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ELI-NP at Magurele - �Pulse and Impulse of ELI� 1) " Polaritonic pulse and coherent X- and gamma rays from Compton (Thomson) backscattering" (MApostol&MGanciu), J. Appl. Phys. 109 013307 (2011) (1-6) 2)�Dynamics of electron�positron pairs in a vacuum polarized by an external radiation �eld� (MA), Journal of Modern Optics, 58 611 (2011) 3)� Classical interaction of the electromagnetic radiation with two-level polarizable matter� (MA), Optik 123 193 (2012) 4)� Coherent polarization driven by external electromagnetic �elds� (MA&MG), Physics Letters A374 4848 (2010) 2
5)�Coupling of (ultra-) relativistic atomic nuclei with pho- tons� (MA&MG), AIP Advances 3 112133 (2013) 6)�Propagation of electromagnetic pulses through the surface of dispersive bodies� (MA), Roum J. Phys. 58 1298 (2013) 7)� Giant dipole oscillations and ionization of heavy atoms by intense electromagnetic pulses� (MA), Roum. Reps. Phys. (2015) 8)� Parametric resonance � in rotation molecular spectra� (MA) 3
INSTITUTE of PHYSICS and NUCLEAR ENGINEERING Magurele-Bucharest Parametric resonance in rotation molecular spectra or Rotation molecular spectra in static electric �elds M Apostol April 2015 4
What can we do with (high-power) lasers and nuclei? 1) Lasers accelerate (plasma) electrons and ions (p); 10 MeV , good �ux 2) Electrons → γ (bremsstrahlung; Compton); 10 MeV ; good �ux 3) Nuclear reactions: �ssion, (p,n)-emission, transmutation, n- sources Improve nuclear data, applications (isotopes, transm) 5
Other, di�erent, new Nuclear Phys Lasers produce strong and very strong electric (magnetic) �elds Nuclei in strong �elds: change of levels → change in reaction rate, decay (Lasers �elds slow ← nuclear processes) → Very similar with Molecules in Strong Fields With a di�erence: Laser �elds are fast ← → molecular processes 6
Strong time-dependent electric �elds: E 0 cos Ω t , Ω = 2 π · 10 15 s − 1 ( 1 eV ) 10 20 w/m 2 → E 0 = 10 9 statvolt/cm (compare at �elds 10 6 ) (Not as high as Schwinger limit 10 13 and non-linear QED!) Accel qE 0 m , velocity qE 0 m Ω , path d = qE 0 m Ω 2 , compare with l (atoms, mols, nuclei) Nuclei: d = 10 − 8 cm ≫ l : shift of en levels Mols: similar, d = 10 − 8 cm ∼ l ; on the border Atoms: d = 0 . 1 µ ≫ l : shift the levels 7
What happens: E m → E m + qcE 0 cos Ω t Ω ℏ ( E m + n Ω) t (coherent states) Dressed states: e − i Transitions, decay, etc 8
Molecular Phys in Strong Fields (ionization, dissociation, chem reactions) Molecular spectroscopy First, in static el �elds (then in fast el �elds) 9
Generalities (well known) Molecules, el dipole moment d = 10 − 18 esu Spherical pendulum (spherical top, spatial, rigid rotator) Coupling time-dependent el �eld = ⇒ (free) rotation (and vibra- tion) spectra ν = 10 11 − 10 13 s − 1 (infrared) 10
