Shows Direct Spontaneous Four-Wave Mixing Dominates in Thin Layers for Photon Pairs

Researchers are increasingly focused on developing integrated photonic technologies that rely on entangled photon pairs. Changjin Son (Max Planck Institute for the Science of Light, Friedrich-Alexander Universität Erlangen-Nürnberg) and Maria Chekhova (Max Planck Institute for the Science of Light, Friedrich-Alexander Universität Erlangen-Nürnberg) et al. have now demonstrated a surprising dominance of direct spontaneous four-wave mixing (SFWM) in ultrathin lithium niobate layers, challenging the conventional understanding that cascaded processes are more efficient. This finding is significant because it unlocks new possibilities for engineering quantum states of light using compact, ‘flat’ platforms and offers a pathway towards more versatile and integrable photon pair sources for quantum communication and computation.

Dominant photon pair generation via direct four-wave mixing in ultrathin lithium niobate is demonstrated

This work focuses on implementing photon pair generation via SFWM within a 10μm-thick lithium niobate (LN) crystal, a second-order nonlinear material. The team achieved this by utilising a 1030nm laser with a pulse duration of 210fs and a repetition rate of 1.023MHz, focused onto the LN sample. Experiments were performed using a Hanbury Brown-Twiss setup to separate entangled photons and analyse their characteristics.
Crucially, the study establishes that the reduced wavevector mismatch in thin layers favours direct SFWM over the typically more efficient cascaded process involving second harmonic generation followed by spontaneous parametric down-conversion. This finding is significant because it alters the predicted efficiency of photon pair generation in these ‘flat’ platforms.

The researchers observed the power dependence of mean photon numbers per pulse for both visible and infrared photons, confirming the dominance of direct SFWM. By carefully controlling the pump power and polarisation, the team demonstrated the generation of photon pairs through SFWM, with detection occurring via single-photon detectors coupled to multi-mode fibres.

The experimental setup included bandpass filters to select specific wavelengths, ensuring accurate detection of the generated photons. This breakthrough reveals new opportunities for quantum state engineering, as the existence of both second- and third-order nonlinear processes within the LN layer broadens the possibilities for manipulating photon pairs. The ability to generate entangled photons directly through SFWM in thin films opens avenues for developing more compact and multifunctional photonic quantum technologies, potentially leading to advancements in quantum communication and computation.

Experimental setup for demonstrating direct spontaneous four-wave mixing in lithium niobate is shown in Figure 1

Scientists investigated photon pair generation using spontaneous four-wave mixing (SFWM) in a thin lithium niobate (LN) crystal. The study aimed to demonstrate that direct SFWM dominates over cascaded processes in such a thin-film geometry, challenging conventional understanding of nonlinear optics. Researchers fabricated a 10μm-thick x-cut LN layer on a 500μm-thick fused silica substrate to facilitate this investigation.

To measure photon pairs, the team employed a Hanbury Brown-Twiss setup, separating entangled photons into two detection arms. A 1030nm laser, delivering pulses of 210fs duration at 1.023MHz repetition rate, served as the pump source. Two half-wave plates and a polarizing beam splitter controlled the pump’s power and polarization before it was focused by a lens L1 into a 100μm spot on the LN sample.

Output photons were then collimated using a 100mm focal length lens L2 with NA=0.5. The separated photons, split by a long-pass dichroic mirror with a 950nm cutoff wavelength, were coupled into multi-mode fibers via lenses L3 and L4. Polarization analysis was performed in each arm using a half-wave plate and a polarizing beam splitter.

Band-pass filters, specifically F2 at 770nm with 10nm bandwidth and F3 at 1550nm with 50nm bandwidth, selected the signal and idler photon detection bands. Single-photon detectors, Perkin&Elmer SPCM-AQRH-16-FC and IDQ ID220, registered detection events, and a time tagger recorded these events triggered by the laser pulses.

This setup enabled precise measurement of photon coincidence counts, revealing a quadratic dependence on pump power consistent with SFWM. Experiments revealed differing power dependencies for visible and infrared photons, with visible photons exhibiting quadratic scaling and infrared photons showing linear behaviour.

