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Optica

Frequency domain Stern–Gerlach effect for photonic qubits and qutrits

Aviv Karnieli, Ady Arie

Published Oct 15, 2018• 37 citations
Publisher

Abstract

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.

DOI
10.1364/optica.5.001297

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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.
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.
In the original formulation of the Hong–Ou–Mandel (HOM) experiment, when two otherwise indistinguishable photons are incident upon the two input ports of a balanced beam splitter, they coalesce, always leaving via the same output port. It is often interpreted that this interference arises due to the indistinguishability of the single photons at the beam splitter; the situation, however, is often more nuanced. Here, we demonstrate an analog of HOM interference between two photons of completely different color. To do so, we utilize a quantum frequency converter based on sum- and difference-frequency generation as an “active” beam splitter—coupling frequency-entangled red and telecom single photons with an octave-spanning energy difference of 282 THz. We achieve an uncorrected two-photon interference visibility beyond 90%. This work presents the first demonstration of HOM interference between two single photons of distinctly different color, deepening our understanding of what underlies quantum interference. It also suggests a novel approach to interfacing photonic qubits in heterogeneous quantum systems where frequency conversion and quantum interference are unified.
In this paper, we propose a novel method for interfering frequency-multiplexed photonic quantum states without the use of optical nonlinear effects, and experimentally demonstrate this technique via frequency-domain Hong-Ou-Mandel (HOM) interference. By cascading the generation of quantum states onto arbitrary orthogonal modes, we can induce interference across any desired frequency mode. Following the generation of quantum states onto the frequency modes, performing measurements in independent frequency bands enables the realisation of a frequency-domain linear optical circuit analogous to linear interference in the spatial domain. We successfully demonstrated programmable quantum interference by controlling the spectral mode functions and measurement bases. Our method offers a new approach to harness the full potential of light's temporal-frequency degrees of freedom, providing a path towards scalable and programmable photonic quantum computing architectures without the need for optical nonlinearities or spatial-mode beam splitters.
The frequency degree-of-freedom, being compatible with well-developed omnipresent optical telecommunication infrastructure, allows for stable, controllable and scalable encoding of quantum information [1] . The HOM effect between independent photons, as a central building block to, e.g., quantum key distribution (QKD), quantum teleportation and entanglement swapping, has been mainly employed within the spatial domain [2] . A key element yet missing to enable scalable and thus real-world frequency-based implementation of quantum computation and non-classical communication, is the demonstration of Hong-Ou-Mandel (HOM) interference between independently created photons of different frequencies. To date, spectral bosonic HOM interference between single photons, produced out of the same continuous-wave (cw)-excited spontaneous parametric down conversion (SPDC) process has been demonstrated [3] , which however does not allow scalability due to the spectral impurity inherent to the proposed approach.
Frequency modes of light are one of the most promising platforms that provide access to high-dimensional quantum states amongst different photonic degrees of freedom capable of high-dimensionality, enabling robust, error-tolerant, and scalable quantum optical information systems. We demonstrate engineering of precisely controlled two-photon high-dimensional states entangled in frequency through time-domain Fourier optical synthesis. We generate and convert a continuous broadband frequency-entangled state into a large range of discrete frequency bins suitable for ITU standards, with spacings ranging from 12.5 GHz to 750 GHz, and observe spectral anticorrelations over 38 frequency bins, including intra-bin pure states at a 100 GHz bin spacing. We characterize the full quantum state dimensionality via Schmidt decomposition and observe lower bounds on the frequency-binned Hilbert-space dimensionalities of at least 289, formed by two entangled qudits with dimension 17. Furthermore, we demonstrate quantum nonlocality via frequency correlations in a transmission experiment over a campus-scale two-node fiber network. This work represents a crucial step towards building a versatile and relatively simple way of generating precisely controlled high-dimensional spectral qudits, with the potential of harnessing in wavelength-multiplexed quantum networks, high-dimensional information processing, and communication of quantum states specifically, and fiber-optic quantum remote sensing.