A theoretical study of the nonlinearity reduction in a four-level system of a potassium atom in the presence of a strong nanosecond laser field, which excites the transition |4S 1/2 ⟩↔|6S 1/2 ⟩ with two photons, is presented. It is shown that the destructive quantum interference between the laser field and the internally generated radiations results in a linear response of the atomic path-1 (|4S 1/2 ⟩↔|6S 1/2 ⟩↔|5P 3/2 ⟩↔|4S 1/2 ⟩) emitted parametric fields. For sufficiently high laser intensities and/or atomic densities, the path-1 emitted fields are driven into saturation, a regime accompanied by a substantial population redistribution among the states. Reasonable agreement between earlier experimental results and the theoretical ones is obtained. It is also shown that upon saturation of path-1, for low atomic density, the path-2 (|4S 1/2 ⟩↔|6S 1/2 ⟩↔|4P 3/2 ⟩↔|4S 1/2 ⟩) is activated. A subtle interplay between laser intensity and atomic density may determine the activation of path-2. Also, it is shown that the path-2 emission |6S 1/2 ⟩↔|4P 3/2 ⟩ is an amplified spontaneous emission process which induces a |4P 3/2 ⟩↔|4S 1/2 ⟩ emission, without population inversion, in a cascade scheme.A theoretical study of the nonlinearity reduction in a four-level system of a potassium atom in the presence of a strong nanosecond laser field, which excites the transition |4S 1/2 ⟩↔|6S 1/2 ⟩ with two photons, is presented. It is shown that the destructive quantum interference between the laser field and the internally generated radiations results in a linear response of the atomic path-1 (|4S 1/2 ⟩↔|6S 1/2 ⟩↔|5P 3/2 ⟩↔|4S 1/2 ⟩) emitted parametric fields. For sufficiently high laser intensities and/or atomic densities, the path-1 emitted fields are driven into saturation, a regime accompanied by a substantial population redistribution among the states. Reasonable agreement between earlier experimental results and the theoretical ones is obtained. It is also shown that upon saturation of path-1, for low atomic density, the path-2 (|4S 1/2 ⟩↔|6S 1/2 ⟩↔|4P 3/2 ⟩↔|4S 1/2 ⟩) is activated. A subtle interplay between laser intensity and atomic density may determine the activation of path-2. Also, it is shown that the path-2 emission |6S 1/2 ⟩↔|4P 3/2 ⟩ is an amplified spontaneous emission process which induces a |4P 3/2 ⟩↔|4S 1/2 ⟩ emission, without population inversion, in a cascade scheme.

Journal of Physics B Atomic Molecular and Optical PhysicsJul 29, 201110 citations

Optical rotary saturation in a gas

Yehiam Prior, J. A. Kash, Erwin Louis Hahn

The optical analog of the nuclear magnetic resonance rotary saturation effect is demonstrated and analyzed. A 9.6-\ensuremath{\mu}m C ${\mathrm{O}}_{2}$ laser resonance excitation of vibrational transitions in gaseous C ${\mathrm{H}}_{3}$ F creates an effective splitting in the interaction representation of the optical two-level system. A radio-frequency standing-wave Stark electric field is tuned in rotary saturation resonance with the splitting. The change in transmitted laser beam intensity, because of rotary resonance, is measured in terms of transient optical signals obtained by the Stark switching method of Brewer and Shoemaker. The measured single and multiphoton rotary saturation resonance signals are compared with perturbation and computer solutions of nonlinear Bloch-Maxwell macroscopic equations. Doppler-free rotary saturation spectra are obtained in the presence of inhomogeneous Doppler broadening by a special scheme of Fourier analysis. A discussion is presented of the coupling of energy between two traveling waves that are in double resonance with the optical two-level system. The concept of spin temperature is discussed in relation to a coherently excited optical level system with a long fluorescence lifetime. The possibility of a cross-relaxation double resonance experiment between an optical system and a spin system is outlined.The optical analog of the nuclear magnetic resonance rotary saturation effect is demonstrated and analyzed. A 9.6-\ensuremath{\mu}m C${\mathrm{O}}_{2}$ laser resonance excitation of vibrational transitions in gaseous C${\mathrm{H}}_{3}$F creates an effective splitting in the interaction representation of the optical two-level system. A radio-frequency standing-wave Stark electric field is tuned in rotary saturation resonance with the splitting. The change in transmitted laser beam intensity, because of rotary resonance, is measured in terms of transient optical signals obtained by the Stark switching method of Brewer and Shoemaker. The measured single and multiphoton rotary saturation resonance signals are compared with perturbation and computer solutions of nonlinear Bloch-Maxwell macroscopic equations. Doppler-free rotary saturation spectra are obtained in the presence of inhomogeneous Doppler broadening by a special scheme of Fourier analysis. A discussion is presented of the coupling of energy between two traveling waves that are in double resonance with the optical two-level system. The concept of spin temperature is discussed in relation to a coherently excited optical level system with a long fluorescence lifetime. The possibility of a cross-relaxation double resonance experiment between an optical system and a spin system is outlined.

