Decoherence
In this chapter, we ask what happens when a quantum system is in contact with its environment. To describe this, we need a more general concept of the quantum state, namely the density matrix. We study the density matrix, and how it describes both classic
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Decoherence
In this chapter, we ask what happens when a quantum system is in contact with its environment. To describe this, we need a more general concept of the quantum state, namely the density matrix. We study the density matrix, and how it describes both classical and quantum uncertainty. This also naturally leads to a description of quantum systems at a non-zero temperature. We conclude this chapter with a short discussion on how entropy arises in quantum mechanics.
7.1 Classical and Quantum Uncertainty In Chap. 1 we considered three simple experiments that went right to the heart of quantum mechanics. In the first two experiments we studied how a very weak laser triggered photodetectors, and we found that light comes in indivisible packets. This led us to hypothesise that light consists of particles, called photons. In the third experiment we set up a Mach–Zehnder interferometer that ensured the photon ended up in detector D2 , and never in detector D1 . When we use high-intensity laser light, this behaviour is completely explained by the classical wave theory of light, and is called interference. We then arrived at the uncomfortable conclusion that a single particle (the photon) can exhibit interference. To explore this further, we modified the third experiment to add quantum non-demolition (QND) detectors in the paths of the interferometer. This served to tell us which path the photons took inside the interferometer. Consequently, the interference pattern was destroyed: the photons no Electronic supplementary material The online version of this chapter (https://doi.org/10.1007/978-3-319-92207-2_7) contains supplementary material, which is available to authorized users.
© Springer International Publishing AG, part of Springer Nature 2018 P. Kok, A First Introduction to Quantum Physics, Undergraduate Lecture Notes in Physics, https://doi.org/10.1007/978-3-319-92207-2_7
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7 Decoherence
longer end up only in detector D2 , but randomly trigger D1 or D2 . We concluded that photons are neither particles, nor waves, and make up a new type of physical objects called quanta with characteristics of both. In this section, we will study this experiment a little further to establish what kind of knowledge we can have about quanta. We will arrive at the notion that there are two kinds of uncertainty: classical and quantum uncertainty. To see this, consider the experiment where we measure the path taken by the photon. In this case we lose the interference and find photons hitting both detector D1 and detector D2 . We can imagine that this experiment is some setup on a bench, with lasers, beam splitters, mirrors, and detectors that are merrily clicking away. Suppose that the outcomes of the photodetectors D1 and D2 as well as the which-path QND detectors are recorded in two data files on a computer, one for the photodetectors, and one for the QND detectors. After a while of taking data we are getting a bit thirsty. Since our presence is not required for the correct running of our automated experiment, we deci
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