Aspect's experiment

Quantum entanglement is a phenomenon first theorized by Erwin Schrödinger in 1935.[3]

Quantum mechanics dictates that once two separate quantum systems (two particles for example) have interacted or if they have a common origin, they cannot be considered as two independent systems. The quantum mechanical formalism postulates that if a first system possesses a ${\displaystyle |\psi \rangle }$ state, and the second a ${\displaystyle |\phi \rangle }$state, then the initial composite system can be represented by the tensor product of both states: ${\displaystyle |\psi \rangle |\phi \rangle }$. Once the interaction takes place and the two systems become entangled, the new composite state of the system, say ${\displaystyle |\Psi \rangle }$, can no longer be written as a tensor product of two separate, individual states. It is a characteristic mark of entanglement that we have a global understanding of the properties of the composite system, and an intrinsic lack of knowledge about the two original separate states. The physical distance between the two systems plays no role in the entangled state (because no position variable is present). The entangled quantum state remains identical—all else being equal—whatever the distances between both systems.

Consequently, any measurement operated on the entangled system is applicable to both elements constituting it: the measure results of both systems are correlated.

The result of the experiment might have shocked Albert Einstein (he died in 1955 long before the experiment was performed) who had a local, realistic outlook on physics. His outlook led him to the conclusion that if the act of measurement influences both systems, then there would exist an influence capable of propagating from one system to the other, at a speed not limited by the speed of light. Quantum mechanical formalism anticipates that the influence of measuring the components of an entangled system has an immediate effect on both components, no matter the distance.

Later in 1935, Albert Einstein, Boris Podolsky, and Nathan Rosen (E.P.R.) imagined a thought experiment which, if one allowed for entangled states to exist, led to a paradox: either some influence travels faster than light (non-causality), or quantum physics is incomplete. None of the two terms of the alternative were admissible at the time, hence the paradox.

This paradox was of great historical importance, but it failed to have an immediate impact. Only Niels Bohr seriously considered the objection it raised, and tried to answer it. But his answer was qualitative, and the paradox remained unsolved. The reality of entanglement remained a matter of opinion, devoid of any direct experimental support. As a matter of fact, the EPR experiment was not practically feasible at the time.

Two major obstacles opposed its undertaking. On one hand, the technical means were insufficient; on the other (and mainly), there seemed to be no effective way of directly measuring the obtained data with quantitative criteria.

The simultaneity of both systems, whatever meaning is attributed to it,[lower-alpha 1] could only be observed by comparing two distant measurements, within the constraints of the speed of light. The simultaneity's influence cannot be causal, nor can it transmit information (which amounts to the same thing). This property is therefore compatible with the theory of relativity, according to which no information can travel faster than the speed of light.

In 1964, Irish physicist John Stewart Bell published an article showcasing quantitative and measurable effects of the EPR experiments. Those are the famous Bell inequalities. These inequalities are quantitative relations which must be verified by measuring correlations between systems which fully obey relativist causality. Any violation of these inequalities would allow for instantaneous remote influence.

These inequalities allowed physicists to remove one of the two obstacles preventing the EPR experiments. But in 1964, the available technical means were still insufficient for the experiment's actual undertaking.

The EPR experiments became conceivable in 1969, when an article demonstrated their technical feasibility.[4]

Following this article, the universities of Harvard and Berkeley set up an experimental protocol and led experiments in 1972. The results were contradictory: Harvard observed concordance with the Bell inequalities (and therefore a contradiction with the predictions of quantum physics), whereas Berkeley's results violated Bell's inequalities (and therefore verified quantum physics).

These experiments notably suffered from an unreliable and unproductive source of entangled particles, which required days of continuous experimentation. But constant controlled experimental conditions are extremely difficult to maintain for such long periods of time, especially for experiments as sensitive as this one. Both results were thus questionable.

In 1976, the same experiment was repeated in Houston using a better and more prolific source of entangled photons which allowed the duration of the experiment to be reduced to 80 minutes. In return, the photons were not optimally polarized, thus preventing the Bell inequalities from appearing clearly. The experiment nevertheless revealed a violation of Bell's inequalities, although it was too weak to constitute a definitive answer.

Additionally, and mainly, these experiments were not sufficiently elaborate to overrule the possibility of correlations (which entail the violation of Bell's inequalities) owing to some classical, slower-than-light influence or signal propagating between the two particles.

In the end, the experimental scheme used in these experiments was far removed from the "ideal" scheme which John Bell used to demonstrate his inequalities: there was therefore no certainty that the Bell inequalities could be applied as they were in such experiments.

Ideal EPR test with a particle source in the middle and detectors P1 and P2 oriented with angles α and β.

The illustration above represents the principle scheme from which John Bell demonstrated his inequalities: a source of entangled photons S simultaneously emits two ${\displaystyle \nu 1}$and ${\displaystyle \nu 2}$ photons whose polarization is prepared so that both photons' state vector is:

${\displaystyle |\psi (\nu 1,\nu 2)\rangle ={1 \over {\sqrt {2}}}\left\{\left|\uparrow ,\uparrow \right\rangle +\left|\rightarrow ,\rightarrow \right\rangle \right\}}$

This formula simply means that the photons are in a superposed state: they are both on a vertical, horizontal or linear polarity with an equal probability.

These two photons are then measured using two polarizers P1 and P2, each with a configurable measuring angle: α and β. the result of each polarizer's measurement can be (+) or (−) according to whether the measured polarization is parallel or perpendicular to the polarizer's angle of measurement.

One noteworthy aspect is that the polarizers imagined for this ideal experiment give a measurable result both in the (−) and (+) situations. Not all real polarizers are able to do this: some detect the (+) situation for example, but are unable to detect anything in the (−) situation (the photon never leaves the polarizer). The first experiments (described above) used the latter sort of polarizer. Alain Aspect's polarizers are much better able to detect both scenarios and therefore much closer to the ideal experiment.

