Ionization of Rydberg atoms in Intense, Single-cycle THz field 4 th year seminar of Sha Li Advisor: Bob Jones Dept. of Physics, Univ. of Virginia, Charlottesville, VA, 22904 April. 15 th, 2013
Outline Outline Background Introduction of Rydberg atoms Brief review of several typical types of field ionization My work Intense THz generation via optical rectification THz streak THz ionization of low-lying Rydberg atoms THz ionization of Rydberg stark states Future Plan Electron Scattering
Rydberg atoms Energy (a.u.) Hydrogen-like atoms Rydberg atoms Valance electron at highly excited orbit, with large principle quantum number n Experience effectively +1 net charge, can be considered as one electron system, but due to finite core size, QUANTUM DEFECT Sketch of a Kepler orbit with low angular momentum 1 En 2( n nl, ) 1 E n 1 E n 3 n 2 r T 3 2 n 2 n 1 3 n 3 2 n=6 n=15 0.38eV 0.06eV 0.13eV 0.008eV 54a 0 338a 0 0.03ps 0.5ps 30THz 2THz 0-0.01-0.02 n=6 n=15-2000 -1000 0 1000 2000 Z (a 0 ) Hydrogen coulomb potential and energy diagram
Examples of Field ionization Examples of Field ionization ω Field ~ω atom
Examples of Field ionization Field ω F >ω atom Half Cycle Pulse: impulsive regime Time F 1 n 2 ~ 1 n R. R. Jones, D. You, and P. H. Bucksbaum, Phys. Rev. Lett. 70, 12361239 (1993)
Examples of Field ionization Field ω F < ω atom, static or quasi-static field. Classical field ionization. Time F = 1 Cn 4 T. F. Gallagher, Rydberg Atoms, Cambridge University Press (1994)
Field Examples of Field ionization ω F < ω atom, Multi-cycle Microwave ionization. n=29 n=28 n=27 n=26 n=25 n=24 n=23 Energy Classical Ionization Limit n=22 Time n=21 n=20-2000 -1000 0 1000 2000 Field (V/cm) F = 1 3n 5 P. Pillet, T. F. Gallagher, et.al Phys. Rev. A 30, 280294 (1984)
THz ionization of low-lying Rydberg atoms Field Our Experiment Low-lying n levels (n=6-15), which require very high field for ionization Oscillating field, but single cycle Very fast pulsed field T~4ps compared to ns or μs scale pulsed field usually used. And very strong peak field strength ~500 kv/cm 0-0.01-0.02 n=6 n=15-2000 -1000 0 1000 2000 Z (a 0 ) But still relatively slow (ω F < ω atom ) compared to the Kepler period of the Rydberg atoms studied: T (n=6-15) range from 0.03ps~0.5ps Time
THz ionization of low-lying Rydberg atoms Field Relatively slow: ω F < ω atom Absolutely fast: ps scale F 1 n? Time
THz generation Characteristics of THz radiation Frequency: ν = 1 THz = 10 12 Hz Period: τ = 1/ν = 1 ps = 10 12 S Wavelength: λ = c/ν = 0.3 mm = 300 μm Wavenumber: 1/λ = 33.3 cm 1 Photon energy: ħω = 4.14 mev Temperature: T = hν/kb = 48 K Xi-Cheng Zhang, Jingzhou Xu, Introduction to THz Wave Photonics, Springer (2009) Yun-Shik Lee, Principles of Terahertz Science and Technology, Springer (2008)
THz generation THz generation via Optical Rectification χ 2 Phase matching LiNbO3 Second order nonlinear effect Difference-frequency mixing among the spectral components contained within the ultrashort pulse bandwidth v g pump v phase THz Large nonlinear coefficient Less THz absorption
THz generation Tilted-Pulse-Front Pumping J. Hebling, Keith A. Nelson, et.al JOSA B, Vol. 25, Issue 7, pp. B6-B19 (2008)
THz generation Field strength (arb. unit) Electro-Optic Sampling n2 1/ 2{1, 1, 2} n1 1/ 2{ 1,1, 2} n n n n 1 0 n 2 0 n 3 0 3 n0 41E 2 3 n0 41E 2 THz THz d ( n n ) E c 1 2 THz 40 30 20 n3 1/ 2{ 2, 2, 0} 10 0-10 -9-8 -7-6 -5-4 -3-2 -1 0-10 1 2 3 4 5 6 7 8 9 10-20 -30-40 time(ps)
THz Streak THz Streak e- p t F() t dt e- e-
THz Streak: Experimental setup THz Streak: Experimental setup 589.8 nm Na beam Na+ & e- THz 390nm 150fs blue Pump LiNbO3 3p 3s 589.8nm Polarizers THz 390nm 150fs blue Delay 589.8 nm 390nm 150fs blue Time
THz Streak: Result THz Streak: Result
THz ionization of low-lying Rydberg atoms THz ionization: Experimental Setup
THz ionization of low-lying Rydberg atoms Ionization Probability Ion yield curve 1 0.8 0.6 0.4 0.2 0 0 100 200 300 400 500 THz field (kv/cm) 10% n=6 n=7 n=8 n=9 n=10 n=11 n=12 n=13 n=14 n=15
THz ionization of low-lying Rydberg atoms THz Field (kv/cm) New Scale Law: F 1!!! n3 300 200 100 Experimental * CMC Simulation 50 F = 1 16n 4 10 6 7 8 9 10 11 12 13 14 15 n
THz ionization of low-lying Rydberg atoms THz Field (kv/cm) 300 200 100 Experimental * CMC Simulation 50 F = 1 16n 4 10 6 7 8 9 10 11 12 13 14 15 n n=15 n=6
Analyze electron energy distributions Electron energy distributions at Max THz field (470 kv/cm)
Probability Analyze electron energy distributions Ionization Probability ΔP Qualitative analysis 1.0 0.8 0.6 10d 0.4 0.2 6d 0.0 0 100 200 300 400 500 1 THz Field (kv/cm) 0.1 0.01 1E-3 1E-4 1 10d 6d 20 40 60 Energy (ev) p Time t F() t dt
Field Analyze electron energy distributions Time
Analyze electron energy distributions Ponderomotive Energy Up: The cycle averaged quiver energy of a free electron in an oscillating electric field: Up = e2 F 2 4mω 2 = F2 4ω 2 (a.u.) 2Up: The max energy a free electron can get from a oscillating electric field that slowly decreases in aptitude: Max energy=2up What if the field have only a few cycles, or even one single cycle?
