Biexciton squeezing due to optical exciton-biexciton conversion

BIEXCITON SQUEEZING DUE TO OPTICAL EXCITON-BIEXCITON CONVERSION

Squeezing is a fully quantum effect of fundamental concern directly exhibiting the quantum-mechanical nature of the electromagnetic field. Production of squeezed states has attracted great attention among the quantum optics community (see Ref. 1 and references therein) over the last two decades and remains a topic of current interest, especially in its extension to massive bosons in atomic system as well as in condensed matter (see, e.g. Refs. 2-5).

In this paper we consider a possible mechanism of generating biexciton squeezed states in a system of interacting photons, excitons and biexcitons. An important property of biexcitons is the anomalously huge probability of quantum transitions with their participation. Gogolin and Rashba⁶ for the first time showed that the optical exciton-biexciton conversion possesses a giant oscillator strength. Similar conclusions were later reported in Refs. 7 and 8. The effective Hamiltonian describing the interaction between photons, excitons and biexcitons in a lowly excited direct-gap semiconductor near the center of Brillouin zone can be constructed after a proper bosonization procedure.⁹ It has a trilinear form as (ℏ = 1 throughout)

H = ωγ⁺γ + Ex⁺x + Em⁺m + f (m⁺γx + x⁺γ⁺m) (1)

where γ⁺, γ (x⁺ , x and m⁺, m) are bosonic operators of photons (excitons and biexcitons) with energy ω (E and E ) and, f measures the optical exciton-biexciton conversion strength which is assumed to be real. The optical exciton-biexciton conversion was intensively exploited in various nonlinear processes in condensed matter such as optical bistability,¹⁰ nonlinear nutation,¹¹ etc. and in quantum optics such as parametric amplification, frequency conversion, Raman scattering (see, e.g. Ref. 12), etc. Recently, nontrivial coherent states for quantum systems gov-erned by the trilinear Hamiltonian (1) have also been introduced.¹³ In a previous publication¹⁴ we already studied squeezed states of biexcitons but used a soluble semiclassical Hamiltonian allowing an exact diagonalization. Here we directly deal with (1) which is fully quantum and not solvable in general. We thus solve it in the short-time limit practically relevant for small samples in which the interac-tion time is in fact very short. We first analytically derive an explicit direction-and time-dependent expression for the biexciton amplitude quadrature variance. Then we investigate the possible evolution of the biexciton from a coherent into a squeezed state in dependence on the initial condition of photons and excitons. The results seem fascinating in the sense that both the degree and direction of biex-citon squeezing are obtainable analytically showing delicate dependences on the parameters involved. Our analysis is perfectly confirmed by numerical tests

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