arXiv subjects

Jorge Villavicencio

Publications and source records attributed to Jorge Villavicencio.

At least 19 recordsLinked to original sources

arXiv2020

Transient quantum beats, Rabi-oscillations and delay-time of modulated matter-waves

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 found that for a system with a bound state, the interplay between the virtual levels with the latter causes a \textit{quantum beat} effect with a beating frequency, $Ω$. We also find a regime characterized by a \textit{time-diffraction} phenomenon that allows to measure unambiguously the delay-time, which can be described by an exact analytical formula. It is found that the delay-time agrees with the phase-time only for the case of strictly monochromatic waves.

quant-ph↗

arXiv2020

Zitterbewegung and Klein-tunneling phenomena for transient quantum waves

We explore the dynamics of relativistic quantum waves in a potential step by using an exact solution to the Klein-Gordon equation with a point source initial condition. We show that in both the propagation, and Klein-tunneling regimes, the Zitterbewegung effect manifests itself as a series of quantum beats of the particle density in the long-time limit. We demonstrate that the beating phenomenon is characterized by the Zitterbewegung frequency, and that the amplitude of these oscillations decays as $t^{-3/2}$. We show that beating effect also manifests itself in the free Klein-Gordon and Dirac equations within a quantum shutter setup, which involve the dynamics of cut-off quantum states. We also find a time-domain where the particle density of the point source is governed by the propagation of a main wavefront, exhibiting an oscillating pattern similar to the diffraction in time phenomenon observed in non-relativistic systems. The relative positions of these wavefronts are used to investigate the time-delay of quantum waves in the Klein-tunneling regime. We show that, depending on the energy difference, ${\cal E}$, between the source and the potential step, the time-delay can be positive, negative or zero. The latter case corresponds to a super-Klein-tunneling configuration, where ${\cal E}$ equals to half the energy of the potential step.

quant-ph↗

arXiv2019

Time-diffraction and Zitterbewegung of two-dimensional massless Dirac excitations

We explore the dynamics of two-dimensional massless Dirac-fermions within a quantum shutter approach, which involves the time-evolution of an initial cut-off plane wave. We show that the probability density is governed by an interplay between {\it diffraction in time} and {\it Zitterbewegung} phenomena, typical of relativistic quantum shutter systems with nonzero mass. The {\it time-diffraction} appears as an oscillatory pattern in the probability density, similar to the effect predicted by Moshinsky in 1952 [Phys. Rev. \textbf{88}, 625] for Schrödinger free matter-waves. The {\it Zitterbewegung} manifests itself as high-frequency oscillations embedded in the time-diffraction profile. We found that these two transient effects are induced by the transverse momentum component of the incident wave, $k_y$, that acts as an effective mass of the system. Furthermore, this effective mass can be manipulated by tuning the incidence angle of the initial quantum state, which allows to control the frequencies of the transients. In particular, we demonstrate that near a normal incidence condition, the {\it Zitterbewegung} appears as a series of {\it quantum beats} in the probability density, with a beating frequency $2k_yv_F$, where $v_F$ is the Fermi velocity.

cond-mat.mes-hall↗

arXiv2019

Heisenberg uncertainty relations for the non-Hermitian resonance state solutions to the Schrödinger equation

Resonance (quasinormal) states correspond to non-Hermitian solutions to the Schrödinger equation obeying outgoing boundary conditions which lead to complex energy eigenvalues and momenta. Following the normalization rule for resonance states obtained from the residue at a complex pole of the outgoing Green's function to the problem, we propose a definition of expectation value for these states and use it to investigate the extent of validity of the Heisenberg uncertainty relations for potentials that vanish after a distance. We derive analytical expressions for the expectation values involving the momentum and the position for a given resonance state and find in model calculations that the Heisenberg uncertainty relations are satisfied for a broad range of potential parameters. A comparison of our approach with that based on the regularization method by Zel'dovich yields very similar results except for resonance energies very close to the energy threshold. Our work shows that the validity of the Heisenberg uncertainty relations may be extended to the non-Hermitian resonance state solutions to the Schrödinger equation.

