Experimental sub-Rayleigh resolution by an unseeded high-gain optical parametric amplifier for quantum lithography

Quantum lithography proposes to adopt entangled quantum states in order to increase resolution in interferometry. In the present paper we experimentally demonstrate that the output of a high-gain optical parametric amplifier can be intense yet exhibits quantum features, namely, sub-Rayleigh fringes, as proposed by [Agarwal et al., Phys. Rev. Lett. 86, 1389 (2001)]. We investigate multiphoton states generated by a high-gain optical parametric amplifier operating with a quantum vacuum input for gain values up to 2.5. The visibility has then been increased by means of three-photon absorption. The present paper opens interesting perspectives for the implementation of such an advanced interferometrical setup.

Figure 1

(Color online) (a) Experimental scheme for quantum lithography based on spontaneous parametric down conversion. The two-photon absorption is simulated through a two-photon coincidence detection. (b) Configuration based on polarization entangled beams.

Figure 2

(Color online) Experimental layout. The radiation generated in the NL crystal is spectrally filtered by an interferential filter (IF) with bandwidth equal to 3 nm and spatially selected adopting a single mode (SM) fiber.

Figure 3

Coherent state as input field. (a) $G_1^{\left(1\right)}$: Count rates $D_1^A$ versus the phase $\phi$. (b) $G_{11}^{\left(2\right)}$: Coincidence counts $\left[D_1^A,D_1^B\right]$ versus the phase $\phi$.

Figure 4

(Color online) (a) $G_{12}^{\left(2\right)}$: Two-photon coincidence counts $\left[D_1^A,D_2\right]$ versus the phase $\phi$ introduced by the Soleil-Babinet compensator $\left(g=1.4\right)$. Circle data: Expected accidental (without correlations) coincidence rates. (b) $G_{11}^{\left(2\right)}$: Two-photon coincidence counts $\left[D_1^A,D_1^B\right]$ versus the phase $\phi$ $\left(g=1.4\right)$. Variations of the detectors signal $\left(\sim 10\%\right)$ due to different couplings of polarizations ${\vec{\pi }}_H$ and ${\vec{\pi }}_V$ with fiber have been corrected by normalizing coincidence counts with signal rates.

Figure 5

(a) Visibility versus nonlinear gain. The continuous line corresponds to the function $V_{\text{max}}\times V_1^{\left(2\right)}\left(g\right)$. (b) Excitation rate versus nonlinear gain. The continuous line corresponds to the function ${\overline{R}}^{\left(2\right)}\left(\alpha g\right)$, where the parameter $\alpha$ has been optimized by fitting the data and reads as 0.85.

Figure 6

(Color online) (a) Circle data: $G_1^{\left(2\right)}$ (two-photon coincidences $\left[D_1^A,D_1^B\right]$) versus the phase $\phi$. Square data: $G_1^{\left(3\right)}$ (three-photon coincidences $\left[D_1^A,D_1^B,D_1^C\right]$) versus the phase $\phi$ $\left(g=2.4\right)$. (b) Excitation rate versus nonlinear gain. The continuous line corresponds to the function ${\overline{R}}^{\left(3\right)}\left(g\right)$. Inset: Visibility $V_1^{\left(3\right)}$ versus nonlinear gain.

Figure 7

(Color online) Effects of coherence on fringe visibility. Square data: Two-photon coincidences counts versus the phase $\phi$ without introducing decoherence. Circle data: Decoherence introduced between the polarization components $\left\{{\vec{\pi }}_H,{\vec{\pi }}_V\right\}$. Triangle data: Decoherence introduced between $\left\{{\vec{\pi }}_{+},{\vec{\pi }}_{-}\right\}$.