A graviton is really really really really really really really really really really really really really really really really really really really really really really really really really really really really really really really really really really really really really really really really hard to detect.
Detecting a photon, for example, is extremely easy. There many types of devices that are able to detect single photons, such as photomultipliers, used in labs around the world. In fact, you don't even need any fancy technology; the human eye can, in principle, detect a single photon. (See The Human Eye and Single Photons.)
However, detecting gravitons is much (much much etc...) harder. A famous example (see [gr-qc/0601043] Can Gravitons Be Detected?) considers an ideal detector with the mass of the planet Jupiter, around
kilograms, placed in close orbit around a neutron star, which is a very strong source of gravitons. A back-of-the-envelope calculation reveals that even in this extremely unrealistic scenario, it would take 100 years to detect a single graviton!
Okay, you say, so let's just make that detector (sometime in the far future when we have the technology to do so) and wait for 100 years. There's a crucial detail that I forgot to mention, however. The star also emits neutrinos in addition to gravitons; in fact, many more neutrinos than gravitons. And neutrinos are much easier to detect than gravitons. In fact, we can calculate that for every graviton that is detected in this scenario, around
neutrinos will be detected. So we will never be able to find the one graviton among the
neutrinos.
Ah, you say, but we can build a neutrino shield and block the neutrinos! But such a shield would need to have a thickness of several light years, and if you try to make it more dense in order to fit between the star and the detector, it would collapse into a black hole...
In conclusion, even with insanely advanced futuristic technology, it would simply be impossible to detect a graviton.
What we have been able to detect, though, are gravitational waves. This amazing discovery by the LIGO experiment was announced on February 11 2016. Gravitational waves are made of lots and lots of gravitons, just like electromagnetic waves are made of lots and lots of photons. A typical gravitational wave is composed of roughly 1,000,000,000,000,000 gravitons per cubic centimeter, therefore it is obviously much easier to detect than a single graviton.
On the other hand, we definitely do not have the technology to detect individual gravitons, and unless some new ingenious way to detect them is found, we will never be able to do so even with much more advanced technology.
What are the consequences of this technological impossibility to detect gravitons? As it turns out, it doesn't really matter! Let me explain.
First, where exactly do gravitons appear in physics? Theoretical physicists are trying to combine general relativity and quantum mechanics into a single theory, called quantum gravity. We do not have a final theory of quantum gravity yet, but we are working very hard on it, and we already understand many aspects of what such a theory should be.
In a theory of quantum gravity, gravitons are the quanta of the gravitational field. Therefore, quantum gravity will use gravitons as part of its formulation, just like the theory of quantum electrodynamics uses photons, which are the quanta of the electromagnetic field.
However, we did not confirm quantum electrodynamics experimentally by detecting photons. Quantum electrodynamics produces predictions that are different from those of classical electrodynamics, and by experimentally testing these predictions we have been able to confirm that the electromagnetic field is indeed quantized.
In a similar way, when we finally have a good candidate for a theory of quantum gravity, it will produce predictions that are different from those of classical gravity. By experimentally testing these predictions, we will be able to confirm that the gravitational field is quantized.
In other words, what we need to do is not detect gravitons; we need to test the predictions of a theory of quantum gravity, as soon as we have such a theory. This will indirectly confirm the existence of gravitons.
