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arXiv:1911.10156

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

Petr P Vasil'ev, Richard V. Penty, Ian H. White

Published Nov 22, 2019• 0 citations
arXivHTMLPDF

Abstract

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

DOI
10.48550/arxiv.1911.10156

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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
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.
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.
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.
A single-photon Fock state has been generated by means of conditional preparation from a two-photon state emitted in the process of spontaneous parametric down-conversion. A recently developed high-frequency homodyne tomography technique has been used to completely characterize the Fock state by means of a pulse-to-pulse analysis of the detectors' difference photocurrent. The density matrix elements of the generated state have been retrieved with a final detection efficiency of about 57%. A comparison has been performed between the phase-averaged tomographic reconstructions of the Wigner function as obtained from the measured density-matrix elements and from a direct Abel transform of the homodyne data. The ability of our system to work at the full repetition rate of the pulsed laser (82MHz)(82\phantom{\rule{0.3em}{0ex}}\mathrm{MHz})(82MHz) substantially simplifies the detection scheme, allowing for more ``exotic'' quantum states to be generated and analyzed.
The presence of negative values in the Wigner quasiprobability distribution is deemed one of the hallmarks of nonclassical phenomena in quantum systems. Here we demonstrate a classical model of squeezed light that, when combined with post-selection on amplitude threshold-crossing detection events, is capable of reproducing observed behavior of single-photon added coherent states. In particular, a classical model of balanced homodyne detection and standard tomographic techniques are used to infer the density matrix in the Fock basis. The resulting Wigner functions exhibit negatively for photon-added vacuum and weak coherent states.
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.