Several years ago, a resonance-shift phenomenon was predicted to exist, termed the stochastic realization shift (SRS), which arises as a consequence of correlated amplitude and frequency variations in a resonant field. An interesting aspect of the phenomenon is that the sign of the SRS in weak and strong fields has been shown to differ. Here, we demonstrate that the SRS may be conveniently studied over a broad range of field strengths via magnetic resonance in an optically pumped alkali-metal vapor. Specifically, we study the SRS in the ground state 0-0 hyperfine transition of ${\mathrm{Rb}}^{87}$ for a field undergoing stochastic (yet correlated) amplitude-frequency fluctuations. Under our experimental conditions we find no evidence for a change in sign of the SRS as the field strength undergoes a transition from weak to strong. Further, our results show that in strong fields the magnitude of the SRS may be influenced by the field's spatial variations. \textcopyright{} 1996 The American Physical Society.Several years ago, a resonance-shift phenomenon was predicted to exist, termed the stochastic realization shift (SRS), which arises as a consequence of correlated amplitude and frequency variations in a resonant field. An interesting aspect of the phenomenon is that the sign of the SRS in weak and strong fields has been shown to differ. Here, we demonstrate that the SRS may be conveniently studied over a broad range of field strengths via magnetic resonance in an optically pumped alkali-metal vapor. Specifically, we study the SRS in the ground state 0-0 hyperfine transition of ${\mathrm{Rb}}^{87}$ for a field undergoing stochastic (yet correlated) amplitude-frequency fluctuations. Under our experimental conditions we find no evidence for a change in sign of the SRS as the field strength undergoes a transition from weak to strong. Further, our results show that in strong fields the magnitude of the SRS may be influenced by the field's spatial variations. \textcopyright{} 1996 The American Physical Society.

Physical Review AJul 1, 19962 citations

Light Shift of Coherent Population Trapping Resonances in Cesium Vapor under the Laser Field with Dual Frequency–Amplitude Modulation

V. I. Vishnyakov, Denis V. Brazhnikov, Mikhail N Skvortsov

Abstract In this study, the light shift of coherent population trapping (CPT) resonances is studied in a miniature glass cell (~0.1 cm3) filled with 133Cs vapor. The atoms exposed to the radiation from a vertical-cavity surface-emitting laser (VCSEL). The laser current is modulated at a microwave frequency (≈4.6 GHz), which leads to the frequency modulation (FM) of output radiation. In addition, the light beam is transmitted through an electro-optic modulator (EOM), which is assembled as a Mach–Zehnder interferometer, acquiring amplitude modulation (AM). This dual (FM–AM) modulation leads to essentially nonlinear behavior of the function describing the light shift of the CPT resonance versus the total optical power in the cell. In particular, this function has an extremum that can be used to suppress the influence of small optical power variations in the cell on the stability of the CPT-based quantum frequency standard (QFS). The proposed scheme is characterized by a number of parameters such as the phase difference between the FM and AM signals as well as the bias voltage at EOM, which are additional degrees of freedom for controlling the behavior of the light shift of the CPT resonance. This can be used for the optimization of the QFS operation regime.Abstract In this study, the light shift of coherent population trapping (CPT) resonances is studied in a miniature glass cell (~0.1 cm3) filled with 133Cs vapor. The atoms exposed to the radiation from a vertical-cavity surface-emitting laser (VCSEL). The laser current is modulated at a microwave frequency (≈4.6 GHz), which leads to the frequency modulation (FM) of output radiation. In addition, the light beam is transmitted through an electro-optic modulator (EOM), which is assembled as a Mach–Zehnder interferometer, acquiring amplitude modulation (AM). This dual (FM–AM) modulation leads to essentially nonlinear behavior of the function describing the light shift of the CPT resonance versus the total optical power in the cell. In particular, this function has an extremum that can be used to suppress the influence of small optical power variations in the cell on the stability of the CPT-based quantum frequency standard (QFS). The proposed scheme is characterized by a number of parameters such as the phase difference between the FM and AM signals as well as the bias voltage at EOM, which are additional degrees of freedom for controlling the behavior of the light shift of the CPT resonance. This can be used for the optimization of the QFS operation regime.

Journal of Experimental and Theoretical PhysicsJun 1, 20243 citations

Nonlinear shift of absorption resonance

O. V. Lukashina, А. Н. Ораевский, Игорь Евгеньевич Проценко

Optics and SpectroscopyMay 1, 19900 citations

Wave/particle duality in monitored Jaynes–Cummings resonances

Th. K. Mavrogordatos

Abstract We operationally uncover aspects of wave/particle duality for the open driven Jaynes–Cummings (JC) model in its strong-coupling limit. We lay special emphasis on the vacuum Rabi resonance, and determine the corresponding normalized intensity-field correlation function via mapping to ordinary resonance fluorescence. We demonstrate that temporal wave–particle fluctuations of light emanating from an established vacuum Rabi resonance are explicitly non-classical, while the limit of vanishing spontaneous emission restores detailed balance. When photon blockade sets in, individual realizations show a rapidly increasing frequency of fluctuations towards the two-photon resonance, arising as a direct consequence of a resolved JC spectrum. About the two-photon resonance peak, spontaneous emissions are more likely to revive a high-frequency quantum beat in the conditioned electromagnetic field amplitude than photons escaping out of the cavity mode. The beat originates from a coherent superposition of the first excited JC couplet states, and sets the background against which nonclassical phase shifts are observed in the conditioned quadrature amplitudes. We also find that the onset of steady-state bimodality reduces the variation of the normalized intensity-field correlation, at the expense of its temporal symmetry.Abstract We operationally uncover aspects of wave/particle duality for the open driven Jaynes–Cummings (JC) model in its strong-coupling limit. We lay special emphasis on the vacuum Rabi resonance, and determine the corresponding normalized intensity-field correlation function via mapping to ordinary resonance fluorescence. We demonstrate that temporal wave–particle fluctuations of light emanating from an established vacuum Rabi resonance are explicitly non-classical, while the limit of vanishing spontaneous emission restores detailed balance. When photon blockade sets in, individual realizations show a rapidly increasing frequency of fluctuations towards the two-photon resonance, arising as a direct consequence of a resolved JC spectrum. About the two-photon resonance peak, spontaneous emissions are more likely to revive a high-frequency quantum beat in the conditioned electromagnetic field amplitude than photons escaping out of the cavity mode. The beat originates from a coherent superposition of the first excited JC couplet states, and sets the background against which nonclassical phase shifts are observed in the conditioned quadrature amplitudes. We also find that the onset of steady-state bimodality reduces the variation of the normalized intensity-field correlation, at the expense of its temporal symmetry.

arXiv:2507.05837The European Physical Journal Special TopicsJul 4, 20251 citation

Theories for multiple resonances

D. Klakow, M. Weber, P.‐G. Reinhard

arXiv:nucl-th/9502027The European Physical Journal ADec 1, 19954 citations

{\mathrm{Rb}}^{87}

for a field undergoing stochastic (yet correlated) amplitude-frequency fluctuations. Under our experimental conditions we find no evidence for a change in sign of the SRS as the field strength undergoes a transition from weak to strong. Further, our results show that in strong fields the magnitude of the SRS may be influenced by the field's spatial variations. \textcopyright{} 1996 The American Physical Society.