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Quantum Electronics and Laser Science Conference

Three-phase biphoton interference

Dmitry Strekalov, Давид Николаевич Клышко, S. P. Kulik, Yanhua H. Shih

Published May 18, 1997• 0 citations
Publisher

Abstract

Parametric downconversion is a nonlinear optical process in which three fields are involved: pump, signal, and idler. The signal and idler separately may have fairly large uncertainty of frequencies and momenta, but if one frequency or momentum is measured, the other one is known with certainty because of the phase matching conditions whose physical meanings are momentum and energy conservations. In addition, the signal and idler pair was also shown to "remember" the phase of the pump photon.

DOI
10.13016/m2hk1s-t847

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Parametric downconversion is a nonlinear optical process in which three fields are involved: pump, signal, and idler. The signal and idler separately may have fairly large uncertainty of frequencies and momenta, but if one frequency or momentum is measured, the other one is known with certainty because of the phase matching conditions whose physical meanings are momentum and energy conservations. In addition, the signal and idler pair was also shown to "remember" the phase of the pump photon.
When a laser beam interacts with a nonlinear crystal, some of the incident photons fission into two lower frequency signal and idler photons through the process of spontaneous parametric downconversion. It is shown that, as a result of the strong positive correlation between signal and idler photons, the normalized intensity cross-correlation function λ12(τ) should be inversely proportional to the downconverted light intensity and ideally should be given by the inverse of the mean number of photons counted in the resolving time. This unusual relationship, which is a reflection of the quantum mechanical character of the downconverted optical field, has been confirmed in photoelectric counting measurements. The experiment makes use of the light from an argon-ion laser oscillating at 351.1 nm interacting with an 8-cm long crystal of KDP. The downconverted light is extracted at 633.5 and 788.0 nm in two directions that satisfy the phase-matching condition and is allowed to fall on two counting photomultipliers. The output pulses are fed to a time-to-digital converter that yields the cross-correlation function.
Quantum states of light, such as single photons, pairs of entangled photons, and squeezed light are a key resource for photonic quantum technologies. All these states can be obtained via the nonlinear optical effect of spontaneous parametric down-conversion (SPDC). In SPDC, a higher-energy photon of a coherent beam (pump) splits in two lower-energy daughter photons, called signal and idler. The photons of such a pair can be entangled in polarization, time/frequency, and position/momentum. Efficient generation of photon pairs requires a high second-order susceptibilityχ(2)\chi^{(2)}χ(2)of the material where it occurs, and the phase matching between the pump and the down-converted photons.
We study a nonlinear interferometer consisting of two consecutive parametric amplifiers, where all three optical fields (pump, signal and idler) are treated quantum mechanically, allowing for pump depletion and other quantum phenomena. The interaction of all three fields in the final amplifier leads to an interference pattern from which we extract the phase uncertainty. We find that the phase uncertainty oscillates around a saturation level that decreases as the mean number N of input pump photons increases. For optimal interaction strengths, we also find a phase uncertainty below the shot-noise level and obtain a Heisenberg scaling . This is in contrast to the conventional treatment within the parametric approximation, where the Heisenberg scaling is observed as a function of the number of down-converted photons inside the interferometer.