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arXiv:1207.1988 · Physical Review A

Nonclassical microwave radiation from the dynamical Casimir effect

J. R. Johansson, Göran Johansson, Christopher M. Wilson, Per Delsing, Franco Nori

Published Apr 4, 2013• 88 citations
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Abstract

We investigate quantum correlations in microwave radiation produced by the dynamical Casimir effect in a superconducting waveguide terminated and modulated by a superconducting quantum interference device. We apply nonclassicality tests and evaluate the entanglement for the predicted field states. For realistic circuit parameters, including thermal background noise, the results indicate that the produced radiation can be strictly nonclassical and can have a measurable amount of intermode entanglement. If measured experimentally, these nonclassicality indicators could give further evidence of the quantum nature of the dynamical Casimir radiation in these circuits.

DOI
10.1103/physreva.87.043804

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We investigate quantum correlations in microwave radiation produced by the dynamical Casimir effect in a superconducting waveguide terminated and modulated by a superconducting quantum interference device. We apply nonclassicality tests and evaluate the entanglement for the predicted field states. For realistic circuit parameters, including thermal background noise, the results indicate that the produced radiation can be strictly nonclassical and can have a measurable amount of intermode entanglement. If measured experimentally, these nonclassicality indicators could give further evidence of the quantum nature of the dynamical Casimir radiation in these circuits.
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A fundamental property of the quantum vacuum is that a time-varying boundary condition for the electro-magnetic field can generate photons from the vacuum, the so-called the dynamical Casimir effect (DCE). The photons are created pairwise and should possess the particular quantum correlations referred to as entanglement. In particular, broadband entanglement sources are useful for two reasons: i) they can be very bright, generating a large number of entangled photons, and ii) the wide frequency content allows shaping the emitted radiation in time. Here we present the observation of entanglement generated in a broadband system using the DCE. The measured sample consists of a superconducting quantum interference device (SQUID) terminating a microwave transmission line. A magnetic flux modulates the SQUID's Josephson inductance at approximately 9~GHz, resulting in a time-varying boundary condition for the quantum vacuum in the transmission line. We detect both quadratures of the microwave radiation emitted at two different frequencies separated by 0.7~GHz. Analysing the measured data and using a careful calibration of the power level emitted from the sample, we determine the purity and type of entanglement using two different methods. We estimate an entanglement rate of 5~Mebit/s (mega entangled bits per second).
We analyze the generation of quantum discord by means of the dynamical Casimir effect in superconducting wave guides modulated by superconducting quantum interferometric devices. We show that for realistic experimental parameters, the conditions for the existence of quantum discord are less demanding than the previously considered for quantum entanglement or nonclassicality. These results could facilitate the experimental confirmation of the quantum nature of the dynamical Casimir effect radiation. Moreover, the states with nonzero discord and zero entanglement generated by the dynamical Casimir effect are a useful resource for quantum cryptography.
We study the Bell's inequality violation by dynamical Casimir radiation with pseudospin measurement. We consider a circuit quantum electrodynamical setup where a relativistically moving mirror is simulated by variable external magnetic flux in a superconducting quantum interference device terminating a superconducting-microwave waveguide. We analytically obtain expectation values of the Bell operator optimized with respect to channel orientations in terms of the system parameters. We consider the effects of local noise in the microwave field modes, asymmetry between the field modes resulting from nonzero detuning, and signal loss. Our analysis provides ranges of the above experimental parameters for which the Bell violation can be observed. We show that the Bell violation can be observed in this setup up to 40mK40\phantom{\rule{0.16em}{0ex}}\text{mK}40mK temperature as well as up to 65% signal loss.
We theoretically investigate the dynamical Casimir effect (DCE) in electrical circuits based on superconducting microfabricated waveguides with tunable boundary conditions. We propose implementing a rapid modulation of the boundary conditions by tuning the applied magnetic flux through superconducting quantum-interference devices that are embedded in the waveguide circuits. We consider two circuits: (i) An open waveguide circuit that corresponds to a single mirror in free space, and (ii) a resonator coupled to a microfabricated waveguide, which corresponds to a single-sided cavity in free space. We analyze the properties of the DCE in these two setups by calculating the generated photon-flux densities, output-field correlation functions, and the quadrature squeezing spectra. We show that these properties of the output field exhibit signatures unique to the radiation due to the DCE, and could, therefore, be used for distinguishing the DCE from other types of radiation in these circuits. We also discuss the similarities and differences between the DCE, in the resonator setup, and the down-conversion of pump photons in parametric oscillators.