The resonance-frequency shift and the energy of molecules with a large change in the permanent dipole moments between the ground and the excited levels under an intense oscillating field are investigated. It is found that the higher-order terms with respect to the Rabi frequency of the Bloch-Siegert shift cannot be neglected for molecules with a large permanent-dipole difference. Some perturbational expressions are derived, and numerical calculations are performed for various sets of parameters.
The resonance-frequency shift and the energy of molecules with a large change in the permanent dipole moments between the ground and the excited levels under an intense oscillating field are investigated. It is found that the higher-order terms with respect to the Rabi frequency of the Bloch-Siegert shift cannot be neglected for molecules with a large permanent-dipole difference. Some perturbational expressions are derived, and numerical calculations are performed for various sets of parameters.
The two-level rotating wave approximation for two-photon excitations in dipolar molecules is modified to include the effects of the Bloch-Siegert shift in the two-photon resonance energy. The resulting analytical results are used to establish a criterion for when Bloch-Siegert effects are important and the relevance of these effects are compared for fixed laser-molecule configurations versus orientationally averaged results. Two-level model molecules, with parallel permanent and transition dipoles, are used in this work and the effects of Bloch-Siegert shifts are discussed for resonance profiles, time-dependent populations of the excited state, and time-averaged excitation rates. Bloch-Siegert shifts can have pronounced effects on resonance energies and the shape of resonance profiles and, for example, on the magnitudes and the temporal locations of the maxima in the temporal evolution of the time-dependent properties of the system.
Expressions are presented for the Bloch-Siegert shift appropriate to electric dipole resonance experiments between excited states, when the maximum change in lifetime due to the applied field is used as the criterion for determining the resonance centre. The results differ from those reported by Silverman and Pipkin (1972) in the magnitude of the power shift, and in that the present authors predict an additional power-independent shift. The effect of neighbouring levels on the power shift is calculated, and shown to be substantial in certain cases.
When trapped atoms are illuminated by weak lasers, off-resonant transitions cause shifts in the frequencies of the vibrational-sideband resonances. These frequency shifts may be understood in terms of Stark shifts of the individual levels or, as proposed here, as a vibrational Bloch-Siegert shift, an effect closely related to the usual (radio-frequency or optical) Bloch-Siegert shift and associated with rapidly oscillating terms when the rotating wave approximation is not made. Explicit analytic expressions are derived and compared to numerical results, and the similarities and differences between the usual and the vibrational Bloch-Siegert shifts are also spelled out.
A dressed-state perturbation theory beyond the rotating wave approximation(RWA) is presented to investigate the interaction between a two-level electronic transition of polar molecules and a quantized cavity field. Analytical expressions can be explicitly derived for both the ground- and excited-state-energy spectrums and wave functions of the system, where the contribution of permanent dipole moments(PDM) and the counter-rotating wave term(CRT) can be shown separately.The validity of these explicit results is discussed by comparison with the direct numerical simulation. Compared to the CRT coupling, PDM results in the coupling of more dressed states and the energy shift is proportional to the square of the normalized permanent dipole difference, and a greater Bloch–Siegert shift can be produced in the giant dipole molecule cavity QED. In addition, our method can also be extended to the solution of the two-level atom Rabi model Hamiltonian beyond the RWA.更多还原
An analytic expression for the absorption spectra of a two-level molecule or atom is derived, within the rotating wave approximation (RWA), which includes the effects of permanent dipole moments and static electric fields. The derivation is for the interaction of the system with a plane-polarized sinusoidal electromagnetic field (EMF) in the semi-classical electric dipole approximation. The RWA resonance profile, and a series of exactly calculated two-level model spectra, are used to investigate some single- and multi-photon spectral effects due to permanent dipoles and static fields, relative to the atomic problem (no permanent dipoles). These effects include the occurrence of even as well as odd photon transitions. Permanent dipole moments can cause narrowing of the resonances, oscillatory fringes around the resonances as a function of frequency, and decreases in the molecule-EMF coupling, relative to the atomic results. Comparisons with exact two-level model spectra are used to study the validity of the RWA results and indicate that several features, such as dynamic backgrounds and shifts of the resonance frequencies from the weak EMF limits of {dollar}\\omega\\sbsp{lcub}\\rm res{rcub}{lcub}\\rm N{rcub}{dollar} = {dollar}\\Delta{dollar}E/N, N = 1,2,3, dots, are missing in the RWA spectra as the coupling increases.;Perturbative corrections to the RWA absorption spectra and the full widths at half maxima for the resonances are derived, neglecting static fields, and used to investigate and explain the effects missing in the RWA; the RWA resonance profile is a zeroth plus first order result obtainable from a time-independent Floquet Hamiltonian secular equation. The usefulness and validity of the perturbative corrections are investigated and it is concluded that these corrections are not useful computationally past second order. However, the corrections are useful in understanding some of the deficiencies of the RWA. These include the shifts of the N-photon resonance positions to low frequency, with respect to {dollar}\\Delta{dollar}E/N, that can occur for molecules with non-zero permanent dipoles; the shift is always to high frequency for atoms. A series of exact model calculations, for "giant dipole" molecules, is also used to discuss the effects of permanent dipole moments on spectra and to establish comparisons with the recent literature on the subject.
The Bloch-Siegert-type shifts and multiple-quantum resonance shifts of a spin-one system subjected to an oscillating radio-frequency applied at right angles to a DC field have been calculated to sixth order in V, the amplitude of the oscillating field, for the single-quantum resonance, and to fourth order in V for the higher resonances. The level crossing criterion appropriate to two-level systems cannot be used here, and a resonance condition based on a previously derived analogue of Shirley's equation for spin-one systems is used instead. The calculation uses degenerate continued-fraction perturbation theory. Numerical calculations were performed in order to obtain the shape of the resonances, and partially check the analytic results. The atomic levels were assumed to be completely stable; the corrections due to finite atomic lifetimes are expected to be small.