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Journal of Physics B Atomic and Molecular Physics

Bloch-Siegert shift in optically oriented199Hg vapour

E. Arimondo, G. Moruzzi

Published Nov 1, 1973• 34 citations
Publisher

Abstract

The Bloch-Siegert shift displayed by a spin 1/2 particle system is measured in a double resonance experiment on the ground state of an optically oriented 199 Hg vapour. The displacement of the nuclear magnetic resonance peaks corresponding to the one and three quantum transitions are studied as a function of the radiofrequency field intensity. Similarly, the displacement of the component of the vapour polarization which is modulated at twice the RF field frequency is observed. The experimental results are compared with the existing theoretical approaches to the Bloch-Siegert effect, and a good agreement is found with the semiclassical theory leading to the continued fraction solution.

DOI
10.1088/0022-3700/6/11/034

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Physical Review A•Feb 1, 1977•18 citations
The Bloch-Siegert shift displayed by a spin 1/2 particle system is measured in a double resonance experiment on the ground state of an optically oriented 199 Hg vapour. The displacement of the nuclear magnetic resonance peaks corresponding to the one and three quantum transitions are studied as a function of the radiofrequency field intensity. Similarly, the displacement of the component of the vapour polarization which is modulated at twice the RF field frequency is observed. The experimental results are compared with the existing theoretical approaches to the Bloch-Siegert effect, and a good agreement is found with the semiclassical theory leading to the continued fraction solution.
The dynamics of a two-level spin system dressed by bichromatic radiation is studied under the conditions of double resonance when the frequency of one (microwave) field is equal to the Larmor frequency of the spin system and the frequency of the other (radio-frequency) field ω rf is close to the Rabi frequency ω 1 in a microwave field. It is shown theoretically that Rabi oscillations between dressed-spin states with the frequency ɛ are accompanied by higher-frequency oscillations at frequencies n ω rf and n ω rf ± ɛ, where n = 1, 2,.... The most intense among these are the signals corresponding to n = 1. The counter-rotating (antiresonance) components of the RF field give rise to a shift of the dressed-state energy, i.e., to a frequency shift similar to the Bloch-Siegert shift. In particular, this shift is manifested as the dependence of the Rabi-oscillation frequency ɛ on the sign of the detuning ω 1 − ω rf from resonance. In the case of double resonance, the oscillation amplitude is asymmetric; i.e., the amplitude at the sum frequency ω rf + ɛ increases, while the amplitude at the difference frequency ω rf − ɛ decreases. The predicted effects are confirmed by observations of the nutation signals of the electron paramagnetic resonance (EPR) of E ′ 1 centers in quartz and should be taken into account to realize qubits with a low Rabi frequency in solids.
The dynamics of a two-level spin system dressed by bichromatic radiation is studied under the conditions of double resonance when the frequency of one (microwave) field is equal to the Larmor frequency of the spin system and the frequency of the other (radio-frequency) field ω_{rf} is close to the Rabi frequency ω_{1} in a micro-wave field. It is shown theoretically that Rabi oscillations between dressed-spin states with the frequency εare accompanied by higher-frequency oscillations at frequencies nω_{rf} and nω_{rf}\pm ε, where n = 1, 2, .... The most intense among these are the signals corresponding to n = 1. The counter-rotating (antiresonance) components of the RF field give rise to a shift of the dressed-state energy, i.e., to a frequency shift similar to the Bloch-Siegert shift. In particular, this shift is manifested as the dependence of the Rabi-oscillation frequency εon the sign of the detuning ω{1} -ω{rf} from resonance. In the case of double resonance, the oscillation amplitude is asymmetric; i.e., the amplitude at the sum frequency ω_{rf} +εincreases, while the amplitude at the difference frequency ω_{rf} -εdecreases. The predicted effects are confirmed by observations of the nutation signals of the electron paramagnetic resonance (EPR) of centers in quartz and should be taken into account to realize qubits with a low Rabi frequency in solids.
We present investigations of radio-frequency (RF) resonances observed in an optically pumped rubidium vapor. By measuring the systematic shifts (the Bloch–Siegert shifts) of RF resonances in low magnetic fields, we demonstrate limitations of the rotating-wave approximation in the case of angular momentum F ≥ 1. The resonance shifts and deformations are characterized in a wide range of parameters and it is shown that the observed behavior is far more complex than in a standard two-level system. It is also demonstrated that the shifts can be controllably turned on or off by switching between the oscillating and rotating magnetic field. Experimental results are supported with numerical calculations, reproducing all features of the observed signals. Besides fundamental aspect of the research, application of rotating magnetic field helps to suppress/evaluate spectroscopic-measurement and precise-metrology systematic errors. The reported study has also important implications for quantum metrology and information processing beyond RWA and standard two-state qubit dynamics.
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.
We present a semiclassical solution for a Zeeman-split, optically pumped, spin-\textonehalf{} system interacting with a strong radio-frequency field. The method of solution presented here is based upon a matrix continued-fraction expansion, and can explain any resonance phenomena which occur for arbitrary geometrical configurations of the pumping beam or the rf field polarization axis. Theoretical predictions of line shapes for some cases are reported and discussed. The solution can also explain some deviations of the observed Bloch-Siegert shift at high rf power from the behavior predicted by a previous semiclassical theory, which can account for simple geometrical configurations only.