Space-time properties of free motion time-of-arrival eigenstates

The properties of the time-of-arrival operator for free motion introduced by Aharonov and Bohm and of its self-adjoint variants are studied. The domains of applicability of the different approaches are clarified. It is shown that the arrival time of the eigenstates is not sharply defined. However, strongly peaked real-space (normalized) wave packets constructed with narrow Gaussian envelopes centred on one of the eigenstates provide an arbitrarily sharp arrival time.Comment: REVTEX, 12 pages, 4 postscript figure

Quantum times of arrival for multiparticle states

Using the concept of crossing state and the formalism of second quantization, we propose a prescription for computing the density of arrivals of particles for multiparticle states, both in the free and the interacting case. The densities thus computed are positive, covariant in time for time independent hamiltonians, normalized to the total number of arrivals, and related to the flux. We investigate the behaviour of this prescriptions for bosons and fermions, finding boson enhancement and fermion depletion of arrivals.Comment: 10 a4 pages, 5 inlined figure

Free motion time-of-arrival operator and probability distribution

We reappraise and clarify the contradictory statements found in the literature concerning the time-of-arrival operator introduced by Aharonov and Bohm in Phys. Rev. {\bf 122}, 1649 (1961). We use Naimark's dilation theorem to reproduce the generalized decomposition of unity (or POVM) from any self-adjoint extension of the operator, emphasizing a natural one, which arises from the analogy with the momentum operator on the half-line. General time operators are set within a unifying perspective. It is shown that they are not in general related to the time of arrival, even though they may have the same form.Comment: 10 a4 pages, no figure

Time-of-arrival distribution for arbitrary potentials and Wigner's time-energy uncertainty relation

A realization of the concept of "crossing state" invoked, but not implemented, by Wigner, allows to advance in two important aspects of the time of arrival in quantum mechanics: (i) For free motion, we find that the limitations described by Aharonov et al. in Phys. Rev. A 57, 4130 (1998) for the time-of-arrival uncertainty at low energies for certain mesurement models are in fact already present in the intrinsic time-of-arrival distribution of Kijowski; (ii) We have also found a covariant generalization of this distribution for arbitrary potentials and positions.Comment: 4 pages, revtex, 2 eps figures include

Ambiguities of arrival-time distributions in quantum theory

We consider the definition that might be given to the time at which a particle arrives at a given place, both in standard quantum theory and also in Bohmian mechanics. We discuss an ambiguity that arises in the standard theory in three, but not in one, spatial dimension.Comment: LaTex, 12 pages, no figure

Enhanced observability of quantum post-exponential decay using distant detectors

We study the elusive transition from exponential to post-exponential (algebraic) decay of the probability density of a quantum particle emitted by an exponentially decaying source, in one dimension. The main finding is that the probability density at the transition time, and thus its observability, increases with the distance of the detector from the source, up to a critical distance beyond which exponential decay is no longer observed. Solvable models provide explicit expressions for the dependence of the transition on resonance and observational parameters, facilitating the choice of optimal conditions

Correcting the quantum clock: conditional sojourn times

Can the quantum-mechanical sojourn time be clocked without the clock affecting the sojourn time? Here we re-examine the previously proposed non-unitary clock, involving absorption/amplification by an added infinitesimal imaginary potential($iV_{i}$), and find it {\it not} to preserve, in general, the positivity of the sojourn time, conditional on eventual reflection or transmission. The sojourn time is found to be affected by the scattering concomitant with the mismatch, however small, due to the very clock potential($iV_{i}$) introduced for the purpose, as also by any prompt scattering involving partial waves that have not traversed the region of interest. We propose a formal procedure whereby the sojourn time so clocked can be corrected for these spurious scattering effects. The resulting conditional sojourn times are then positive definite for an arbitrary potential, and have the proper high- and low-energy limits.Comment: Corrected and rewritten, RevTeX, 4 pages, 2 figures (ps files) include

Single-photon source based on FWM with adjustable linear SOP

We present a setup able to generate and detect single photons in optical fibers using the stimulated four-wave mixing (FWM) process. The results show an accurate generation of single photons at four different linear states of polarization (SOPs), with angles 0, 45, 90 and -45 degrees. The detection was performed in back-to-back configuration and after transmission over an optical fiber with a length up to 10 m

Bohmian arrival time without trajectories

The computation of detection probabilities and arrival time distributions within Bohmian mechanics in general needs the explicit knowledge of a relevant sample of trajectories. Here it is shown how for one-dimensional systems and rigid inertial detectors these quantities can be computed without calculating any trajectories. An expression in terms of the wave function and its spatial derivative, both restricted to the boundary of the detector's spacetime volume, is derived for the general case, where the probability current at the detector's boundary may vary its sign.Comment: 20 pages, 12 figures; v2: reference added, extended introduction, published versio