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Quantum Electronics and Laser Science Conference

Quantum tomography of the single-photon Fock state

Alexander I. Lvovsky, Thomas Aichele, Hauke Hansen, Oliver J. Benson, J. Mlynek, Stephan Schiller

Published Nov 13, 2002• 0 citations
Publisher

Abstract

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.

DOI
10.1109/qels.2001.962178

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•Jan 1, 2014•0 citations
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.
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.
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.
A new class of non-classical light states has been experimentally generated and their complete phase-space characterization has been achieved by quantum homodyne tomography. Such states are produced by the action of the photon creation operator on a coherent light field and are thus the result of the elementary excitation process of a classical field by a single quantum. Being intermediate between a single-photon Fock state and a coherent one, they offer the unique opportunity to closely follow the smooth evolution between the particle-like and the wave-like behavior of the light field.
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 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.