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Physical Review A

State-selective Rabi and Ramsey magnetic resonance line shapes

G. Xu, Daniel J. Heinzen

Published Feb 1, 1999• 23 citations
Publisher

Abstract

We carry out state-selective Rabi and Ramsey magnetic-resonance experiments on ground-state ${}^{133}\mathrm{Cs}(\mathrm{F}=4)$ atoms. Novel line shapes are obtained, which exhibit very sharp features with a width much smaller than the inverse duration of the magnetic-resonance pulse. The sensitivity of ordinary magnetic-resonance experiments with total spin $\mathrm{F}\mathrm{}>1/2$ is significantly less than the Heisenberg limit, which can be exactly realized only with maximally correlated spin states. We show that the state-selective resonances yield sensitivity very close to the Heisenberg limit, without any state preparation beyond ordinary optical pumping.

DOI
10.1103/physreva.59.r922

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Cs and Rb atomic vapors have been optically pumped in their ground states. The optical/rf-field configuration used allowed for the optical detection of magnetic resonance spectra with subkilohertz resolution by a pump–probe beam technique, in which the free-precessional motion of spins is recorded in the time domain. A six-level system serves as a model to describe the dependence of the observed spectra on the optical frequencies involved. With an intense laser beam applied during the free-precession period, Zeeman light-shift effects are observed. The spatial electric-field distribution of the laser beams and particle diffusion have to be taken into account to let us explain the observed magnetic resonance line shapes adequately.
New studies of Na2{\mathrm{Na}}_{2}Na2​ hyperfine structure (hfs) by the laser-induced-fluorescence molecular-beam magnetic-resonance technique are described which show that state selection and detection by strong optical fields can produce rf-magnetic-resonance spectra which differ drastically from the Rabi shape, even though the optical and rf fields do not act simultaneously on the molecules. We suggest that in the case of optically unresolved ground-state sublevels these effects are due to the creation of ground-state coherence by absorption and stimulated-emission cycles in the laser field, and we present a model calculation which exhibits the essential features of the observed spectra. We also give a proof that no model based only upon populations can explain the negative signals we observe.
Large-amplitude oscillations are predicted in the free-induction decay (FID) of atomic or spin two-level quantum systems that are coherently prepared by a resonant electromagnetic field in the form of a square amplitude pulse of duration TTT. The effect should be detectable in nuclear magnetic resonance (NMR) or in optical resonance experiments when the transition line shape is inhomogeneously broadened (${T}_{2}^{*}\ensuremath{\ll}{T}_{2}$) and the applied field is intense enough that the pulse area $\ensuremath{\chi}T\ensuremath{\ge}2\ensuremath{\pi}$, where $\ensuremath{\chi}$ is the Rabi frequency. Physically, the effect is due to Rabi oscillations which are generated in the preparative stage and are then reproduced because of atomic memory in the radiative period which follows. The atomic polarization derived from the Bloch equations assumes the form of an integral over the inhomogeneous line shape, and can be evaluated numerically for arbitrary linewidth $\ensuremath{\sigma}$ or analytically when $\ensuremath{\sigma}\ensuremath{\rightarrow}\ensuremath{\infty}$. The characteristics of the oscillation are unusual since the oscillation frequency, which is of order $\ensuremath{\chi}$, increases with time while the oscillation envelope vanishes identically for times $t\ensuremath{\ge}2T$. Coherent emission is therefore confined to one pulse width TTT immediately following the pulse. Previous NMR and infrared FID experiments with small-area pulses ($\ensuremath{\chi}T\ensuremath{\le}4\ensuremath{\pi}$), interpreted erroneously in terms of an edge echo effect, support the oscillatory FID behavior described here. For the case $\ensuremath{\chi}T>4\ensuremath{\pi}$, an experimental test would be even more decisive, as the oscillations are more pronounced.
We observe very narrow (\ensuremath{\sim}200 Hz) magnetic resonance lines in alkali vapors with atomic densities much greater than usual and with cell dimensions much smaller than usual. The Zeeman resonance frequency is shifted downward by a large factor, but the spin-exchange broadening vanishes in the high-density limit. This new regime affords important new possibilities for investigating basic interactions in dense alkali vapors, and it also opens the way to miniaturized optically pumped devices.
A density matrix description of magnetic resonance is constructed, with detailed application to spin J = 1 (or greater) particles. Different types of “monitoring” or “measurement” operators employed in atomic beam, induction, and optical experiments are constructed, and used as a compact introductory basis for the description of resonance line shapes and other characteristics of these experiments. Of particular interest are the similarities and unique differences between the optical experiments known by the names “optical pumping,” “double resonance,” and “light beats” on the one hand, and magnetic induction and atomic beam experiments on the other.
Precise control of magnetic fields is a frequent challenge encountered in experiments with atomic quantum gases. Here we present a simple method for performing in situ monitoring of magnetic fields that can readily be implemented in any quantum-gas apparatus in which a dedicated field-stabilization approach is not feasible. The method, which works by sampling several Rabi resonances between magnetically field sensitive internal states that are not otherwise used in a given experiment, can be integrated with standard measurement sequences at arbitrary fields. For a condensate of 87Rb atoms, we demonstrate the reconstruction of Gauss-level bias fields with an accuracy of tens of microgauss and with millisecond time resolution. We test the performance of the method using measurements of slow resonant Rabi oscillations on a magnetic-field sensitive transition and give an example for its use in experiments with state-selective optical potentials.