Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Predictions for cooling a solid to its ground state

Author: William C. Troy
Journal: Quart. Appl. Math. 71 (2013), 331-338
MSC (2010): Primary 82B10
DOI: https://doi.org/10.1090/S0033-569X-2012-01294-3
Published electronically: October 23, 2012
MathSciNet review: 3087426
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Abstract: A major goal of quantum computing research is to drain all quanta $ (q)$ of thermal energy from a solid at a positive temperature $ T_{0}>0,$ leaving the object in its ground state. In 2010 the first complete success was reported when a quantum drum was cooled to its ground state at $ T_{0}=20{\rm mK.}$ However, current theory, which is based on the Bose-Einstein equation, predicts that the temperature $ T \to 0$ as $ q \to 0.$ We prove that this discrepancy between experiment and theory is due to previously unobserved errors in low temperature predictions of the Bose-Einstein equation. We correct this error and derive a new formula for temperature which proves that $ T \to T_{0}>0$ as $ q \to 0.$ Simultaneously, the energy decreases to its `supersolid' ground state level as $ q \to 0^{+}.$ For experimental data our temperature formula predicts that $ T_{0}= 9.8{\rm mK,}$ in close agreement with the $ 20{\rm mK}$ experimental result. Our results form a first step towards bridging the gap between existing theory and the construction of useful quantum computing devices.

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Additional Information

William C. Troy
Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: troy@math.pitt.edu

DOI: https://doi.org/10.1090/S0033-569X-2012-01294-3
Keywords: Bose-Einstein equation, temperature
Received by editor(s): July 21, 2011
Published electronically: October 23, 2012
Article copyright: © Copyright 2012 Brown University

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