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Journal articles on the topic 'Tunneling Time'

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Published: 9 March 2023

Last updated: 10 March 2023

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1

Nimtz, Günter, and Horst Aichmann. "Zero-Time Tunneling – Revisited." Zeitschrift für Naturforschung A 72, no. 9 (August 28, 2017): 881–84. http://dx.doi.org/10.1515/zna-2017-0172.

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AbstractSince 1931, the nonclassical process of tunneling was conjectured to have a zero-time delay in the barrier. These theories have been rejected and denied. However, photonic and recent electronic tunneling experiments have proven the zero-time prediction. Tunneling is due to virtual wave packets in electromagnetic, elastic, and Schrödinger wave fields up to the macroscopic level. In this article we cite theoretical and experimental studies on zero-time tunneling, which have proven this striking behavior.

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2

Davies, P. C. W. "Quantum tunneling time." American Journal of Physics 73, no. 1 (January 2005): 23–27. http://dx.doi.org/10.1119/1.1810153.

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3

Van Labeke, Daniel, Jean-Marie Vigoureux, and Gilles Parent. "Photon tunneling time." Ultramicroscopy 71, no. 1-4 (March 1998): 11–20. http://dx.doi.org/10.1016/s0304-3991(97)00061-2.

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4

Xiao, Zhi, Hai Huang, and Xiang-Xiang Lu. "Resonant tunneling dynamics and the related tunneling time." International Journal of Modern Physics B 29, no. 08 (March 30, 2015): 1550052. http://dx.doi.org/10.1142/s0217979215500526.

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In close analogy with optical Fabry–Pérot (FP) interferometer, we rederive the transmission and reflection coefficients of tunneling through a rectangular double barrier (RDB). Based on the same analogy, we also get an analytic finesse formula for its filtering capability of matter waves, and with this formula, we reproduce the RDB transmission rate in exactly the same form as that of FP interferometer. Compared with the numerical results obtained from the original finesse definition, we find the formula works well. Next, we turn to the elusive time issue in tunneling, and show that the "generalized Hartman effect" can be regarded as an artifact of the opaque limit βl → ∞. In the thin barrier approximation, phase (or dwell) time does depend on the free inter-barrier distance d asymptotically. Further, the analysis of transmission rate in the neighborhood of resonance shows that, phase (or dwell) time could be a good estimate of the resonance lifetime. The numerical results from the uncertainty principle support this statement. This fact can be viewed as a support to the idea that, phase (or dwell) time is a measure of lifetime of energy stored beneath the barrier. To confirm this result, we shrink RDB to a double Dirac δ-barrier. The landscape of the phase (or dwell) time in k and d axes fits excellently well with the lifetime estimates near the resonance. As a supplementary check, we also apply phase (or dwell) time formula to the rectangular well, where no obstacle exists to the propagation of particle. However, due to the self-interference induced by the common cavity-like structure, phase (or dwell) time calculation leads to a counterintuitive "slowing down" effect, which can be explained appropriately by the lifetime assumptions.

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5

PARK, CHANG-SOO. "TUNNELING TIME OF A PARTICLE: TWO-DIMENSIONAL APPROACH." Modern Physics Letters B 21, no. 26 (November 10, 2007): 1733–50. http://dx.doi.org/10.1142/s0217984907014218.

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A two-dimensional problem of tunneling of a particle is studied to propose an experiment to measure tunneling time. We consider a 2D rectangular barrier in which the particle undergoes both tunneling and free lateral motion at the same time. The two processes are coupled by the same tunneling time, which leads to a simple relation between the tunneling time and the corresponding lateral shift such that L = vτ. Since the lateral speed v is constant the tunneling time can be obtained by measuring the lateral shift. The shifted length can be controlled by an initial lateral speed and become over a hundred nanometers when the particle is provided with sufficient initial lateral speed. The present model may also be used for examining the relationships between characteristic tunneling times suggested in previous articles. We also demonstrate physical differences between the 2D problem of a particle tunneling and the frustrated total internal reflection of electromagnetic waves.

