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Journal of the Optical Society of America B

Multichannel homodyne detection for quantum optical tomography

Georgios Roumpos, Steven T. Cundiff

Published Apr 22, 2013• 18 citations
Publisher

Abstract

We present a multichannel optical homodyne detection setup suitable for measurements of quantum light statistics with ultrafast time resolution. We employ the setup to measure light statistics of diode lasers driven by both a direct and a pulsed current source. In particular, we measure the time-resolved second-order correlation function g(2) and photon number distribution. Our results provide information about the dynamics of the lasing transition.

DOI
10.1364/josab.30.001303

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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.
Abstract Recent progress in ultrafast optics facilitates the investigation of the dynamics of highly multimode quantum states of light. Yet, the complete tomographic reconstruction of optical quantum states with prior unknown statistics and dynamics is still challenging, since state-of-the-art tomographic methods require the measurement of orthogonal and distinguishable modes. Here, we propose a tomography scheme based on time-domain quadrature correlation measurements and theoretically demonstrate its ability to reconstruct highly multimode Gaussian states. In contrast to (eight-port) homodyne detection, the two local oscillator pulses are shorter in time and are (independently) time-delayed against the pulsed quantum state. The distinguishable mode structure is obtained in post-processing from the correlation measurement data by orthogonalization. We show that the number of reconstructable modes increases with the number of time delays used and decreases with the temporal extent of the local oscillator. Additionally, we compare dual-pulse homodyne detection and electro-optic sampling. By analysing the (quantum) correlations present in the measurement data, we show how thermalisation of the quantum state during detection leads to the requirement of correlation measurements. Furthermore, we open an avenue to extending our tomography scheme to non-Gaussian states.
We measured the time-domain quantum statistics of a pulsed, high-repetition-rate optical field by balanced homodyne detection. The measuring apparatus discriminates the time scales on which intrinsic quantum fluctuations prevail from those scales for which technical noise is overwhelming. A tomographic reconstruction of weak coherent states with various average photon numbers demonstrates the potential ability of the system to measure high-repetition-rate, time-resolved signals. Possible extensions to other physical situations are discussed.
We prove that the photon-number distribution of an arbitrary single-mode optical state can be calculated directly from the phase-averaged quadrature amplitude distribution, measured using optical homodyne detection. We experimentally demonstrate the application of this result by measuring the ultrafast (subpicosecond), time-resolved photon-number statistics of a weak field from a pulsed diode laser. Also presented is a numerical calculation of the photon-number distribution of a quadrature-squeezed vacuum state.