Optimised spectral purity of unfiltered photons via pump and nonlinearity shaping

Abstract

Photonic quantum technologies rely on the efficient generation and interference of indistinguishable photons. Exceptional achievements in this respect have been obtained by domain engineering of quasi-phase-matched parametric down-conversion sources, demonstrating high two-photon interference visibility using only moderate bandpass spectral filtering. Here, we optimised the spectral purity and indistinguishability of photons from telecom-wavelength sources by combining Gaussian quasi-phase-matching with Gaussian pump spectral shaping. Without spectral filtering, we used time-of-flight spectrometry to estimate an upper bound spectral purity of 99.9272(6)%, and achieved visibilities of up to 98.5(8)% in two-photon interference experiments with independent sources.

Figures (11)

• Figure 1: Joint spectral amplitude optimisation under group velocity matching conditions. Panels show the results of different combinations of nonlinearity profiles (top) and pump spectra (left): (a) constant QPM nonlinearity with hyperbolic secant pump, (b) constant QPM nonlinearity with Gaussian-shaped pump, (c) Gaussian-engineered nonlinearity with hyperbolic secant pump, (d) Gaussian-engineered nonlinearity with Gaussian-shaped pump. On the top, dashed red lines indicate the nonlinear crystal boundaries, and $\sigma$ denotes the width of the Gaussian nonlinearity profile. The pump intensity spectra on the left assume flat spectral phases $\varphi(\lambda)$ (dashed blue lines) with widths ($\Delta_{\mathrm{PEF}}$ for hyperbolic secant, $\sigma_{\mathrm{PEF}}$ for Gaussian) chosen to maximise the spectral purity $P$ of each case. The reported values show the ideal purity calculated through Schmidt decomposition and the weights of the first five Schmidt modes.
• Figure 2: Spectral purity analysis. (a) Maximum purity (blue dots) and optimal $\sigma_{\mathrm{PEF}}$ (orange dots) as a function of the nonlinear profile width $\sigma/L$ normalised to the crystal length. Red stars mark the working point $\sigma/L = 1/6.04$. The inset displays the Gaussian target function $g_{\mathrm{ideal}}$ at this optimal width. (b) Purity as functions of normalised width $\sigma/L$ and pump spectral width $\sigma_{\mathrm{PEF}}$. The red star marks the optimal working point ($\sigma = L/6.04$, $\sigma_{\mathrm{PEF}} = \qty{0.308}{\nano\meter})$. (c) Comparison between the target field amplitude at $\sigma/L=1/6.04$ and the actual field obtained using the domain engineering in the lower panel. Light and dark grey regions have inverted nonlinearity signs. The inset demonstrates the accuracy of target field tracking.
• Figure 3: Experimental scheme. (a) A femtosecond (fs) pulsed laser operating at a repetition rate of 76 is spectrally shaped by a spatial light modulator (SLM) positioned at the Fourier plane of a folded 4$f$ pulse shaper. A concave mirror ($f=\qty{500}{\milli\meter}$) maps different wavelengths of the first-order diffracted beam to specific pixels of the SLM. The beam is reflected with a slight vertical tilt, offsetting the incoming and outgoing beams. Amplitude shaping is achieved by combining the polarisation rotation imposed on each wavelength by the SLM with the polarisation rejection carried out by the Glan-Taylor (GT) polariser. A beam sampler sends part of the beam to the spectrometer, while the rest is sent to the down-conversion sources. The inset shows an example of pump spectrum before and after pulse shaping (the dashed line is the spectral phase for transform-limited pulses) (b) The beam is split to the two sources and focused with lenses of focal length $f_{\mathrm{lens}}=\qty{500}{\milli\meter}$. Each source consists of a custom apodised-KTP crystal inside a Sagnac loop Fedrizzi2007. The four down-converted photons at telecom wavelengths are separated from the pump beam using dichroic mirrors (DM) and lowpass filters (LPF). Depending on the measurements to perform, photons undergo a certain single-particle transformation $U$, and single-count and coincidence events between the photons and the laser trigger signal are detected using superconducting nanowire single-photon detectors (SNSPDs) via a time-tagging system. (c) In the time-of-flight spectrometry measurements, the signal and idler photons from each source are sent to commercial plug-and-play dispersion compensation modules that introduce different relative time delays depending on the frequencies of the photons. A 2D histogram is acquired by recording three-fold coincidences between the trigger signal and the down-converted photons for several combinations of time delays between these channels. The JSI in the inset is reconstructed from this histogram by knowing the chromatic dispersion of the dispersion compensation modules. (d) In the heralded two-photon interference measurements, four-fold coincidences are recorded when interfering the two idler photons from each source at a polarisation-maintaining fibre beam splitter (FBS) while varying their relative time delay at the FBS.
• Figure 4: Results Gaussian spectral shaping. (a) Shaped pump amplitude spectrum ($\sqrt{I}$) and corresponding Gaussian fit (red line) with $\sigma_{\mathrm{PEF}}=\qty{0.321(1)}{\nano\meter}$. FWHM is defined as full width at half maximum of the intensity. (b) Expected purity as a function of the pump bandwidth. The red marker indicates the purity expected from the FWHM in panel (a), with a reduction from the maximum purity of $\approx 10^{-4}\%$. (c) Calculated purity and pulse duration (solid lines), at $\sigma_{\mathrm{PEF}}=\qty{0.321}{\nano\meter}$, as a function of group delay dispersion from the pump spectral shaping. The panel uses dual x-axes: displacement $\Delta$ from optimal grating-to-mirror distance $f$ (upper scale) and corresponding GDD (lower scale). The intersection between the measured pulse duration of 1.21(2) (red dashed line and shaded uncertainty region) and the simulated curve defines the two GDD intervals (dashed black lines and grey-shaded areas) and the corresponding $\Delta$. The intersection of the GDD intervals with the simulated purity establishes the maximum purity of 99.16(43).
• Figure 5: Time-of-flight spectrometry and two-photon interference results. (a) JSA reconstructed from TOFS, with purity of $\qty{99.90}{\percent}$ and estimated maximum purity of 99.9272(6) (see Appendix \ref{['appendix:max purity']}). (b) Heralded TPI measurement from different sources at a pump power of 5.8 mW, integrating each point over 10 minutes. The red line indicates the fit to the data, and the shaded area is the associated one-sigma uncertainty region. Using only lowpass filters, we obtained a fitted visibility of $\qty{98.5 \pm 0.8}{\percent}$ and a visibility of $\qty{98.5(4)}{\percent}$ extracted from the minimum data and the average of the four maxima.