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Phase dealy time and superluminal propagation in barrier tunneling

Swarnali Bandopadhyay, A. M. Jayannavar

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

In this work we study the behaviour of Wigner phase delay time for tunneling in the reflection mode. Our system consists of a circular loop connected to a single wire of semi-infinite length in the presence of Aharonov-Bohm flux. We calculate the analytical expression for the saturated delay time. This saturated delay time is independent of Aharonov- Bohm flux and the width of the opaque barrier thereby generalizing the Hartman effect. This effect implies superluminal group velocities as a consequence. We also briefly discuss the concept called collapse or space destroyer.

Related papers

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We study the nature of tunneling phase time for various quantum mechanical structures such as networks and rings having potential barriers in their arms. We find the generic presence of the Hartman effect, with superluminal velocities as a consequence, in these systems. In quantum networks, it is possible to control the "super arrival" time in one of the arms by changing the parameters on another arm which is spatially separated from it. This is yet another quantum nonlocal effect. Negative time delays (time advancement) and "ultra Hartman effect" with negative saturation times have been observed in some parameter regimes. In the presence and absence of Aharonov-Bohm (AB) flux, quantum rings show the Hartman effect. We obtain the analytical expression for the saturated phase time. In the opaque barrier regime, this is independent of even the AB flux thereby generalizing the Hartman effect. We also briefly discuss the concept of "space collapse or space destroyer" by introducing a free space in between two barriers covering the ring. Further, we show in presence of absorption that the reflection phase time exhibits the Hartman effect in contrast to the transmission phase time.

arXiv:quant-ph/0511089•International Journal of Modern Physics B•Apr 20, 2007•8 citations

Energy storage in superluminal barrier tunneling: Origin of the Hartman effect

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We show that the anomalously short delay times observed in barrier tunneling have their origin in energy storage and its subsequent release. The observed group delay is proportional to the energy stored. This delay is not a propagation delay and should not be linked to a velocity since evanescent waves do not propagate. The "Hartman effect", in which the group delay becomes independent of thickness for opaque barriers, is shown to be a consequence of the saturation of stored energy with barrier length.

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Tunneling Times and "Superluminal" Tunneling: A brief Review

V. S. Olkhovsky, Erasmo Recami

In the First Part of this paper [that was submitted for pub. in 1991 and appeared in print in Phys. Reports 214 (1992) 339] we critically review the main theoretical definitions and calculations of the sub-barrier tunnelling and reflection times. Moreover, within conventional QM, we propose a new definition of such durations, on the basis of a recent general formalism of ours. At last, we discuss a surprising result: that QM predicts tunnelling through opaque barriers to take place with Superluminal group-velocities. In the Second Part [that appeared in print later, in J. de Physique-I 5 (1995) 1351] we, e.g., present the results of some numerical calculations (based on our equations) on the penetration and return times during tunnelling INSIDE a rectangular potential barrier, and set forth suitable definitions also of the variances, or dispersions, for the transmission and reflection time-durations. The numerical evaluations confirm that our approach implied, and implies, the existence of Superluminal tunnelling (that we called "Hartman effect"): an effect that in these days is receiving --at Cologne, Berkeley, Florence and Vienna-- indirect, but interesting, experimental verifications. More detailed reviews of the same topics are in the LANL Archive cond-mat/9802126 (and in an Appendix to physics/9712051, where the data are summarized of the experiments that --in four different sectors of physics-- seem to indicate the existence of Superluminal motions).

arXiv:cond-mat/9802162•Feb 15, 1998•1 citation

Superluminal tunnelling through successive barriers: Does QM predict infinite group-velocities?

Erasmo Recami

The phenomenon of one-dimensional non-resonant tunnelling is analyzed through two or more successive (opaque) potential barriers, separated by intermediate free regions R, just by exploiting the relevant solutions to the Schroedinger equation. The total traversal time has been shown by us to be independent not only of the barrier widths (the so-called ‘Hartman effect’), but also of the R-widths: so that the effective group velocity in the regions R, between two successive barriers, can be regarded as practically infinite. Such a prediction has been theoretically confirmed and generalized (as well as interpreted in terms of ‘super-oscillations’) by Aharonov et al. A recent experiment by Longhi et al. supported the predictions by considering two successive gratings in an optical fibre, that is, by having recourse to two ‘classical barriers’ (which allow simulating the tunnelling, due to the known formal identity between the Schrödinger and the Helmholtz equation).

Journal of Modern Optics•Apr 1, 2004•34 citations

Physical mechanism for apparent superluminality in barrier tunneling

Herbert G. Winful

Tunneling without distortion is not a propagation phenomenon but a quasistatic process in which the slowly varying envelope of the input pulse modulates the amplitude of a standing wave in the barrier. Because the envelope has a bandwidth that is small compared to the cutoff frequency of the barrier it does not propagate; it merely stands and waves. The envelope of the reflected and transmitted fields can adiabatically follow the envelope of the input pulse with only a small delay proportional to the energy stored in the barrier. The Hartman effect, in which the delay becomes independent of barrier length, is explained on the basis of saturation of stored energy with increasing length. Because the delay is not a propagation delay, it should not be linked to a velocity of propagation. True evanescent waves have zero speed and not infinite velocity as often asserted.

