Dynamical Casimir Effect in a Superconducting Coplanar Waveguide
J. R. Johansson · G. Johansson · C. M. Wilson · Franco Nori
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In one page
Nobody can shake a mirror at a useful fraction of the speed of light, and that alone is why the dynamical Casimir effect — Gerald Moore’s 1970 prediction that a fast enough mirror turns the vacuum’s virtual photons into real ones — had never been seen. Working between RIKEN and Chalmers, J. R. Johansson, Göran Johansson, Christopher Wilson and Franco Nori show how to build the mirror out of circuitry instead. Their design is a superconducting coplanar waveguide, a microwave line on a chip, closed at one end by a SQUID: a loop whose inductance you tune with a magnetic flux. Tuning the flux changes the line’s effective length, so the boundary moves although nothing material does, and it can move at a good fraction of the speed of light in the line. They compute the outgoing spectrum, show the quantum part peaks at half the drive frequency where the thermal background does not, and estimate about a hundred thousand photons a second drawn out of empty space.
Why it matters hereChapter 2 rests on the vacuum being a real medium with modes you can push on, and this is the blueprint that made pushing on them practical — swap the impossible relativistic mirror for a flux-tuned boundary on a chip. Chapter 6 is the payoff: the light leaving the line was paid for out of the ground state of the field. The measurements followed within two years, at Chalmers, /library/stm-b8989fce8d, and in a different circuit at Aalto, /library/stm-c395407d90.
What it claims
01Two parallel mirrors in empty space are attracted to each other because of the vacuum fluctuations of the electromagnetic field, since the density of modes between them differs from the density outside; this effect of quantum electrodynamics was predicted by Casimir in 1948 and has since been verified experimentally.Introduction, opening paragraph
Settled physics02If the mirrors move there is also a mismatch between the vacuum modes at different instants of time, and this was predicted to create real photons out of vacuum fluctuations; the same dynamical Casimir effect holds for a single mirror under nonuniform acceleration. The photon production rate is non-negligible only when the mirror velocity approaches the speed of light, which rules out massive mirrors and is why the effect had not yet been verified.Introduction, paragraphs 2 and 3
Settled physics03A coplanar waveguide terminated to ground through a SQUID has a boundary condition set by the magnetic flux threading the loop, which is equivalent to a short-circuited transmission line of tunable length. Because no massive mirror is moving, the velocity of the effective boundary can approach the speed of light in the line, so photon production from the vacuum can be made experimentally detectable.Paragraph beginning ’Here we show’; Fig. 1 and the effective length of Eq. (5)
Designed, not yet built04For a small-amplitude harmonic drive the output photon flux density separates into three parts: elastically reflected thermal photons and up-converted thermal photons, both of classical origin, and a third term that is purely quantum mechanical and originates in the vacuum fluctuations. The spectrum of that quantum radiation is identical to the spectrum of the single-mirror dynamical Casimir effect.Eq. (11) and the paragraph following it
Published and peer-reviewed05The quantum radiation can be told apart from the thermal background by its shape: the quantum flux density is parabolic with a maximum at half the driving frequency, whereas the reflected thermal field peaks at zero frequency and at the driving frequency. The photons are created in correlated pairs whose frequencies sum to the driving frequency, giving a squeezing spectrum with maximum squeezing at half the drive.Paragraph following Eq. (11); Fig. 2
Published and peer-reviewed06For typical superconducting-circuit parameters — a SQUID plasma frequency near 36 gigahertz, a drive at half of it, 90 femtofarad junction capacitance, about 55 ohms characteristic impedance and a wave velocity of about 1.2 times ten to the eighth metres per second — the quantum contribution exceeds the classical one across a wide band, the crossover with thermal noise falls near 70 millikelvin, and the production rate in a 100 megahertz band around half the drive is about a hundred thousand photons per second, which is clearly detectable with lock-in techniques and long integration.Estimates accompanying Figs. 2 and 3; Eq. (10)
Designed, not yet built
Read it · abstract
Abstract
We investigate the dynamical Casimir effect in a coplanar waveguide (CPW) terminated by a superconducting quantum interference device (SQUID). Changing the magnetic flux through the SQUID parametrically modulates the boundary condition of the CPW, and thereby, its effective length. Effective boundary velocities comparable to the speed of light in the CPW result in broadband photon generation which is identical to the one calculated in the dynamical Casimir effect for a single oscillating mirror. We estimate the power of the radiation for realistic parameters and show that it is experimentally feasible to directly detect this nonclassical broadband radiation.
J. R. Johansson (RIKEN and Chalmers), G. Johansson and C. M. Wilson (Microtechnology and Nanoscience, Chalmers University of Technology), and Franco Nori (RIKEN and the University of Michigan). Physical Review Letters 103, 147003 (2009). Preprint: arXiv:0906.3127 [cond-mat.supr-con].
(Abstract only. The input-output derivation of the tunable boundary condition, the sideband expansion, the spectra of Figures 2 and 3 and the analysis of SQUID asymmetry are at the source — see the rights note above. The preprint is free to read at arXiv.)
The way in
https://doi.org/10.1103/PhysRevLett.103.147003Licence checked on the source itself: the arXiv posting 0906.3127 [cond-mat.supr-con] carries the arXiv non-exclusive distribution licence, which is not a Creative Commons licence, and the published version, Physical Review Letters 103, 147003 (2009), is under the APS default licence. This sheet therefore carries the summary, the claims and the authors’ own abstract, and sends the reader to the source. The preprint is free to read at arXiv. Claim locators cite the preprint, whose equation and figure numbering matches the published Letter.
How to cite it
J. R. Johansson, G. Johansson, C. M. Wilson, Franco Nori (2009) Dynamical Casimir Effect in a Superconducting Coplanar Waveguide. doi:10.1103/PhysRevLett.103.147003
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