Динамика туннелирования

1. Динамика туннелирования Л. Келдыш ФИАН Конференция к 100-летию И. Я. Померанчука ИТЭФ, 5 Июня 2013г.

2. План • 1. Нелинейная ионизация атомов: Многоквантовый фотоэффект и Туннельный эффект • 2. Электрофотопоглощение в кристаллах

3. Tunneling – Quantum Mechanical penetration of particles through potential barriers Nuclear α-decay (Gamov, 1928) Atom Ionization by electric field (Openheimer, 1928) Cold emission of electrons from metals (Fowler and Nordheim, 1928)

5. Two ways of atoms’ ionization by the electrc field Photoeffect – high frequency, linear Ionization rate Tunneling – low frequency, highly nonlinear Ionization rate How do these effects compete at optical fields?

6. Parameters and scales Coulomb (atomic) units - More convenient - (generally • ) Field frequency – Typically for powerful lasers . Field strength – Intensity scale

16. Photoelectron Energy Spectrum

19. Ultrashort Pulses (USP)

20. Предельно короткие импульсы (В. С. Попов, 2000: ЛК, 2000) Half-cycle (HCP) pulses: And OCP-pulses:

21. No problem to solve numerically forany particular pulseshapeoff(t). Because of the extreme nonlinearity does not reduce to the sum of independent harmonics contributions. Number and energies of absorbed photons not defined exactly. No moreseparate channels.

23. Still some general features exist. • Characteristic parameter ranges: • Lowest fields - Linear absorbtion due to highest harmonics usually exponentially small.

24. 2. Highest fields - • universal tunneling ionization. Main contribution – "jet" with momentum ~ from the narrow part of the pulse, close to the field maximum. If two or more maxima of - coherent contributions, interference. For periodicwave – "quantization" of ejected electron energies.

25. Intermediate (moderate field strength) range – - strongpulse shape sensitivity. No general rule (formula). Defined predominately by the narrow vicinity of thef(t) singularity in the complex t-plane, closest to the real axis

27. for Lorentzian and for solitonlike pulse

28. Electroabsorption in Semiconductors Under Strong THz Pulses

29. Tunneling assisted electro-photoabsorption • Dynamic cwelectroabsorption • Electroabsorption under THz pulses • Tunneling vsmultiphoton assisted processes

30. Tunneling Assisted Photoabsorption

31. Interband electro-photoabsorption Tunneling through the barrier under the electric field action (Fowler and Nordheim, 1928) H – the energy barrier height. Valence electron becomes capable of absorbing the photon , while penetrating into the energy gap to the depth ("barrier") Absorption coefficient Effective absorption threshold red shift under static field

32. Electroabsorption Spectrum

33. Electroabsorption Under Strong cw Field

34. Dynamic electro-photoabsorption. Y. Yacobi, 1968 Jauho and Johnsen, 1996Nordstrom et al.,1998 ac fields. Ladder of (multi)photon replicas - absorption of the optical photon assisted by a few fir photons. Electroabsorptionunder USP. (LK, 2005) Pulse durationT~1psec 10fsec- THz range. Half-cycle type –unipolar splash. The problem completely equivalent to the multiquantum photoeffect with(I, Eg)Egћω. Then parameters and

35. Absorption Change

36. The total absorption in the pulse and Tunneling for λ>1, i. e. and "multiphoton" processes for λ<1, i. e.

37. Full lines for solitonlike HC pulse E(t)~cosh-2(t/T), dotted lines for the static field of the same strength. ForT=30 fsec unit of Δ corresponds in GaAs to ~20 meV, the unity of f - to ~50 kV/cm field strength(5 MW/cm2 intensity).