New Measures Quantify Broadband Quantum Entanglement

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Quantum entanglement, a phenomenon once confined to science fiction, is now observable across macroscopic and microscopic scales, with applications ranging from quantum teleportation to stealth jet detection. However, current entanglement criteria and measures, which rely on mode-based inseparability, prove insufficient for broadband emission sources such as spasers—plasmonic nanolasers that radiate over very broad bandwidths. This limitation hinders the full harvesting of entanglement potential in technologies like ultrafast nano-control and nano-imaging, especially when using near-field detectors. To address this, researchers introduce new criteria and measures for entanglement in wavepackets, focusing on total entanglement between two wavepackets, entanglement between a wavepacket and an ensemble, and the nonclassicality of a single wavepacket.

The key finding is that these newly developed criteria enable the quantification of total entanglement across all modes in wavepackets, overcoming the insufficiencies of traditional mode-based approaches that only detect entanglement between carrier frequencies. This advancement ensures compatibility with near-field detectors and captures the full nonclassical correlations in broadband systems.

The methodology involves extending entanglement notions to wavepackets by replacing single-mode operators with summations over spatial modes. For wavepacket-wavepacket entanglement, the researchers define annihilation operators that integrate over spatial positions, allowing for convergent criteria such as analogues of the Simon-Peres-Horodecki and Hillery-Zubairy tests. Similarly, for ensemble-wavepacket entanglement, collective operators are adapted to wavepacket sums. Nonclassicality in a wavepacket is assessed by examining noise reduction below the standard quantum limit or by generating entanglement at a beam-splitter output, accounting for contributions from squeezed or entangled constituent modes.

Results analysis reveals that for wavepackets emitted from initially entangled cavities or atoms, the Hillery-Zubairy criterion shows entanglement increasing as wavepackets leave the sources and approaching a constant value thereafter. In spontaneous emission from a single atom, entanglement with the emitted wavepacket evolves similarly, while superradiant emission from an atomic ensemble exhibits enhanced correlations due to collective decay. Nonclassicality is demonstrated when constituent modes are squeezed or entangled, leading to reduced noise in the wavepacket, as confirmed through beam-splitter tests that reveal entanglement generation.

In context, the findings matter because they address the motivations outlined in the paper: the need for entanglement measures in broadband emitters like spasers, which are crucial for developing fast-response nano-technologies and improving efficiency in quantum devices such as heat engines. The criteria ensure that maximum entanglement can be harnessed, particularly in near-field detection scenarios where traditional methods fail, thereby supporting advancements in quantum plasmonics and miniaturized laser applications.

Limitations of the study include the unresolved issue that entanglement negativity, unlike logarithmic negativity, is not established as a quantifiable measure, and the criteria may not fully capture all non-Gaussian states without beam-splitter augmentation. Additionally, the approach faces challenges in continuous mode distributions, where infinitesimal contributions require careful handling to avoid ambiguities in noise calculations.

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