Abstract
Photon pair states and multiple-photon squeezed states have many applications in quantum information science. In this paper, Green functions are derived for spontaneous four-wave mixing in the low- and high-gain regimes. Nondegenerate four-wave mixing in a strongly-birefringent medium generates signal and idler photons that are associated with only one pair of temporal (Schmidt) modes, for a wide range of pump powers and arbitrary pump shapes. The Schmidt coefficients (expected photon numbers) depend sensitively on the pump powers, and the Schmidt functions (shapes of the photon wavepackets) depend sensitively on the pump powers and shapes, which can be controlled.
Highlights
Photons are a key resource for quantum information science [1,2,3,4]
Nondegenerate four-wave mixing in a strongly-birefringent medium generates signal and idler photons that are associated with only one pair of temporal (Schmidt) modes, for a wide range of pump powers and arbitrary pump shapes
Pairs of signal and idler photons can be generated by spontaneous three-wave mixing (TWM) in a second-order nonlinear medium [5], which is driven by one pump wave [6], and spontaneous four-wave mixing (FWM) in a third-order nonlinear medium [7], which can be driven by one or two pump wave(s) [8]
Summary
Photons are a key resource for quantum information science [1,2,3,4]. Pairs of signal and idler photons can be generated by spontaneous three-wave mixing (TWM) in a second-order nonlinear medium [5], which is driven by one pump wave [6], and spontaneous four-wave mixing (FWM) in a third-order nonlinear medium [7], which can be driven by one or two pump wave(s) [8]. They enable many aspects of continuous-variable (CV) quantum information [23, 24], including quantum key-distribution [25, 26], quantum teleportation [27, 28] and quantum-enhanced metrology [29, 30], which utilizes phase squeezing [31, 32], number squeezing [33, 34] and number-difference squeezing [35, 36] to reduce measurement errors below the shot-noise limit To work well, these applications require the signal and idler photons to occupy single pairs of temporal modes (wavepackets with specific shapes).
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