Frequency domain Stern–Gerlach effect for photonic qubits and qutrits

Aviv Karnieli,Ady Arie

doi:10.1364/optica.5.001297

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.

Highlights

Nonlinear optical processes are widely used as platforms for the generation and manipulation of non-classical states of light
As with the qubit case, this spatial separation of orthogonal eigenstates might prove beneficial to quantum information processing using frequency domain qutrits [24,25,26]
We have shown that paraxial photons propagating in specially engineered nonlinear media exhibit the properties of 2D

Summary

INTRODUCTION

Nonlinear optical processes are widely used as platforms for the generation and manipulation of non-classical states of light. In spite of the growing advancements in this field, quantum effects incorporating the spatial degree of freedom, in a manner that allows for a spatially separated projection on frequency-basis eigenstates, have been rarely explored to date These spectral-to-spatial beam splitters are expected to benefit scalability, when higher dimensional qudits are concerned, since they do not rely on additional optical elements such as frequency converters, waveplates, and dichroic prisms. Massive particles carrying internal angular momenta (either spin or orbital) These photons can interact with an external effective field, the components of which are given by the external optical pump fields coupling the different frequencies. We propose an analogous Stern–Gerlach (SG) effect for photons, which has been recently described for classical light [11] Such an effect allows for the spatial separation of orthogonal frequency-superposition states, thereby realizing a projection of the quantum state on a different basis otherwise inaccessible within a single nonlinear interaction. The effect proposed allows for a realization, using a single optical element, of spectral-to-spatial beam splitters and tritters, all-optically controlled by the pump field, with applications to quantum information processing in the frequency domain

SG EFFECT FOR PHOTONIC QUBITS

H SFG d r

QUTRIT CASE

CONCLUSIONS