This linear scaling of IR photons was attributed to spontaneous parametric down-conversion (SPDC) within the LN crystal, generating signal photons at 1550nm and undetected idler photons at 3.078μm. The team calculated the second-order correlation function g(2) as g(2)(0) = ⟨Ncc⟩ / (⟨Nvis⟩⟨NIR⟩), fitting the data to g(2) = 1 + a/P2, where ‘a’ is a fitting parameter and ‘P’ is the pump power. A g(2) value exceeding 2, coupled with its inverse square relationship to pump power, confirmed the detection of correlated photon pairs generated via SFWM.

Visible and infrared photon rate scaling differentiates spontaneous four-wave mixing from parametric down-conversion in these experiments

Scientists demonstrated spontaneous four-wave mixing (SFWM) photon pair generation in a thin layer of lithium niobate (LN). The team implemented SFWM in a second-order nonlinear crystal, a 20m-thick LN layer, to investigate the dominance of direct SFWM over cascaded processes. Experiments revealed a quadratic dependence of the mean photon number per pulse for visible photons, ⟨Nvis⟩, and a linear dependence for infrared photons, ⟨NIR⟩, at a pump wavelength of 1030nm.

Measurements confirm that the quadratic scaling of ⟨Nvis⟩ is indicative of SFWM, while the linear scaling of ⟨NIR⟩ suggests a contribution from spontaneous parametric down-conversion (SPDC). The researchers recorded mean photon numbers of ⟨Nvis⟩ and ⟨NIR⟩ as a function of pump power, observing distinct behaviours.

Data shows that the visible photon rate exhibited a quadratic increase, while the infrared photon rate increased linearly. Tests prove that the coherence length for SPDC in the thin LN layer is 15m, exceeding the sample thickness, and while idler photons were not detected, the signal photon generation rate from SPDC was significant.

Importantly, SPDC did not affect coincidence detection because the idler photons were not present in the visible arm. Scientists measured the number of coincidence counts per pulse, ⟨Ncc⟩, as a function of pump power, finding a quadratic dependence consistent with SFWM. The second-order correlation function, g(2), was calculated as g(2)(0) = ⟨Ncc⟩ / (⟨Nvis⟩⟨NIR⟩), resulting in a fitting curve of g(2) = 1 + a/P2, where ‘a is a fitting parameter and ‘P is the pump power.

Measurements confirm that g(2) exceeded the thermal value of 2, and its inverse dependence on the mean photon number of SFWM, scaling as P2, indicated the detection of correlated photon pairs. Further investigation involved examining the contribution of the cascaded process by detecting photon pairs from SPDC pumped at 515nm.

The team measured a conversion efficiency of 2 × 10−2%/W for second harmonic generation, corresponding to 30 μW of SH power generated from 400mW of 1030nm pumping. Analysis revealed that the cascaded process generated only 4 × 10−8 pairs per pulse, representing just 5% of the total photon pair rate. The phase-matching functions for SFWM, SHG, and SPDC were compared, demonstrating that the nonlinear coherence length for SFWM was significantly larger, leading to a more efficient direct process.

Direct spontaneous four-wave mixing surpasses cascaded processes in lithium niobate photon pair generation, offering higher efficiency

Scientists have demonstrated that direct spontaneous four-wave mixing (SFWM) dominates photon pair generation in a thin layer of lithium niobate, challenging the conventional understanding that cascaded processes are more efficient. This research focused on generating photon pairs using SFWM in a second-order nonlinear crystal, specifically a thin layer of lithium niobate, exploiting both second and third-order nonlinear optical processes.

Measurements of the correlation function and the efficiency of second harmonic generation were undertaken to characterise the photon pair generation. The study reveals that the wavevector mismatch for SFWM is significantly smaller than that for both second harmonic generation and spontaneous parametric down-conversion, leading to a substantially larger phase-matching function for SFWM.

Theoretical modelling, incorporating the phase-matching functions for each process, confirms that the efficiency of direct SFWM exceeds that of the cascaded process, even though the latter involves both SHG and SPDC. Calculations show that the rate of photon pair generation through direct SFWM is considerably higher than through the cascaded route, with the cascaded process accounting for only 5% of the total photon pair rate under the conditions tested.

The authors acknowledge that their analysis assumes a non-depleted pump and a simplified model for the nonlinear susceptibilities. Future research could explore the impact of pump depletion and more complex material properties on the observed dominance of direct SFWM. These findings have implications for the design of integrated photonic devices, suggesting that thin-film platforms can efficiently generate entangled photons via direct SFWM, offering opportunities for state engineering and multi-functional photonics without relying on cascaded nonlinearities.