Quantum mechanical Stern–Gerlach (SG)-like effects are unusual to explore in the domain of optics due to the absence of any interaction of photons or optical waves with the conventional magnetic field. A few recent investigations point toward the possibility of observing an SG-like effect in nonlinear optics via wedge-shaped poling in a long lithium niobate (LN) crystal to generate a spatially varying analogous magnetic field ( B → A ). This leads to two different propagation directions for the mutually orthogonal states formed by superposition of signal and idler modes (states) with opposite phases. In this work, we present theoretical formalism to show an equivalent SG-like splitting in a frequency downconversion process and experimentally validate the assertion by producing a suitable transverse gradient in B → A through an in-homogeneous pump wavefront. The experimental results show SG-like splitting in an optical parametric generation (OPG) process using a widely used periodically poled LN (PPLN) crystal and a pump laser exhibiting a suitable spatial beam profile. The experimentally measured deviation angle for the mutual beam closely matches with the prediction from theoretical formalism using a Gaussian pump wavefront.
Quantum mechanical Stern–Gerlach (SG)-like effects are unusual to explore in the domain of optics due to the absence of any interaction of photons or optical waves with the conventional magnetic field. A few recent investigations point toward the possibility of observing an SG-like effect in nonlinear optics via wedge-shaped poling in a long lithium niobate (LN) crystal to generate a spatially varying analogous magnetic field ( B → A ). This leads to two different propagation directions for the mutually orthogonal states formed by superposition of signal and idler modes (states) with opposite phases. In this work, we present theoretical formalism to show an equivalent SG-like splitting in a frequency downconversion process and experimentally validate the assertion by producing a suitable transverse gradient in B → A through an in-homogeneous pump wavefront. The experimental results show SG-like splitting in an optical parametric generation (OPG) process using a widely used periodically poled LN (PPLN) crystal and a pump laser exhibiting a suitable spatial beam profile. The experimentally measured deviation angle for the mutual beam closely matches with the prediction from theoretical formalism using a Gaussian pump wavefront.
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.
The Stern-Gerlach experiment, a seminal quantum physics experiment, demonstrated the intriguing phenomenon of particle spin quantization, leading to applications in matter-wave interferometry and weak-value measurements. Over the years, several optical experiments have exhibited similar behavior to the Stern-Gerlach experiment, revealing splitting in both spatial and angular domains. Here we show, theoretically and experimentally, that the Stern-Gerlach effect can be extended into the time and frequency domains. By harnessing Kerr nonlinearity in optical fibers, we couple signal and idler pulses using two pump pulses, resulting in the emergence of two distinct eigenstates whereby the signal and idler are either in phase or out of phase. This nonlinear coupling emulates a synthetic magnetization, and by varying it linearly in time, one eigenstate deflects towards a higher frequency, while the other deflects towards a lower frequency. This effect can be utilized to realize an all-optical, phase-sensitive frequency beam splitter, establishing a new paradigm for classical and quantum data processing of frequency-bin superposition states.
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.
The Stern-Gerlach (SG) effect, discovered almost a century ago, has become a paradigm of quantum mechanics. Surprisingly there is little evidence that the original scheme with freely propagating atoms exposed to gradients from macroscopic magnets is a fully coherent quantum process. Specifically, no high-visibility spatial interference pattern has been observed with such a scheme, and furthermore no full-loop SG interferometer has been realized with the scheme as envisioned decades ago. On the contrary, numerous theoretical studies explained why it is a near impossible endeavor. Here we demonstrate for the first time both a high-visibility spatial SG interference pattern and a full-loop SG interferometer, based on an accurate magnetic field, originating from an atom chip, that ensures coherent operation within strict constraints described by previous theoretical analyses. This also allows us to observe the gradual emergence of time-irreversibility as the splitting is increased. Finally, achieving this high level of control over magnetic gradients may facilitate technological applications such as large-momentum-transfer beam splitting for metrology with atom interferometry, ultra-sensitive probing of electron transport down to shot-noise and squeezed currents, as well as nuclear magnetic resonance and compact accelerators.
The Stern-Gerlach (SG) experiment reported in 1922 was an important milestone in the history of physics. The passing of a collimated neutral beam of silver atoms through a long, strong and asymmetrical magnet caused the atoms of silver out of a horizontal slit to split roughly into two separate beams forming a hollow lip figure (as seen on a plate held normal to the beam) instead of being a filled-in lip figure as suggested by some theoretical calculations. The SG results were thought to indicate that the observed phenomenon can not be explained using classical physics. Following a classical numerical approach by the author using a double-slit geometry, results are given for a 3D numerical SG type experiment showing clearly that a binary beam splitting is possible for certain conditions using an inverse square relation as the only source of forces- thus giving the possibility of a classical interpretation to the problem. For simplicity, we use what is mathematically equivalent- a dipole of charges to represent the magnetic dipole of the atom, and sets of fixed charges or potential surfaces around the path of the beam to represent the poles of a magnet. Although not exactly following the SG setup, the present results, nonetheless, are useful in showing the clear discrete behavior that can be caused by the combination of a fixed boundary, a strong field asymmetry and the highly nonlinear mapping of the inverse square law of forces coupled with the spin direction of a particle.
Nonlinear crystals are typically used when interaction of different frequencies of light is requested. In classical optics these nonlinear phenomena are used for second-harmonic generation, sum-frequency generation, optical parametric amplification and many other effects. In quantum optics, dealing with optical interaction on the level of individual photons, the most prominent process is spontaneous parametric down-conversion (SPDC),1 where the crystal is pumped by intensive laser light and the crystal can mediate the splitting of a pump photon to a photon pair. The two generated photons are typically called signal and idler. Influence of magnetic field on these nonlinear processes was not thoroughly tested yet. This topic deserves intensive study both from theoretical and experimental point of view, because the magnetic field can decrease the symmetry of the nonlinear crystal and so it may allow to use new types of phase-matching conditions. We started to test the SPDC process in BBO crystals. Nonlinear magneto-optic tensor of this material is not known and we can hardly predict it. According to our first theoretical derivations the efficiency of the nonlinear processes has to oscillate when rotating the magnetic-field orientation.