Abstract
We present in this paper a general model for determining the quantum properties of the light generated by a synchronously pumped optical parametric oscillator (SPOPO) operating below threshold. This model considers time and frequency on an equal footing, which allows us to find new quantum properties, related for example to the carrier envelope offset (CEO) phase, and to consider situations that are close to real experiments. We show that, in addition to multimode squeezing in the so-called ‘supermodes’, the system exhibits quadrature entanglement between frequency combs of opposite CEO phases. We have also determined the quantum properties of the individual pulses and their quantum correlations with the neighboring pulses. Finally, we determine the quantum Cramer–Rao limit for an ultra-short time delay measurement using a given number of pulses generated by the SPOPO.
Highlights
We present in this paper a general model to determine the quantum properties of the light generated by a synchronously pumped Optical Parametric Oscillator (SPOPO) operating below threshold
There has been a rising interest for OPOs pumped by trains of ultrashort pulses, because of their promising properties: firstly, with such pumps, the efficiency of the nonlinear process can be increased further and the oscillation threshold lowered; SPOPO time/frequency quantum analysis secondly the fact that the system generates light which spans over thousands of spaced frequency modes (“frequency combs“) opens the way to the efficient generation of highly multimode non-classical light [10, 11, 12]; in addition such sources can be used for the quantum metrology of ultra-short time delays [13]
We have presented in this paper a novel time-frequency model for determining the quantum properties of OPOs below threshold based on a general inputoutput formalism that we have applied to the SPOPO case
Summary
The validity of which requires that the spectral width of the phase matching function Φ(ω, ω ) is much larger than the repetition rate T0−1, and that the pump pulses are localized around the center of each period and have a temporal width much smaller than T0 These conditions are generally satisfied in practice with SPOPOs ultrashort pulses. These frequency combs are continuous trains of pulses with a CEO half of that of the pump. For θ = 0, SPOPOs generate pairs of entangled frequency combs with opposite frequency shifts, or in the time domain continuous trains of pulses whose CEOs are symmetric with respect to. This corresponds to the two regimes of the degenerate OPO above threshold [18]
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