• Acta Physica Sinica
  • Vol. 69, Issue 18, 184204-1 (2020)
Ze-Hui Zhai*, Wen-Jing Hao, Jian-Li Liu, and Xi-Ya Duan
Author Affiliations
  • School of Physics and Electronic Engineering, Shanxi University, Taiyuan 030006, China
  • show less
    DOI: 10.7498/aps.69.20200589 Cite this Article
    Ze-Hui Zhai, Wen-Jing Hao, Jian-Li Liu, Xi-Ya Duan. Filter cavity design and length measurement for preparing Schrödinger cat state[J]. Acta Physica Sinica, 2020, 69(18): 184204-1 Copy Citation Text show less

    Abstract

    Optical Schr?dinger cat state is not only one of the basic elements of quantum mechanics, but also a pivotal resource of continuous-variable quantum information. The non-Gaussian operation in its preparation can also be a key technology in distilling continuous-variable squeezing and entanglement. In the experimental preparation, a small part of a beam of vacuum squeezing is separated and detected as the trigger of appearance of Schr?dinger cat state. Filter operation in the trigger optical path is important since it affects dark counts of single photon detector, frequency mode matching of trigger mode and signal mode, and preparing rate of the Schr?dinger cat state, etc. In this paper, we describe the design of optical filter in the trigger path and the measurement of the filter cavity length. According to the design, filter cavity length $ {l_{{\rm{FC}}}}$ should satisfy $ {\rm{189}}\;{\text{μm}} > {l_{{\rm{FC}}}} > {\rm{119}}\;{\text{μm}}$. This cavity length is too small to be measured with a ruler. To measure the cavity length, we introduce an optical method, in which Gouy phases of Hermite Gaussian transverse modes TEM00 and TEM10 are used. When the cavity length is scanned, resonant peaks and the corresponding scanning voltages are recorded. From theoretical derivation, the cavity length is related to the filter cavity piezo response to the scanning voltage $ {\varPsi '_{\rm{G}}}$, the slope rate of piezo scanning voltage $ U'$, and the time distance between TEM00 and TEM10 resonant peaks $ \Delta t$. The finally measured cavity length is ${l_{{\rm{FC}}}} = ({\rm{141}} \pm 28)~{\text{μm}}$, which satisfies the design requirement. The measurement error mainly originates from inaccurate fitting of $ {\varPsi '_{\rm{G}}}$ and $ U'$, and readout error of $ \Delta t$. It is shown that the error of $ {\varPsi '_{\rm{G}}}$ is dominant since less data are used in the curve fitting. The measurement error is expected to be reduced if much more data of piezo response to scanning voltage are collected and used to fit $ {\varPsi '_{\rm{G}}}$ with higher order polynomials. The proposed measurement method of short cavity length needs neither wide tuning laser nor any peculiar instrument, and does not depend on any dispersion property of the cavity, and hence it has a certain generality. It can be hopefully used in many other optical systems, such as cavity quantum electrodynamics, where ultrashort cavity plays a central role.
    Ze-Hui Zhai, Wen-Jing Hao, Jian-Li Liu, Xi-Ya Duan. Filter cavity design and length measurement for preparing Schrödinger cat state[J]. Acta Physica Sinica, 2020, 69(18): 184204-1
    Download Citation