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We demonstrate a new technique for the suppression of noise associated with the laser source in atomic clocks based on coherent population trapping (CPT). The technique uses differential detection of the transmission of linearly and circularly polarized beams that propagate through different parts of a single rubidium vapor cell filled with a buffer gas mixture. The common-mode noise associated with the laser frequency and amplitude noise is suppressed by the differential detection of the two laser beams. The CPT signal, which is present only in the circularly polarized laser beam, is unaffected. The implementation of the technique requires only a change of the polarization of part of the laser beam and an additional photodiode. The technique is simple and applicable to CPT frequency references where a major source of noise is the laser, such as compact and chip-scale devices.