Efficient Robust Spontaneous Parametric Down-Conversion via Detuning Modulated Composite Segments Designs

TL;DR

The paper tackles the sensitivity of SPDC-based photon-pair sources to environmental and fabrication variations. It introduces detuning modulated composite segmentation (DMCS), a framework that applies composite-pulse ideas to $SU(1,1)$ SPDC dynamics to cancel error terms up to high order, thereby boosting robustness without sacrificing substantial brightness. The authors derive the theoretical underpinnings, design specific DMCS crystal segments, and validate the approach experimentally on a 2 cm KTP crystal for degenerate 532 nm → 1064 nm conversion, reporting a sevenfold improvement in stability against temperature fluctuations and favorable comparison to both standard PP and thin-crystal designs. The work demonstrates that DMCS can deliver stable, high-fidelity entangled photon sources suitable for quantum information tasks and suggests broader applicability to other $\mathrm{SU}(1,1)$ systems and nonlinear processes, potentially enabling more robust quantum technologies while reducing power requirements.

Abstract

Spontaneous Parametric Down Conversion (SPDC) holds a pivotal role in quantum physics, facilitating the creation of entangled photon pairs, heralded single photons and squeezed light, critical resources for many applications in quantum technologies. However, their production is susceptible to physical variations, posing limitations on their robust utility. To overcome these limitations, this work introduces a method to significantly enhance the reliability of entangled photon pair generation. This approach involves introducing a composite design scheme to the SPDC process. The design is based on the development of a theoretical composite segments framework for SU(1,1), offering increased error resilience and robustness of the process. The practical application is experimentally demonstrated by modulating the nonlinear coefficient of a KTP crystal for degenerate 532 nm to 1064 nm conversion, resulting in an effective sevenfold improvement in stability of photon-pair generation and coincidence rate against temperature fluctuations compared to conventional quasi-phase-matching techniques. Furthermore, the presented concept is applicable to other physical systems that exhibit SU(1,1) dynamics. This methodology can create a leap forward in quantum technologies by significantly enhancing stability and error tolerance, thus paving the way for a new generation of entangled photon sources, holding promise for quantum information processing, communication, and precision measurement applications.

Figures (15)

• Figure 1: (a) Perfect phase matching and the periodically poled QPM design: A non-linear crystal is poled periodically to compensate for the phase mismatch of the desired frequency conversion. (b) DMCS crystal, in which the crystal has modulated segments with different poling periods and lengths. (c) The normalized rate of generated pairs along the crystal while assuming that it lies in the Rayleigh range and the process is under plane wave approximation. All dynamics in the plotted non-zero deviation temperature plots are already in the harmonic regime. Yet, for short enough crystals, they do not differ from the hyperbolic perfect solution. (d) We show for different temperature deviations how the normalized rate of generated pairs changes along the crystal and demonstrate that the process result is robust under these deviations. (e) Blue is the generation rate of the periodically poled design and purple is the rate for DMCS. As can be seen, the DMCS case is much less sensitive to $\Delta k$ (the gray horizontal axis) and, hence, to temperature (the purple horizontal axis). We show perfect phase matching at $\Delta k=0$, and five representative points that are not phase-matched.
• Figure 2: Geometrical representation of SPDC dynamics: All the possible SPDC states are mapped to a surface of a hyperboloid, and the pair generation rate is proportional to $w$. (a) The geometrical representation of the SPDC process under the undepleted pump approximation for PP design. All six path trajectories from 1(c) are plotted. The continuous red line is the perfect phase matching, and all of the dotted lines are at the five deviated temperatures. The blue continuous line describes $w$, at the end of the process as $\Delta T$ changes from -2.4°C to +2.4°C. (b) The quantum $uvw$-vector trajectory on the hyperboloid representation of the SU(1,1) dynamics of our 2 cm DMCS crystal at the designated temperature (the continuous lines) and at 1°C deviation from it (the dotted lines). As one can see, while the $w$ value at the end of the crystal is 6.7 times lower than the PP crystal (for the same pump intensity), it is much more robust to errors: $w(\Delta T = 0\text{°C}) = 5.545 \cdot 10^{-5}$, $w(\Delta T = 1\text{°C}) = 5.398 \cdot 10^{-5}$ (not in the figure) and $w(\Delta T = 2.4\text{°C}) = 5.579 \cdot 10^{-5}$.
• Figure 3: Comparison of numerical and experimental results for a PP crystal and a DMCS crystal. (a)-(d) normalized count-rate vs. temperature deviation from the desired work temperature and the signal wavelength ((a) and (c)) or signal angle ((b) and (d)) for the PP ((a)-(b)) and DMCS ((c)-(d)) crystals, the white dashed line matches the conditions in the experiment. (e) the experimental setup - a 532.25 nm CW pump laser passes through a nonlinear crystal that creates a type-0 colinear SPDC process. The crystal rests on a kinetic stage that allows switching between different poling designs, and its temperature is controlled with a precision of 0.1°C. After the light passes through the crystal, the remaining pump is filtered out. The generated SPDC photons are focused into a fiber that collects them into a superconducting nanowire single photon detector. (f) experimental and numerical results - the normalized count rate of PP (red) and DMCS (blue) crystals relative to their maximal rates versus the temperature deviation from the desired work temperature. The markers are the experimental results and the continuous line marks the numerical simulations predictions.
• Figure 4: Comparison of the normalized coincidence rate of the PP and DMCS crystals. (a) the experiment setup - we add a 50:50 fiber coupler and a second detector that allows counting coincidence between the outputs, using a time-tagger. (b)-(c) normalized absolute value of the phase matching function of periodically poled and DMCS crystals inside a 3 nm wavelength window matching the line filter used in the system. (d) The absolute value of the normalized pump spectral amplitude, the JSI of the crystals can be calculated by multiplying the phase matching function with the pump spectral amplitude. The wider phase matching function allows the DMCS crystal to maintain a stable sum over the JSI when the temperature changes and the phase matching function shifts along the diagonal. (e) experimental results - the normalized coincidence count rate of the DMCS (blue) and PP (red) crystals. The DMCS crystal displays a 2°C robustness width which is almost a seven-fold improvement compared to 0.296°C of the PP crystal.
• Figure A.1: The sensitivity of $\Delta k$: we show in (a), (b), (c) how $\Delta k$ varies as each parameter changes while keeping the others at their optimal values, in (d) how the rate of generated entangles pairs change with $\Delta k$, and in (e) how $\Delta k$ varies as $T$ and $\theta_s$ change while keeping $\lambda_s=1064$nm.