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6

Dumont, Randall S., and T. L. Marchioro II. "Tunneling-time probability distribution." Physical Review A 47, no. 1 (January 1, 1993): 85–97. http://dx.doi.org/10.1103/physreva.47.85.

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7

Buttiker, Markus, and Rolf Landauer. "Traversal time for tunneling." IBM Journal of Research and Development 30, no. 5 (September 1986): 451–54. http://dx.doi.org/10.1147/rd.305.0451.

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8

Azbel', M. Ya. "Time, tunneling and turbulence." Uspekhi Fizicheskih Nauk 168, no. 06 (June 1998): 613–23. http://dx.doi.org/10.3367/ufnr.0168.199806b.0613.

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9

Azbel', M. Ya. "Time, tunneling and turbulence." Physics-Uspekhi 41, no. 6 (June 30, 1998): 543–52. http://dx.doi.org/10.1070/pu1998v041n06abeh000402.

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10

Mullen, Kieran, Eshel Ben-Jacob, Yuval Gefen, and Zeev Schuss. "Time of Zener tunneling." Physical Review Letters 62, no. 21 (May 22, 1989): 2543–46. http://dx.doi.org/10.1103/physrevlett.62.2543.

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11

Büttiker, M., and R. Landauer. "Traversal Time for Tunneling." Physica Scripta 32, no. 4 (October 1, 1985): 429–34. http://dx.doi.org/10.1088/0031-8949/32/4/031.

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12

Landauer, Rolf. "Traversal Time in Tunneling." Berichte der Bunsengesellschaft für physikalische Chemie 95, no. 3 (March 1991): 404–10. http://dx.doi.org/10.1002/bbpc.19910950332.

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13

Laikhtman, B., and E. L. Wolf. "Tunneling time and effective capacitance for single electron tunneling." Physics Letters A 139, no. 5-6 (August 1989): 257–60. http://dx.doi.org/10.1016/0375-9601(89)90151-5.

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14

Nimtz, Günter, and Horst Aichmann. "All waves have a zero tunneling time." Zeitschrift für Naturforschung A 76, no. 4 (February 19, 2021): 295–97. http://dx.doi.org/10.1515/zna-2020-0299.

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Abstract Zero tunneling time and thereby a faster than light traversal velocity was calculated nearly a hundred years ago and has been observed recently. We report about experimental results and estimations, which confirm the zero time tunneling for elastic as well as for electromagnetic and Schrödinger waves. Zero time tunneling was first observed with microwaves 1992 (H. Aichmann and G. Nimtz, Found. Phys., vol. 44, p. 678, 2014; A. Enders and G. Nimtz, J. Phys. I, vol. 2, p. 169, 1992). In 2008, zero time was also observed for tunneling electrons (P. Eckle, A. N. Pfeiffer, C. Cirelli, et al., Science, vol. 322, p. 1525, 2008). Presumably, this effect took place with atoms quite recently (R. Ramos, D. Spierings, I. Racicot, and A. M. Steinberg, Nature, vol. 583, p. 529, 2020). The Einstein relation E 2 = (ħk)2 c 2 is not satisfied in the tunneling process, since the wave number k is imaginary (E is the total energy, ħ the Planck constant, and c the vacuum velocity of light), Zero time tunneling is described by virtual photons (A. Stahlhofen and G. Nimtz, Europhys. Lett., vol. 76, p. 189, 2006). The tunneling process itself violates the Special Theory of Relativity. Remarkably, Brillouin conjectured that wave mechanics is valid for all waves independent of their field (L. Brillouin, Wave Propagation in Periodic Structures, Chap. VIII, New York, Dover Publications, 1953).

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15

ZHAO, XIAN-GENG, and MING JUN ZHU. "TUNNELING TIME BETWEEN TWO BIASED QUANTUM WELLS." Modern Physics Letters B 13, no. 12n13 (June 10, 1999): 385–90. http://dx.doi.org/10.1142/s0217984999000488.

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We study the dynamics of double-well systems under the influence of time-dependent external fields. A tunneling time describing the coherent tunneling between two quantum wells is obtained analytically by the use of perturbation theory. We illustrate two examples to show the advantage of our theory, in which the phenomenon of localization/delocalization can be addressed uniformly by the tunneling time.