Special situations (less known) External static electric �eld (highly-oscillating �elds?) Internal static electric �eld (polar matter; pyroelectrics, ferro- electrics) Low temperatures Heavy polar impurities 11
Free rotations: Approx azimuthal rotations+zenithal oscillations ϕ 2 sin 2 θ ) = L 2 H = 1 l 2 = 1 θ 2 + ˙ 2 Ml 2 ( ˙ 2 M ˙ 2 I L x = Mr 2 ( − ˙ ϕ sin θ cos θ cos ϕ ) , L y = Mr 2 ( ˙ ϕ sin θ cos θ sin ϕ , θ sin ϕ − ˙ θ cos ϕ − ˙ L z = Mr 2 ˙ ϕ sin 2 θ [ ] ∂ 2 1 1 ∂θ (sin θ ∂ ∂ L 2 = − ℏ 2 ∂θ ) + sin 2 θ ∂ϕ 2 sin θ Y lm , ℏ 2 l ( l + 1) , l = 0 , 1 , ... ; L z = − i ℏ ∂ ∂ϕ , L z Y lm = ℏ mY lm , m = − l, − l + 1 , ...l .; degeneracy 2 l + 1 12
Classical eqs of motion ϕ 2 sin θ cos θ , I d ϕ sin 2 θ ) = 0 ¨ θ = ˙ dt ( ˙ ϕ = L z /I sin 2 θ ; conserved L ˙ L 2 H = 1 θ 2 + z 2 I ˙ 2 I sin 2 θ z / 2 I sin 2 θ , minimum for E�ective potential function U eff = L 2 θ = π/ 2 , δϑ = θ − π/ 2 θ 2 + L 2 2 I δθ 2 + L 2 H ≃ 1 z z 2 Iδ ˙ 2 I Precession ϕ = ω 0 t , ω 0 = L z /I , oscillation δθ = A cos( ω 0 t + δ ) 13
Coupling : H int ( t ) = − dE cos θ cos ωt Eqs ϕ 2 sin θ cos θ − dE ¨ θ = ˙ I sin θ cos ωt , ϕ sin 2 θ ) = 0 ; I d dt ( ˙ L 2 z U eff = 2 I sin 2 θ Harmonic-oscillator 0 δθ = − dE θ + ω 2 δ ¨ I cos ωt where ω 0 = L z /I = ℏ m/I 14
Solution δθ = a cos ωt + b sin ωt ω − ω 0 γ dE ( ω − ω 0 ) 2 + γ 2 , b = − dE a = 2 Iω 0 2 Iω 0 ( ω − ω 0 ) 2 + γ 2 typical resonance Approx: L z ≃ L ( m ≃ l , L 2 x + L 2 y ≪ L 2 z ≃ L 2 ) Mean absorbed power 2 dEbω 0 = d 2 E 2 θ cos ωt = − 1 γ P = − dEδ ˙ ( ω − ω 0 ) 2 + γ 2 4 I 15
QM (exact) ω 0 = ( E l +1 − E l ) / ℏ = ( ℏ /I )( l + 1) ∂ | c lm | 2 = πd 2 E 2 | (cos θ ) lm | 2 δ ( ω 0 − ω ) 2 ℏ 2 ∂t � � � ( l + 1) 2 − m 2 � (cos θ ) lm = (cos θ ) l +1 ,m ; l,m = − i (2 l + 1)(2 l + 3) ∂ | c lm | 2 ∑ l ∑ l = πd 2 E 2 m = − l | (cos θ ) lm | 2 δ ( ω 0 − ω ) = P q = ℏ ω 0 ω 0 m = − l ∂t 2 ℏ = d 2 E 2 ( ω − ω 0 ) 2 + γ 2 = d 2 E 2 γ γ 6 I ( l + 1) 2 6 ℏ ω 0 ( l + 1) ( ω − ω 0 ) 2 + γ 2 16
Finite temperatures P q,th = πd 2 E 2 ω 0 × 2 ℏ m = − l | (cos θ ) lm | 2 [ e − β ℏ 2 l ( l +1) / 2 I − e − β ℏ 2 ( l +1)( l +2) / 2 I ] × ∑ l δ ( ω 0 − ω ) /Z ∑ (2 l + 1) e − β ℏ 2 l ( l +1) / 2 I = 2 I Z = β ℏ 2 l =0 is the partition function ( ) 2 β ℏ 2 P q,th = πd 2 E 2 e − β ℏ 2 l ( l +1) / 2 I δ ( ω 0 − ω ) = 12 I ( l + 1) 3 I ( ) 2 β ℏ 2 e − β ℏ 2 l ( l +1) / 2 I = 1 2 P q ( l + 1) I 17
Typical values: I = 10 − 38 g · cm 2 (molecular mass M = 10 5 elec- tronic mass m = 10 − 27 g , the dipole length r = 10 − 8 cm ( 1 �)), and get ℏ /I = 10 11 s − 1 ≃ 1 K ( ω 0 = ℏ m/I , or ω 0 = ℏ ( l + 1) /I ) Room temperature β ℏ 2 ( l + 1) /I ≪ 1 ) (many levels) 18
Harmonic oscillator , energy levels ℏ ω 0 ( n + 1 / 2) , n = 0 , 1 , 2 ... , ω 0 = L z /I = ℏ m/I , m = 0 , 1 , 2 ... ; ω 0 = ℏ m/I → q-m frequency ω 0 = ( E l +1 − E l ) / ℏ = ( ℏ /I )( l + 1) Transitions n → n + 1 , absorbed power P n = πd 2 E 2 ( n + 1) δ ( ω 0 − ω ) 4 I Total power N P n = πd 2 E 2 ∑ P osc = m ( m + 1 / 2) δ ( ω 0 − ω ) 2 I n =0 √ √ ℏ ( N + 1) N + 1 ( δθ ) N +1 ,N = = ≪ 1 2 Iω 0 2 m 19
