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arXiv:1306.1151 · Physical Review Letters

Magic Frequencies in Atom-Light Interaction for Precision Probing of the Density Matrix

Menachem Givon, Yair Margalit, Amir Waxman, David Tal, David Groswasser, Yonathan Japha, R. Folman

Published Aug 1, 2013• 3 citations
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Abstract

We analyze theoretically and experimentally the existence of a magic frequency for which the absorption of a linearly polarized light beam by a vapor of alkali-metal atoms is independent of the population distribution among the Zeeman sublevels and the angle between the beam and a magnetic field. The phenomenon originates from a peculiar cancellation of the contributions of higher moments of the atomic density matrix, and is described using the Wigner-Eckart theorem and inherent properties of Clebsch-Gordan coefficients. One important application is the robust measurement of the hyperfine population.

DOI
10.1103/physrevlett.111.053004

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We analyze theoretically and experimentally the existence of a magic frequency for which the absorption of a linearly polarized light beam by a vapor of alkali-metal atoms is independent of the population distribution among the Zeeman sublevels and the angle between the beam and a magnetic field. The phenomenon originates from a peculiar cancellation of the contributions of higher moments of the atomic density matrix, and is described using the Wigner-Eckart theorem and inherent properties of Clebsch-Gordan coefficients. One important application is the robust measurement of the hyperfine population.
Coherent-population-trapping resonance in vapor cell is a quantum interference effect that appears in the two-photon transitions between the ground-state hyperfine levels of alkali-metal atoms and is often utilized in miniature and centimeter-scale clock devices. To quantitatively understand and predict the performance of this phenomenon, it is necessary to consider the transitions and relaxations between all hyperfine Zeeman sublevels involved in the different excitation processes of the atom. In this paper, we constructed a computational multilevel atomic model of the Liouville density-matrix equation for 32 Zeeman sublevels involved in the D1{D}_{1}D1​ line of 133Cs^{133}\mathrm{Cs}133Cs irradiated by two frequencies with circularly polarized components and then simulated the amplitude and shape of the resonance spectrum of the transmitted light through centimeter-scale Cs-vapor cells. We show that the numerical solutions of the equation and analytical investigations adequately explain a variety of the characteristics observed in the experiment.
A scheme for concentrating a large fraction (\ensuremath{\sim}100%) of the alkali-metal atoms in an atomic vapor in any single magnetic sublevel of the ground state is developed. This is experimentally demonstrated in the 87Rb^{87}\mathrm{Rb}87Rb vapor. The atomic vapor is optically pumped to a high degree of spin polarization after which two radio-frequency \ensuremath{\pi} pulses are applied to transfer the atomic population from the (2,2) or (2,-2) (F,MF{\mathit{M}}_{\mathit{F}}MF​) state to the (2,0) sublevel of the ground state. The resulting distribution is diagnosed using a microwave field tuned to the hyperfine transition (6834 MHz).
Atoms are not two-level systems, and their rich internal structure often leads to complex phenomena in the presence of light. Here, we analyze off-resonant light scattering including the full hyperfine and magnetic structure. We find a set of frequency detunings where the induced atomic dipole is the same irrespective of the Zeeman state, and where two-photon transitions that alter the atomic state turn off. For alkali-metal atoms and alkaline-earth-metal ions, if the hyperfine splitting is dominated by the magnetic dipole moment contribution, these detunings approximately coincide. Therefore, at a given ``magical'' detuning, all Zeeman states in a hyperfine manifold behave almost identically, and can be traced out to good approximation. This feature prevents state decoherence due to light scattering, which impacts quantum optics experiments and quantum information applications.
We report an unusual phenomenon, peculiar sign reversals of the ground-state magnetic resonances and of the zero-dip resonance (Zeeman resonance at zero field) of optically pumped, alkali-metal vapors. These anomalies occur when a weak circularly polarized D1D1D1 laser light is tuned to pump atoms predominantly from the lower ground-state hyperfine multiplet. One can understand the signal reversals in a simple, semiquantitative way with reference to the spin-temperature distribution. Quantitative computer simulations are in excellent agreement with observations.
In the optical excitation of atoms with polarized light, producing excited atoms, only some of the Zeeman sublevels of the excited state are actually reached, so that large differences of population can be built up between Zeeman sublevels or between hyperfine structure (hfs) levels. This property can be used to detect radio-frequency resonance in optically excited atomic states. These resonances produce a characteristic change in intensity or in the degree of polarization of the light re-emitted. Zeeman intervals, Stark effects, and hfs intervals can be measured in this manner. (The Stark constant of the 63P1 level of Hg and the electric quadrupole moments of the alkali atoms have been obtained in this way.)The technique of “optical pumping” gives a way to concentrate atoms in some of the Zeeman sublevels of one of the hfs levels of the ground state.Atomic orientation has been obtained with the Na atom, in an atomic beam and in the vapor in equilibrium with the metal. The orientation effects have been studied by detection of radio-frequency resonance signals in the ground state. Orientation can be increased many times by adding a variable pressure of a foreign gas to the pure Na vapor. Because of the coupling between nuclear spin and electron spin, nuclear orientation is produced at the same time as atomic orientation.
We report an unusual phenomenon, peculiar sign reversals of the ground-state magnetic resonances and of the zero-dip resonance (Zeeman resonance at zero field) of optically pumped, alkali-metal vapors. These anomalies occur when a weak circularly polarized D1D1D1 laser light is tuned to pump atoms predominantly from the lower ground-state hyperfine multiplet. One can understand the signal reversals in a simple, semiquantitative way with reference to the spin-temperature distribution. Quantitative computer simulations are in excellent agreement with observations.