Purification of photon subtraction from continuous squeezed light by filtering

Photon subtraction from squeezed states is a powerful scheme to create good approximation of so-called Schrödinger cat states. However, conventional continuous-wave-based methods actually involve some impurity in squeezing of localized wave packets, even in the ideal case of no optical losses. Here, we theoretically discuss this impurity by introducing mode match of squeezing. Furthermore, here we propose a method to remove this impurity by filtering the photon-subtraction field. Our method in principle enables creation of pure photon-subtracted squeezed states, which was not possible with conventional methods.

Figure 1

Optical setup of our method inserting a filter cavity in the photon-subtraction path. Unlike conventional methods, by taking the bandwidth of the filter $\mathrm{\Gamma }$ narrower than that of the OPO $\gamma$, the resulting photon-subtracted squeezed states become purer.

Figure 2

Normalized correlation functions $N\left(r_{\gamma ,\epsilon }\right)\left(t\right)$ in the time domain, obtained by numerical calculations, for $\gamma =1$. Solid blue line: both-side exponential function corresponding to the limit of $\epsilon \to 0$. Dashed orange line: $\epsilon =0.3$. Dotted green line: $\epsilon =0.7$. The latter two correspond to the squeezing degrees of about 5.4 and 15.1 dB, respectively, at $\omega =0$.

Figure 3

Equivalent amount of losses $L$ as a function of the relative bandwidth of the wave-packet mode function ${\gamma }_{\text{rel}}$. Solid blue line: $\epsilon /\gamma =0.03$. Dashed orange line: $\epsilon /\gamma =0.3$. Dotted green line: $\epsilon /\gamma =0.7$. They correspond to the squeezing degrees of about 0.5, 5.4, and 15.1 dB, respectively, at $\omega =0$. The traces are almost overlapped. In particular, $L\approx 0.1$ at ${\gamma }_{\text{rel}}=1$.

Figure 4

Mode functions to show the mode match of squeezing to heralded single-photon wave packets, for the case without filtering, for $r\left(t\right)\propto exp(-\gamma |t\left|\right)$ with $\gamma =1$. Solid blue line: $N\left(r\right)\left(t\right)$. Dashed orange line: $N(r*r)\left(t\right)$.

Figure 5

Mode functions to show the mode match of squeezing to heralded single-photon wave packets, for the case with filtering, for $r\left(t\right)\propto exp(-\gamma |t\left|\right)$ with $\gamma =1$ and $h\left(t\right)\propto exp(-\mathrm{\Gamma }t)u\left(t\right)$ with $\mathrm{\Gamma }=0.4$. Solid blue line: $N(h^R*r)\left(t\right)$. Dashed orange line: $N(h^R*r*r)\left(t\right)$. Dotted green line: $N\left(h^R\right)\left(t\right)$.

Figure 6

The mode-matching rate in Eq. (56).