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Journal of Experimental and Theoretical Physics Letters

Quantum Entanglement at the Superradiance of a Condensate of Electron–Hole Pairs in Semiconductor Heterostructures

Petr P Vasil'ev

Published Dec 1, 2024• 4 citations
Publisher

Abstract

The quantum properties of superradiant pulses generated at the radiative recombination of an electron–hole condensate in semiconductor heterostructures at room temperature have been studied using optical homodyne tomography. Signatures of the quantum entanglement of superradiant states, which are superpositions of two coherent states, have been revealed. It has been demonstrated that reconstructed Wigner functions under certain conditions are very similar to the Wigner functions of the Schrödinger cat states.

DOI
10.1134/s0021364024603348

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The quantum properties of superradiant pulses generated at the radiative recombination of an electron–hole condensate in semiconductor heterostructures at room temperature have been studied using optical homodyne tomography. Signatures of the quantum entanglement of superradiant states, which are superpositions of two coherent states, have been revealed. It has been demonstrated that reconstructed Wigner functions under certain conditions are very similar to the Wigner functions of the Schrödinger cat states.
Abstract Advanced quantum technologies require sources of non-Gaussian and non-classical light. For the understanding of properties of quantum light it is necessary to reconstruct its quantum state. Here, we use time-domain optical homodyne tomography for the quantum state recognition and reconstruction of the femtosecond optical field from a nonequilibrium superradiant coherent electron–hole state formed in a semiconductor GaAs/AlGaAs heterostructure. We observe severe deviations from the Poissonian statistics of the photons associated with the coherent state when the transformation from lasing to superradiance occurs. The estimated Mandel parameter Q of the superradiant states is in the range of 1.08–1.89. The reconstructed Wigner functions show large areas of negative values, a characteristic sign of non-classicality, demonstrating the quantum nature of the generated superradiant emission. The photon number distribution and Wigner function of the superradiant state are very similar to those of the displaced Fock state.
For the visualization of quantum states, the approach based on Wigner functions can be very effective. Homodyne detection has been extensively used to obtain the density matrix, Wigner functions and tomographic reconstructions of optical fields for many thermal, coherent or squeezed states. Here, we use time-domain optical homodyne tomography for the quantum state recognition and reconstruction of the femtosecond optical field from a nonequilibrium superradiant coherent electron-hole state formed in a semiconductor laser structure. We observe severe deviations from the Poissonian statistics of the photons associated with the coherent laser state when the transformation from lasing to superradiance occurs. The reconstructed Wigner functions show large areas of negative values, a characteristic sign of non-classicality, demonstrating the quantum nature of the generated superradiant emission. The photon number distribution and Wigner function of the SR state are very similar to those of the displaced Fock state
The effect of the nonstationary condensation of electron-hole pairs in GaAs/AlGaAs p-i-n heterostructures at room temperature under the conditions of generation of superradiance pulses was demonstrated in an explicit form. It was found that a dramatic decrease in spontaneous emission from the entire conduction band and a rapid electron transition to the very bottom of the band occurred at the earliest stages of the development of a superradiance pulse. The condensation of electrons at the band bottom resulted in the formation of a nonequilibrium coherent cooperative state, the recombination of which was observed previously as high-power femtosecond superradiance pulses.
Rabi oscillations in semiconductor heterostructures generating superradiance at room temperature have been studied experimentally and theoretically. An anomalously long oscillation decay time has been observed experimentally in structures with a low- Q cavity. A theoretical model of the dynamics of the coherent interaction of an electron–hole system with an electromagnetic field in such a cavity, which is based on the classical Maxwell–Bloch equations, predicts a decay time more than an order of magnitude shorter than that measured experimentally. It is suggested that one of the possible reasons for this effect may be the presence of quantum feedback arising from two counterpropagating electromagnetic waves, which mediate the interaction of two coherent electron–hole ensembles and lead to their quantum entanglement with the electromagnetic field.
A review of an experimental study of superradiance in semiconductor inorganic structures is presented. It is demonstrated that unique properties of superradiant emission are determined by unusual properties of electrons and holes, namely, the formation of BCS-like state in a system of collectively paired electrons and holes. This can adequately explain all features of superradiance, including its femtosecond pulse duration, record peak power, optical spectrum, spatial and temporal coherency and macroscopically large fluctuations. The effect of non-equilibrium condensation of electrons and holes in the phase domain at room temperature is experimentally demonstrated. The critical temperature of condensation in a strongly degenerate system of electrons and holes is finally theoretically estimated.
The spectra of spontaneous emission accompanying the generation of femtosecond superradiant pulses in GaAs/AlGaAs heterostructures are studied. It is clearly demonstrated that spontaneous emission spectra of electron–hole pairs, which have been left in the semiconductor after the formation of a coherent collective e–h state, correspond to the strong overheating of carriers. This phenomenon can be explained by the effect of dynamic cooling and nonequilibrium condensation of collectively paired carriers at the bottoms of the bands during the superradiant emission, which was observed earlier.