quant-ph↗

arXiv2012

Hermitian and non-Hermitian formulations of the time evolution of quantum decay

This work discusses Hermitian and non-Hermitian formulations for the time evolution of quantum decay, that involve respectively, continuum wave functions and resonant states, to show that they lead to an identical description for a large class of well behaved potentials. Our approach is based on the analytical properties of the outgoing Green's function to the problem in the complex wave number plane.

quant-ph↗

arXiv2006

Full time nonexponential decay in double-barrier quantum structures

We examine an analytical expression for the survival probability for the time evolution of quantum decay to discuss a regime where quantum decay is nonexponential at all times. We find that the interference between the exponential and nonexponential terms of the survival amplitude modifies the usual exponential decay regime in systems where the ratio of the resonance energy to the decay width, is less than 0.3. We suggest that such regime could be observed in semiconductor double-barrier resonant quantum structures with appropriate parameters.

quant-ph↗

arXiv2005

Quantum shutter approach to tunneling time scales with wave packets

The quantum shutter approach to tunneling time scales (G. Garc\'{ı}a-Calderón and A. Rubio, Phys. Rev. A \textbf{55}, 3361 (1997)), which uses a cutoff plane wave as the initial condition, is extended in such a way that a certain type of wave packet can be used as the initial condition. An analytical expression for the time evolved wave function is derived. The time-domain resonance, the peaked structure of the probability density (as the function of time) at the exit of the barrier, originally found with the cutoff plane wave initial condition, is studied with the wave packet initial conditions. It is found that the time-domain resonance is not very sensitive to the width of the packet when the transmission process is in the tunneling regime.

quant-ph↗

arXiv2003

Transient time-domain resonances and the time scale for tunneling

Transient {\it time-domain resonances} found recently in time-dependent solutions to Schrödinger's equation are used to investigate the issue of the tunneling time in rectangular potential barriers. In general, a time frequency analysis shows that these transients have frequencies above the cutoff frequency associated with the barrier height, and hence correspond to non-tunneling processes. We find, however, a regime characterized by the barrier opacity, where the peak maximum $t_{max}$ of the {\it time-domain resonance} corresponds to under-the-barrier tunneling. We argue that $t_{max}$ represents the relevant tunneling time scale through the classically forbidden region.

quant-ph↗

arXiv2003

Equivalence between the real time Feynman histories and the quantum shutter approaches for the "passage time" in tunneling

We show the equivalence of the functions $G_{\rm p}(t)$ and $|Ψ(d,t)|^2$ for the ``passage time'' in tunneling. The former, obtained within the framework of the real time Feynman histories approach to the tunneling time problem, using the Gell-Mann and Hartle's decoherence functional, and the latter involving an exact analytical solution to the time-dependent Schrödinger equation for cutoff initial waves.

quant-ph↗

arXiv2002

Tunneling time scale of under-the-barrier forerunners

Time-dependent analytical solutions to Schrödinger's equation with quantum shutter initial conditions are used to investigate the issue of the tunneling time of forerunners in rectangular potential barriers. By using a time-frequency analysis, we find the existence of a regime characterized by the opacity of the barrier, where the maximum peak of a forerunner measured at the barrier transmission edge $x=L$ corresponds to a genuine tunneling process. The corresponding time scale represents the tunneling time of the forerunner through the classically forbidden region.

quant-ph↗

arXiv2002

The role of the buildup oscillations on the speed of resonant tunneling diodes

The fastest tunneling response in double barrier resonant structures is investigated by considering explicit analytic solutions of the time dependent Schrödinger equation. For cutoff initial plane waves, we find that the earliest tunneling events consist on the emission of a series of propagating pulses of the probability density governed by the buildup oscillations in the quantum well. We show that the fastest tunneling response comes from the contribution of incident carriers at energies different from resonance, and that its relevant time scale is given by $τ_r=π\hbar /| E-ε| $, where $ε$ is the resonance energy and $E$ is the incidence energy.

