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Design and characterization of wideband balanced homodyne detectors for quantum homodyne tomography

Erick Barrios Barocio

Published Jan 1, 2012• 0 citations
Publisher

Abstract

This thesis reports the realization and applications of a versatile wideband balanced homodyne detector operating in the time domain and intended for Quantum Optical Tomography. The detector can work with high repetition rate lasers used for the production and measurement of the electric field quadratures of quantum states of light. Full characterization of the detector by shot-noise measurements and by verifying its capability to reconstruct the density matrix and Wigner function of various states of interest is given. By overcoming photodiodes response mismatch, high frequency electronics issues and by choosing an appropriate optical set-up, a high level of common mode suppression (52.4dB) and a low electronic noise gave a shot-to-electronic noise ratio of I3dB for a Local Oscillator with 6.2 x 108 photons-per-pulse on a ~ 100MHz bandwidth. Results for the characterization of a single-photon Fock state are presented. An average efficiency of 56% was obtained for the generation/detection of the state.

DOI
10.11575/prism/4702

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This thesis reports the realization and applications of a versatile wideband balanced homodyne detector operating in the time domain and intended for Quantum Optical Tomography. The detector can work with high repetition rate lasers used for the production and measurement of the electric field quadratures of quantum states of light. Full characterization of the detector by shot-noise measurements and by verifying its capability to reconstruct the density matrix and Wigner function of various states of interest is given. By overcoming photodiodes response mismatch, high frequency electronics issues and by choosing an appropriate optical set-up, a high level of common mode suppression (52.4dB) and a low electronic noise gave a shot-to-electronic noise ratio of I3dB for a Local Oscillator with 6.2 x 108 photons-per-pulse on a ~ 100MHz bandwidth. Results for the characterization of a single-photon Fock state are presented. An average efficiency of 56% was obtained for the generation/detection of the state.
We present a high-speed time-domain shot-noise-limited balanced homodyne detector that is suitable for the detection of the quantum states of nanosecond pulsed optical fields. The detector can detect the quantum noise of individual nanosecond optical pulses at a repetition rate of 40 MHz and achieve a signal-to-noise ratio of above 14.5 dB at a local oscillator power of 9.9×107 photons per pulse. The stability of the detector is characterized via an Allan variance measurement, and superior stability is observed. The detector is especially applicable in the fields of quantum optics and quantum information, where high-speed time-domain detection of nanosecond pulsed optical field quadratures is required.
This thesis is concerned with the generation of non-classical quantum states of light, the photon-level manipulation of quantum states and the accurate tomography of both quantum states and quantum processes. In optics, quantum information can be encoded and processed in both discrete and continuous variables. Hybrid approaches combining for example homodyne detection with conditional state preparation and manipulation are gaining increasing prominence. The development and characterization of a time-domain balanced homodyne detector (BHD) is presented. The detector has a bandwidth of 80 MHz, a signal-to-noise ratio of 14.5 dB and an efficiency of 86% making it well-suited to pulse-to-pulse measurement of quantum optical states. The BHD is employed to perform quantum state tomography (QST) of non-classical multi-photon Fock states generated by spontaneous parametric down-conversion. A detailed investigation of the mode-matching between the local oscillator used for homodyne detection and the generated Fock states is presented. The one-, two- and three-photon Fock states are reconstructed with a combined preparation and detection efficiency exceeding 50%. Fock states have a number of applications in quantum state engineering, where non-classical ancilla states and conditional measurements enable photon-level manipulation of quantum states. Fock state filtration (FSF) is investigated - an example of a post-selected beam splitter which is a basic building block for many quantum state engineering protocols. A model is developed incorporating the effect of experimental imperfections. An experimental implementation of a Fock state filter is fully characterized by means of coherent-state quantum process tomography (QPT). The reconstructed process is found to be consistent with the model. The filter preferentially removes the single-photon component from an arbitrary input quantum state. Calibration of optical detectors in the quantum regime is discussed. Quantum detector tomography (QDT) is reviewed and contrasted with a new technique for performing QST with a calibrated detector known as the fitting of data patterns (FDP). The first experimental characterization of a BHD is performed by probing the detector with phase-averaged coherent states. The FDP method is shown to be applicable to the estimation of quantum processes, where a detector response is not assumed - thus demonstrating the versatility of the FDP approach as a new method in the quantum tomography toolbox.
Low-noise, efficient, phase-sensitive time-domain optical detection is essential for foundational tests of quantum physics based on optical quantum states and the realization of numerous applications ranging from quantum key distribution to coherent classical telecommunications. Stability, bandwidth, efficiency, and signal-to-noise ratio are crucial performance parameters for effective detector operation. Here we present a high-bandwidth, low-noise, ultra-stable time-domain coherent measurement scheme based on balanced homodyne detection ideally suited to characterization of quantum and classical light fields in well-defined ultrashort optical pulse modes.
The Wigner function is a quasi-probability distribution of quantum states of light that describes the probability amplitude of any state through their marginal distribution. The Wigner function can be reconstructed through quantum tomography which uses the information obtained from light quadratures to reconstruct a 3d image of the Wigner function. Light quadratures can be obtained by means of balanced homodyne detection (BHD). BHD uses a controlled interference between the quantum field to be characterized and a local oscillator, which is a coherent source with well-defined frequency and phase. The main feature of a BHD is its ability to measure extremely small noise signals, even below the quantum vacuum limit for squezeed light. To obtain precise measurements in BHD it is necessary to characterize the noise sources in the electronics of the BHD such as Johnson noise and fundamental noises such as shot noise. To characterize the noise in the BHD, time based and frequency-based measurements were performed to find the quantum to classical noise ratio (QCNR). QCNR measures the capacity of the BHD to distinguish quantum noise. A high QCNR allows us to make reliable measurements of the light quadratures. For this project we developed a circuit based on the one presented by Lang et al. in low noise balanced homodyne detector for quantum noise measurements.
A balanced homodyne detection scheme with nanosecond time resolution and sub-shot-noise sensitivity has been developed and successfully tested yielding an efficient detection scheme for high-speed quantum-optical measurements and communication protocols, for example, quantum cryptography. The parameters of the detector and its precise balancing allow complete characterization of quantum states created by femtosecond light pulses that include the measurement of photon number, optical phase, and statistical properties with a high signal-to-noise ratio for the whole bandwidth from DC to several tens of megahertz. The electronic part of the detector is based on a commercially available amplifier that provides ease of construction and use while yielding good performance.
We design and experimentally characterize a balanced homodyne detector optimized for high-repetition-rate (100 MHz) pulsed optical sources. Unlike conventional transimpedance-amplifier architectures, which suffer from nonlinearities and dynamic instabilities with ultrashort pulses, our approach allows to directly amplify the photocurrent extracted at the common photodiode node without feedback loops. A theoretical model describing the detector response, noise, and pulse-to-pulse correlations is developed, providing quantitative predictions for the signal variance, signal-to-noise ratio (SNR), and inter-pulse correlations. Implemented with two matched InGaAs photodiodes illuminated by a 1030 nm mode-locked laser at 100 MHz, the detector exhibits excellent linearity and shot-noise-limited scaling of the signal variance with optical power. Optimizing the temporal integration window yields a maximum SNR of about 14 dB, while correlation measurements confirm negligible inter-pulse correlations. These results demonstrate that the proposed architecture offers a robust and simple solution for high-speed pulsed homodyne detection, suitable for quantum optics and continuous-variable quantum information applications.