HYSTERESIS AND BLEACHING OF ABSORPTION BY ELECTRONS ON HELIUM
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1 HYSERESIS AND BLEACHING O ABSORPION BY ELECRONS ON HELIUM D. Ryvkin, 1 M.J. La, and M.I. Dykman 1 1 Dpartmnt of Physics and Astronomy, Michigan Stat Univrsity Royal Holloway, Univrsity of London Dynamics for slow nrgy rlaxation Absorption blaching Many-lctron hystrsis
2 Microwav absorption and saturation Stark-shift transition frquncy by a fild to tun to 1- rsonanc + V E.1 mm - 56 mm E R α = α = 1 Rlaxation rat, MH Rlativ absorption E. Collin t al., PRL (00 Intrprtation: absorption saturation in a two-lvl systm
3 Convntional absorption saturation φ Narly rsonant driving: H = 1 xp( iω t + h.c. n n n = 1 Ecw1 Wak fild absorption: σ = χ, χ = 0 /[ 0 + ( ω1 ω ] 1 Wak-fild linwidth is 0 = + φ Powr absorbd pr unit tim is σ ω Strong fild absorption: σ = χ /( + χ Elctrons: bands of in-plan motion instad of nrgy lvls
4 ω p = ( π n 3/ / m 1/ >> Elctron rlaxation mchanisms Elctron-lctron coupling: thrmaliation of in-plan motion ovr tim Elctron in-plan momntum distribution ε α = 4 α = 3 α = α = αβ = π q V ρ αα αβ ( p 1 ω p, On-ripplon/vapor atoms scattring is quasi-lastic 1/ and short-wavlngth, αβ q intraband scattring, intrband scattring, p δ m Enrgy rlaxation: two-ripplon/phonon scattring k ( p + q m xp( p ρ αβ β α = n n + ε 1 α αα αβ q >> n ε β / m ( α β ( h = 1 << αβ << ( k B = 1 ω p
5 H Mastr quation for many-lctron systm = = 1 xp( iω t + h.c. n n ild Hamiltonian for spatially uniform rsonant radiation n rquncy dtuning is small: δω = ω ( ε, ε 1 δω << ω 1 Ecw1 Short-wavlngth scattring, > ω = p 3/ ( π n / m ffctivly singl-lctron kintic quation for a strongly corrlatd lctron systm 1/ In th band indx rprsntation & αα ρ β α α & ρ 1 αα αβ ββ βα = ( ρ ρ + ( δ, 1 δ, Im( ρ 1 = ( iδω + ρ + i 0 * ( ρ ρ Ando, 1978 αβ βα Dtaild balanc for fast in-plan thrmaliation = xp[( ε ε / ] α β
6 Enrgy rlaxation d Enrgy balanc quation = + ω Im( * ρ 1 Microscopic mchanisms: dt Enrgy diffusion from on-ripplon scattring wo-ripplon scattring, Dcay into phonons: modulation of th H dilctric constant, q << q V 1 8π q 1 + q << q1, ( r = d r' δε ( r' E ( r, r', E( r, r' = / r r ' q, q q 1 q wo-ripplon scattring, kinmatic coupling: 1 = 1 10 / 3 ( / ω, h << / hω, hω hω
7 Distribution ovr bands 1 Slow nrgy rlaxation, : th rat of fild inducd transitions dos not hav to bat th rat of 1 rlaxation. Excitd stats ar populatd and absorption is χ >> 1 << blachd alrady for du to lctron hating, ε α = 4 α = 3 α = α =1 1 χ = 0 /( 0 + δω Rmindr: absorption saturation for a two-lvl systm rquirs χ > 1 thrmal distribution ovr bands in th stationary rgim αα ρ = Z 1 ( xp( εα / χω / Z( ( Equation for lctron tmpratur ω = 1 nrgy is countd off ε1 1 k χ Z << ( α α = xp( ε / 1
8 Z( Absorption dcras I χ ω / Absorption dcras: thrmal population of ( σ = 1 th stat and blaching Constant nrgy rlaxation rat approximation 3 / ( χ / 7 = / ω
9 Absorption dcras II χ ω / Z( Absorption dcras: thrmal population of ( σ = 1 th stat and blaching Kinmatic two-ripplon scattring 3 / 3 /13 x / 9 x = / ω
10 Many-lctron lin shift Strongly corrlatd lctron liquid for 1/ (π n >> Diffrnt distanc from H surfac in diffrnt stats lads to dpndnc of lctron transition frquncy on stats of nighboring lctrons: many-lctron Stark shift ε ε ε ε + Ω( 1 1 Many narst nighbors: man-fild approximation Ω ( H m ( n 4 r 3 nm n m ( ( n 11 m ν / r 3 nm νν ρ νν ( ρ ρ d 1 αα 3 / 8.9 n s Enrgy balanc quation χ ω / ω = Z( ( 1 with χ = χ( = [ δω Ω( ]
11 Slf-consistnt quation for tmpratur Z ( = χ (, = 1 1/ ω * χ ( δω = Ω( [ dω/ d ] >> 0 has a narrow pak for if Constant nrgy rlaxation rat approximation * Ω, Ry Many-lctron bistability wak fild Z( 1 1/ strong fild bistability Z( 1 1/ χ ( χ ( δω / 0 = 1, δω = 0.001Ry
12 Slf-consistnt quation for tmpratur Z ( = χ (, = 1 1/ ω * χ ( δω = Ω( [ dω/ d ] >> 0 has a narrow pak for if * Kinmatic two-ripplon scattring Ω, Ry Many-lctron bistability wak fild Z( 1 1/ 0 strong fild bistability Z( 1 1/ 0 χ( 0 χ( 0 δω / 0 = 10, δω = 0.003Ry
13 Conclusions Absorption saturation is accompanid by blaching from lctron hating. Many-lctron shift of transition frquncy lads to absorption hystrsis for low hlium tmpraturs Elctron nrgy rlaxation can b studid via nonlinar absorption xprimnts
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