Coherent Magnetic Response at Optical Frequencies Using Atomic Transitions

In optics, the interaction of atoms with the magnetic field of light is almost always ignored since its strength is many orders of magnitude weaker compared to the interaction with the electric field. In this article, by using a magnetic-dipole transition within the $4f$ shell of europium ions, we show a strong interaction between a green laser and an ensemble of atomic ions. The electrons move coherently between the ground and excited ionic levels (Rabi flopping) by interacting with the magnetic field of the laser. By measuring the Rabi flopping frequency as the laser intensity is varied, we report the first direct measurement of a magnetic-dipole matrix element in the optical region of the spectrum. Using density-matrix simulations of the ensemble, we infer the generation of coherent magnetization with magnitude $5.5\times {10}^{-3}\mathrm{A}/\mathrm{m}$, which is capable of generating left-handed electromagnetic waves of intensity $1\mathrm{nW}/{\mathrm{cm}}^2$. These results open up the prospect of constructing left-handed materials using sharp transitions of atoms.

Popular Summary

Over the last two decades, there has been a growing interest in a new generation of optical tools using materials that are not available in nature. These materials offer the promise of devices with unique capabilities such as super-resolution lenses and optical cloaks. For these materials to work, they must interact strongly with both the magnetic and the electric field of light. However, the interaction of atoms with the magnetic field is almost always ignored since its strength is many orders of magnitude weaker than the electric field. We show, for the first time, a strong interaction between the magnetic field of a laser beam and an ensemble of atoms.

We shone a laser through a special crystal doped with europium atoms, which have a very complex electronic structure. The structure is such that, for a specific wavelength of light (527.5 nm), the electrons prefer to interact with the magnetic field of light instead of the electric field. For this to happen, it is essential that (i) the crystal is cooled to a temperature of 4 K, and (ii) the color of light is very precise (the wavelength should be accurate at the level of one part in ten billion). By measuring how much light is transmitted through the crystal as the laser intensity is varied, we are able to deduce the strength of the magnetic interaction.

Our results demonstrate one way to create materials with unusual optical properties. Future work could also use interactions between electrons and the magnetic field of a laser to study quantum interference.

Figure 1

The simplified experimental schematic. The experiment starts with an infrared external cavity diode laser (ECDL) at a wavelength of 1055 nm. The ECDL is locked to a reference cavity which is constructed from ultralow expansion glass. The fiber amplifier produces an optical power exceeding 5 W while maintaining the frequency stability of the ECDL. The fiber amplifier output is frequency doubled using cavity-based second harmonic generation with a periodically poled KTP (PPKTP) crystal. The output of the second harmonic generation cavity is split into two beams and acousto-optic modulators (AOM) are used to precisely control frequency and timing. The Eu:YSO crystal is housed in a continuous-flow liquid-helium cryostat.

Figure 2

The levels of the $4f$ shell of ${\mathrm{Eu}}^{+3}$ ions with an energy below $20000{\mathrm{cm}}^{-1}$. We use the ${{}^{7}F}_0\to {{}^{5}D}_1$ magnetic-dipole transition at a wavelength of 527.5 nm. The hyperfine structure of the ${{}^{153}\mathrm{Eu}}^{+3}$ isotope with a nuclear spin of $I=5/2$ is also shown (the ordering of the upper hyperfine levels is not known). The numbers in the brackets are the projection of the nuclear spin angular momentum, $|\pm m_I⟩$. The upper plot shows the transmission of a weak probe laser beam as its frequency is scanned across the magnetic-dipole transition. We observe an inhomogeneously broadened line (which is due to variations in the crystal field and crystal strains) with a width of 1.6 GHz, and a peak absorption of $\exp (-1.8)$. The lower plot shows the measurement of the homogeneous linewidth. Here, following excitation to the ${}^5{D}_1$ level, we record the fluorescence from the ${}^5{D}_0$ level to the ground $F$ manifold. The initial sharp rise in the fluorescence is due to phonon-induced relaxation from ${}^5{D}_1$ to ${}^5{D}_0$, which results in a homogeneous linewidth of $\mathrm{\Gamma }=2\pi \times 4.8\mathrm{kHz}$ (corresponding to a nonradiative lifetime of $\tau =33\mu \mathrm{s}$). The slow decay in the fluorescence is due to the radiative lifetime of the ${}^5{D}_0$ level.

Figure 3

The transmission of the probe laser beam through the crystal as the duration of the Rabi pulse is varied. We observe a clear Rabi cycle with a frequency approaching 1 MHz. The Rabi oscillation quickly dephases due to a number of processes, such as the variation of the magnetic-dipole matrix element among various hyperfine transitions. The solid line is a numerical simulation that solves the density matrix for a large number of atoms whose absolute transition frequencies are spread through the inhomogeneous profile, causing different hyperfine transitions to be resonant with the laser. The lower plot shows the inferred magnetization from the same simulations. See text for details.

Figure 4

The observed Rabi flopping frequency as the laser intensity is varied for 23 different Rabi flopping experiments. From the square-root fit to the data points (the solid line), we deduce a magnetic-dipole matrix element of $\mu =(0.063\pm 0.005){\mu }_B$. The right-hand panels show six specific flopping experiments (probe transmission versus Rabi pulse duration) as the laser intensity is varied from 5630 to $1510\mathrm{W}/{\mathrm{cm}}^2$.

Figure 5

Fluorescence from the crystal as a function of the angle of incidence for $S$-polarized [diamonds, schematic (a)] and $P$-polarized [triangles, schematic (b)] light. The fluorescence signal is normalized to take into account both the change in the Fresnel reflection losses from the surfaces and the path-length change of the beam as the crystal is rotated. The large increase in the fluorescence for $S$-polarized light (a) is due to a change of the direction of the angle of the magnetic field with the optical axes. In contrast, when the angle of the electric field is varied (b), there is negligible change in the fluorescence. This shows that during ${{}^{7}F}_0\to {{}^{5}D}_1$ excitation, light interacts with the magnetic field of light instead of the electric field.

Figure 6

The inferred real (dashed line) and imaginary (solid line) parts of the magnetic susceptibility as the laser frequency is scanned across the ${{}^{7}F}_0\to {{}^{5}D}_1$ transition. See Appendix pp7 for details.

Figure 7

Total fluorescence from the crystal as a function of the angle of incidence for light propagating along the $D_2$ axis (a), (b) and along the $b$ axis (c), (d) of the crystal. The measurements (c) and (d) suffer from low signal-to-noise ratio, but the overall trend is clear. For each propagation direction, the fluorescence depends sensitively on the direction of the magnetic field.