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Frequency and time-resolved photon correlations [1] involve studying the photon statistics of a quantum source while considering both the detection times and the frequencies of emitted photons. In the case of a continuously driven two-level system, it is well-known that including the frequency of photons reveals a rich landscape of correlations beyond the expected antibunching behavior [2]. Furthermore, in the time-dependent case, where a two-level system is excited by finite pulses, the photon statistics oscillate between antibunching and bunching, depending on whether the pulse area is odd or even. However, this model does not account for correlations between photons of different frequencies [3].
In this work, we explore the time-dependent, frequency-filtered photon statistics of a two-level system under pulsed excitation. Our results show that the photon statistics for a given pulse are not fixed but can range from bunching to uncorrelated emission to antibunching, depending on the frequency filters applied. This reveals that, much like the continuous wave (cw) case, time-dependent photon statistics offer a rich variety of features, highlighting the intricate interplay between pulse area, photon frequencies, and correlations in the time-dependent regime.
This approach could therefore contribute to simplify the current pulsed driven schemes for generating entanglement, where subsequential excitation of emitters leads to photon number entanglement [4]. Instead, just by adequately selecting the relevant frequency windows, one could potentially select the number of photons in early and late time bins that lead to the desired entanglement of the state.
[1] E. del Valle, A. Gonzalez-Tudela, F. P. Laussy, C. Tejedor, and M. J. Hartmann. Theory of Frequency-Filtered and Time-Resolved N -Photon Correlations. Physical Review Letters, 109(18):183601, October 2012.
[2] Juan Camilo Lopez Carreno, Elena del Valle, and Fabrice P. Laussy. Photon Correlations from the Mollow Triplet: Photon Correlations from the Mollow Triplet. Laser & Photonics Reviews, 11(5):1700090, September 2017.
[3] Fischer, K., Hanschke, L., Wierzbowski, J. et al. Signatures of two-photon pulses from a quantum two-level system. Nature Phys 13, 649–654 (2017).
[4] Wein, S.C., Loredo, J.C., Maffei, M. et al. Photon-number entanglement generated by sequential excitation of a two-level atom. Nat. Photon. 16, 374–379 (2022).
