We develop a nonstandard concept of atomic clocks where the blackbodyradiation shift (BBRS) and its temperature fluctuations can be dramaticallysuppressed (by one to three orders of magnitude) independent of theenvironmental temperature. The suppression is based on the fact that in asystem with two accessible clock transitions (with frequencies v1 and v2) whichare exposed to the same thermal environment, there exists a "synthetic"frequency v_{syn} (v1-e12 v2) largely immune to the BBRS. As an example, it isshown that in the case of ion 171Yb+ it is possible to create a clock in whichthe BBRS can be suppressed to the fractional level of 10^{-18} in a broadinterval near room temperature (300\pm 15 K). We also propose a realization ofour method with the use of an optical frequency comb generator stabilized toboth frequencies v1 and v2. Here the frequency v_{syn} is generated as one ofthe components of the comb spectrum and can be used as an atomic standard.
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