Joint spectrum mapping of polarization entanglement in spontaneous parametric down-conversion

Polarization-entangled photon pairs can be efficiently prepared into pure Bell states with a high fidelity via type-II spontaneous parametric down-conversion (SPDC) of narrow-band pump light. However, the use of femtosecond pump pulses to generate multiphoton states with precise timing often requires spectral filtering to maintain a high quality of polarization entanglement. This typically reduces the efficiency of photon pair collection. We experimentally map the polarization correlations of photon pairs from such a source over a range of down-converted wavelengths with a high spectral resolution and find strong polarization correlations everywhere. A spectrally dependent imbalance between contributions from the two possible decay paths of SPDC is identified as the reason for a reduction in entanglement quality observed with femtosecond pump pulses. Our spectral measurements allow us to predict the polarization correlations for arbitrary filter profiles when the frequency degree of freedom of the photon pairs is ignored.

Figure 1

(Color online) Schematic of the spontaneous parametric down-conversion (SPDC) setup. A femtosecond-pumped SPDC process generates photon pairs in single-mode optical fibers which pass through polarization filters and subsequent grating monochromators.

Figure 2

(Color online) Polarization correlations measured in the H∕V and $+45∕-45°$ bases. The bottom trace in each panel represents pair coincidences from consecutive pulses. For the lower panel, $5\text{‐}\mathrm{nm}$- (FWHM) wide interference filters are inserted. Without spectral filters (upper panel), we observe direct visibilities of $V_{\mathrm{HV}}=94.8\%\pm 0.2\%$ and $V_{45}=68.4\%\pm 0.3\%$ without correcting for higher order contributions; with spectral filters, the corresponding values are $V_{\mathrm{HV}}=93.6\pm 0.4\%$ and $V_{45}=81.6\pm 0.3\%$.

Figure 3

(Color online) The joint spectra of coincidence counts for ${\mathrm{H}}_1{\mathrm{V}}_2$ polarizations (upper panel) and ${\mathrm{V}}_1{\mathrm{H}}_2$ (lower panel) polarization are different. Exchange of the ${\lambda }_1$ and ${\lambda }_2$ axis maps one onto the other. These joint spectra show the covariance between ${\lambda }_1$ and ${\lambda }_2$, which decreases with the broadening of the pump light. Different widths between the marginal (solid trace) and the single-photon event spectrum (dotted trace), as well as differences between ordinary and extraordinary polarization, are apparent.

Figure 4

(Color online) A joint spectrum of coincidences measured for a $+45°∕-45°$ polarization combination (upper panel) reveals a pattern with the maximum coincidence rate at the degenerate wavelengths for a source adjusted to observe singlet Bell states $\mid {\Psi }^{-}⟩$. The joint spectrum measured for a $+45°∕+45°$ polarization combination (lower panel) exhibits four regions of higher count rate. These regions correspond to area with an imbalance of $a$ and $b$. At the position of the degenerate wavelengths in the center, the coincidence rate is close to zero.

Figure 5

(Color online) Polarization correlations at three different wavelength pairs where one photon is projected onto $+45°$ polarization. The maximum of coincidences ranges from $-45°$ polarization for a maximally entangled singlet Bell state $\left(C\right)$ to the horizontal $\left(A\right)$ or vertical $\left(B\right)$ polarization.

Figure 6

(Color online) Map of the visibility $V_{45}$ of polarization correlations for different sets of wavelengths (upper panel). We find a significant local increase compared to the global value obtained in Fig. 2. Points $A$, $B$, and $C$ correspond to the three detailed visibility measurements shown in Fig. 5. The lower panel indicates the angle $\gamma$ for the maximal count rates, ranging from $-45°$ polarization for the singlet Bell state at $\left(C\right)$ in the center towards horizontal polarization $\left(A\right)$ for dominating ${\mid \mathrm{V}⟩}_1{\mid \mathrm{H}⟩}_2$ contributions or vertical polarization $\left(B\right)$ for prevailing ${\mid \mathrm{H}⟩}_1{\mid \mathrm{V}⟩}_2$ contributions.

Figure 7

Entanglement quality. The upper panel illustrates the entanglement entropy $S$ as a function of both wavelengths ${\lambda }_1$ and ${\lambda }_2$ for a model distribution of nonoverlapping contributions for ${\mid \mathrm{H}⟩}_1{\mid \mathrm{V}⟩}_2$ and ${\mid \mathrm{V}⟩}_1{\mid \mathrm{H}⟩}_2$ decay paths in SPDC according to Eq. (3). The lower panel shows $S({\lambda }_1,{\lambda }_2)$ obtained from experimental polarization correlations in the $+45°∕-45°$ basis of Fig. 3. The entanglement is maximal at positions with balanced contributions for both decay paths.

Figure 8

(Color online) Visibility $V_{45}$ (open circles) and normalized coincidence rates (solid squares) as a function of fixed filter bandwidth $\Delta {\lambda }_f$. The values were obtained by virtual filtering using the spectral map of visibility measurements leading to Fig. 6. The experimental point (solid circle) corresponds to a real filter with $\Delta {\lambda }_f=5\mathrm{nm}$, resulting in $V_{45}=81.6\%$. Our result is consistent with predictions in [27].