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New Journal of Physics

Wigner function and photon number distribution of a superradiant state in semiconductor heterostructures

Petr P Vasil'ev, Richard V. Penty

Published Jul 8, 2020• 12 citations
Publisher

Abstract

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.

DOI
10.1088/1367-2630/aba3e8

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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 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.
States with explicit quantum character, such as squeezed vacuum and bright squeezed light, as well as coherent states and incoherent superpositions of coherent states were generated and analysed by tomographical methods. Wigner functions, photon-number distributions, density matrices and phase distributions were reconstructed with high accuracy. Features such as photon number oscillations, sub-Poissonian and super-Poissonian photon statistics, bifurcations of the phase distribution, and loss of coherence were observed, demonstrating the usefulness of quantum state reconstruction as an analysing tool in quantum optics experiments.
We report about the realization and the applications of an efficient pulsed optical homodyne apparatus operating in the time domain at the high repetition rates characteristic of commonly used mode-locked lasers for the analysis of quantum light states. We give a full characterization of our system by shot-noise measurements and by verifying its capability to work in a gated configuration at lower acquisition rates. We demonstrate the potential of this high-frequency time-domain detector by applying it to the reconstruction of the density matrix elements and of the Wigner functions of various field states by means of quantum tomography. Results are shown for the complete characterization of simple coherent states with low average photon number, of single-photon Fock states and of the so-called single-photon added coherent states, which result from the elementary excitation of a classical wave-like field. Wigner functions with negative values are observed for the non-classical states and an overall efficiency of about 60% is obtained for the generation/detection system.
Summary form only given. The single photon Fock state is one of the most fundamental states of the light field. It is highly non-classical and reveals the wave-particle duality of light most strikingly. Its marginal distributions are of non-Gaussian shape and its Wigner function exhibits a strong negativity around the origin of phase space. Although the reconstruction of the Fock state has already been performed for the motional state of trapped beryllium ions, in the optical domain this task has not been resolved so far, the main difficulty being the lack of coherent single-photon sources. We present results of applying the technique of optical homodyne tomography to the single photon Fock state prepared by conditional measurements on a photon pair produced in parametric down conversion.
Quantum state tomography and the reconstruction of the photon number distribution are techniques to extract the properties of a light field from measurements of its mean and fluctuations. These techniques are particularly useful when dealing with macroscopic or mesoscopic systems, where a description limited to the second order autocorrelation soon becomes inadequate. In particular, the emission of nonclassical light is expected from mesoscopic quantum dot systems strongly coupled to a cavity or in systems with large optical nonlinearities. We analyze the emission of a quantum dot-semiconductor optical amplifier system by quantifying the modifications of a femtosecond laser pulse propagating through the device. Using a balanced detection scheme in a self-heterodyning setup, we achieve precise measurements of the quadrature components and their fluctuations at the quantum noise limit1. We resolve the photon number distribution and the thermal-to-coherent evolution in the photon statistics of the emission. The interferometric detection achieves a high sensitivity in the few photon limit. From our data, we can also reconstruct the second order autocorrelation function with higher precision and time resolution compared with classical Hanbury Brown-Twiss experiments.