Non-Hermitian engineering for brighter broadband pseudothermal light

We show that non-Hermitian engineering can play a positive role in quantum systems. This is in contrast to the widely accepted notion that optical losses are a drawback that must be eliminated or, at least, minimized. We take advantage of the interplay between nonlinear interactions and loss to show that spectral-loss engineering can relax phase-matching conditions, enabling generation of broadband pseudothermal states at new frequencies. This opens the door for utilizing the full potential of semiconductor materials that exhibit giant nonlinearities but lack the necessary ingredients for achieving quasi-phase-matching. This in turn may pave the way for building on-chip quantum light sources.

Figure 1

(a) A phase-matched material facilitates pair creation (internal arrows pointing out), generating intense output in modes $a$ and $b$. (b) Away from phase-matching, oscillations in the fields' relative phases spawn two competing processes: pair creation (outward arrows) and recombination (inward arrows), generating negligible output in modes $a$ and $b$. (c) Adding loss in mode $a$ of a non-phase-matched material suppresses recombination without disrupting pair creation, generating enhanced output in mode $b$.

Figure 2

(a) Spectral density $n_a$ in mode $a$ for various loss rates ${\gamma }_b$ in mode $b$. (b) Optimal loss rate ${\gamma }_{\mathrm{opt}}$. Loss becomes beneficial away from phase matching ($\mathrm{\Delta }k=0$). (c) Enhancement due to loss defined as $n_a$ for $\gamma ={\gamma }_{\mathrm{opt}}$ divided by $n_a$ for $\gamma =0$. Other parameters are $\xi L_0=1.0$ and $z/L_0=1$. The enhancement factor defined by the output state value of $n_a^{{\gamma }_{\mathrm{opt}}}/n_a^{\gamma =0}$ is shown in (c). Clearly, several orders of magnitude improvement can be observed outside the standard phase-matching regime. $L_0$ is a nominal unit length. All plotted quantities are dimensionless.

Figure 3

Properties of the generated light for various values of loss parameter ${\gamma }_b$. (a) Spectral density $n_a$ in mode $a$. (b) Spectral density $n_b$ in mode $b$. (c) The correlation parameter $m$. (d) The entanglement of formation (EoF) between modes $a$ and $b$. Other parameters are $\xi L_0=1.0$ and $\mathrm{\Delta }k{L}_0=11.5$. Vertical axes have different scales, while horizontal axes are the same. $L_0$ is a nominal unit length. All plotted quantities are dimensionless.

Figure 4

Comparison between output predicted by quantum and classical models, using optimal loss parameter $\gamma L_0={\gamma }_{\mathrm{opt}}{L}_0=22.7$, squeezing parameter $\xi L_0=1.0$, and phase mismatch $\mathrm{\Delta }k{L}_0=11.5$. The spectral density $n_a$ in mode $a$ is plotted for smaller $[n_a\left(0\right)=0.2]$ and bigger $[n_a\left(0\right)=20]$ seeds in (a) and (b) respectively. The correlation parameter $m$ is plotted for smaller and bigger seeds in (c) and (d). The entanglement of formation (EoF) between modes $a$ and $b$ is plotted for smaller and bigger seeds in (e) and (f) respectively. For output predicted by the classical model, the EoF evaluates to be numerically zero, indicating no entanglement, as expected. Horizontal axes are the same in all plots. $L_0$ is a nominal unit length. All plotted quantities are dimensionless.