A schematic diagram of the GaAs/AlGaAs MQW structure. We assume that the MQW structure is grown along the

*z*-axis, with a period of 400 nm, and each quantum well consists of one GaAs layer of thickness 5 nm (sandwiched between two AlGaAs slabs). The exciton energy

*ω*_{0} of a single quantum well is set to be 1.514 eV, such that the resonant photon wavelength

*λ* = 2

*πc*/

*ω*_{0}≈ 820 nm. A pair of identical photons with wavevector

*k*_{0} could be produced by a two-photon down-conversion crystal. One of the photons is directed to the detector-1 (D1) and the other along the growth direction of the MQW. (b) The inequality

[Eq. (13)] as a function of time for the state |

*q*〉 = |

*k*_{0}〉(red dashed curve) and

(black solid curve) in a MQW system containing 200 periods. The region above the blue dashed line indicates the violation regime. In plotting this panel, the coupling constant

*g* = 8.3 meV, between

and |

*k*_{0}〉, is determined from the period of the Rabi-like oscillations in . The photon loss

*κ* = 3.3 meV is obtained from the width of the Lorentzian fitting (the green dashed-dotted curve in the inset of . Here we have set the excitonic polarization decay rate

*γ* as the spontaneous emission rate of the general GaAs/AlGaAs quantum well

*γ* =

*Γ*_{QW} = 100 (1/ns).

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