Broadband pseudothermal states with tunable spectral coherence generated via nonlinear optics

Abstract

It is well known that the reduced state of a two-mode squeezed vacuum state is a thermal statei.e. a state whose photon-number statistics obey a geometric distribution. More exotic broadband states can be realized as the reduced state of two spectrally-entangled beams generated using nonlinear optics. We show that these broadband "pseudothermal" states are tensor products of states in spectral Schmidt modes, whose photon-number statistics obey a geometric distribution. We study the spectral and temporal coherence properties of these states and show that their spectral coherence can be tuned-from perfect coherence to complete incoherence-by adjusting the pump spectral width. In the limit of a cw pump, these states are tensor products of true thermal states, but with different temperatures at each frequency. This could be an interesting state of light for investigating the interplay between spectral, temporal, and photon-number coherences.

Non-Hermitian engineering for brighter broadband pseudothermal light

“…This work could be extended in a number of ways. One could consider the effect of optical loss on pseudothermal states with interesting coherence properties, such as those generated by pulsed pump lasers [47]. Furthermore, it would be interesting to consider frequency-dependent loss in the context of spectral shaping.…”

“…In the absence of optical loss, the state generated by the operator P will be a spectrally entangled twin-beam state, i.e., a manifold of twomode squeezed vacua (see Appendix B). Despite a cw pump, the spectrum of each individual beam will be broad, as opposed to cw, with a bandwidth that gets more narrow as the length of the nonlinear region increases [47]. The reduced state of each beam will thus be a broadband pseudothermal state.…”

“…Concretely, if the input state is a vacuum state, the generated light is necessarily described by a two-mode squeezed vacuum state, and thus the reduced state of each mode is a pseudothermal state-i.e. a state with an arbitrary spectrum (not necessarily blackbody), but with thermal photon-number statistics at each frequency [47].…”

“…Nonlinear processes such as spontaneous parametric down conversion (SPDC) or spontaneous four wave mixing (SFWM) can generate spectrally entangled twin beams. The reduced state of each beam, obtained by tracing out the other component, can be thought of as a broadband "pseudothermal" state [47] whose spectral coherence can be tuned-from perfect coherence to complete incoherence-by adjusting the pump spectral width.…”

“…where r(ω) is the dispersive nonlinear coupling coefficient and it is a function of optical properties of the material [47] (in the low-gain regime, r(ω) is the phase-matching function parameterized in terms of ω). The reduced state of, say, beam a is then given by:…”