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arXiv:0802.0333 · Physical Review A

Magneto-optical Stern-Gerlach effect in an atomic ensemble

Yu Guo, Lan Zhou, Le‐Man Kuang, C. P. Sun

Published Jul 23, 2008• 46 citations
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Abstract

We study the birefringence of quantized polarized light in a magneto-optically manipulated atomic ensemble as a generalized Stern-Gerlach effect of light. To explain this engineered birefringence microscopically, we derive an effective Shr\"odinger equation for the spatial motion of two orthogonally polarized components, which behave as a spin with an effective magnetic moment leading to a Stern-Gerlach split in a nonuniform magnetic field. We show that the electromagnetically-induced-transparency mechanism can enhance the magneto-optical Stern-Gerlach effect of light in the presence of a control field with a transverse spatial profile and a nonuniform magnetic field.

DOI
10.1103/physreva.78.013833

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We study the birefringence of quantized polarized light in a magneto-optically manipulated atomic ensemble as a generalized Stern-Gerlach effect of light. To explain this engineered birefringence microscopically, we derive an effective Shr"odinger equation for the spatial motion of two orthogonally polarized components, which behave as a spin with an effective magnetic moment leading to a Stern-Gerlach split in a nonuniform magnetic field. We show that the electromagnetically-induced-transparency mechanism can enhance the magneto-optical Stern-Gerlach effect of light in the presence of a control field with a transverse spatial profile and a nonuniform magnetic field.
We study the optical control for birefringence of a polarized light by an atomic ensemble with a tripod configuration, which is mediated by the electromagnetically induced transparency with a spatially inhomogeneous laser. The atomic ensemble splits the linearly polarized light ray into two orthogonally polarized components, whose polarizations depend on quantum superposition of the initial states of the atomic ensemble. Accompanied with this splitting, the atomic ensemble behaves as a birefringent lens, which allows one polarized light ray passing through straightly while focuses the other light of vertical polarization with finite aberration of focus.
Electromagnetically induced transparency allows for light transmission through dense atomic media by means of quantum interference of absorption amplitudes. Media exhibiting electromagnetically induced transparency have interesting properties, such as very slow group velocities. Associated with the slow light propagation are quasiparticles, so-called dark polaritons, which are mixtures of a photonic and an atomic contribution. Here, we demonstrate that these excitations behave as particles with a nonzero magnetic moment, which is in clear contrast to the properties of a free photon. It is found that circularily polarized light passing through a rubidium gas cell under the conditions of electromagnetically induced transparency is deflected by a small magnetic field gradient. The deflection angle is proportional to the propagation time of an optical pulse through the cell. The observed beam deflection can be understood by assuming that dark state polaritons have an effective magnetic moment. This is attributed to the spin wave contribution that develops upon entry of light into the medium. Our experiment can be described in terms of a Stern-Gerlach experiment for the dark polaritons.
We propose a scheme to exhibit Stern-Gerlach deflection of high-dimensional vector optical solitons at a weak-light level in a cold atomic gas via electromagnetically induced transparency. We show that the propagating velocity and generation power of such solitons can be reduced to ${10}^{\ensuremath{-}6}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}c$ (ccc is light speed in vacuum) and lowered to magnitude of nanowatt, respectively. The stabilization of the solitons is realized by using an optical lattice potential formed by a far-detuned laser field, and trajectories of them are deflected significantly by using a transversal Stern-Gerlach gradient magnetic field. Deflection angles of the solitons can be of magnitude of ${10}^{\ensuremath{-}3}$ rad when propagating several millimeters. Different from atomic Stern-Gerlach deflection, deflection angles of the solitons can be distinct for different polarization components and can be manipulated in a controllable way. The result obtained can be described in terms of the Stern-Gerlach effect for vector optical solitons with quasispin and effective magnetic moment.
Abstract Stern‐Gerlach (SG) effect, initially found for unveiling the existence of quantized electron spins, is now a general concept describing a state‐dependent separation. It is widely explored in optics to achieve a function of optical splitting, but the current schemes always require a polarization‐ or wavelength‐dependent process, thus showing limitations for broader applications. Here, spatial modes of an optical field are employed as another degree of freedom to demonstrate an SG effect. Two modes of a pair of coupled waveguides are found to be in analog to the electron spins. They are able to undergo a splitting upon a spatially‐dependent waveguide coupling, which plays the role of a non‐uniform magnetic field. In an experiment, such a splitting is realized in two coupled non‐parallel slab waveguides, and its strength is adjusted at ease by varying the parameters of this proposed structure. This SG‐related optical splitting may find applications in the field of optical sensing and signal processing.
We propose a scheme to realize an optical Thirring model and create temporal optical Thirring solitons in a tripod-type atomic gas via double electromagnetically induced transparency (EIT). We show that giant enhancement of the cross-phase modulation for the two polarization components of the probe pulse can be obtained under the condition of the double EIT, and hence the optical Thirring model can be realized. We also show that the system supports stable temporal optical Thirring solitons, which have ultralow generation power and ultraslow propagation velocity. In particular, these temporal optical Thirring solitons may experience a significant Stern-Gerlach deflection when a gradient magnetic field is applied to the system. The results reported here are useful not only for extending the research realm of nonlinear magneto-optics but also for the application in precision measurements, such as the detection of microgradient magnetic fields.
Abstract The Stern–Gerlach (SG) effect provided the first direct experimental evidence of the quantization of electron spin. Although some analog SG effects have been proposed in optical systems, finding a perfect optical analog for the SG effect remains a challenge. Here, a novel optical SG effect is demonstrated in periodically poled electro‐optical crystals. Induced by an applied electric field, the principal axes of crystal rock periodically along the propagation direction of light. When the quasi‐phase‐matching condition is satisfied, the electro‐optical coupling process within the periodically poled crystal can be accurately described by the Schrödinger–Pauli equation for spin‐1/2 particles. The output photons can be deflected toward opposite directions according to their intrinsic spin angular momentum (circular polarizations), since the transversely varying duty cycle of crystal arises an effective magnetic‐field gradient. Moreover, the output photons can be separated according to two arbitrary orthogonal polarization states, allowing us to construct high‐speed electro‐optically tunable polarization beam splitters for arbitrary orthogonal polarization states. Therefore, the optical SG effect provides not only a perfect optical analog for the quantum SG effect but also a useful optical element for optics and quantum physics.