Quantum Entanglement DIY

Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently — instead, a quantum state may be given for the system as a whole.

Measurements of physical properties such as position, momentum, spin, polarization, etc., performed on entangled particles are found to be appropriately correlated. For example, if a pair of particles is generated in such a way that their total spin is known to be zero, and one particle is found to have clockwise spin on a certain axis, then the spin of the other particle, measured on the same axis, will be found to be counterclockwise; because of the nature of quantum measurement. However, this behavior gives rise to paradoxical effects: any measurement of a property of a particle can be seen as acting on that particle (e.g., by collapsing a number of superposed states); and in the case of entangled particles, such action must be on the entangled system as a whole. It thus appears that one particle of an entangled pair “knows” what measurement has been performed on the other, and with what outcome, even though there is no known means for such information to be communicated between the particles, which at the time of measurement may be separated by arbitrarily large distances.

An entangled system is defined to be one whose quantum state cannot be factored as a product of states of its local constituents (e.g., individual particles). If entangled, one constituent cannot be fully described without considering the other(s). Note that the state of a composite system is always expressible as a sum, or superposition, of products of states of local constituents; it is entangled if this sum necessarily has more than one term.

Quantum systems can become entangled through various types of interactions. Entanglement is broken when the entangled particles decohere through interaction with the environment; for example, when a measurement is made.

As an example of entanglement: a subatomic particle decays into an entangled pair of other particles. The decay events obey the various conservation laws, and as a result, the measurement outcomes of one daughter particle must be highly correlated with the measurement outcomes of the other daughter particle (so that the total momenta, angular momenta, energy, and so forth remains roughly the same before and after this process). For instance, a spin-zero particle could decay into a pair of spin-½ particles. Since the total spin before and after this decay must be zero (conservation of angular momentum), whenever the first particle is measured to be spin up on some axis, the other (when measured on the same axis) is always found to be spin down. (This is called the spin anti-correlated case; and if the prior probabilities for measuring each spin are equal, the pair is said to be in the singlet state.)

Experiment Description

The experiment described in this post is the repetition of the famous experiment of Wu – Shaknov in which it will demonstrate the angular correlation of gamma photons emitted from the annihilation of the positron and subsequently scattered by a compton scatterer.

We have already described in the post on the annihilation of the positron that the two gamma photons of 511 keV, for the conservation of momentum, are emitted on the same line but in opposite directions. From theoretical considerations also it is known that they have spin phased out by π/2 . The two photons that result from the annihilation of the positron have all what is need in order to form a single quantum system, from which it follows that the two gamma photons are entangled one to another.

The following diagram represents the experiment setup. The Na22 source of gamma photons is placed in between two lead ingots, with a hole in the center to give rise to two collimated beams of gamma rays. The collimated beams hit two iron cylinders that act as compton scatterer. The SiPM detectors with LYSO scintillator crystal are placed laterally so as to capture the radiation scattered at around 90° angle. One detector is maintained in a fixed position, while the other is positioned parallel to the first and subsequently placed orthogonal. The two detectors are operated in coincidence mode to detect only the photon pairs generated by the same annihilation.

The two gamma photons produced from annihilation have spin phased out by π/2 and their state of entangled photons should ensure that this angular correlation manifests itself with different counting rates in relation to the relative position of the two detectors. In particular, you should have the greater count rate when the two detectors are positioned orthogonal and minimum when they are parallel, the ratio between the two counting rates should have a value equal to 2.

 

 

The same experiment has been carried out using a PSoC (programmable system on chip) instead of the bunch of components shown in the image above. The link to this newest post is the following : PSoC Coincidence Detector – II

Measurements Results

Geometrical data

Lead Bricks : 150x150x50 mm
Hole : diameter 10 mm
Iron scatterer : cylinder diameter 12 mm x 30 mm long
Scintillation Crystal : LYSO 4x4x20 mm
Position of the crystal : touching the scatterer
Distance of the crystal : around 10 mm down the scatterer front face
Distance of the scatterer face between the source : 50 mm

False Coincidence likelyhood

If we assume that the coincidence circuit has a time resolution of τ, then the probability of accidental coincidence is:
P = 2τC1C2 = 2 x 2,5 x 10-7 x C1 x C2
Τ = 250 nsec
C1 = counting rate on crystal 1
C2 = counting rate on crystal 2

Without scatterer and tuning the threshold of discriminator around 100keV the following counting rates are obtained :

C1 = 96 CPS
C2 = 97 CPS
P = 2 x 2,5 x 10^-7 x 96 x 97 = 4,66 x 10^-3 s^-1 or 0,280 CPM

Background Measurements Data

Time = 12 h = 720 min
N pulses = 221
σ = √N = 14,9
σ² = N = 221
From these data we can calculate the following value of background rate :
0,31 ± 0,02 CPM

Parallel detector Measurements Data

Time = 20 h = 1200 min
N pulses = 878
σ = √N = 29,63
σ² = N = 878
From these data we can calculate the following value of the rate :
0,732 ± 0,025 CPM (background not subtracted)
Subtracting the background
σ = 0,068
0,422 ±  0,068 CPM (background subtracted)

Orthogonal detector Measurements Data

Time = 24 h = 1440 min
N pulses = 1435
σ = √N = 37,88
σ² = N = 1435
From these data we can calculate the following value of the rate :
0,997 ±  0,026 CPM (background not subtracted)
Subtracting the background
σ = 0,068
0,687 ± 0,068 CPM (background subtracted)

Detector_ǁ = 0,422 ± 0,068 CPM
Detector_Ⱶ = 0,687 ± 0,068 CPM

Detector _Ⱶ / Detector _ǁ = 0,687 / 0,422 = 1,63

These values are compatible with the theoretical predictions (and the experimental verification made, for example, in the experiment of Wu-Shaknov) establishing a greater counting rate in the case where the detectors are orthogonal. This is considered a confirmation that the emitted gamma photons are polarized at planes shifted by 90° phase.
This result is compatible with the hypothesis that the two gamma photons are entangled.

Improvements

The electronic part has been greatly improved with SiPM preamplifier and with a PSOC chip which does the “coincidence job”. The image below shows the new setup. This posts explain this new setup : PSoC Coincidence Detector – I , PSoC Coincidence Detector – II .

Acknowledgements and References

We thank AdvanSiD, especially Claudio and Alessandro , for providing the SiPM modules used in the experiments.
We thank Professor  Clifford John Bland for suggestions, support, and computer simulations.
Article in “Scientific American” with description of a similar experiment : How to build your own quantum entanglement experiment.

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