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The All-Optical Stern-Gerlach Effect in Space and in Time

Ady Arie

Published Jan 1, 2024• 0 citations
Publisher

Abstract

Lightwaves can be split into two beams or two pulses, each comprising a frequency-bin superposition, in the presence of a nonlinear coupling gradient, representing the nonlinear optics analog of the celebrated Stern-Gerlach effect for atoms.
DOI
10.1364/cleo_si.2024.sth3p.5

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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.
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.
In the optical Stern-Gerlach effect the interaction of a two-level atom with an optical-field gradient causes a state-selective deflection that leads to a splitting of the atomic trajectory. The semiclassical approach to this problem actually predicts a splitting of the atomic beam into two paths, similar to the well-known magnetic Stern-Gerlach effect for spin 1/2. Here we study a model in which the quantum nature of the field is taken into account and we show, in particular, that for an initial coherent state of the cavity light the optical Stern-Gerlach effect manifests itself as a splitting of the atomic beam into two groups containing, however, many spots. \textcopyright{} 1996 The American Physical Society.