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Physical Review A

Coherent population trapping as a magnetic-field diagnostic for hydrogen plasmas

D. R. Farley, James M. Mitrani, S. Cohen

Published Mar 12, 2012• 3 citations
Publisher

Abstract

Coherent population trapping (CPT) is theoretically examined as a magnetic-field diagnostic for high-\ensuremath{\beta} hydrogen plasma. Time-dependent quantum mechanical Bloch equations, which describe the evolution of the 2$s$ and 3$p$ level populations of the hydrogen atom under CPT conditions, were solved numerically. When the frequency difference of two copropagating lasers equals the energy difference between the atoms' levels subject to the local magnetic field, a discernable CPT dark line in the H\ensuremath{\alpha} emission is predicted, enabling the possibility of noninvasive, localized magnetic-field measurements. The effects of fine and hyperfine level structure, Doppler broadening, plasma-generated electric fields, and degree-of-hydrogen ionization are included in the model. A shift in dark-line position of 15$%$ of the linewidth is predicted to be caused by contributions from the entire H\ensuremath{\alpha} manifold. The laser-induced H\ensuremath{\alpha} fluorescence is estimated to be an order of magnitude stronger than the background H\ensuremath{\alpha} emission.

DOI
10.1103/physreva.85.033412

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Coherent population trapping (CPT) is theoretically examined as a magnetic-field diagnostic for high-\ensuremath{\beta} hydrogen plasma. Time-dependent quantum mechanical Bloch equations, which describe the evolution of the 2sss and 3ppp level populations of the hydrogen atom under CPT conditions, were solved numerically. When the frequency difference of two copropagating lasers equals the energy difference between the atoms' levels subject to the local magnetic field, a discernable CPT dark line in the H\ensuremath{\alpha} emission is predicted, enabling the possibility of noninvasive, localized magnetic-field measurements. The effects of fine and hyperfine level structure, Doppler broadening, plasma-generated electric fields, and degree-of-hydrogen ionization are included in the model. A shift in dark-line position of 15% of the linewidth is predicted to be caused by contributions from the entire H\ensuremath{\alpha} manifold. The laser-induced H\ensuremath{\alpha} fluorescence is estimated to be an order of magnitude stronger than the background H\ensuremath{\alpha} emission.
An analysis is presented of the feasibility of measurements of local poloidal magnetic fields in toroidal magnetic fusion devices using coherent population trapping (CPT) in hydrogen-like probing atoms. A measurement scheme is examined in which CPT suppresses the resonance fluorescence from a probing beam of light neutrals with Zeeman-split levels. Feasibility requirements for CPT in three- and five-level systems are discussed. As a result, a theory of CPT-based magnetometry is developed for a system significantly more complex than the conventional three-level Λ system. A theoretical analysis shows that this technique can be used to measure a local safety factor in a toroidal device to an accuracy of a few percent.
We report our study on coherent population trapping (CPT) in a $\ensuremath{\Lambda}$ configuration coupled by magnetic dipole interactions. The $\ensuremath{\Lambda}$ configuration is formed by bichromatic radio-frequency fields coupling a pair of Zeeman sublevels in one hyperfine level of an alkali-metal atom to another sublevel in the other hyperfine level. The Zeeman sublevel at the apex is coupled to a state in the nPnPnP manifold via an optical transition on one of the spectroscopic DDD lines to induce optical pumping to a dark state. The configuration is closed without leakage to other Zeeman sublevels. We use lithium atoms in an optical trap for our experimental study. The system allows independent control of the main parameters characterizing CPT, which include the upper-state decay rate and the decoherence rate as well as the Rabi frequencies. By turning off the applied fields, the system is frozen so that its quantum state can be measured precisely. We studied the line shapes and dynamics of the CPT system, and measured the phase relation of the dark superposition state to find excellent agreement with theory. The possible application of the scheme as a method to cool optically trapped atoms below the recoil limit in a manner analogous to velocity-selective coherent population trapping is discussed.
We consider the coherent-population-trapping (CPT) phenomenon in a sodium atomic vapor. The experiment leading to the first observation of CPT is revisited with an improved experimental setup and a larger range of magnetic-field strengths. From the analysis of the ground-state hyperfine splitting as a function of the applied magnetic field, we conclude that we have observed the whole spectrum of dark resonances within the D1 line corresponding to the nonabsorbing coherent superposition of two Zeeman sublevels of two different components of the 32S1/2 level. This was not obvious a priori because the transition probabilities at high magnetic-field strengths, as applied in the experiment, have to be taken into account. The differences in the contrast of the various black lines are explained in terms of pumpings outside the interaction scheme preparing the nonabsorbing state. Possible applications of CPT in high magnetic fields are discussed.
Summary form only given. We have performed experimental investigations of the coherent population trapping (CPT) phenomenon at a single hyperfine transition at the D/sub 1/ and D/sub 2/ lines of Rb in a cell, inserted inside a magnetic shield. For observation of CPT dark resonances at a single hyperfine transition the Zeeman degeneracy has to be removed. This was achieved by applying a homogeneous magnetic field H/sub 1/, parallel to the laser beam and scanned in both directions around zero value. Additional coil produced constant magnetic or RF electromagnetic field H/sub 2/ perpendicular to the beam propagation. The fluorescence signal was registered in order to investigate the influence of the additional electromagnetic field on the dark line parameters. It was observed that the width and the contrast of the dark line are very sensitive to the applied field H/sub 2./ Increasing the value/amplitude of H/sub 2/ causes increase of the width and decrease of the contrast of the CPT resonances.
Atomic hydrogen has been loaded into a 1-K deep magnetic trap through the use of a dilution refrigerator. Evaporative cooling has been used to cool the trapped hydrogen into the submillikelvin temperature regime. These techniques have produced a sample with density of 8 × 1013 cm-3 at a temperature of 100 μK. At this density a transition to a Bose-Einstein condensate is predicted to occur at a temperature of 30 μK. These results have been obtained with a magnetic trap that has been constructed to accommodate upcoming experiments based on laser spectroscopy of the 1S-2S two photon transition in the trapped hydrogen. A frequency doubled narrow linewidth cw dye laser system has been constructed to excite the 1S-2S transition. The excitation will be detected by the observation of electric field-induced Lyman-alpha fluorescence. The optical detection system should yield improved sample density and temperature diagnostic capabilities that will facilitate a closer approach to the quantum degenerate regime. Additionally the cold, confined hydrogen gas offers the possibility of improving the level of resolution of Doppler-free hydrogen 1S-2S laser spectroscopy by several orders of magnitude.
Coherent population trapping(CPT)magnetometer is based on coherent population trapping coherent dark states,using an all-optical method to measure the magnetic field with high accuracy.In our experiment,we used the method of injection locking to get the two color lasers with locked phase and large frequency difference,which equald to the hyperfine splitting of the cesium atoms′ground states,and observed the CPT transmission signals.We added the longitudinal magnetic field which was along the laser propagation direction,and observed the widen CPT transmission peak and the splitting signals.For the magnetic field of medium intensity,we got the magnetic field value by measuring the splitting spacing,and for the weak region,the value could be obtained by the relation of current and magnetic field.In our experiment,we could measure the static field with several nT.