Given the apparatus and the initial state of polarization given to the photons, quantum mechanics is able to predict the probabilities of measuring (+,+), (−,−), (+,−) and (−,+) on the polarizers (P1,P2), oriented on the (α,β) angles. As a reminder:

${\displaystyle P_{++}(\alpha ,\beta )=P_{--}(\alpha ,\beta )={1 \over 2}\cos ^{2}(\alpha -\beta )}$

${\displaystyle P_{+-}(\alpha ,\beta )=P_{-+}(\alpha ,\beta )={1 \over 2}\sin ^{2}(\alpha -\beta )}$

A maximal violation of Bell's inequalities is predicted for |α−β| = 22.5°

Alain Aspect (with the notable collaboration of physicists Philippe Grangier, Gérard Roger and Jean Dalibard) set up several increasingly complex experiments between 1980 and 1982.

Only his most complex experiment, which took place in 1982 and is the closest to the initial specifications, will be described here.

The first experiments testing Bell's inequalities possessed low-intensity photon sources and necessitated a continuous week to complete. One of Alain Aspect's first improvements consisted in using a photon source several orders of magnitude more efficient. This source allowed a detection rate of 100 photons per second, thus shortening the length of the experiment to 100 seconds.

The source used is a calcium radiative cascade, excited with a krypton laser.

One of the main points of this experiment was to make sure that the correlation between the measurements P1 and P2 had not been the result of "classical" effects, especially experimental artefacts.

As an example, when P1 and P2 are prepared with fixed angles α and β, it can be surmised that this state generates parasitic correlations through current or mass loops, or some other effects. As a matter of fact, both polarizers belong to the same setup and could influence one another through the various circuits of the experimental device, and generate correlations upon measurement.

One can then imagine that the fixed orientation of the polarizers impacts, one way or the other, the state the photon couple is emitted with. In such a case, the correlations between the measurement results could be explained by hidden variables within the photons, upon their emission. Alain Aspects had mentioned these observations to John Bell himself.

One way of ruling out these kinds of effects is to determine the (α,β) orientation of the polarizers at the last moment—after the photons have been emitted, and before their detection—and to keep them far enough from each other to prevent any signal from reaching any one of them.

This method assures that the orientation of the polarizers during the emission has no bearing on the result (since the orientation is yet undetermined during emission). It also assures that the polarizers do not influence each other, being too distant from one another.

As a consequence, Aspect's experimental set-up has polarizers P1 and P2 set 6 metres apart from the source, and 12 metres apart from one another. With this setup, only 20 nanoseconds elapse between the emission of the photons and their detection. During this extremely short period of time, the experimenter has to decide on the polarizers' orientation and to then orient them.

Since it is physically impossible to modify a polarizer's orientation within such a time span, two polarizers—one for each side—were used and pre-oriented in different directions. A high-frequency shunting randomly oriented towards one polarizer or the other. The setup corresponded to one polarizer with a randomly tilting polarization angle.

Since it was not possible either to have the emitted photons provoke the tilting, the polarizers shunted periodically every 10 nanoseconds (asynchronously with the photon's emission) thus assuring the referral device would tilt at least once between the emission of the photon and its detection.

Another important characteristic of the 1982 experiment was the use of two-channel polarizers which allowed a measurable result in situations (+) and (−). The polarizers used until Aspect's experiment could detect situation (+), but not situation (−). These single-channel polarizers had two major inconveniences:

• Situation (−) was difficult to discriminate from an experimentation mistake.
• They had to be scrupulously calibrated.

The two-channel polarizers Aspect used in his experiment avoided these two inconveniences and allowed him to use Bell's formulas directly to calculate the inequalities.

Technically, the polarizers he used were polarizing cubes which transmitted one polarity and reflected the other one, emulating a Stern-Gerlach device.

Bell's inequalities establish a theoretical curve of the number of correlations (++ or −−) between the two detectors in relation to the relative angle of the detectors ${\displaystyle (\alpha -\beta )}$. The shape of the curve is characteristic of the violation of Bell's inequalities. The measures' matching the shape of the curve establishes, quantitatively and qualitatively, that Bell's inequalities have been violated.

Aspect's experiments unambiguously confirmed the violation, as predicted the Copenhagen interpretation of quantum physics, thus undermining Einstein's local realistic outlook on quantum mechanics and local hidden variable scenarios. In addition to being confirmed, the violation was confirmed in the exact way predicted by quantum mechanics, with a statistical agreement of up to 242 standard deviation.[7]

Given the technical quality of the experiment, the scrupulous avoidance of experimental artefacts, and the quasi-perfect statistical agreement, this experiment convinced the scientific community at large that quantum physics violated Bell's inequalities and, consequently, that quantum physics was non-local.

After the results, some physicists legitimately tried to look for flaws in Aspect's experiment and to find out how to improve it to resist criticism.

Some theoretical objections can be raised against the setup:

• the quasi-periodical aspect of the shunting oscillations hinders the validity of the experiment because it can induce correlations through quasi-synchronization resulting from two referrals;
• the correlations (+,+), (−,−) etc. were counted in real time, at the moment of detection. Each polarizer's two (+) and (−) channels were therefore linked by physical circuits. Once more, correlations may be induced.

The ideal experiment, which would negate any imaginable possibility of induced correlations should:

• use purely random shunting;
• record the (+) or (−) results on each side of the device, without any physical link between the two sides. The correlations would be calculated after the experiment, by comparing the recorded results of both sides.

The conditions of the experiment also suffered from a detection loophole.[1]