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Ideal Detection of Entanglement Through Stimulated Disentanglement

Nir Nechushtan, Han‐Zhong Zhang, Yosef London, Mallachi-Elia Meller, Haia Amichai, Eliyahu Cohen, Avi Pe’er

Published Jan 1, 2025• 0 citations
Publisher

Abstract

We demonstrate efficient detection of time-energy entanglement by stimulating the disentangling interaction (sum-frequency generation). We measure both the time-difference and energy-sum correlations simultaneously, lifting the key limitations of standard detection methods.
DOI
10.1364/cleo_fs.2025.ff100_5

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Abstract Standard detection of entanglement relies on local measurements of the individual particles, evaluating their correlations in post-processing. For time-energy entangled photons, either times (t1,t2)(t_1,t_2)(t1​,t2​) or energies (E1,E2)(E_1,E_2)(E1​,E2​) are measured, but not both due to the mutual quantum uncertainty, providing only partial information of the entanglement. In principle, a global detector could recover the complete information of entanglement in a single shot if it could measure the combined correlated variables (t1−t2)(t_1-t_2)(t1​−t2​) and (E1+E2)(E_1+E_2)(E1​+E2​) without measuring the individual energies or times. Such a global measurement is possible using the reverse disentangling interaction, like sum-frequency generation (SFG), but nonlinear interactions at the single-photon level are exceedingly inefficient. We overcome this barrier by stimulating the nonlinear SFG interaction with a strong pump, thereby measuring both the energy-sum (SFG spectrum) and the time-difference (response to group delay/dispersion) simultaneously and efficiently. We generate biphotons with extreme time-energy entanglement (octave-spanning spectrum of 113THz) and measure a relative uncertainty between time-difference and energy-sum of Δ(t1−t2)Δ(E1+E2)≈2∙10−13hΔ(t_1-t_2)Δ(E_1+E_2)≈2∙10^{-13}hΔ(t1​−t2​)Δ(E1​+E2​)≈2∙10−13h, violating the classical bound by more than 12 orders of magnitude. The presented coherent SFG dramatically enhances the detection SNR compared to standard methods since it ideally rejects erroneous coincidences in both time and energy, paving the way for sensing applications, such as quantum illumination (radar) and more.
We analyze the dynamics of sum-frequency generation (SFG) and difference-frequency generation (DFG) for broadband input fields. We demonstrate that amplitude modulation of the input fields significantly affects conversion efficiency of SFG and DFG, but frequency modulation does not affect conversion efficiency. Analytic results for SFG and DFG output-field intensities are thereby available for arbitrary fields. Self- and cross-phase modulation can affect the dynamics in the limit of very high field strengths, but these effects are of higher nonlinearity and therefore usually negligible. The quantum efficiency of DFG is shown to be generally higher than SFG, but the energy efficiency is much lower if the difference frequency is significantly less than the input frequencies. Optimal SFG quantum conversion efficiency for such systems approaches that of second-harmonic generation only if the quantum fluence (total number of photons) in the two input beams are equal. Optimal DFG quantum conversion efficiency occurs when the number of photons of frequency ${\mathrm{\ensuremath{\omega}}}_{2}$ is small yet sufficient for significant stimulation. A recently developed method for obtaining efficient SFG for multimode input fields is theoretically analyzed. The method involves using an arrangement with two or more nonlinear mixing crystals with a time-delay line situated between the crystals that delays one of the fundamental fields relative to the other. The efficiency in the second crystal depends on the cross-correlation function of the two fundamental fields upon leaving the first nonlinear crystal. The time-delay method is not effective for multimode DFG.