Entangled Photons Essay

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Chapter 1 Production of entangled photons Roll Number : MP12014 Name : S.Srikanth 1.1 Introduction Quantum entanglement occurs when a group of particles interact in a way, such that their quantum state cannot be described independently. As a consequence, all measurables such as position, momentum, polarization etc, are correlated. This is remarkable and sometimes seems paradoxical. The debate on this phenomena dates back to the days of Einstein, recalling the seminal work "The EPR paradox" [1]. This phenomena can be attributed solely to the nature of quantum measurement which deviates radically from classical measurements. Many experiments since have con rmed the validity of such a phenomena. We will not delve deep into these debates. Photon Entanglement Consider a system of two photons, label them signal and idler (historical reasons!). The photons can be distinguished as they are heading in dif- ferent directions. We assume that the photons have the polarization state described by the following wave function [2]: j Belli = 1 p2 (jV isjV ii + jHisjHii) (1.1) 12 CHAPTER 1. PRODUCTION OF ENTANGLED PHOTONS where jV i and jHi refer to horizontal or vertical polarizations and subscripts indicate signal or idler. The notation in the above equation means that the states are entangled and hence, cannot be factored into simple product of signal and idler states. If the polarizations of the photons are measured in the H,V basis there are two possible outcomes: both vertical or both horizontal. Now one can choose to measure in the rotated basis jV i = cos jV i sin jHi (1.2) jH i = sin jV i + cos jHi (1.3) The polarizers are rotated at an angle and measurements are made. It can be seen plainly that, on measurement both the photons are in... ... middle of paper ... ...2 sin2lcos)+C (1.11) where A is number of entangled pairs and C is an o set.O set is necessary as some coincidences are observed even when = 00; = 900. Hence, we now have a way to count the number of entangled pairs. We need to calibrate the above equation and a rough idea of purity of the entangled states can be found by nding N(00; 00):N(900,900) etc. 1.5 Summary and Discussion Non-locality is a major theme pondered over in fundamental physics. As pointed out by Einstein quantum mechanics seems to give rise to "spooky actions at distance". A method to produce entangled photons using a laser source and a non-linear crystal has been explained. The6 CHAPTER 1. PRODUCTION OF ENTANGLED PHOTONSBibliography [1] Arvind and Arvind, Quantum tomography Physical Review A73, 211- 215 (2014). [2] Neilson and Chuang, Quantum Computation and Quantum Informa- tion ........ 7
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