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One entanglement can hide another!

​A theoretical physicist at the IPhT and his partners at the EPFL (Switzerland) and MIT (USA) have just revealed a temporal form of quantum entanglement. For the first time, this has allowed them to demonstrate a very strong entanglement between a photon and a phonon, in a diamond crystal at room temperature. Their experiment makes it possible to probe the coherence of single phonons on very short time scales, which opens the door to the search for materials for ultrafast quantum technologies.

Published on 19 February 2021

Even though the entanglement of two distant quantum states is more and more popularized among the general public, it remains a difficult concept to grasp. In its "simplest" version, two distinct photons are "joined" in the same quantum state, which is manifested as a close correlation between their individual polarization states. While the measurement of the first photon indicates a random polarization, the second is always polarized in the same direction as its "twin"!

Physicists have imagined two "nested" entanglements, which are much more difficult to describe. The first brings together a photon and a quantum of crystalline vibration (i.e. a phonon). The emission of the photon is very strongly correlated with the creation of the phonon, although it is undetectable. The second entanglement brings together two successively created photon–phonon pairs. While the measurement of the photon (which is possible this time) indicates a random creation time, the phonon is always created at the same time!

As a result, the measurements of these temporally entangled states violate the "Bell inequalities". This not only demonstrates the strength of the entanglement between the two moments of creation of the photon–phonon pairs, but also that of the entanglement linking the photon and phonon – a world first.

This experiment also allowed the researchers to measure the coherence time of a single phonon, despite its brevity (on the order of a few picoseconds). The technique they used can be applied to all kinds of crystals (powders, synthetic materials, etc.). And perhaps it can eventually be used to unveil a material suitable for the development of ultrafast quantum technologies ...

Behind the scenes of this experiment ... 

How is the photon–phonon entanglement produced?

A diamond crystal at room temperature is illuminated by two successive ultra-short laser pulses (labeled "write" and "read"), separated by a few picoseconds (10-12 s). Their wavelengths are tuned precisely to the energy levels of the diamond.

In some very rare cases, one of the write photons is converted into a quantum of crystal vibration (phonon) and a photon of lesser energy (Stokes photon). In this case, a few picoseconds later, a read photon is absorbed at the same time as the phonon by the crystal, which emits a photon of higher energy (anti-Stokes photon).

These events occur very rarely (one time in a thousand), in spite of the large number of photons that make up the ultra-short laser pulse. But when they do occur, the creation of a Stokes photon is always accompanied by the creation of a phonon. The number of Stokes photons is thus closely correlated with the number of phonons, which is itself closely correlated with the number of anti-Stokes photons. These correlations are quantum in nature: the Stokes-phonon pair is entangled in the sense that it is both absent and present. This leads to an entanglement of the Stokes–anti-Stokes photon pairs, something that is difficult to demonstrate experimentally.

What does the temporal entanglement of the two photon–phonon pairs consist of?

To overcome this difficulty, the researchers used two successive sets of write-read pulses ("early" and "late") separated by 3 nanoseconds (10-9 s), with each set capable of generating photon–phonon pairs. In this way, they demonstrated that the creation time of the Stokes and anti-Stokes photon pairs is indefinite: the pairs are thus temporally entangled.

It is as though the form of entanglement by presence (there is a photon–phonon pair) or absence (there is no photon–phonon pair) was transformed into temporal entanglement between "there is a Stokes–anti-Stokes early photon pair" and "there is a Stokes–anti-Stokes late photon pair". The measurements show that these two states are simultaneously possible.

Furthermore, it is possible to probe the coherence time of the phonon by varying the time difference between the write and read photons.

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