Modeling of the thermalization of trapped paraexcitons inCu2Oat ultralow temperatures

Abstract

We theoretically analyze the relaxation of paraexcitons in cuprous oxide due to exciton-phonon and excitonexciton scattering. Particular attention is paid to the evolution of the distribution function as well as to the cooling process of the exciton gas. The results underline the importance of interexcitonic collisions at moderate and higher densities which prevent the formation of the typical bottleneck and accelerate the thermalization at ultralow temperatures significantly. Furthermore, we discuss the impact of strain on the exciton-phonon coupling and show that the overall cooling process of the excitons benefits from strain induced effects. However, for very low lattice temperatures (T 1.0 K), the process of thermalization is slow, and the excitons might not reach the lattice temperature within their finite lifetime.

Biexciton as a Feshbach resonance and Bose–Einstein condensation of paraexcitons in Cu2O

“…Among two terms of Γ p , Gx x depends on stress via A (see table 1), while Γ ph is stress-independent. As a matter of fact, at low temperatures the interaction of paraexcitons with phonons consists of their interaction with longitudinal acoustic phonons, which does not depend on stress, and that with transverse acoustic phonons, which is negligibly weak [57]. For T=1.2 K, where Γ ph =80 neV, we compute Gx x and A by iterations in the stress range from 0.2 kbar to 2 kbar for the density reported in [10][11][12][13].…”

“…On contrast, the loss rate A ∝ Γ p , which at low densities and small inhomogeneity equals Γ ph . Because interaction of excitons with longitudinal acoustic phonons is stress-independent and that with transverse acoustic ones is weak, 42 we assume the value of Γ ph at 1.2 K under moderate stress to be the same 80 neV as measured under zero stress. 43 Neglecting in the following inhomogeneity of the strain field, we put Γ p Γ x−x + Γ ph with Γ x−x = n (A + K) computed by iterations and obtain A for different S at a particular density.…”

Multicomponent exciton gas in cuprous oxide: cooling behaviour and the role of Auger decay

“…The first stage of the time evolution of the exciton gas is characterised by the local thermalisation of the excitonic momentum distribution. This process is very fast, within about 1 ns local equilibrium is reached even for low densities of 10 12 cm −3 [15]. The thermalisation turns out to be essentially determined by exciton-exciton (X-X) collisions.…”

“…The cooling process of the excitons can be investigated looking at the 'effective' temperature defined by the averaged kinetic energy per particle [15]. Again, the X-X collisions are crucial for the cooling efficiency.…”

“…Again, the X-X collisions are crucial for the cooling efficiency. However, at very low temperatures of the helium bath below 0.1 K, the cooling is not efficient enough to ensure that the excitons reach the bath temperature within their lifetime [15]. This does not yet rule out the possibility that there are zones within the trap where the local temperature is less than the global effective temperature.…”