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arXiv:1912.11505 · npj Quantum Information

Joint measurement of time–frequency entanglement via sum frequency generation

Han Liu, Amr Saher Helmy

Published Aug 3, 2020• 10 citations
arXivHTMLPDF

Abstract

Abstract We propose, analyze, and evaluate a technique for the joint measurement of time–frequency entanglement between two photons. In particular, we show that the frequency sum and time difference of two photons could be simultaneously measured through the sum-frequency generation process, without measuring the time or frequency of each individual photon. We demonstrate the usefulness of this technique by using it to design a time–frequency entanglement based continuous variable superdense coding and a quantum illumination protocol. Performance analysis of these two protocols suggests that the joint measurement of strong time–frequency entanglement of non-classical photon pairs can significantly enhance the performance of joint-measurement based quantum communication and metrology protocols.

DOI
10.1038/s41534-020-00293-y

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Abstract We propose, analyze, and evaluate a technique for the joint measurement of time–frequency entanglement between two photons. In particular, we show that the frequency sum and time difference of two photons could be simultaneously measured through the sum-frequency generation process, without measuring the time or frequency of each individual photon. We demonstrate the usefulness of this technique by using it to design a time–frequency entanglement based continuous variable superdense coding and a quantum illumination protocol. Performance analysis of these two protocols suggests that the joint measurement of strong time–frequency entanglement of non-classical photon pairs can significantly enhance the performance of joint-measurement based quantum communication and metrology protocols.
We propose, analyze, and evaluate a technique for the joint measurement of time-frequency entanglement between two photons. In particular, we show that the frequency sum and time difference of two photons could be simultaneously measured through the sum-frequency generation process, without measuring the time or frequency of each individual photon. We demonstrate the usefulness of this technique by using it to design a time-frequency entanglement based continuous variable superdense coding and a quantum illumination protocol. Performance analysis of these two protocols suggests that the joint measurement of strong time-frequency entanglement of non-classical photon pairs can significantly enhance the performance of joint-measurement based quantum communication and metrology protocols.
We propose, analyze and evaluate a technique for the joint measurement of time-frequency entanglement between two photons. In particular, we show that the frequency sum and time difference of two photons could be simultaneously measured through the sum-frequency generation process, without measuring the time or frequency of each individual photon. We demonstrate the usefulness of this technique by using it to design a time-frequency entanglement based continuous variable superdense coding and a quantum illumination protocol. Performance analysis of these two protocols suggests that the joint measurement of strong time-frequency entanglement of non-classical photon pairs can significantly enhance the performance of joint-measurement based quantum communication and metrology protocols.
We present an experimental scheme that realizes joint measurement of photon-number sum and phase-difference operators on a two-mode field. The proposed scheme only involves linear optical elements and photon detectors with single-photon sensitivity. Furthermore, we demonstrate that such a measurement setup can be applied to generate two-mode N-photon entangled states from a pair of squeezed vacuum states. These N-photon entangled states are useful resources for quantum-information processing, high-precision frequency measurement, and quantum optical lithography.
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.
Single photons provide a natural platform for quantum communication and quantum networking, as they can be entangled in many degrees of freedom and maintain coherence over long-distance links. However, while their minimal interactions with the environment isolate them from detrimental noise, it can make them difficult to measure and manipulate. In particular, manipulation on the ultrafast timescale is necessary to fully exploit the energy-time (or spectral) photonic degree of freedom. Full control over the spectral properties of single photons is key to many quantum technologies and opens the door to natural high-dimensional quantum encodings. \n \nIn this thesis, we theoretically and experimentally examine the use of nonlinear optical processes mediated by strong laser pulses as a method to control the spectral properties of ultrafast single photons. By mixing single-photon pulses with strong escort pulses that have been shaped through dispersion in a nonlinear crystal, the shape of the escort is imprinted on the photon, resulting in a custom-tailored upconverted pulse. We theoretically examine this process for quadratic spectral phases and show that it has the potential to be simultaneously effective and efficient for the customization of single-photon spectral waveforms, and can be performed in an entanglement-conserving manner. \n \nWe then experimentally demonstrate the range of this technique through three applications. First, we show that sum-frequency generation with shaped pulses can be used to coherently measure time-bin encoded photons with bin separations on the order of picoseconds, well below the timing resolution of our detectors. Secondly, we show that this technique can be adapted to convert a train of pulses to a frequency comb, which can be read out in a straightforward manner using diffraction-based spectrometry. We also show here that this process can be performed in a polarization-maintaining fashion, and demonstrate that entanglement with a partner photon is conserved with high fidelity. Finally, we show that this process can be viewed as a time lens, which modulates a temporal waveform in an analogous fashion to a lens focusing a beam of light. We apply the time lens to a photon from an energy-time entangled pair, and show negative magnification of the joint spectrum through a reversal of the spectral correlations. Such processes could find application in quantum state engineering and high-speed single-photon measurement.