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Acta Physica Sinica

Fidelity of the photon subtracted (or added) squeezed vacuum state and squeezed cat state

L uuml Jing-Fen, Ma Shan-Jun

Published Jan 1, 2011• 5 citations
Publisher

Abstract

In this paper, the fidelity of photon subtracted (or added) squeezed vacuum state with arbitrary number of photons and squeezed cat state is derived analytically. The result shows that whether the photon is added or subtracted, the maximum fidelity increases with the increase of the change of photon number, and the amplitude of the superposition state corresponding to the maximum fidelity also increases. In addition, for the same number of subtracted or added photons, the amplitude of the superposition state corresponding to the maximum fidelity in the case of added photon is larger than in the case of subtracted photon, but the maximum fidelity in the case is smaller. Although it is more difficult to make photon added than photon subtracted the photon added can be used as an important method to obtain cat state of large amplitude.

DOI
10.7498/aps.60.080301

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In this paper, the fidelity of photon subtracted (or added) squeezed vacuum state with arbitrary number of photons and squeezed cat state is derived analytically. The result shows that whether the photon is added or subtracted, the maximum fidelity increases with the increase of the change of photon number, and the amplitude of the superposition state corresponding to the maximum fidelity also increases. In addition, for the same number of subtracted or added photons, the amplitude of the superposition state corresponding to the maximum fidelity in the case of added photon is larger than in the case of subtracted photon, but the maximum fidelity in the case is smaller. Although it is more difficult to make photon added than photon subtracted the photon added can be used as an important method to obtain cat state of large amplitude.
We study how photon addition and subtraction can be used to generate squeezed superpositions of coherent states (SSCSs) in free-traveling fields with high fidelities and large amplitudes. It is shown that an arbitrary NNN-photon subtraction results in the generation of a SSCS with nearly the perfect fidelity (F>0.999)(F>0.999)(F>0.999) regardless of the number of photons subtracted. In this case, the amplitude of the SSCS increases as the number of the subtracted photons gets larger. For example, two-photon subtraction from a squeezed vacuum state of 6.1dB6.1\phantom{\rule{0.3em}{0ex}}\mathrm{dB}6.1dB can generate a SSCS of $\ensuremath{\alpha}=1.26$, while in the case of the four-photon subtraction a SSCS of a larger amplitude $\ensuremath{\alpha}=1.65$ is obtained under the same condition. When a photon is subtracted from a squeezed vacuum state and another photon is added subsequently, a SSCS with a lower fidelity $(F\ensuremath{\approx}0.96)$ yet higher amplitude $(\ensuremath{\alpha}\ensuremath{\approx}2)$ can be generated. We analyze some experimental imperfections including inefficiency of the detector used for the photon subtraction.
Optical cat states, the nonclassical superposition of two quasi-classical coherent states, serve as a basis for gedankenexperiments testing quantum physics on mesoscopic scales and are increasingly recognized as a resource for quantum information processing. Here, we report the first experimental realization of optical cat states by adding a photon to a squeezed vacuum state; so far only photon-subtraction protocols have been realized. Photon addition gives us the advantage of using heralded signal photons as experimental triggers, and we can generate cat states at rates exceeding $2.3\ifmmode\times\else\texttimes\fi{}{10}^{5}$ counts per second. Our most highly squeezed vacuum input state shows \ensuremath{-}8.9 dB squeezing, but such squeezing entails some degradation---in this case, 15.1 dB antisqueezing. Even so, our approach enables us to synthesize a state with a maximum cat amplitude of $|\ensuremath{\alpha}|\ensuremath{\approx}1.77$ whose Wigner distribution still shows pronounced negative parts. Our experimental implementation with controlled photon addition demonstrates a powerful and robust building block for advanced quantum state engineering and shows that heralded photon addition can be controlled well and performed at high rates.
A new kind of non-Gaussian quantum state is introduced by applying nonlocal coherent superposition (τa + sb) m of photon subtraction to two single-mode squeezed vacuum states, and the properties of entanglement are investigated according to the degree of entanglement and the average fidelity of quantum teleportation. The state can be seen as a single-variable Hermitian polynomial excited squeezed vacuum state, and its normalization factor is related to the Legendre polynomial. It is shown that, for τ = s, the maximum fidelity can be achieved, even over the classical limit (1/2), only for even-order operation m and equivalent squeezing parameters in a certain region. However, the maximum entanglement can be achieved for squeezing parameters with a π phase difference. These indicate that the optimal realizations of fidelity and entanglement could be different from one another. In addition, the parameter τ/s has an obvious effect on entanglement and fidelity.
Optical "Schrödinger cat" states, the non-classical superposition of two quasi-classical coherent states, serve as a basis for gedanken experiments testing quantum physics on mesoscopic scales and are increasingly recognized as a resource for quantum information processing. Here, we report the first experimental realization of optical "Schrödinger cats" by adding a photon to a squeezed vacuum state, so far only photon-subtraction protocols have been realized. Photon-addition gives us the advantage of using heralded signal photons as experimental triggers, and we can generate "Schrödinger cats" at rates exceeding 8.5×1048.5 \times 10^48.5×104 counts per second; at least one order of magnitude higher than all previously reported realizations. Wigner distributions with pronounced negative parts are demonstrated at down to -8.89 dB squeezing, even when the initial squeezed vacuum input state has low purity. Benchmarking against such a degraded squeezed input state we report a maximum fidelity of more than 80% with a maximum cat amplitude of ∣α∣≈1.66|α| \approx 1.66∣α∣≈1.66. Our experiment uses photon-addition from pairs, one of those photons is used for monitoring, giving us enhanced control; moreover the pair production rates are high and should allow for repeated application of photon-addition via repeat-stages.
Abstract In this paper, using the linear entropy criterion to quantify the degree of entanglement, we demonstrate that the addition of photons can enhance the entanglement degree of the photon-added two-mode squeezed vacuum states (PATMSVSs). Besides, the entanglement degree can approach ideal in case of squeezing parameter or number of added photons is high. When using PATMSVSs as entanglement resources to teleport a coherent state via a canonical protocol, the results show that the average fidelity of the quantum teleportation process is enhanced by the photon addition operation. The average fidelity increases as the number of photons added to the two-mode increases. In addition, we show that an enhancement in average fidelity can also be achieved by increasing the squeezing parameter of the TMSVS.