IEEE Journal of Selected Topics in Quantum Electronics•Jan 1, 2003•22 citations
In this work we study the behaviour of Wigner phase delay time for tunneling in the reflection mode. Our system consists of a circular loop connected to a single wire of semi-infinite length in the presence of Aharonov-Bohm flux. We calculate the analytical expression for the saturated delay time. This saturated delay time is independent of Aharonov- Bohm flux and the width of the opaque barrier thereby generalizing the Hartman effect. This effect implies superluminal group velocities as a consequence. We also briefly discuss the concept called collapse or space destroyer.
We study the nature of tunneling phase time for various quantum mechanical structures such as networks and rings having potential barriers in their arms. We find the generic presence of the Hartman effect, with superluminal velocities as a consequence, in these systems. In quantum networks, it is possible to control the "super arrival" time in one of the arms by changing the parameters on another arm which is spatially separated from it. This is yet another quantum nonlocal effect. Negative time delays (time advancement) and "ultra Hartman effect" with negative saturation times have been observed in some parameter regimes. In the presence and absence of Aharonov-Bohm (AB) flux, quantum rings show the Hartman effect. We obtain the analytical expression for the saturated phase time. In the opaque barrier regime, this is independent of even the AB flux thereby generalizing the Hartman effect. We also briefly discuss the concept of "space collapse or space destroyer" by introducing a free space in between two barriers covering the ring. Further, we show in presence of absorption that the reflection phase time exhibits the Hartman effect in contrast to the transmission phase time.
We show that the anomalously short delay times observed in barrier tunneling have their origin in energy storage and its subsequent release. The observed group delay is proportional to the energy stored. This delay is not a propagation delay and should not be linked to a velocity since evanescent waves do not propagate. The "Hartman effect", in which the group delay becomes independent of thickness for opaque barriers, is shown to be a consequence of the saturation of stored energy with barrier length.
Recent papers suggest that tunneling wave packets traverse the region of allowed propagation between two potential barriers with superluminal group velocity and in a time independent of barrier separation. This phenomenon has been termed the "generalized Hartman effect" and extended to multiple barriers. Here we show that this delay time is not a transit time but a cavity lifetime. It does not imply superluminal velocity. Reported experimental verifications of this effect are reinterpreted.
In the First Part of this paper [that was submitted for pub. in 1991 and appeared in print in Phys. Reports 214 (1992) 339] we critically review the main theoretical definitions and calculations of the sub-barrier tunnelling and reflection times. Moreover, within conventional QM, we propose a new definition of such durations, on the basis of a recent general formalism of ours. At last, we discuss a surprising result: that QM predicts tunnelling through opaque barriers to take place with Superluminal group-velocities. In the Second Part [that appeared in print later, in J. de Physique-I 5 (1995) 1351] we, e.g., present the results of some numerical calculations (based on our equations) on the penetration and return times during tunnelling INSIDE a rectangular potential barrier, and set forth suitable definitions also of the variances, or dispersions, for the transmission and reflection time-durations. The numerical evaluations confirm that our approach implied, and implies, the existence of Superluminal tunnelling (that we called "Hartman effect"): an effect that in these days is receiving --at Cologne, Berkeley, Florence and Vienna-- indirect, but interesting, experimental verifications. More detailed reviews of the same topics are in the LANL Archive cond-mat/9802126 (and in an Appendix to physics/9712051, where the data are summarized of the experiments that --in four different sectors of physics-- seem to indicate the existence of Superluminal motions).
The phenomenon of one-dimensional non-resonant tunnelling is analyzed through two or more successive (opaque) potential barriers, separated by intermediate free regions R, just by exploiting the relevant solutions to the Schroedinger equation. The total traversal time has been shown by us to be independent not only of the barrier widths (the so-called ‘Hartman effect’), but also of the R-widths: so that the effective group velocity in the regions R, between two successive barriers, can be regarded as practically infinite. Such a prediction has been theoretically confirmed and generalized (as well as interpreted in terms of ‘super-oscillations’) by Aharonov et al. A recent experiment by Longhi et al. supported the predictions by considering two successive gratings in an optical fibre, that is, by having recourse to two ‘classical barriers’ (which allow simulating the tunnelling, due to the known formal identity between the Schrödinger and the Helmholtz equation).
Tunneling without distortion is not a propagation phenomenon but a quasistatic process in which the slowly varying envelope of the input pulse modulates the amplitude of a standing wave in the barrier. Because the envelope has a bandwidth that is small compared to the cutoff frequency of the barrier it does not propagate; it merely stands and waves. The envelope of the reflected and transmitted fields can adiabatically follow the envelope of the input pulse with only a small delay proportional to the energy stored in the barrier. The Hartman effect, in which the delay becomes independent of barrier length, is explained on the basis of saturation of stored energy with increasing length. Because the delay is not a propagation delay, it should not be linked to a velocity of propagation. True evanescent waves have zero speed and not infinite velocity as often asserted.