Kinetics of a Superconductor Excited with a Femtosecond Optical Pulse

Abstract

Superconducting state dynamics following excitation of a superconductor with a femtosecond optical pulse is studied in terms of a phenomenological Rothwarf and Taylor model. Analytical solutions for various limiting cases are obtained. The model is found to account for the intensity and temperature dependence of both photoinduced quasiparticle density, as well as pair-breaking and superconducting state recovery dynamics in conventional as well as cuprate superconductors.In recent years numerous studies of non-equilibrium carrier dynamics in superconductors (SC) have been performed utilizing femtosecond real-time techniques [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Research focused on the identification of relaxation processes and direct measurements of the relaxation times.One of the open issues at the moment is whether cuprates are in the so called phonon bottleneck regime as conventional SCs [19], or in the weak bottleneck regime, where relaxation is governed by the biparticle recombination kinetics [9,17,18]. The theoretical model that has been most commonly used to interpret the dynamics is a phenomenological Rothwarf-Taylor (RT) model which describes the evolution of quasiparticle (QP) and high frequency phonon (HFP) populations via a set of two non-linear differential equations [20], which were shown recently[21] to follow from the general set of kinetic equations for a SC [22]. While the RT model has been known for almost 40 years, no rigorous attempt to solve it has been made thus far, and neither has a comparison to the experimental data been made.In this Letter we present a detailed study of the evolution of the SC state following excitation by ultrashort laser pulse using the RT model. We have obtained analytical solutions of the model in the limit of a strong and a weak bottleneck, which are in excellent agreement with numerical simulations. The solutions enable comparison of the model to the experimental results. We show that RT model can account for most of the experimental observations in conventional as well as cuprate SC, and that both conventional and cuprates SCs are in the strong bottleneck regime, where SC state recovery is governed by the HFP decay dynamics.Rothwarf and Taylor have pointed out that the phonon channel should be considered when studying the SC relaxation [20]. When two QPs with energies ≥ ∆, where ∆ is the SC gap, recombine a HFP (ω > 2∆) is created. Since HFP can subsequently break a Cooper pair creating two QPs the SC recovery is governed by the decay of the HFP population. The dynamics of QP and HFP populations is determined by [20]:Here n and N are concentrations of QPs and HFPs, respectively, η is the probability for pair-breaking by HFP absorption, and R the bare QP recombination rate with the creation of a HFP. N T is the concentration of HFP in thermal equilibrium at temperature T , and γ their decay rate. I 0 and J 0 represent the external sources of QPs and HFPs, respectively [12]. Physically γ is governed by the fastest of the two processes: ...

Hot electron relaxation in the heavy-fermionYb1−xLuxAl3compound using femtosecond optical pump-probe spe

“…Since HFP can subsequently excite EHP, the recovery is essentially governed by the decay of the HFP population. 9,11 In the low excitation limit, as in this case, the T dependencies of both amplitude of the induced reflectivity change A, and are governed by the T dependence of the number density of thermally excited EHPs, n T . It was shown 11 that n T ϰ A −1 − 1, where A͑T͒ = A͑T͒ / A͑T → 0͒ and…”

“…4,5 Both T and excitation density dependence of the relaxation process can be well accounted for by the phenomenological Rothwarf-Taylor ͑RT͒ model, 5,9-11 which was originally developed to describe the relaxation in superconductors driven out of equilibrium. [9][10][11] We should note that the alternative model presented in Refs. 6 and 7 is essentially also a bottleneck model.…”

Electron relaxation in metals: Theory and exact analytical solutions

“…7 and 8͒ found a relaxation process below T c , which is distinct from the equilibration of hot carriers in the normal state. A relatively strong e-ph coupling, Ӎ 0.9, 8 and a rapid decrease in the photoresponse decay rate with decreasing temperature 15 were found in YBa 2 Cu 3 O 6.5 , and the phonon bottleneck 12,[16][17][18] or a biparticle recombination 15,19 were observed below T c . More recently, a time-resolved photoemission spectroscopy 20 and the standard pump-probe optical measurements 21 have been performed on Bi 2 Sr 2 CaCu 2 O 8+␦ .…”

Signatures of nonadiabatic BCS state dynamics in pump-probe conductivity

“…In the past few years, fueled by recent advances in femtosecond terahertz (THz) laser technology 3 , many experimental 4-17 and theoretical [18][19][20][21][22][23][24][25][26][27][28][29][30][31] studies have focused on the ultrafast time response of the BCS state subjected to nonadiabatic perturbations. For example, Matsunaga et al 4,5 have employed THz pump-THz probe spectroscopy to investigate the nonadiabatic dynamics of superconducting thin films after the injection of Bogoliubov quasiparticles with energies just above the gap edge.…”