate the actual physical content of such a measurement in terms of atomic dynamical variables, taking into account the finite width of the laser beam. Different operation regimes are identified, in particular the ones in which the quantum current density may be obtained.

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Introduction

Cited by 104 publications

References 144 publications

Space-time-symmetric extension of nonrelativistic quantum mechanics

Space-time-symmetric extension of nonrelativistic quantum mechanics

Attosecond chronoscopy of photoemission

On atomic time-of-arrival measurements with a laser of finite beam width

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