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arXiv:1703.02786 · Physical Review A

Negative Wigner function at telecommunication wavelength from homodyne detection

Christoph Baune, Jaromı́r Fiurášek, Roman Schnabel

Published Jun 19, 2017• 19 citations
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Abstract

Quantum states of light having a Wigner function with negative values represent a key resource in quantum communication and quantum information processing. Here we present the generation of such a state at the telecommunication wavelength of 1550 nm. The state is generated by means of photon subtraction from a weakly squeezed vacuum state and is heralded by the ``click'' of a single photon counter. Balanced homodyne detection is applied to reconstruct the Wigner function, also yielding the state's photon-number distribution. The heralding photons are frequency up-converted to 532 nm to allow for the use of a room-temperature (silicon) avalanche photodiode. The Wigner function reads $W(0,0)=\ensuremath{-}0.063\ifmmode\pm\else\textpm\fi{}0.004$ at the origin of phase space, which certifies negativity with more than 15 standard deviations.

DOI
10.1103/physreva.95.061802

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Quantum states of light having a Wigner function with negative values represent a key resource in quantum communication and quantum information processing. Here we present the generation of such a state at the telecommunication wavelength of 1550 nm. The state is generated by means of photon subtraction from a weakly squeezed vacuum state and is heralded by the ``click'' of a single photon counter. Balanced homodyne detection is applied to reconstruct the Wigner function, also yielding the state's photon-number distribution. The heralding photons are frequency up-converted to 532 nm to allow for the use of a room-temperature (silicon) avalanche photodiode. The Wigner function reads W(0,0)=\ensuremath−0.063\ifmmode±\else\textpm\fi0.004W(0,0)=\ensuremath{-}0.063\ifmmode\pm\else\textpm\fi{}0.004W(0,0)=\ensuremath−0.063\ifmmode±\else\textpm\fi0.004 at the origin of phase space, which certifies negativity with more than 15 standard deviations.
In the field of continuous-variable quantum information processing, non-Gaussian states with negative values of the Wigner function are crucial for the development of a fault-tolerant universal quantum computer. While several non-Gaussian states have been generated experimentally, none have been created using ultrashort optical wave packets, which are necessary for high-speed quantum computation, in the telecommunication wavelength band where mature optical communication technology is available. In this paper, we present the generation of non-Gaussian states on wave packets with a short 8-ps duration in the 1545.32 nm telecommunication wavelength band using photon subtraction up to three photons. We used a low-loss, quasi-single spatial mode waveguide optical parametric amplifier, a superconducting transition edge sensor, and a phase-locked pulsed homodyne measurement system to observe negative values of the Wigner function without loss correction up to three-photon subtraction. These results can be extended to the generation of more complicated non-Gaussian states and are a key technology in the pursuit of high-speed optical quantum computation.
The presence of negative values in the Wigner quasiprobability distribution is deemed one of the hallmarks of nonclassical phenomena in quantum systems. Here we demonstrate a classical model of squeezed light that, when combined with post-selection on amplitude threshold-crossing detection events, is capable of reproducing observed behavior of single-photon added coherent states. In particular, a classical model of balanced homodyne detection and standard tomographic techniques are used to infer the density matrix in the Fock basis. The resulting Wigner functions exhibit negatively for photon-added vacuum and weak coherent states.
The squeezed light field is a kind of important continuous variable quantum resource.It has wide applications in precision measurement and quantum information processing.Quantum storage is the foundations of quantum repeater and long distance quantum communication,and alkali metal atoms are an ideal quantum storage medium due to long ground state coherent time. With the rapid development of quantum storage technology in atomic medium,the preparation of the squeezed light which resonates with alkali metal atoms has become one of the research hotspots in the field of quantum information.In this paper,we report the generation of squeezed vacuum at 795 nm (resonant on the rubidium D1 transition line) by using an optical parametric oscillation based on a periodically poled KTiOPO4 crystal. The generated squeezed light field is detected by a balanced homodyne detector,and the squeezing of-3 dB and anti-squeezing of 5.8 dB are observed at a pump power of 45 mW.By using a maximum likelihood estimation,the density matrix of the squeezed light field is reconstructed.The time-domain signals from the balanced homodyne detector are collected to acquire the noise distribution of the squeezed light under different phase angles.The likelihood function is established for the measured quadrature components.An identity matrix is chosen as an initial density matrix,and the density matrix of the squeezed field is obtained through an iterative algorithm.The diagonal elements of the density matrix denote the photon number distribution,which includes not only even photon number states but also odd photon number states.The occurrence of odd photon number states mainly comes from the system losses and the imperfect quantum efficiency of detector.The Wigner function in phase space is calculated through the density matrix,and the maximum value of the Wigner function is 0.309.The standard deviation of the squeezed component is 64.4% of that of the vacuum state,corresponding to the squeezing degree of-3.8 dB.The standard deviation of the anti-squeezing component is 1.64 times that of the vacuum state,corresponding to the anti-squeezing degree of 4.3 dB.We theoretically calculate the photon number distribution and the Wigner function of the vacuum squeezed field,and compare the results obtained by theoretical calculation with those obtained by maximum likelihood reconstruction.The probability of vacuum state|0 obtained by maximum likelihood reconstruction is greater,and the probability of photon number state|n(n=1,2,) is smaller than the corresponding theoretical calculation results.From the theoretical calculation,the maximum value of Wigner function is 0.231,and the short axis and long axis of noise range deduced from the contours of the Wigner function are larger than the results from the maximum likelihood reconstruction.The possible reasons for the discrepancy are as follows. 1) The phase scanning is nonuniform during the measurement of the quadrature components.2) The low-frequency electronic noise is not completely filtered out in the datum acquisition process.3) The datum points of measured quadrature components are not enough.In conclusion,we produce a vacuum squeezed field of 795 nm,and obtain the photon number distribution and the Wigner function in phase space through maximum likelihood estimation and theoretical calculation,respectively.This work will provide an experimental basis for generating the Schrodinger cat state.
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.
Telecommunication wavelength with well-developed optical communication technologies and low losses in the waveguide are advantageous for quantum applications. However, an experimental generation of non-classical states called non-Gaussian states at the telecommunication wavelength is still underdeveloped. Here, we generate highly-pure-single-photon states, one of the most primitive non-Gaussian states, by using a heralding scheme with an optical parametric oscillator and a superconducting nano-strip photon detector. The Wigner negativity, the indicator of non-classicality, of the generated single photon state is -0.228 ± 0.004, corresponded to 85.1 ± 0.7% of single photon and the best record of the minimum value at all wavelengths. The quantum-optics-technology we establish can be easily applied to the generation of various types of quantum states, opening up the possibility of continuous-variable-quantum-information processing at the telecommunication wavelength.