Physical Review ADec 1, 19789 citations

Relaxation of two-level systems

Ya. D. Klubis

Journal of Applied SpectroscopyJan 1, 19710 citations

Relaxation of a single two-level system

J. Łuczka

Czechoslovak Journal of PhysicsJun 1, 19860 citations

Anomalous Loss Reduction Below Two-Level System Saturation in Aluminum Superconducting Resonators

Tamin Tai, Jingnan Cai, Steven M. Anlage

Superconducting resonators are widely used in many applications such as qubit readout for quantum computing, and kinetic inductance detectors. These resonators are susceptible to numerous loss and noise mechanisms, especially the dissipation due to two-level systems (TLS) which become the dominant source of loss in the few-photon and low temperature regime. In this study, capacitively-coupled aluminum half-wavelength coplanar waveguide resonators are investigated. Surprisingly, the loss of the resonators is observed to decrease with a lowering temperature at low excitation powers and temperatures below the TLS saturation. This behavior is attributed to the reduction of the TLS resonant response bandwidth with decreasing temperature and power to below the detuning between the TLS and the resonant photon frequency in a discrete ensemble of TLS. When response bandwidths of TLS are smaller than their detunings from the resonance, the resonant response and thus the loss is reduced. At higher excitation powers, the loss follows a logarithmic power dependence, consistent with predictions from the generalized tunneling model (GTM). A model combining the discrete TLS ensemble with the GTM is proposed and matches the temperature and power dependence of the measured internal loss of the resonator with reasonable parameters.Superconducting resonators are widely used in many applications such as qubit readout for quantum computing, and kinetic inductance detectors. These resonators are susceptible to numerous loss and noise mechanisms, especially the dissipation due to two-level systems (TLS) which become the dominant source of loss in the few-photon and low temperature regime. In this study, capacitively-coupled aluminum half-wavelength coplanar waveguide resonators are investigated. Surprisingly, the loss of the resonators is observed to decrease with a lowering temperature at low excitation powers and temperatures below the TLS saturation. This behavior is attributed to the reduction of the TLS resonant response bandwidth with decreasing temperature and power to below the detuning between the TLS and the resonant photon frequency in a discrete ensemble of TLS. When response bandwidths of TLS are smaller than their detunings from the resonance, the resonant response and thus the loss is reduced. At higher excitation powers, the loss follows a logarithmic power dependence, consistent with predictions from the generalized tunneling model (GTM). A model combining the discrete TLS ensemble with the GTM is proposed and matches the temperature and power dependence of the measured internal loss of the resonator with reasonable parameters.

arXiv:2109.11742Sep 24, 20210 citations

The optical analog of the nuclear magnetic resonance rotary saturation effect is demonstrated and analyzed. A 9.6-\ensuremath{\mu}m C

{\mathrm{O}}_{2}

laser resonance excitation of vibrational transitions in gaseous C

{\mathrm{H}}_{3}

F creates an effective splitting in the interaction representation of the optical two-level system. A radio-frequency standing-wave Stark electric field is tuned in rotary saturation resonance with the splitting. The change in transmitted laser beam intensity, because of rotary resonance, is measured in terms of transient optical signals obtained by the Stark switching method of Brewer and Shoemaker. The measured single and multiphoton rotary saturation resonance signals are compared with perturbation and computer solutions of nonlinear Bloch-Maxwell macroscopic equations. Doppler-free rotary saturation spectra are obtained in the presence of inhomogeneous Doppler broadening by a special scheme of Fourier analysis. A discussion is presented of the coupling of energy between two traveling waves that are in double resonance with the optical two-level system. The concept of spin temperature is discussed in relation to a coherently excited optical level system with a long fluorescence lifetime. The possibility of a cross-relaxation double resonance experiment between an optical system and a spin system is outlined.