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arXiv:quant-ph/9911014 · Physical Review A

First-order interference of nonclassical light emitted spontaneously at different times

Yoon-Ho Kim, Maria V. Chekhova, S. P. Kulik, Yanhua H. Shih, Morton H. Rubin

Published Apr 14, 2000• 19 citations
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Abstract

We study the first-order interference in spontaneous parametric down-conversion generated by two pump pulses that are well distinguishable in time. The observed modulation in the angular distribution of the signal photon can only be explained in terms of a quantum-mechanical description based on biphoton states. The condition for observing interference in the signal channel is shown to depend on the parameters of the idler photon.

DOI
10.1103/physreva.61.051803

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We study the first-order interference in spontaneous parametric down-conversion generated by two pump pulses that are well distinguishable in time. The observed modulation in the angular distribution of the signal photon can only be explained in terms of a quantum-mechanical description based on biphoton states. The condition for observing interference in the signal channel is shown to depend on the parameters of the idler photon.
We have experimentally demonstrated two-photon interference between biphoton amplitudes arising from two well-separated pump pulses. It is important to note the following. 1) The pump pulse intensity was low enough so that single counting rates of the detectors were kept much smaller than pulse repetition rates: the probability of having one spontaneous parametric down conversion (SPDC) photon pair per pulse in our experiment is negligible. Hence the interference cannot be explained as two SPDC photons from two pump pulses (one SPDC photon pair from each pulse) interfering at the detectors. The two pump pulses simply provide two biphoton amplitudes which could result in coincidence counts, and interference occurs between these two biphoton amplitudes only when they are indistinguishable. 2) The BBO crystal in our experiment was only 100 /spl mu/m thick, so the two-pulse did not exist in BBO at the same time at any moment. 3) Due to the delays in the interferometer (/spl tau/ /spl tau//sub 1/), the signal-idler never met at the beamsplitter. Therefore, the existence of two-photon interference cannot be viewed as the interference between the signal and idler photons. These three points again emphasize the fact that it is the indistinguishability of the two-photon Feynman alternatives for the biphoton amplitudes which is responsible for the two-photon quantum interference effects.
A ${\ensuremath{\chi}}^{(2)}$ nonlinear optical crystal is pumped by two temporally well-distinguishable femtosecond laser pulses to generate entangled photon pairs in the process of spontaneous parametric down-conversion. We have observed first- and second-order interference between amplitudes generated from the first and the second pump pulse as a function of the time delay between the two pump pulses. The criteria for first- and second-order interference are found to be very different, which reflect the quantum entanglement nature of the state of spontaneous parametric down-conversion.
Although induced coherence is generally associated with induced or stimulated emission, in the process of spontaneous parametric downconversion of light induced coherence can be generated on its own. This is demonstrated in an experiment in which the signal beams from two coherently pumped downconverters come together and interfere whenever the idler beam from the first downconverter (DC1) passes through and is aligned with the second downconverter (DC2). Misaligning the idlers, or blocking the first idler, makes the interference disappear. More generally, the degree of coherence can be controlled by varying the amplitude of the idler from DC1 that reaches DC2. The interpretation of this nonclassical interference is discussed in terms of the interpretation of the wave function or state vector of the emitted photon.
Interference has been observed in the mixing of signal photons produced by spontaneous down-conversion in two nonlinear crystals, when the optical path difference through the interferometer greatly exceeds the coherence length of the light. The interference shows up as a periodic modulation of the spectrum. We demonstrate that the interference is nonclassical and connected with the entangled state of the signal and idler photons, by transferring the long optical delay from the path of the signal photons to the path of the idler photons. Even though the idlers are not interfering directly, the effect is found to be unchanged, but the interference is lost when the idler photons are blocked. We discuss the extent to which one photon carries the modulated spectrum.
Summary form only given. Pairs of entangled photons display a complex quantum state that cannot be represented through a product of single-particle states. The spontaneous parametric down-conversion (SPDC) process, that takes place when a laser pulse pumps a second-order nonlinear crystal has become recently a convenient source of such nonclassical states of light in quantum optics experiments. Nonstationary effects are mainly observed when the pump pulse temporal duration is significantly shorter than the characteristic interaction time in the nonlinear crystal. We introduce a nonstationary theory of SPDC to describe the results of fourth-order quantum-interference experiments when no spectral filtering is applied to the down-converted fields. Experiments involving nonlinear SPDC crystals with three different lengths were performed. The ultraviolet laser pulses were obtained from a Ti:sapphire femtosecond laser with a second-harmonic generator. These pulses were used to pump nonlinear crystals to initiate the process of nonstationary spdc and generate orthogonally-polarized photon pairs. These pairs then went into a polarization interferometer, and the coincidence counts of the detectors at the two output ports of the interferometer were recorded.