Abstract
We present a scheme for simulating relativistic quantum physics in circuit quantum electrodynamics. By using three classical microwave drives, we show that a superconducting qubit strongly coupled to a resonator field mode can be used to simulate the dynamics of the Dirac equation and Klein paradox in all regimes. Using the same setup we also propose the implementation of the Foldy–Wouthuysen canonical transformation, after which the time derivative of the position operator becomes a constant of the motion.
Highlights
Feynman [1] is credited for introducing the idea of a quantum simulator
At his keynote speech during the 1st Conference on Physics and Computers in 1981, he claimed that because the laws of Nature are not those of classical mechanics, it would be better to build a quantum simulation of a physical problem under the same quantum mechanical laws
We show how the physics of relativistic quantum mechanics can be simulated in a very different setting: that of circuit quantum electrodynamics and superconducting qubits
Summary
Feynman [1] is credited for introducing the idea of a quantum simulator. At his keynote speech during the 1st Conference on Physics and Computers in 1981, he claimed that because the laws of Nature are not those of classical mechanics, it would be better to build a quantum simulation of a physical problem under the same quantum mechanical laws. For relativistic electrons, one can estimate a Zitterbewegung with an amplitude of about 10−4 nm and a frequency of 1021 Hz, making its eventual detection very demanding There is another interesting property of the Dirac equation related to the behavior of relativistic Dirac particles under the effect of an external scalar potential, dψ i hdt. Klein found that equation (4) for a relativistic Dirac particle allows for propagating solutions beyond the potential barrier [10]. The position and momentum of the Dirac particle are encoded in its phase-space or field quadrature representation This opens up new possibilities for combining intracavity fields with propagating quantum microwaves [26,27,28] in scalable quantum network architectures [29] with delocalized and/or sequential interactions
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