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arXiv:quant-ph/0406090 · Physical Review A

Tomographic reconstruction of the single-photon Fock state by high-frequency homodyne detection

Alessandro Zavatta, Silvia Viciani, Marco Bellini

Published Nov 23, 2004• 133 citations
arXivHTMLPDF

Abstract

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 $(82\phantom{\rule{0.3em}{0ex}}\mathrm{MHz})$ substantially simplifies the detection scheme, allowing for more ``exotic'' quantum states to be generated and analyzed.

DOI
10.1103/physreva.70.053821

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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.
We present the experimental approach to the determination of the Fock-States density matrix via the optical homodyne tomography. The single photon state is generated by Spontaneous Parametric Down Conversion (SPDC) in a nonlinear crystal pumped by the Second Harmonic of a picosecond dye laser. The fundamental frequency of the dye-laser realizes the local oscillator for the homodyne measurement. In this paper we describe the experimental apparatus and discuss the possibility to realize the quantum tomography of the single-photon state and, in the future, of the n-photon state. The experimental determination of the field state prepared in a coherent state with different mean photon numbers is also presented.
We have reconstructed the quantum state of optical pulses containing single photons using the method of phase-randomized pulsed optical homodyne tomography. The single-photon Fock state 1> was prepared using conditional measurements on photon pairs born in the process of parametric down-conversion. A probability distribution of the phase-averaged electric field amplitudes with a strongly non-Gaussian shape is obtained with the total detection efficiency of (55+/-1)%. The angle-averaged Wigner function reconstructed from this distribution shows a strong dip reaching classically impossible negative values around the origin of the phase space.
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.
Displaced Fock states of the electromagnetic field have been synthesized by overlapping the pulsed optical single-photon Fock state ∣1〉|1〉∣1〉 with coherent states on a high-reflection beam splitter and completely characterized by means of quantum homodyne tomography. The reconstruction reveals nonclassical properties of displaced Fock states, such as negativity of the Wigner function and photon number oscillations. To our knowledge, this is the first time complete tomographic reconstruction has been performed on a highly nonclassical optical state.
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.
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.