Title: Bayesian tomography of high-dimensional on-chip biphoton frequency combs with randomized measurements
Abstract Owing in large part to the advent of integrated biphoton frequency combs, recent years have witnessed increased attention to quantum information processing in the frequency domain for its inherent high dimensionality and entanglement compatible with fiber-optic networks. Quantum state tomography of such states, however, has required complex and precise engineering of active frequency mixing operations, which are difficult to scale. To address these limitations, we propose a solution that employs a pulse shaper and electro-optic phase modulator to perform random operations instead of mixing in a prescribed manner. We successfully verify the entanglement and reconstruct the full density matrix of biphoton frequency combs generated from an on-chip Si3N4microring resonator in up to an 8 × 8-dimensional two-qudit Hilbert space, the highest dimension to date for frequency bins. More generally, our employed Bayesian statistical model can be tailored to a variety of quantum systems with restricted measurement capabilities, forming an opportunistic tomographic framework that utilizes all available data in an optimal way. more »« less
Imany, Poolad; Lingaraju, Navin B.; Alshaykh, Mohammed S.; Leaird, Daniel E.; Weiner, Andrew M.
(, Science Advances)
null
(Ed.)
Control over the duration of a quantum walk is critical to unlocking its full potential for quantum search and the simulation of many-body physics. Here we report quantum walks of biphoton frequency combs where the duration of the walk, or circuit depth, is tunable over a continuous range without any change to the physical footprint of the system—a feature absent from previous photonic implementations. In our platform, entangled photon pairs hop between discrete frequency modes with the coupling between these modes mediated by electro-optic modulation of the waveguide refractive index. Through control of the phase across different modes, we demonstrate a rich variety of behavior: from walks exhibiting enhanced ballistic transport or strong energy confinement, to subspaces featuring scattering centers or local traps. We also explore the role of entanglement dimensionality in the creation of energy bound states, which illustrates the potential for these walks to quantify high-dimensional entanglement.
Chang, Kai-Chi; Cheng, Xiang; Sarihan, Murat Can; Vinod, Abhinav Kumar; Lee, Yoo Seung; Zhong, Tian; Gong, Yan-Xiao; Xie, Zhenda; Shapiro, Jeffrey H.; Wong, Franco N. C.; et al
(, npj Quantum Information)
Abstract Qudit entanglement is an indispensable resource for quantum information processing since increasing dimensionality provides a pathway to higher capacity and increased noise resilience in quantum communications, and cluster-state quantum computations. In continuous-variable time–frequency entanglement, encoding multiple qubits per photon is only limited by the frequency correlation bandwidth and detection timing jitter. Here, we focus on the discrete-variable time–frequency entanglement in a biphoton frequency comb (BFC), generating by filtering the signal and idler outputs with a fiber Fabry–Pérot cavity with 45.32 GHz free-spectral range (FSR) and 1.56 GHz full-width-at-half-maximum (FWHM) from a continuous-wave (cw)-pumped type-II spontaneous parametric downconverter (SPDC). We generate a BFC whose time-binned/frequency-binned Hilbert space dimensionality is at least 324, based on the assumption of a pure state. Such BFC’s dimensionality doubles up to 648, after combining with its post-selected polarization entanglement, indicating a potential 6.28 bits/photon classical-information capacity. The BFC exhibits recurring Hong–Ou–Mandel (HOM) dips over 61 time bins with a maximum visibility of 98.4% without correction for accidental coincidences. In a post-selected measurement, it violates the Clauser–Horne–Shimony–Holt (CHSH) inequality for polarization entanglement by up to 18.5 standard deviations with anS-parameter of up to 2.771. It has Franson interference recurrences in 16 time bins with a maximum visibility of 96.1% without correction for accidental coincidences. From the zeroth- to the third-order Franson interference, we infer an entanglement of formation (Eof) up to 1.89 ± 0.03 ebits—where 2 ebits is the maximal entanglement for a 4 × 4 dimensional biphoton—as a lower bound on the 61 time-bin BFC’s high-dimensional entanglement. To further characterize time-binned/frequency-binned BFCs we obtain Schmidt mode decompositions of BFCs generated using cavities with 45.32, 15.15, and 5.03 GHz FSRs. These decompositions confirm the time–frequency scaling from Fourier-transform duality. Moreover, we present the theory of conjugate Franson interferometry—because it is characterized by the state’s joint-temporal intensity (JTI)—which can further help to distinguish between pure-state BFC and mixed state entangled frequency pairs, although the experimental implementation is challenging and not yet available. In summary, our BFC serves as a platform for high-dimensional quantum information processing and high-dimensional quantum key distribution (QKD).
