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Conference on Lasers and Electro-Optics

Photon subtraction and single photon squeezing schemes for generation of Schrodinger cat-like states under experimental imperfections

Setsuo Suzuki, K. Tsujino, Fumihiko Kannari, Masahide Sasaki

Published Jan 1, 2005• 0 citations
Publisher
DOI
10.1109/iqec.2005.1561086

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Schrödinger cat state is an important non-classical state, and it can be used in quantum teleportation, quantum computation and quantum repeater. Schrödinger cat state is usually obtained experimentally by subtracting one photon from a squeezed-vacuum state. The fidelity between a photon-subtracted squeezed state and a cat state can be very high under suitable parameters. However, the quality of the generated state will be affected by the imperfect experimental conditions. In this paper, the effect of imperfect experimental conditions on the generation of cat state is theoretically calculated and analyzed. The input squeezed-vacuum field is represented by Weyl characteristic function, which contains the fluctuation variance of the squeezed and amplified noises. The characteristic function of generated state is obtained by using the transmission matrix of beam splitter and the measurement operator of single-photon detector. We acquire the expression of Wigner function of generated state by the Fourier transform of the Weyl characteristic function. The fidelity is calculated by using the formula F=1/π∫d2ζC1(ζ)C|cat->(ζ), where C1(ζ) and C|cat->(ζ) represent Weyl characteristic function of the generated state and the Schrodinger cat state, respectively. The imperfection of the input squeezed state, the imperfection of the single-photon detector and the loss of the balanced homodyne detection are included in our theoretical model. We calculate the Wigner function at the phase-space origin W(0) and the fidelity in terms of different experimental parameters. The results show that the fidelity and negativity of W(0) decrease with squeezing purity decreasing. A pure squeezed-vacuum state is composed of even photon number states. In the case of impure squeezing, some odd photon number states appear in the photon number distribution. After subtracting one photon from the impure squeezing state, the generated state consists of not only odd photon number state but also even photon states, which degrades the fidelity of the generated state. The lower squeezing purity is required to meet the demand for W(0)<0 under the condition of higher squeezing degree. There is an optimal squeezing degree to maximize the fidelity of generated state with impure squeezing. The use of inefficient on-ff single-photon detector and the loss of the balanced homodyne detection will further reduce the fidelity of the generated state. Under the practical experimental condition:squeezing degree s=-3 dB, the squeezing purity μ=99% and the quantum efficiency of balanced homodyne detection η=98%, the fidelity of generated state can reach 0.88 with using a commercially available on-off single-photon detector. This work can provide theoretical guidance for generating a high-quality Schrödinger cat state.
Measurement-induced nonlinear operation in linear optics is a promising technique to realize quantum computation and communications. Such an operation has been demonstrated via the generation of photon-subtracted squeezed states, namely, Schrödinger-cat states. Nielsen and Mølmer have proposed an efficient scheme to generate the cat states with larger amplitudes relative to previous experimental results. We present a simple experimental implementation of their scheme and analyze it while considering experimental imperfections. Our study indicates that the current photon detection technology meets the conditions necessary for their operation.
We proposed and analyzed a scheme to generate large-size Schr\"odinger cat states based on linear operations of Fock states, squeezed vacuum states, and conditional measurements. By conducting conditional measurements via photon number detectors, two unbalanced small-amplitude Schr\"odinger kitten states combined by a beam splitter can be amplified to a large-size cat state with the same parity. According to simulation results, two Schr\"odinger odd kitten states with amplitudes of $|\ensuremath{\beta}|=1.06$ and $|\ensuremath{\beta}|=1.11$ generated from one-photon-subtracted 3 dB squeezed vacuum states, are amplified to an odd cat state of $|\ensuremath{\beta}|=1.73$ with a fidelity of F=99F=99%F=99. A large-size Schr\"odinger odd cat state with $|\ensuremath{\beta}|=2.51$ and F=97.30F=97.30%F=97.30 is predicted when 5.91 dB squeezed vacuum states are employed. According to the analysis on the impacts of experimental imperfections in practice, Schr\"odinger odd cat states of $|\ensuremath{\beta}|>2$ are available. A feasible configuration based on a quantum frequency comb is developed to realize the large-size cat state generation scheme we proposed.