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Optics Express

All-optical Stern-Gerlach effect in the time domain

Gil Bashan, Avishay Eyal, Moshe Tur, Ady Arie

Published Feb 12, 2024• 4 citations
Publisher

Abstract

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.

DOI
10.1364/oe.510722

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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.
Multi-color photons are prominent candidates for carrying quantum information, as their unlimited dimensionality allows for novel qudit-based schemes. The generation and manipulation of such photons takes place in nonlinear optical media, and the coupling between the different frequency bins can be engineered to obtain the desired quantum state. Here, we propose the design of a frequency-domain Stern–Gerlach effect for photons, where quantum entanglement between the spatial and spectral degrees of freedom is manifested. In this scheme, orthogonal frequency-superposition states can be spatially separated, resulting in a direct projection of an input state onto the frequency-superposition basis. We analyze this phenomenon for two-color qubits and three-color qutrits, and present a generalized wavelength-domain analog of the Hong–Ou–Mandel interference with distinguishable photons. Our results pave the way toward realization of single-element, all-optically controlled spectral-to-spatial beam splitters and tritters that can benefit quantum information processing in the frequency domain.
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.
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.
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.