Cheng, Xiang; Chang, Kai-Chi; Sarihan, Murat Can; Mueller, Andrew; Spiropulu, Maria; Shaw, Matthew D.; Korzh, Boris; Faraon, Andrei; Wong, Franco N. C.; Shapiro, Jeffrey H.; et al
(, Communications Physics)
Abstract High-dimensional quantum entanglement is a cornerstone for advanced technology enabling large-scale noise-tolerant quantum systems, fault-tolerant quantum computing, and distributed quantum networks. The recently developed biphoton frequency comb (BFC) provides a powerful platform for high-dimensional quantum information processing in its spectral and temporal quantum modes. Here we propose and generate a singly-filtered high-dimensional BFC via spontaneous parametric down-conversion by spectrally shaping only the signal photons with a Fabry-Pérot cavity. High-dimensional energy-time entanglement is verified through Franson-interference recurrences and temporal correlation with low-jitter detectors. Frequency- and temporal- entanglement of our singly-filtered BFC is then quantified by Schmidt mode decomposition. Subsequently, we distribute the high-dimensional singly-filtered BFC state over a 10 km fiber link with a post-distribution time-bin dimension lower bounded to be at least 168. Our demonstrations of high-dimensional entanglement and entanglement distribution show the singly-filtered quantum frequency comb’s capability for high-efficiency quantum information processing and high-capacity quantum networks.
Abstract Dual-comb interferometry harnesses the interference of two laser frequency combs to provide unprecedented capability in spectroscopy applications. In the past decade, the state-of-the-art systems have reached a point where the signal-to-noise ratio per unit acquisition time is fundamentally limited by shot noise from vacuum fluctuations. To address the issue, we propose an entanglement-enhanced dual-comb spectroscopy protocol that leverages quantum resources to significantly improve the signal-to-noise ratio performance. To analyze the performance of real systems, we develop a quantum model of dual-comb spectroscopy that takes practical noises into consideration. Based on this model, we propose quantum combs with side-band entanglement around each comb lines to suppress the shot noise in heterodyne detection. Our results show significant quantum advantages in the uW to mW power range, making this technique particularly attractive for biological and chemical sensing applications. Furthermore, the quantum comb can be engineered using nonlinear optics and promises near-term experimentation.
Patrick, Link; Wysocki, Gerard
(, Journal of Physics B: Atomic, Molecular and Optical Physics)
Abstract Faraday rotation spectroscopy and absorption spectroscopy are performed simultaneously in a dual comb spectroscopy arrangement with quantum cascade laser combs operating at ∼8μm. The system uses free-running laser combs that provide ∼70 cm−1spectral coverage and ∼2 MHz spectral resolution. Detection of NO2in an equilibrium mixture with N2O4and N2O is used to demonstrate selective measurements of paramagnetic NO2in the presence of spectrally interfering diamagnetic species.
Lu, Hsuan-Hao, Myilswamy, Karthik V., Bennink, Ryan S., Seshadri, Suparna, Alshaykh, Mohammed S., Liu, Junqiu, Kippenberg, Tobias J., Leaird, Daniel E., Weiner, Andrew M., and Lukens, Joseph M. Bayesian tomography of high-dimensional on-chip biphoton frequency combs with randomized measurements. Nature Communications 13.1 Web. doi:10.1038/s41467-022-31639-z.
Lu, Hsuan-Hao, Myilswamy, Karthik V., Bennink, Ryan S., Seshadri, Suparna, Alshaykh, Mohammed S., Liu, Junqiu, Kippenberg, Tobias J., Leaird, Daniel E., Weiner, Andrew M., & Lukens, Joseph M. Bayesian tomography of high-dimensional on-chip biphoton frequency combs with randomized measurements. Nature Communications, 13 (1). https://doi.org/10.1038/s41467-022-31639-z
Lu, Hsuan-Hao, Myilswamy, Karthik V., Bennink, Ryan S., Seshadri, Suparna, Alshaykh, Mohammed S., Liu, Junqiu, Kippenberg, Tobias J., Leaird, Daniel E., Weiner, Andrew M., and Lukens, Joseph M.
"Bayesian tomography of high-dimensional on-chip biphoton frequency combs with randomized measurements". Nature Communications 13 (1). Country unknown/Code not available: Nature Publishing Group. https://doi.org/10.1038/s41467-022-31639-z.https://par.nsf.gov/biblio/10381693.
@article{osti_10381693,
place = {Country unknown/Code not available},
title = {Bayesian tomography of high-dimensional on-chip biphoton frequency combs with randomized measurements},
url = {https://par.nsf.gov/biblio/10381693},
DOI = {10.1038/s41467-022-31639-z},
abstractNote = {Abstract Owing in large part to the advent of integrated biphoton frequency combs, recent years have witnessed increased attention to quantum information processing in the frequency domain for its inherent high dimensionality and entanglement compatible with fiber-optic networks. Quantum state tomography of such states, however, has required complex and precise engineering of active frequency mixing operations, which are difficult to scale. To address these limitations, we propose a solution that employs a pulse shaper and electro-optic phase modulator to perform random operations instead of mixing in a prescribed manner. We successfully verify the entanglement and reconstruct the full density matrix of biphoton frequency combs generated from an on-chip Si3N4microring resonator in up to an 8 × 8-dimensional two-qudit Hilbert space, the highest dimension to date for frequency bins. More generally, our employed Bayesian statistical model can be tailored to a variety of quantum systems with restricted measurement capabilities, forming an opportunistic tomographic framework that utilizes all available data in an optimal way.},
journal = {Nature Communications},
volume = {13},
number = {1},
publisher = {Nature Publishing Group},
author = {Lu, Hsuan-Hao and Myilswamy, Karthik V. and Bennink, Ryan S. and Seshadri, Suparna and Alshaykh, Mohammed S. and Liu, Junqiu and Kippenberg, Tobias J. and Leaird, Daniel E. and Weiner, Andrew M. and Lukens, Joseph M.},
}
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