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arXiv:2403.04432

Wavepacket interference of two photons through a beam splitter: from temporal entanglement to wavepacket shaping

Zhaohua Tian, Qi Liu, Yu Peng Tian, Ying Gu

Published Mar 7, 2024• 0 citations
arXivHTMLPDF

Abstract

Quantum interferences based on beam splitting are widely used for entanglement. However, the quantitative measurement of the entanglement in terms of temporal modes and wavepacket shaping facilitated by this entanglement remain unexplored. Here we analytically study the interference of two photons with different temporal shapes through a beam splitter (BS), then propose its application in temporal entanglement and shaping of photons. The temporal entanglement described by Von Neumann entropy is determined by the splitting ratio of BS and temporal indistinguishability of input photons. We found that maximum mode entanglement can be achieved with a 50/50 BS configuration, enabling the generation of a Bell state encoded in temporal modes, independent of the exact form of the input photons. Then, detecting one of the entangled photons at a specific time enables the probabilistic shaping of the other photon. This process can shape the exponentially decaying (ED) wavepacket into the ED sine shapes, which can be further shaped into Gaussian shapes with fidelity exceeding 99\%. The temporal entanglement and shaping of photons based on interference may solve the shape mismatch issues in large-scale optical quantum networks.

DOI
10.48550/arxiv.2403.04432

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Quantum interferences based on beam splitting are widely used for entanglement. However, the quantitative measurement of the entanglement in terms of temporal modes and wavepacket shaping facilitated by this entanglement remain unexplored. Here we analytically study the interference of two photons with different temporal shapes through a beam splitter (BS), then propose its application in temporal entanglement and shaping of photons. The temporal entanglement described by Von Neumann entropy is determined by the splitting ratio of BS and temporal indistinguishability of input photons. We found that maximum mode entanglement can be achieved with a 50/50 BS configuration, enabling the generation of a Bell state encoded in temporal modes, independent of the exact form of the input photons. Then, detecting one of the entangled photons at a specific time enables the probabilistic shaping of the other photon. This process can shape the exponentially decaying (ED) wavepacket into the ED sine shapes, which can be further shaped into Gaussian shapes with fidelity exceeding 99%. The temporal entanglement and shaping of photons based on interference may solve the shape mismatch issues in large-scale optical quantum networks.
Quantum interferences based on beam splitting are widely used for entanglement. However, the quantitative measurement of the entanglement in terms of temporal modes and wavepacket shaping facilitated by this entanglement remain unexplored. Here we analytically study the interference of two photons with different temporal shapes through a beam splitter (BS) and then propose its application in temporal entanglement and shaping of photons. The temporal entanglement described by Von Neumann entropy is determined by the splitting ratio of BS and temporal indistinguishability of input photons. We found that maximum mode entanglement can be achieved with a 50/50 BS configuration, enabling the generation of a Bell state encoded in temporal modes, independent of the exact form of the input photons. Then, detecting one of the entangled photons at a specific time enables the probabilistic shaping of the other photon. This process can shape the exponentially decaying (ED) wavepacket into the ED sine shapes, which can be further shaped into Gaussian shapes with a fidelity exceeding 99%. The temporal entanglement and shaping of photons based on interference may solve the shape mismatch issues in large-scale optical quantum networks.
In this work, we present a comprehensive analytical study of a lossless quantum beam splitter (BS) with transmission coefficient T and reflection coefficient R. Using the unitary operator representation and binomial expansion, we derive the exact probability distribution P_k for detecting k photons in one output port when the input ports are prepared in Fock states |N>_0 |M>_1. The balanced configuration R = T = 1/2 and N = M is examined in detail: we prove that destructive quantum interference suppresses all odd photon numbers at the outputs, leaving only even photon counts. The special case N = M = 1 reproduces the famous Hong-Ou-Mandel (HOM) dip with P_1 = 0. Beyond photon statistics, we demonstrate that the beam splitter functions as a deterministic, tunable source of photon-number entanglement. By tracing over one output mode, we construct the reduced density matrix rho_2 and compute the von Neumann entropy S = - sum_k P_k log2 P_k, a direct measure of entanglement between the two output ports. For the balanced case with N = M = 1, we obtain S = 1 ebit, i.e., maximal Bell-state entanglement. For larger equal photon numbers, the entropy increases monotonically. Our results transform the passive beam splitter into a deterministic source of photon-number entanglement, with direct applications in optical quantum computing, interferometry, and quantum information processing. Numerical three-dimensional plots of the probability distribution are provided, and all derivations are supported by rigorous algebra and a full appendix.
Abstract By applying phase modulation across different frequencies, metasurfaces possess the ability to manipulate the temporal dimension of photons at the femtosecond scale. However, there remains a fundamental challenge to shape the single wavepacket at the nanosecond scale by using of metasurfaces. Here, it is proposed that the single photon temporal shape can be converted through the multi‐photon wavepacket interference on a single metasurface. By selecting appropriate input single‐photon temporal shapes and metasurfaces beam splitting ratio, controllable photon shape conversion can be achieved with high fidelity. For examples, photons with an exponentially decaying profile can be shaped into a Gaussian profile; by tuning the relative time delays of input photons, Gaussian‐shaped photons can be transformed into exponentially decaying or rising profiles through the same metasurface. The proposed mechanism provides a compact way for solving the temporal shape mismatch issues in quantum networks, facilitating the realization of high‐fidelity on‐chip quantum information processing.
We propose an experimentally feasible scheme to generate various types of entangled states of light fields by using beam splitters and single-photon detectors. Two beams of light fields are incident on two beam splitters respectively with each beam being asymmetrically split into two parts in which one part is supposed to be so weak that it contains at most one photon. We let the two weak output modes interfere at a third beam splitter. A conditional joint measurement on both weak output modes may result in an entanglement between the other two output modes. The conditions for the maximal entanglement are discussed based on the concurrence. Several specific examples are also examined.
Abstract The interference of two independent single-photon pulses impinging on a beam splitter is analysed in a generalised time-resolved manner. Different aspects of the phenomenon are elaborated using different representations of the single-photon wave packets, like the decomposition into single-frequency field modes or spatio-temporal modes matching the photonic wave packets. Both representations lead to equivalent results, and a photon-by-photon analysis reveals that the quantum-mechanical two-photon interference can be interpreted as a classical one-photon interference once a first photon is detected. A novel time-dependent quantum-beat effect is predicted if the interfering photons have different frequencies. The calculation also reveals that full two-photon fringe visibility can be achieved under almost any circumstances by applying a temporal filter to the signal. PACS 42.50.Dv, 42.50.Ct 1