quant-ph↗

arXiv2002

Quantum-wave evolution in a step potential barrier

By using an exact solution to the time-dependent Schrödinger equation with a point source initial condition, we investigate both the time and spatial dependence of quantum waves in a step potential barrier. We find that for a source with energy below the barrier height, and for distances larger than the penetration length, the probability density exhibits a {\it forerunner} associated with a non-tunneling process, which propagates in space at exactly the semiclassical group velocity. We show that the time of arrival of the maximum of the {\it forerunner} at a given fixed position inside the potential is exactly the traversal time, $τ$. We also show that the spatial evolution of this transient pulse exhibits an invariant behavior under a rescaling process. This analytic property is used to characterize the evolution of the {\it forerunner}, and to analyze the role played by the time of arrival, $3^{-1/2}τ$, found recently by Muga and Büttiker [Phys. Rev. A {\bf 62}, 023808 (2000)].

quant-ph↗

arXiv2002

Transient tunneling effects of resonance doublets in triple barrier systems

Transient tunneling effects in triple barrier systems are investigated by considering a time-dependent solution to the Schrödinger equation with a cutoff wave initial condition. We derive a two-level formula for incidence energies $E$ near the first resonance doublet of the system. Based on that expression we find that the probability density along the internal region of the potential, is governed by three oscillation frequencies: one of them refers to the well known Bohr frequency, given in terms of the first and second resonance energies of the doublet, and the two others, represent a coupling with the incidence energy $E$. This allows to manipulate the above frequencies to control the tunneling transient behavior of the probability density in the short-time regime

quant-ph↗

arXiv2002

Delay time and tunneling transient phenomena

Analytic solutions to the time-dependent Schrödinger equation for cutoff wave initial conditions are used to investigate the time evolution of the transmitted probability density for tunneling. For a broad range of values of the potential barrier opacity $α$, we find that the probability density exhibits two evolving structures. One refers to the propagation of a {\it forerunner} related to a {\it time domain resonance} [Phys. Rev. A {\bf 64}, 0121907 (2001)], while the other consists of a semiclassical propagating wavefront. We find a regime where the {\it forerunners} are absent, corresponding to positive {\it time delays}, and show that this regime is characterized by opacities $α< α_c$. The critical opacity $α_c$ is derived from the analytical expression for the {\it delay time}, that reflects a link between transient effects in tunneling and the {\it delay time}

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.

quant-ph↗

arXiv2000

Dynamical analysis of the buildup process near resonance

The time evolution of the buildup process inside a double-barrier system for off-resonance incidence energies is studied by considering the analytic solution of the time dependent Schrödinger equation with cutoff plane wave initial conditions. We show that the buildup process exhibits invariances under arbitrary changes on the system parameters, which can be successfully described by a simple and easy-to-use one-level formula. We find that the buildup of the off-resonant probability density is characterized by an oscillatory pattern modulated by the resonant case which governs the duration of the transient regime. This is evidence that off-resonant and resonant tunneling are two correlated processes, whose transient regime is characterized by the same transient time constant of two lifetimes.

quant-ph↗

arXiv2000

Exact relativistic time evolution for a step potential barrier

We derive an exact analytic solution to a Klein-Gordon equation for a step potential barrier with cutoff plane wave initial conditions, in order to explore wave evolution in a classical forbidden region. We find that the relativistic solution rapidly evanesces within a depth $2x_p$ inside the potential, where $x_p$ is the penetration length of the stationary solution. Beyond the characteristic distance $2x_p$, a Sommerfeld-type precursor travels along the potential at the speed of light, $c$. However, no spatial propagation of a main wavefront along the structure is observed. We also find a non-causal time evolution of the wavefront peak. The effect is only an apparent violation of Einstein causality.

quant-ph↗

arXiv2000

Early times in tunneling

Exact analytical solutions of the time-dependent Schrödinger equation with the initial condition of an incident cutoff wave are used to investigate the traversal time for tunneling. The probability density starts from a vanishing value along the tunneling and transmitted regions of the potential. At the barrier width it exhibits, at early times, a distribution of traversal times that typically has a peak $τ_p$ and a width $Δτ$. Numerical results for other tunneling times, as the phase-delay time, fall within $Δτ$. The Büttiker traversal time is the closest to $τ_p$. Our results resemble calculations based on Feynman paths if its noisy behaviour is ignored.

quant-ph↗