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J. G. Muga

Publications and source records attributed to J. G. Muga.

At least 163 records · Page 9Linked to original sources
arXiv2003

Tunneling dynamics in relativistic and nonrelativistic wave equations

We obtain the solution of a relativistic wave equation and compare it with the solution of the Schroedinger equation for a source with a sharp onset and excitation frequencies below cut-off. A scaling of position and time reduces to a single case all the (below cut-off) nonrelativistic solutions, but no such simplification holds for the relativistic equation, so that qualitatively different ``shallow'' and ``deep'' tunneling regimes may be identified relativistically. The nonrelativistic forerunner at a position beyond the penetration length of the asymptotic stationary wave does not tunnel; nevertheless, it arrives at the traversal (semiclassical or Büttiker-Landauer) time "tau". The corresponding relativistic forerunner is more complex: it oscillates due to the interference between two saddle point contributions, and may be characterized by two times for the arrival of the maxima of lower and upper envelops. There is in addition an earlier relativistic forerunner, right after the causal front, which does tunnel. Within the penetration length, tunneling is more robust for the precursors of the relativistic equation.

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arXiv2003

Atomic time-of-arrival measurements with a laser of finite beam width

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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arXiv2003

Suppression of Rabi oscillations for moving atoms

The well-known laser-induced Rabi oscillations of a two-level atom are shown to be suppressed under certain conditions when the atom is entering a laser-illuminated region. For temporal Rabi oscillations the effect has two regimes: classical-like, at intermediate atomic velocities, and quantum at low velocities, associated respectively with the formation of incoherent or coherent internal states of the atom in the laser region. In the low velocity regime the laser projects the atom onto a pure internal state that can be controlled by detuning. Spatial Rabi oscillations are only suppressed in this low velocity, quantum regime.

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arXiv2003

Explicit solution for a Gaussian wave packet impinging on a square barrier

The collision of a quantum Gaussian wave packet with a square barrier is solved explicitly in terms of known functions. The obtained formula is suitable for performing fast calculations or asymptotic analysis. It also provides physical insight since the description of different regimes and collision phenomena typically requires only some of the terms.

quant-ph↗
arXiv2002

A measurement-based approach to quantum arrival times

For a quantum-mechanically spread-out particle we investigate a method for determining its arrival time at a specific location. The procedure is based on the emission of a first photon from a two-level system moving into a laser-illuminated region. The resulting temporal distribution is explicitly calculated for the one-dimensional case and compared with axiomatically proposed expressions. As a main result we show that by means of a deconvolution one obtains the well known quantum mechanical probability flux of the particle at the location as a limiting distribution.

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arXiv2002

Transient response of a quantum wave to an instantaneous potential step switching

The transient response of a stationary state of a quantum particle in a step potential to an instantaneous change in the step height (a simplified model for a sudden bias switch in an electronic semiconductor device) is solved exactly by means of a semianalytical expression. The characteristic times for the transient process up to the new stationary state are identified. A comparison is made between the exact results and an approximate method.

quant-ph↗
arXiv2002

Bounds and enhancements for the Hartman effect

The time of passage of the transmitted wave packet in a tunneling collision of a quantum particle with a square potential barrier becomes independent of the barrier width in a range of barrier thickness. This is the Hartman effect, which has been frequently associated with ``superluminality''. A fundamental limitation on the effect is set by non-relativistic ``causality conditions''. We demonstrate first that the causality conditions impose more restrictive bounds on the negative time delays (time advancements) when no bound states are present. These restrictive bounds are in agreement with a naive, and generally false, causality argument based on the positivity of the ``extrapolated phase time'', one of the quantities proposed to characterize the duration of the barrier's traversal. Nevertheless, square wells may in fact lead to much larger advancements than square barriers. We point out that close to thresholds of new bound states the time advancement increases considerably, while, at the same time, the transmission probability is large, which facilitates the possible observation of the enhanced time advancement.

quant-ph↗
arXiv2002

Time scale of forerunners in quantum tunneling

The forerunners preceding the main tunneling signal of the wave created by a source with a sharp onset or by a quantum shutter, have been generally associated with over-the-barrier (non-tunneling) components. We demonstrate that, while this association is true for distances which are larger than the penetration lenght, for smaller distances the forerunner is dominated by under-the-barrier components. We find that its characteristic arrival time is inversely proportional to the difference between the barrier energy and the incidence energy, a tunneling time scale different from both the phase time and the Büttiker-Landauer (BL) time.

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arXiv2002

Quantum time-of-flight measurements: kick clock versus continuous clock

The measurement of time durations or instants of ocurrence of events has been frequently modelled ``operationally'' by coupling the system of interest to a ``clock''. According to several of these models the operational approach is limited at low energies because the perturbation of the clock does not allow to reproduce accurately the corresponding ideal time quantity, defined for the system in isolation. We show that, for a time-of-flight measurement model that can be set to measure dwell or arrival times, these limitations may be overcome by extending the range of energies where the clock works properly using pulsed couplings rather than continuous ones.

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arXiv2001

Asymptotic behaviour of the probability density in one dimension

We demonstrate that the probability density of a quantum state moving freely in one dimension may decay faster than 1/t. Inverse quadratic and cubic dependences are illustrated with analytically solvable examples. Decays faster than 1/t allow the existence of dwell times and delay times.

quant-ph↗
arXiv2001

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.

quant-ph↗
arXiv2001

Characteristic times in one dimensional scattering

This chapter reviews several quantities that have been proposed in scattering theory to characterize the temporal aspects of one dimensional collisions: the dwell time, the delay time, the decay time, and times characterizing transient effects or the attainment of stationary conditions. Some aspects of tunnelling times are also discussed.

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arXiv2001

Generalizations of Kijowski's time-of-arrival distribution for interaction potentials

Several proposals for a time-of-arrival distribution of ensembles of independent quantum particles subject to an external interaction potential are compared making use of the ``crossing state'' concept. It is shown that only one of them has the properties expected for a classical distribution in the classical limit. The comparison is illustrated numerically with a collision of a Gaussian wave packet with an opaque square barrier.

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arXiv2000

Comment on "Measurement of time of arrival in quantum mechanics"

The analysis of the model quantum clocks proposed by Aharonov et al. [Phys. Rev. A 57 (1998) 4130 - quant-ph/9709031] requires considering evanescent components, previously ignored. We also clarify the meaning of the operational time of arrival distribution which had been investigated.

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arXiv2000

Comment on "Foundations of quantum mechanics: Connection with stochastic processes"

Recently, Olavo has proposed several derivations of the Schrodinger equation from different sets of hypothesis ("axiomatizations") [Phys. Rev. A 61, 052109 (2000)]. One of them is based on the infinitesimal inverse Weyl transform of a classically evolved phase space density. We show however that the Schrodinger equation can only be obtained in that manner for linear or quadratic potential functions.

quant-ph↗
arXiv2000

Model for the arrival-time distribution in fluorescence time-of-flight experiments

An operational arrival-time distribution is defined as the distribution of detection times of the first photons emitted by two level atoms in resonance with a perpendicular laser beam in a time of flight experiment. For ultracold Cesium atoms the simulations are in excellent agreement with the theoretical ideal time-of-arrival distribution of Kijowski.

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arXiv2000

Effect of classically forbidden momenta in one dimensional quantum scattering

The transmitted wave that results from a collision of a wave packet which is initially to the left of a potential barrier depends in general on the amplitudes of negative momenta of the initial state. The exact form of this dependence is shown and the importance of this classically forbidden effect is illustrated with numerical examples. Special care is taken to account properly for bound states.

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