Tunable frequency-bin multimode squeezed vacuum states of light

Squeezed states are a versatile class of quantum states with applications ranging from quantum computing to high-precision detection. We propose a method for generating tunable squeezed vacuum states of light with multiple modes encoded in frequency bins. Our method uses custom-engineered spontaneous parametric down-conversion pumped by a pulse-shaped pump field. The multimode squeezed states are generated in a single pass and can be tuned in real time by adjusting the properties of the pump field. Exploring new quantum states of light, encoded in new degrees of freedom, can be a fruitful path toward discovering new quantum applications.

Figure 1

(a) Five-peak target phase-matching function as defined in Eq. (17) (with $c_m=\sqrt{2}/\sqrt{\pi }L{\sigma }_{k}5, {\sigma }_k=2.5/L$, and $\delta k=24{\sigma }_k$) and corresponding custom phase-matching function generated by the custom-poled crystal shown in (b). We took ${\sigma }_k=2.5/L$ to ensure that the target nonlinearity profile fits within the length of the crystal. The custom-poled crystal has $N=1073$ domains of width $w=18.63\mu \text{m}$. The domain width was chosen to match the phase-matching conditions of type-II KTP in the symmetric group-velocity-matched regime.

Figure 2

(a) Five-peak phase-matching function as defined by Eq. (11) with $\sigma$ and $\delta \omega$ related to ${\sigma }_k$ and $\delta k$ in Fig. 1 via Eqs. (18) and (19). (b) Five-peak pump function as defined in Eq. (10) with the same $\sigma$ and $\delta \omega$ as the PMF. (c) Resulting joint spectral amplitude as defined in Eq. (8).

Figure 3

(a) Three-peak target phase-matching function as defined in Eq. (17) (with $c_0=\sqrt{2}/\sqrt{\pi }L5{\sigma }_k$ and $c_1=c_{-1}=3c_0/2$) and corresponding custom phase-matching function generated by the custom-poled crystal shown in (b). The parameters ${\sigma }_k, \delta k, N$, and $w$ are the same as in Fig. 1. (c) Resulting joint spectral amplitude as defined in Eq. (8) for a three-peak phase-matching function and a three-peak pump function with $\sigma$ and $\delta \omega$ the same as in (a). (d) The JSA in (c) with a filter applied to both the signal and idler modes, with a transmission function $\{1-exp[-{({\omega }_s-{\mathrm{\Omega }}_s)}^2/4{\sigma }_f^2)\}\{1-exp[-{({\omega }_i-{\mathrm{\Omega }}_i)}^2/4{\sigma }_f^2]\}$, where ${\sigma }_f=2\sigma$.

Figure 4

(a) Real part and (b) imaginary part of the five-peak target phase-matching function as defined in Eq. (17) (with $c_m=\sqrt{2}/\sqrt{\pi }L5{\sigma }_k, {\sigma }_k=2.5/L$, and $\delta k=24{\sigma }_k$) and (c) real part and (d) imaginary part of the corresponding amplitude function. We took ${\sigma }_k=2.5/L$ to ensure that the target nonlinearity profile fits within the length of the crystal. The custom-poled crystal has $N=1073$ domains of width $w=18.63\mu \text{m}$. The domain width was chosen to match the phase-matching conditions of type-II KTP in the symmetric group-velocity-matched regime.