In spontaneous parametric down-conversion, a strong pump drives a second-order nonlinear optical susceptibility, producing paired output photons in initially unseeded modes. The two outputs are conventionally called the signal photon and idler photon. They need not have equal frequencies. For a monochromatic pump, conservation of energy gives
Efficient bulk generation also requires phase matching: the nonlinear source and emitted waves must remain in phase. In the ideal plane-wave geometry this is . Different refractive indices and propagation directions determine which pairs satisfy it. A finite interaction length supplies a mismatch bandwidth rather than an infinitely sharp wavevector constraint. [ref]
At weak gain, the SPDC pair state contains a large vacuum component and a small pair amplitude. Detecting one output conditions the other, producing a heralded single-photon source. This is probabilistic: stronger pumping also increases unwanted multiple-pair events. Experiments collect two output modes with optical filters and single-photon detectors, comparing coincident detections with background counts. [ref]
Sources of Nonclassical Light for Quantum Networks by NIST. Spontaneous Parametric Down-Conversion and Figure 2, pair generation and heralding
A signal photon is the photon assigned to a designated signal mode in a photon-pair process such as spontaneous parametric down-conversion. Its partner is called the idler photon. The labels identify modes or experimental roles; they do not universally mean the higher-energy and lower-energy photon.
For a narrowband pump, pair production obeys . Spatial and polarization correlations also depend on the phase matching arrangement. Detecting the idler can herald the presence of the signal, but heralding efficiency depends on collection and loss. At degeneracy, signal and idler can have equal frequencies while remaining distinguishable by propagation direction or another mode label.
An idler photon is the partner of a signal photon in a specified nonlinear optical process. In spontaneous parametric down-conversion, one pump photon supplies the energy of the pair, .
The idler can be measured to herald a signal photon or to condition a correlation measurement. It is not a physically expendable photon: losses in its channel reduce heralding rates and can bias an uncorrected coincidence sample. When the two output modes have the same frequency, the signal/idler distinction comes from their assigned spatial, polarization or experimental roles rather than from energy ordering.
Detection of one member of a pair conditions the other mode towards a one-photon state. Imperfect collection reduces heralding efficiency; unresolved spectral correlations can leave a mixed state, and multiple pairs can contaminate the heralded output. Filtering can improve purity while reducing brightness. Heralding is conditional preparation, not deterministic conversion of every pump pulse.
The weak-gain state generated by an undepleted pump contains a vacuum term and a photon-pair amplitude. A continuum pair amplitude combines the pump spectrum with a phase-matching factor . Its joint spectrum determines spectral correlations and the purity attainable by heralding one partner.
For two collected spatial modes , each with polarizations , put . The one-pair state is a Bell state. The normalized two-pair component isThis follows by expanding and using the bosonic creation operator identity . The three orthogonal normalized Fock states have equal probability . A tensor product of independently labelled pairs is a different multimode description; identifying its labels without renormalization changes its norm.
For an ideal undepleted pump and one collected pair of spatial modes, the two orthogonal polarization-pair creation terms generate two commuting two-mode squeezed vacua. If , either squeezed pair has geometric occupation probability . Adding their pair counts gives equal-weight possibilities, hence . Thus and at weak gain. Different unresolved temporal or spectral modes need not obey this single-mode formula.
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Spontaneous Parametric Down-Conversion (SPDC) is a quantum optics process in which a single photon interacts with a nonlinear crystal to produce two lower-energy photons, commonly referred to as "signal" and "idler" photons. This process is significant in quantum mechanics and quantum optics, as it is one of the primary methods for generating entangled photon pairs, which are essential for various applications in quantum information science, such as quantum cryptography, quantum computing, and quantum teleportation.
You can then detect one of the photons, and when you do you know that the other one is there as well and ready to be used. two photon interference experiment comes to mind, which is the basis of photonic quantum computer, where you need two photons to be produced at the exact same time to produce quantum entanglement.
Features Alan Migdall of the National Institute of Standards and Technology. Produced by the Joint Quantum Institute (JQI).
Mentions that this phenomena is useful to determine the efficiency of a single photon detector, as you have the second photon of the pair as a control.
Also briefly describes how the input energy and momentum must balance out the output energy and momentum of the two photons coming out (determined by the output frequency and angle).
Shows the crystal close up of the crystal branded "Cleveland Crystals Inc.". Mentions that only one in a billion photon gets scattered.
Also shows a photomultiplier tube.
Then shows their actual optical table setup, with two tunnels of adjustable angle to get photons with different properties.
Very short whiteboard video by Peter Mosley from the University of Bath, but it's worth it for newbs. Basically describes spontaneous parametric down-conversion.
One interesting thing he mentions is that you could get single photons by making your sunglasses thicker and thicker to reduce how many photons pass, but one big downside problem is that then you don't know when the photon is going to come through, that becomes essentially random, and then you can't use this technique if you need two photons at the same time, which is often the case, see also: two photon interference experiment.