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16

Kullie, Ossama. "Tunneling Time in Attosecond Experiments and Time Operator in Quantum Mechanics." Mathematics 6, no. 10 (October 8, 2018): 192. http://dx.doi.org/10.3390/math6100192.

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Attosecond science is of a fundamental interest in physics. The measurement of the tunneling time in attosecond experiments, offers a fruitful opportunity to understand the role of time in quantum mechanics (QM). We discuss in this paper our tunneling time model in relation to two time operator definitions introduced by Bauer and Aharonov–Bohm. We found that both definitions can be generalized to the same type of time operator. Moreover, we found that the introduction of a phenomenological parameter by Bauer to fit the experimental data is unnecessary. The issue is resolved with our tunneling model by considering the correct barrier width, which avoids a misleading interpretation of the experimental data. Our analysis shows that the use of the so-called classical barrier width, to be precise, is incorrect.

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17

Bhattacharya, Samyadeb, and Sisir Roy. "Dissipative Effect and Tunneling Time." Advances in Mathematical Physics 2011 (2011): 1–13. http://dx.doi.org/10.1155/2011/138358.

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The quantum Langevin equation has been studied for dissipative system using the approach of Ford et al. Here, we have considered the inverted harmonic oscillator potential and calculated the effect of dissipation on tunneling time, group delay, and the self-interference term. A critical value of the friction coefficient has been determined for which the self-interference term vanishes. This approach sheds new light on understanding the ion transport at nanoscale.

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18

Landauer, R., and Th Martin. "Barrier interaction time in tunneling." Reviews of Modern Physics 66, no. 1 (January 1, 1994): 217–28. http://dx.doi.org/10.1103/revmodphys.66.217.

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19

Huang, Z. H., P. H. Cutler, T. E. Feuchtwang, E. Kazes, H. Q. Nguyen, and T. E. Sullivan. "Model studies of tunneling time." Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films 8, no. 1 (January 1990): 186–91. http://dx.doi.org/10.1116/1.577061.

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20

Yamada, Norifumi. "Quasi-Distribution of Tunneling Time." Acta Physica Hungarica A) Heavy Ion Physics 19, no. 3-4 (April 1, 2004): 329–32. http://dx.doi.org/10.1556/aph.19.2004.3-4.31.

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21

Hagmann, Mark J. "Transit time for quantum tunneling." Solid State Communications 82, no. 11 (June 1992): 867–70. http://dx.doi.org/10.1016/0038-1098(92)90710-q.

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22

Xu, Dai-Yu, Towe Wang, and Xun Xue. "Quantum Tunneling Time: Relativistic Extensions." Foundations of Physics 43, no. 11 (September 14, 2013): 1257–74. http://dx.doi.org/10.1007/s10701-013-9744-2.

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23

Chen, Ming-Quey, and M. S. Wang. "Traversal time for quantum tunneling." Physics Letters A 149, no. 9 (October 1990): 441–44. http://dx.doi.org/10.1016/0375-9601(90)90213-8.

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24

Cahay, M., K. T. Dalton, G. S. Fisher, and A. F. M. Anwar. "Tunneling time through resonant tunneling devices and quantum-mechanical bistability." Superlattices and Microstructures 11, no. 1 (January 1992): 113–17. http://dx.doi.org/10.1016/0749-6036(92)90371-b.

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25

Huang, Zheng. "Rashba Spin-Orbit Effect on Traversal Time in Parabolic-Well Magnetic Tunneling Junction." Applied Mechanics and Materials 707 (December 2014): 338–42. http://dx.doi.org/10.4028/www.scientific.net/amm.707.338.

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Based on the phase time definition,we study theoretically the transmission coefficients and the spin-tunneling time in parabolic-well magnetic tunneling junction with a tunnel barrier in the presence of Rashba spin-orbit interaction. The significant quantum size, quantum coherence, and Rashba spin-orbit interaction are considered simultaneously. It is found that the tunneling time strongly depends on the spin orientation of tunneling electrons. We also find that as the length of the semiconductor increases, the spin tunneling time shows curved increase. It exhibits useful instructions for the design of spin electronic devices.

