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Theory of generated four-wave mixing for two-photon creation of exciton condensate in C2O

Belousov, I.V., Beloussov, I.V., Ketterson, J., Arapan, L.V., Sun, Y.

Published Dec 1, 2005• 0 citations
OpenAlex

Abstract

The experimental situation in which excitons in Cu2O are pumped directly into a state with wave vector = k0 by two counter-propagating laser pulses, and subsequently probed by a third, time-delayed, pulse has been theoretically investigated. It has been shown that additional electromagnetic waves are excited in the system. A specific configuration of two pump pulses and one probe pulse has been found to generate only one additional electromagnetic wave. The dependence of the time-integrated photon number in this wave on the delay time between pump and probe pulses for some values of the detuning has been investigated.

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The experimental situation in which excitons in Cu2O are pumped directly into a state with wave vector = k0 by two counter-propagating laser pulses, and subsequently probed by a third, time-delayed, pulse has been theoretically investigated. It has been shown that additional electromagnetic waves are excited in the system. A specific configuration of two pump pulses and one probe pulse has been found to generate only one additional electromagnetic wave. The dependence of the time-integrated photon number in this wave on the delay time between pump and probe pulses for some values of the detuning has been investigated.
The experimental situation in which excitons in Cu 2 O are pumped directly into a state with wave vector k → = 0 → by two counter-propagating laser pulses , and subsequently probed by a third, time-delayed, pulse has been theoretically investigated. It has been shown that additional electromagnetic waves are excited in the system. A specific configuration of two pump pulses and one probe pulse has been found to generate only one additional electromagnetic wave. The dependence of the time-integrated photon number in this wave on the delay time between pump and probe pulses for some values of the detuning has been investigated.
We propose and examine theoretically a four-wave-mixing experiment in which excitons in Cu2O{\text{Cu}}_{2}\text{O}Cu2​O are pumped directly into a state with wave vector k=0\mathbf{k}=\mathbf{0}k=0 by two counter-propagating cross-polarized laser pulses and which is subsequently probed by a third time-delayed pulse. Approximate analytical solutions of the time evolution equations are found which describe the time dependence of the exciton and photon densities. Most importantly, we obtain the dependence of the resulting phase-conjugated signal versus the delay time td{t}_{d}td​ between the probe and pump pulses. It is shown that the total number of photons generated in the course of the experiment is proportional to the areas of all three incoming pulses. The dependence of the resulting time-integrated signal on the delay time td{t}_{d}td​ is the same as the exciton density dependence on the time ttt. Hence, one may directly study the time evolution of the exciton condensate. The approximate analytical results are compared with a numerical solution of the evolution equations for a wide range of incident pulse intensities. It is noted that an exciton condensate arising by an alternate route can also be probed through a phase-conjugated two-photon process.
We propose and theoretically investigate a two-photon four wave mixing experiment to probe for BEC of excitons in Cu2O thin films. A relatively simple set of equations describing the dynamics of the system is obtained for a particular configuration of the exciting beams, and numerical and approximate analytical solutions are found. The resulting phase-conjugated signal vs. the delay time between the pump and probe pulses yields a direct measure of the time evolution of the exciton condensate, and exhibit peaks when the film thickness is a multiple of a half wavelength of light.
We propose and theoretically investigate a two-photon four-wave mixing experiment to probe for Bose-Einstein condensation of excitons in Cu2O{\text{Cu}}_{2}\text{O}Cu2​O thin films. A relatively simple set of equations describing the dynamics of the system is obtained for a particular configuration of the three incident beams, and numerical and approximate analytical solutions are found. When one takes into account the boundary conditions, which result in reflections from the interfaces, the characteristics of the resulting phase-conjugated signal will exhibit Fabry-Perot-type oscillations. For film thicknesses equal to a multiple of a half wavelength in the film the resulting signal is enhanced by more than an order of magnitude relative thicknesses that are an odd multiple of a quarter wavelength. In this case the contribution from accompanying excitonic condensates with wave vectors $\ifmmode\pm\else\textpm\fi{}2\mathbf{k}$ is minimal. Therefore, the resulting phase-conjugated signal vs the delay time between the pump and probe pulses yields a direct measure of the time evolution only of the exciton condensate with wave vector k=0\mathbf{k}=\mathbf{0}k=0.
We present a time-dependent calculation for four-wave mixing using a combination of long, short, and time delayed laser pulses in the context of electromagnetically induced transparency. Two transform limited nanosecond lasers are used to create a highly coherent mixture of the ground state and an excited state via a two-photon process. Once the induced transparency is established, a laser with short pulse length is injected after a suitable delay to generate four-wave mixing. We show that the wave mixing process is phase matched for all detunings, and with appropriately selected atomic coherence and populations, near 100% photon flux conversion efficiency can be obtained, independent of the intensity of the short pulse laser. In addition, we show that for small detunings for the short pulse laser, the four-wave mixing field travels with the speed of light in vacuum and suffers no pulse distortion even though the medium is highly dispersive at the frequency of the generated wave. These advantages open a door for future applications of the scheme for highly efficient, very stable UV generation.
The quantum beats (QB) in the time-dependent absorption intensity of the probe pulse and the spontaneous luminescence one in Cu2O crystal at the condition of double optical resonance are studied theoretically. It is assumed that the pump is performed by the CO2 laser pulse, which couples dynamically the 1s (Γ 5 + ) and 2p (Γ 4 - , Γ 5 - , Γ 3 - , Γ 2 - ) excitonic states and leads to their splitting into two or three quasienergy levels. The frequency of the probe pulse is in the region of the Γ 5 + exciton resonance. The respective intensities for different directions of the electric field E L of the pump, the polarization ξ of the probe pulse, and the observation q are obtained. The QB take place with the doubled Raby frequency, which at different E L , ξ, and q includes different sets of matrix elements of dipole transitions between 1s (Γ 5 + ) and 2p (Γ 4 - , Γ 5 - , Γ 3 - , Γ 2 - ) levels. These unknown matrix elements can be obtained, measuring the period of the QB.