Inverse design of spontaneous parametric downconversion for generation of high-dimensional qudits

Abstract

Spontaneous parametric downconversion (SPDC) in quantum optics is an invaluable resource for the realization of high-dimensional qudits with spatial modes of light. One of the main open challenges is how to directly generate a desirable qudit state in the SPDC process. This problem can be addressed through advanced computational learning methods; however, due to difficulties in modeling the SPDC process by a fully differentiable algorithm, progress has been limited. Here, we overcome these limitations and introduce a physically constrained and differentiable model, validated against experimental results for shaped pump beams and structured crystals, capable of learning the relevant interaction parameters in the process. We avoid any restrictions induced by the stochastic nature of our physical model and integrate the dynamic equations governing the evolution under the SPDC Hamiltonian. We solve the inverse problem of designing a nonlinear quantum optical system that achieves the desired quantum state of downconverted photon pairs. The desired states are defined using either the second-order correlations between different spatial modes or by specifying the required density matrix. By learning nonlinear photonic crystal structures as well as different pump shapes, we successfully show how to generate maximally entangled states. Furthermore, we simulate all-optical coherent control over the generated quantum state by actively changing the profile of the pump beam. Our work can be useful for applications such as novel designs of high-dimensional quantum key distribution and quantum information processing protocols. In addition, our method can be readily applied for controlling other degrees of freedom of light in the SPDC process, such as spectral and temporal properties, and may even be used in condensed-matter systems having a similar interaction Hamiltonian.

Direct generation of spatially entangled qudits using quantum nonlinear optical holography

“…The simulation tool is nonperturbative and accounts for diffraction. It assumes the undepleted pump approximation and paraxial propagation dynamics ( 31 , 42 ). For the HG 10 nonlinear hologram, both the measured and simulated coefficients form a maximally entangled Bell state.…”

“…The binary modulation of the nonlinearity can be shaped in an arbitrary manner, in contrast to pump beams that must satisfy the Helmholtz equation. This enables the design of structures with a modulation pattern that varies along the propagation axis, for example, in a segmented manner, as well as cascaded patterns having different poling periods, facilitating all-optical control over the generated states ( 8 , 16 , 31 , 33 ). These segments may use various degrees of freedom: (i) Different phases between each segment will enable coherent destructive or constructive interference between states generated in a consecutive manner.…”

“…These external shaping methods have since been the main driving force behind high-dimensional quantum state engineering. To this day, while theoretically proposed by a number of works (31)(32)(33)(34), the crystal degree of freedom was not demonstrated experimentally for spatial encoding of quantum light.…”

Partial Bell-State Measurement with Type-II Parametric Down Conversion: Extracting Phase Information from the Zeropoint Field (I)

“…Type-II PDC is widely used as a source of entangled states in optical experiments for testing Bell inequalities [ 7 , 8 , 9 , 10 , 11 , 12 ] and the implementation of quantum communication schemes [ 13 , 14 , 15 , 16 , 17 , 18 ]. A monochromatic pumping laser impinges on one side of a nonlinear crystal, giving rise to pairs of conjugated beams with orthogonal polarisations.…”

Highly Efficient 3D Nonlinear Photonic Crystals in Ferroelectrics

“…[ 14–16 ] They also have great potentials for generations of high dimensional entangled states in the spatial basis and for the exploration of optical analogues of spin dynamics in magnetization textures, such as the topological Hall effect. [ 17–19 ]…”