Compares well with the exact q-m result - h-osc satisfactory approx 20
Strong Static El Field H = 1 θ 2 + ˙ ϕ 2 sin 2 θ ) − dE 0 cos θ 2 I ( ˙ Cons of L z I d ϕ sin 2 θ ) = 0 dt ( ˙ E�ective potential function L 2 z U eff = 2 I sin 2 θ − dE 0 cos θ 21
dE 0 ≫ L 2 ⇒ E 0 ≫ T/d = 4 × 10 4 esu (1 . 2 × Assume: z /I ∼ T = 10 9 V/m ) Very high; atomic �elds 4 . 8 × 10 6 esu Polar matter ( e.g. , pyroelectrics, ferroelectrics), OK! Low temperatures, free molecular rotations hindered dipoles quenched, execute small rotations and vibrations Transitions from free rotations to small vibrations around quenched positions in polar matter is seen in the curve of the heat capacity vs temperature (Pauling, 1930) 22
Similarly, sstrong static electric �elds may appear locally near polar impurities with large moments of inertia, embedded in polar matter. z /IdE 0 ) 1 / 4 ≃ ( T/dE 0 ) 1 / 4 ≪ 1 U eff minimum, for θ 0 ≃ ( L 2 Harmonic oscillator U eff ≃ − dE 0 + 2 dE 0 δθ 2 H ≃ 1 θ 2 + 1 0 δθ 2 − dE 0 2 Iω 2 2 Iδ ˙ √ dE 0 /I ≫ 10 12 s − 1 (Rabi's frequency, 1936) ω 0 = 2 Worth noting: frequency ω 0 given by the static �eld E 0 23
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Coupling: H int = − dE ( t )(sin α sin θ cos ϕ + cos α cos θ ) [ ] H 1 int = − 1 cos( ω + 1 2 ω 0 ) t + cos( ω − 1 2 dE sin α 2 ω 0 ) t δθ , 2 dE cos α cos ωt · δθ 2 . H 2 int = 1 H 1 int : transitions n → n + 1 , resonance frequency Absorbed power 16 Iω 0 d 2 E 2 Ω( n + 1) sin 2 αδ ( ω − Ω) = π P q = 16 Iω 0 d 2 E 2 Ω( n + 1) sin 2 α γ 1 ( ω − Ω) 2 + γ 2 , γ → 0 + = (resonance), Ω = 1 2 ω 0 , 3 2 ω 0 . 25
Temperature dependence [ e − β ℏ ω 0 n − e − β ℏ ω 0 ( n +1) ] 16 Iω 0 d 2 E 2 Ω ∑ π P q,th = n =0 ( n + 1) × × sin 2 αδ ( ω − Ω) / ∑ n =0 e − β ℏ ω 0 n where the summation over n is, in principle, limited. √ √ n + 1 ≪ θ 0 ≃ ( L 2 z /IdE 0 ) 1 / 4 = Validity: ℏ / 2 Iω 0 ( δθ ) n +1 ,n = ⇒ n ≪ 80 Extend the summation, P q,th independent of temperature y ≃ L 2 ≫ L 2 Validity: L 2 x + L 2 z . 26
Parametric resonance ′ = H + H 2 int = 1 θ 2 + 1 2 Iω 2 0 (1 + h cos ωt ) δθ 2 2 Iδ ˙ H E ( h = 2 E 0 cos α ), Mathieu's eq θ + ω 2 δ ¨ 0 (1 + h cos ωt ) δθ = 0 Periodic solutions, aperiodic solutions, which may grow inde�- nitely with increasing the time for ω near 2 ω 0 /n , n = 1 , 2 , 3 ... Initial conditions, thermal �uctations, class sol ine�ective 27
QM: di�erent! Transitions n → n + 2 (double quanta abs, Goeppert-Mayer, 1931) Absorbed power ∂ | c n +2 ,n | 2 = πh 2 64 ℏ ω 3 P q = 2 ℏ ω 0 0 ( n + 1)( n + 2) δ (2 ω 0 − ω ) = ∂t = h 2 γ 64 ℏ ω 3 (2 ω 0 − ω ) 2 + γ 2 , γ → 0 + 0 ( n + 1)( n + 2) ∑ P q,th = πh 2 64 ℏ ω 3 n =0 ( n + 1)( n + 2) × 0 [ e − β ℏ ω 0 (2 n +1) − e − β ℏ ω 0 (2 n +3) ] [∑ n =0 e − β ℏ ω 0 n ] 2 × δ (2 ω 0 − ω ) / 28
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