Analyze electron energy distributions 100.2 ev ~0.25THz and ~322 kv/cm F(t)=F 0 sin(ωt) ΔP = F t dt t0 E = (2P 0 P + ( P) 2 )/2 Up = F2 4ω 2 18. 5 ev Max energy~ 5. 4 Up!!!
Energy (a.u.) THz ionization of Rydberg Stark states What if the Rydberg atoms are initially prepared in Stark states? 11p 10d F = 1 Cn 4 11s Field (kv/cm) Na n=10, m=0 Stark manifold
Field (arb. unit) THz ionization of Rydberg Stark states Na+/e- elec. ion +/ 0.15 0.14 0.13 0.12 0.11 elec. ion 0.1 0.09 0 1 2 3 4 5 6 7 8 9 nth stark level
THz ionization of Rydberg Stark states Landau-Zener Transition Simplest case: 2-level H(F)= E 1(F) 1 2 E 1 2 E E 2(F) E 2 E + E E + E 1 E E: coupling/quantum defect P dia =e 2πΓ E 1 E E E 2 Γ= (1 2 E)2 = ( 2 E)2 de1 dt de2 dt de1 F 1 df de2 df F
THz ionization of Rydberg Stark states THz field E + E + E E F 0 E F E + E + t E E F 0 E F
THz ionization of Rydberg Stark states What may influence the result? Aptitude of static field Direction of static field (Relative to THz) Initial stark level Asymmetry of THz and THz slew rate
THz ionization of Rydberg Stark states Multi-level Landau-Zener Transitions () t i H( t) ( t) t ien ( t) Cn( t) n( t) e n Spherical basis n, l, m > : Ψ n, E n ( t ) t i E fn i C ( t) C ( t) H ( t) e f n fn n Parabolic/Diabatic basis n, k, m > : Ψ n, E n (t) i C ( t) C ( t) H ( t) e f n fn n Adiabatic/Local basis : (no good quantum #) t 0 i E Ψ n (t), E n (t) fn t ( t ) dt
THz ionization of Rydberg Stark states Still working on numerical simulation codes!
Future plan Future plan Electron Scattering Electron been dragged back by THz to the nucleus and knocks off more electrons.
Conclusion Conclusion Intense THz generation via optical rectification Can generate THz with peak field strength as high as 500 kv/cm THz streak & Electron energy distributions Can measure THz waveform inside the chamber. Electrons from ionization of lower n states have higher energies Electron energy distribution shows the asymmetry of the field In THz streak, have electrons with energy exceed 2Up. THz ionization of low-lying Rydberg atoms and Rydberg stark states Ionization of low-lying Rydberg atoms: Scales as 1/n^3 Ionization of Rydberg stark states: Shows the asymmetry and fast property of THz field.
Thank you!
Field Analyze electron energy distributions Time
THz ionization of Rydberg Stark states Numerical Simulation: 2 -Level Γ= (1 2 E)2 = ( 2 E)2 de1 dt de2 dt de1 F 1 df de2 df Initially in state, with a linear ramp F = kt from very large negative time to very large positive time. work in 1>, 2> basis P1 P1 500k 50k 10k 5k k E 10 E E 2 E + E E + E 1 25 E E 50 E E 1 E E E 2 100 E F t t +
THz ionization of low-lying Rydberg atoms signal/pi (arb. u.) 8.0E-06 7.0E-06 6.0E-06 5.0E-06 4.0E-06 3.0E-06 2.0E-06 1.0E-06 0.0E+00 0 100 200 300 400 500 600 Energy/n^3 arb. u. 3s-nd excitation prob. curves 6d/0.3846 7d/0.6631 8d/0.7692 9d/0.9077 10d/1 sig i i. Pe PN i 3s E Pe 3 n sig P N P sig P E 3 n E n N e 3s 3 3s
Analyze electron energy distributions Time of Flight (ToF) spectrometer MCP md 2 2d1eU d2 t t0 ( v0 v0 ) eu md 2 2d1eU v0 md d2 T (ns) v0 d d1 U -U (V)