Study and characterisation of polarisation entanglement JABIR M V Photonic sciences laboratory, PRL

Plan of talk What is entanglement ? Why we need entangled system ? Question on completeness of QM Bell-CHSH inequality for discrete variables Source of entanglement Measuring entangled state Experimental setup and results

What is entanglement ? Suppose we have a composite system which composes of two subsystems and, if we can write then it is a product state. then we call it is an entangled state. Pairs or groups of particles in 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.

Why we need entangled system ? Quantum teleportation Quantum cryptography Quantum computation

Question on completeness of QM EPR questioned element of reality and locality of Quantum theory Assertion 1 Quantum mechanics is complete if incompatible quantities can not have simultaneous reality 2 Quantum mechanics is incomplete if incompatible quantities can have simultaneous reality Measurement by Alice does not change Bob’s system- locality Bob’s spin component is predetermined - realism

Measurement of position on electron and momentum on positron give simultaneous reality Assertion one is failed- Quantum description of physical reality is incomplete Introduce local hidden variable to explain this contrary non-seperable system

Bell-CHSH inequality for discrete variables Hidden variable theory: Hidden variables must exist which determine EPR results being necessary to extend quantum mechanics to a complete local and realistic theory. Bell’s role: One can find bounds between a local and nonlocal prediction of quantum mechanics. Clauser, Horne, Shimony and Holt (CHSH) inequality : Experimental adaptation of Bell’s inequality λ - hidden variable ; p(λ) - probability distribution which determines measurement results.

Bell-CHSH inequality for discrete variables A(a,λ), A(a’,λ) and B(b,λ), B(b’,λ) – two measurement outcomes for particle A and B. a, a’, b and b’ projection angle Possible outcomes are ±1 Principle of locality - A(a,λ), A(a’,λ) independent of B(b,λ), B(b’,λ) and vice versa Thus the correlation value E of the measurement on particle A and B...(1)

Using the constraints of A and B, a parameter S can be defined as Lets calculate possible outcome (2) ±1 0 ±2 0 ±2 1) 2) 3) 4)

Using the constraints of A and B, a parameter S can be defined as.... (2) ±1 0 ±2 0 ±2 Using inequality we can derive the CHSH inequality as

CHSH inequality For local realistic system, and for entangled system Here, Where, is the coincidence counts at angle a and b of corresponding analysers

EPR-Bell states There are mainly four maximally entangled bipartite system called EPR-Bell states.

Sources of entanglement One of the popular source of entanglement is spontaneous parametric down converted photons.

Type-Ι phase matching for positive uniaxial ( ) for negative uniaxial crystal ( )

Type- ΙΙ phase matching for negative uniaxial crystal ( ) for positive uniaxial crystal ( ) A B

Measuring entangled states Characterisation is done by projective measurements. Here we use polarizer for project to desired state single state of photons which we can pass through PA So the coincidence count, For diagonal projection- For linear projection-

For linear projection,

Experimental Setup 1. Blue diode laser 2. Half wave plate 3. Cascaded BIBO crystal 4. Polarising beam splitter 5. Interference 6. Collimator 7. Single photon counting module(SPCM) 8. Time to digital converter 10. Half wave plate

Experimental Setup 1 1. Blue diode laser 2. Half wave plate 3. Cascaded BIBO crystal 4. Polarising beam splitter 5. Interference 6. Collimator 7. Single photon counting module(SPCM) 8. Time to digital converter 10. Half wave plate

Analyser -IAnalyser -II

Result and discussion

CHSH inequality Where, is the coincidence counts at angle a and b of corresponding analysers

Visibility, V=91.5±0.2% Bell’s parameter S = ± The state which we have produced is,