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arXiv:1212.4412 · Optics Express

Experimental generation of multi-photon Fock states

Merlin Cooper, Laura J. Wright, Christoph Söller, Brian J. Smith

Published Feb 25, 2013• 107 citations
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Abstract

We experimentally demonstrate the generation of multi-photon Fock states with up to three photons in well-defined spatial-temporal modes synchronized with a classical clock. The states are characterized using quantum optical homodyne tomography to ensure mode selectivity. The three-photon Fock states are probabilistically generated by pulsed spontaneous parametric down conversion at a rate of one per second, enabling complete characterization in 12 hours.

DOI
10.1364/oe.21.005309

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We experimentally demonstrate the generation of multi-photon Fock states with up to three photons in well-defined spatial-temporal modes synchronized with a classical clock. The states are characterized using quantum optical homodyne tomography to ensure mode selectivity. The three-photon Fock states are probabilistically generated by pulsed spontaneous parametric down conversion at a rate of one per second, enabling complete characterization in 12 hours.
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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.
Multi-photon Fock states have diverse applications such as optical quantum information processing. For the implementation of quantum information processing, Fock states should be generated within the telecommunication wavelength band, particularly in the C-band (1530-1565 nm). This is because mature optical communication technologies can be leveraged for transmission, manipulation, and detection. Additionally, to achieve high-speed quantum information processing, Fock states should be generated in optical pulses with as short a duration as possible, as this allows embedding lots of information in the time domain. In this paper, we successfully generate picosecond pulsed multi-photon Fock states (single-photon and two-photon states) in the C-band with Wigner negativities for the first time, which are verified by pulsed homodyne tomography. In our experimental setup, we utilize a single-pixel superconducting nanostrip photon-number-resolving detector (SNSPD), which is expected to facilitate the high-rate generation of various quantum states. This capability stems from the high temporal resolution of SNSPDs (several tens of picoseconds in our case and also in general) allowing us to increase the repetition frequency of pulsed light from the conventional MHz range to the GHz range, although in this experiment the repetition frequency is limited to 10 MHz due to the bandwidth of the homodyne detector. Consequently, our experimental setup is anticipated to serve as a prototype of a high-speed optical quantum state generator for ultrafast quantum information processing at telecommunication wavelength.
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.
Generation of multi-photon states (such as for instance three- and four-photon states) is one of the most challenging problems of modern quantum optics. In many works the authors claim to have produced such states by means of overlapping photon pairs generated in spontaneous parametric down-conversion (SPDC). Moreover three- and four-photon states generated this way have been used for observing Greenberger-Horne-Zeilinger (GHZ) polarization states testing Bell's inequalities for spin-1 quantum systems preparing W-states and other applications. In this paper we show that the criterion for obtaining three- or four-photon states is the behavior of the corresponding normalized Glauber's correlation function. Calculations carried out for the case of SPDC or even PDC in the stimulated regime demonstrate that these processes are not capable of generating three- or four-photon states: photon statistics reveals typically two-photon behaviour. We suggest a method of measuring higher-order correlation functions in the pulsed regime which allows one to study multi-photon correlations for these and many other processes.