We examine in this paper the spectral characteristics of a coherent population trapping (CPT) maser in order to evaluate the frequency stability achievable by this kind of passive frequency standard. The peculiar features of the coherent microwave emission associated with the coherent population trapping phenomenon are theoretically examined taking into account the impact of the various noise contributions on the physical principle of operation. The theoretical predictions are then compared with the experimental results obtained with a laboratory prototype of
87Rb CPT maser. The measured frequency stability is mainly limited in the short term by the system thermal noise and in the medium term by the thermal drift and turns out to be in agreement with the computations within a factor of 2.
Abstract We develop a theory of modulation response of the coherent population trapping (CPT) resonance. We consider the simplest three-level atom, but take into account the polychromatic spectrum of the pumping and probing light produced by pure FM modulation of single frequency field. The analysis based on the density matrix equations rigorously includes the most important for applications range of modulation parameters where modulation frequency and deviation are comparable with or greater than the CPT linewidth, so the response of the atomic medium is not adiabatic. Some theoretical results, in particular the possibility of using a quadrature response to modulation to suppress light shift, are compared with the experiment carried out with a diode laser (VCSEL) and 87 Rb atoms.
Abstract Motivated by recent developments in atomic frequency standards employing the effect of coherent population trapping (CPT), we propose a theoretical framework for describing the CPT resonances. Our extended model includes several realistic experimental factors not accounted for in the standard approaches, namely, the FM-based technique for generating the error signal, skewed laser spectrum, etc. We provide a simple yet non-trivial analytical solution revealing the magnitude and structure of the light shift. The performance of the model is checked against numerical simulations, the agreement is good to perfect.
We have developed an effective mathematical model to calculate the coherent population trapping (CPT) resonance in periodically modulated light, when the modulation frequency
f varies near the fractional part of hyperfine splitting in the ground state
Δhfs/N (where
N=1,2,...). In such polychromatic field, only two frequency components that are most resonant with atomic optical transitions are taken into account accurately, while all other off-resonant components are taken into account using the second-order perturbation theory in the field. Within the presented concept, equation for atomic density matrix is obtained, in which the contribution of all off-resonant components is reduced to the appearance of two new operators (non-diagonal, in general case): the shift operator and relaxation operators. In the case of three-level
Λ-system, the adequacy of presented effective model was verified by numerical calculations of various dependencies, in which we did not find visual differences from the exact calculations. In addition to a significant mathematical simplification, our model provides a clear physical picture of various features of CPT spectroscopy in a periodically modulated laser field, including effects that have not been discussed in the scientific literature before. In particular, we show that the widespread viewpoint that the CPT resonance shift is determined by usual ac Stark shifts of the lower levels is, in general, fundamentally incorrect, since the contribution to the light shift due to beats at the frequency
Δhfs between different off-resonant frequency components can be comparable (or even dominate) with the standard ac Stark shift. Therefore, even if we have detailed information on the modulated field spectrum (e.g. using a spectrum analyzer), this is, in general, absolutely insufficient to determine the light shift of CPT resonance.