HY390 HY390 hoton ntanglement Laboratory protocol
Goals. Learn how to create and detect pairs of photons entangled in polarization.. Test the lauser Horne Shimony and Holt version of the Bell inequality [3]. Introduction The hidden variable theory was introduced for the first time in 933 by instein odolsky and Rosen in their famous article []. In a thought experiment known as the R paradox they presented a situation which led them to infer that quantum mechanics is not a complete theory. The answer that there is no need of hidden variable for quantum mechanics to be complete came from Bell [] 96. quipment neither exhaustive nor detailed - Two identical b-barium borate BBO crystals Mounted face-to-face with one crystal rotated by 90 0 - SM-AQR-3 silicon AD Based single photon counters. - ounter I I660 B - InGa laser diode mw wavelength 05 nm. - Quartz plate - Half wave plate - polarizer - olaroid near IR linear polarizing films - olored glass long pass filters - Fiber couplers - rails - Homemade circuit for coincidence counting - Optical breadboard ntanglement The polarization entangled states is produced by using the method of Kwiat et al[]. We use two thin types-i down conversion crystals rotated by 90 with each other Fig. The polarization of the input photons is fixed by a polarizer and a half-wave plate to 5 so that half of the light is vertically polarized and the other part is horizontally polarized. The horizontally polarized light is down-converted by the first crystal and the vertically one is done by the second crystal. At the output of the two crystals we produce a set of two thin cones of down converted light. The wave length of the input light pump is 05 nm and the one of the down-converted photons is 80nm.
Laser olarizer Half Wave late Quartz late BBO Figure : Typical experiment for down-conversion production The cones overlap is such that it is impossible to know from which crystal does light come from. This confirms the entangled state of photons and there is no way to separate the state of two photons created at the same time. The first crystal down converts the horizontally polarized photon into vertically polarized ones: H i S The second crystal down-converts the vertically one into horizontally photons: H H i S i and s stand for idler and signal they represent the two entangled photons and p corresponds to the pomp photon source. The entangled state is described by: T l is the polarization of the pump photon. If this polarization makes 5 with respect to H or then the entangled state is given by: i T H H e a represents the phase induced by the second crystal due the birefringence on photons downconverted by the first crystal. The difference of phase can be adjusted by means of birefringent crystal like a quartz plate. If is fixed to 0 then i cos l H H sin l e 3 H H b 3
A polarizer projects the state of light into the direction of the transmission angle of the polarizer. If this direction is vertical or horizontal H then the eigenstate of the polarizer are and H and any polarization state of light is given by: H. 5 If the polarizer is turned by an angle relative to the horizontal then the eigen state are also rotated by the same angle. H H H cos H sin sin H cos 6 Question: Show that the basis change does not affect the shape of equation b. H` H` ` ` 7 The measurement of the idler and signal photons is done by two polarizers set at and The state of each photon is described by: p sin H cos sin H cos 8 Question : - Show that the probability of joint detection in H state is:
H H H p sin sin 9 i s - What is the probability of joint detection in state? Question 3: Show that the probability of a coincidence detection of the idler and the signal in the vertical polarization is given by: T cos for 0 an l i s 0 Hidden variable theory HT: In terms of hidden variable theory a photon with as polarization will register vertical in front of a polarizer set along the vertical axis if and H horizontal if. If the polarizer is set to an angle then the general rule giving the polarization of the photon with polarization is; Question : 3 0 otherwise HT Show that according the hidden variable theory HT the probability of coincidence is: HT HT HT d 0 The corresponding quantum mechanical probability is given by 0. Draw on the same graph both curves corresponding to 0 and. Bell inequality: Bell theory proved that it is impossible to reconcile HT theory with quantum mechanics even if 0 and equations present very close graphs. In our lab we will test the lauser Horne Shimony and Holt a close version of the Bell inequality. For that purpose you will need the following measurements: 5
S HH H H 3 S doesn t seem to have any physical meaning; it happens that it has a critical value that distinguishes realistic local theory HT from quantum mechanics. According to Bell the following inequality should be verified by any realistic hidden variable theory. a b a c b c lauser Horne Shimony and Holt reformulated this inequality in a form that was easier to test experimentally. The new form is given by: S Our experiment will prove that entangled states violate this inequality. xperiment: lease consult the teaching assistant for detailed experimental procedures. The source beam is set for l by means of a polarizer and a half wave plate and is fixed to zero with a quartz plate. The crystals are designed to down convert about 3. The total acquisition time for each data is 5s and for statistical purpose you should take 5 records per data. - Record coincidence and single detection rates I S and as a function of detector angle for angles. Increment the rail angle by from to 8 degrees - You will take data I S and by scanning from 0 to 30 with an increment of 0. a- Take a scan with 0 b- Take a scan with 5 c- Take a scan with 90 d- Take a scan with 35 3- Take a scan with each 505 90 for and.5.5 67.5and. 5 6
7 From these data calculate S and S by using the following formula: S References: - A. instein B. odolsky and. Rosen an quantum-mechanical description of physical reality be considered complete? hys. Rev. 7 777 780 935. - J. S. Bell On the instein odolsky Rosen paradox hysics ~Long Island ity.y.! 95 00 96. This article is reprinted in Ref. 3. 3- J. F. lauser and A. Shimony Bell s theorem-experimental tests and implications Rep. rog. hys. 88 97 978. - 7J. F. lauser M. A. Horne A. Shimony and R. A. Holt roposed experiment to test local hidden-variable theories hys. Rev. Lett. 3 5 880 88 969. 5-. G. Kwiat. Waks A. G. White I. Applebaum and. H. berhard 6- Ultrabright source of polarization-entangled photons hys. Rev. A 60 R773 R776 999. 7-. D. Mermin Is the moon there when nobody looks? Reality and the Quantum theory hys. Today 38 ~ 38 7 985.