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26

Gaponenko, S. V., and D. V. Novitsky. "Tunneling time of electromagnetic radiation trough an ideal plasma layer." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 58, no. 2 (July 5, 2022): 231–36. http://dx.doi.org/10.29235/1561-2430-2022-58-2-231-236.

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In this paper, we derived the relation for the phase time of electromagnetic radiation tunneling through an ideal plasma layer in a dielectric for frequencies ω below the plasma frequency ωp in the limit of low transparency of the layer. Within the framework of the model under consideration, the tunneling time is found to be independent of the layer thickness and determined only by the ω and ωp values. For lower frequencies the tunneling time tends to the limit defined by the inverse plasma frequency which allows us to treat the tunneling process in this case as a ‘splash’ of a plasma layer as a whole entity to form the transmitted radiation. Since the transmittance of the plasma layer is very low, the result obtained does not allow us to speak about superluminal energy transfer.

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27

Kullie, Ossama. "Time Operator, Real Tunneling Time in Strong Field Interaction and the Attoclock." Quantum Reports 2, no. 2 (April 7, 2020): 233–52. http://dx.doi.org/10.3390/quantum2020015.

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Attosecond science, beyond its importance from application point of view, is of a fundamental interest in physics. The measurement of tunneling time in attosecond experiments offers a fruitful opportunity to understand the role of time in quantum mechanics. In the present work, we show that our real T-time relation derived in earlier works can be derived from an observable or a time operator, which obeys an ordinary commutation relation. Moreover, we show that our real T-time can also be constructed, inter alia, from the well-known Aharonov–Bohm time operator. This shows that the specific form of the time operator is not decisive, and dynamical time operators relate identically to the intrinsic time of the system. It contrasts the famous Pauli theorem, and confirms the fact that time is an observable, i.e., the existence of time operator and that the time is not a parameter in quantum mechanics. Furthermore, we discuss the relations with different types of tunneling times, such as Eisenbud–Wigner time, dwell time, and the statistically or probabilistic defined tunneling time. We conclude with the hotly debated interpretation of the attoclock measurement and the advantage of the real T-time picture versus the imaginary one.

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28

Bracher, C., and M. Kleber. "Minimum tunneling time in quantum motion." Annalen der Physik 510, no. 7-8 (December 1998): 687–94. http://dx.doi.org/10.1002/andp.199851007-813.

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29

Nimtz, G., and A. A. Stahlhofen. "Universal tunneling time for all fields." Annalen der Physik 520, no. 6 (June 5, 2008): 374–79. http://dx.doi.org/10.1002/andp.20085200603.

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30

Dragoman, D. "Tunneling time asymmetry in semiconductor heterostructures." IEEE Journal of Quantum Electronics 35, no. 12 (1999): 1887–93. http://dx.doi.org/10.1109/3.806604.

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31

Zhang, Chao, and Narkis Tzoar. "Virtual Process in Time-dependent Tunneling." Physica Scripta T25 (January 1, 1989): 333–35. http://dx.doi.org/10.1088/0031-8949/1989/t25/060.

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32

McCutchen, Charles W. "Photon Tunneling Goes Back in Time." Physics Today 48, no. 10 (October 1995): 104. http://dx.doi.org/10.1063/1.2808232.

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33

Shu, Zheng, Xiaolei Hao, Weidong Li, and Jing Chen. "General way to define tunneling time." Chinese Physics B 28, no. 5 (May 2019): 050301. http://dx.doi.org/10.1088/1674-1056/28/5/050301.

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34

Zhai, Feng, Yong Guo, and Bing-Lin Gu. "Tunneling time in magnetic barrier structures." European Physical Journal B 29, no. 1 (September 2002): 147–52. http://dx.doi.org/10.1140/epjb/e2002-00273-y.

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35

van Houselt, Arie, and Harold J. W. Zandvliet. "Colloquium: Time-resolved scanning tunneling microscopy." Reviews of Modern Physics 82, no. 2 (May 17, 2010): 1593–605. http://dx.doi.org/10.1103/revmodphys.82.1593.

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36

Camus, N., E. Yakaboylu, L. Fechner, M. Klaiber, M. Laux, Y. Mi, K. Z. Hatsagortsyan, T. Pfeifer, C. H. Keitel, and R. Moshammer. "Experimental Evidence for Wigner’s Tunneling Time." Journal of Physics: Conference Series 999 (April 2018): 012004. http://dx.doi.org/10.1088/1742-6596/999/1/012004.

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37

Ergenzinger, Klaus. "Multiphoton ionization as time-dependent tunneling." Physical Review A 55, no. 1 (January 1, 1997): 577–88. http://dx.doi.org/10.1103/physreva.55.577.

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38

Schulman, L. S. "Jump time in Landau-Zener tunneling." Physical Review A 58, no. 2 (August 1, 1998): 1595–96. http://dx.doi.org/10.1103/physreva.58.1595.

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39

de Aquino, Veríssimo M., Valdir C. Aguilera-Navarro, Mario Goto, and Hiromi Iwamoto. "Tunneling time through a rectangular barrier." Physical Review A 58, no. 6 (December 1, 1998): 4359–67. http://dx.doi.org/10.1103/physreva.58.4359.

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40

Landsman, A. S., T. Zimmermann, and S. Mishra. "Tunneling time in strong field ionisation." Journal of Physics: Conference Series 635, no. 9 (September 7, 2015): 092138. http://dx.doi.org/10.1088/1742-6596/635/9/092138.

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41

Turok, Neil. "On quantum tunneling in real time." New Journal of Physics 16, no. 6 (June 5, 2014): 063006. http://dx.doi.org/10.1088/1367-2630/16/6/063006.

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42

Nitzan, Abraham, Joshua Jortner, Joshua Wilkie, Alexander L. Burin, and Mark A. Ratner. "Tunneling Time for Electron Transfer Reactions." Journal of Physical Chemistry B 104, no. 24 (June 2000): 5661–65. http://dx.doi.org/10.1021/jp0007235.

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43

Kira, M., I. Tittonen, W. K. Lai, and S. Stenholm. "Semiclassical computations of time-dependent tunneling." Physical Review A 51, no. 4 (April 1, 1995): 2826–37. http://dx.doi.org/10.1103/physreva.51.2826.

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44

Keski-Vakkuri, Esko, and Per Kraus. "Tunneling in a time-dependent setting." Physical Review D 54, no. 12 (December 15, 1996): 7407–20. http://dx.doi.org/10.1103/physrevd.54.7407.

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45

Kelkar, N. G., H. M. Castañeda, and M. Nowakowski. "Quantum time scales in alpha tunneling." EPL (Europhysics Letters) 85, no. 2 (January 2009): 20006. http://dx.doi.org/10.1209/0295-5075/85/20006.

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46

Kotler, Zvi, and Abraham Nitzan. "Traversal time for tunneling: Local aspects." Journal of Chemical Physics 88, no. 6 (March 15, 1988): 3871–78. http://dx.doi.org/10.1063/1.453835.

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47

Moretti, P., D. Mugnai, A. Ranfagni, and M. Cetica. "Traversal time in macroscopic quantum tunneling." Physical Review A 60, no. 6 (December 1, 1999): 5087–90. http://dx.doi.org/10.1103/physreva.60.5087.

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48

Burgess, C. P. "Quantum tunneling and imaginary‐time paths." American Journal of Physics 59, no. 11 (November 1991): 994–98. http://dx.doi.org/10.1119/1.16659.

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49

BANDOPADHYAY, SWARNALI, and A. M. JAYANNAVAR. "PHASE TIME FOR A TUNNELING PARTICLE." International Journal of Modern Physics B 21, no. 10 (April 20, 2007): 1681–704. http://dx.doi.org/10.1142/s0217979207036941.

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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.

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50

Stein, Benjamin P. "Observing electron tunneling in real time." Physics Today 60, no. 6 (June 2007): 27. http://dx.doi.org/10.1063/1.2754592.

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