Versatile engineering of multimode squeezed states by optimizing the pump spectral profile in spontaneous parametric down-conversion

Introduction We study the quantum correlations induced by spontaneous parametric down-conversion of a frequency comb and how they can be manipulated to produce useful states for quantum information tasks. We first derive a... [ view full abstract ]

Introduction

We study the quantum correlations induced by spontaneous parametric down-conversion of a frequency comb and how they can be manipulated to produce useful states for quantum information tasks.

We first derive a theoretical method to find the output state corresponding to a pump with an arbitrary spectral profile. Our interest stems from the availability of pulse shapers that can change the spectral profile with no hardware changes, thus giving rise to a versatile setup to produce entangled states of light. 

To explore the potential of the setup, we take an objective-oriented approach and run an optimization algorithm to numerically find the pump profiles maximizing some target functions. These include the number of independently squeezed modes and the variances of nullifiers defining cluster states used in many continuous-variable quantum information protocols. We take into account the physical limitations of the pulse-shaper, so that our results are readily applicable to experiments using existing technology.

Results

As an example, we apply the method to concentrate or flatten the distribution of squeezing factors. This turns out to be useful for the optical realization of complex quantum networks [2].

We then turn to the optimization of a four-modes cluster state whose nodes correspond to frequency bands modes (frexels). Figure lin4frexels shows (a) the four frexels π_j and (b) two possible ways of assigning them to the nodes of a four-modes cluster. Figure NullsOptResults shows the results of the optimization of the pump spectral profile to reduce the average noise of the nullifiers of a four-modes linear cluster. (a) shows the nullifiers’ noise reduction in dB for a Gaussian pump and for the optimal profiles found optimizing the pump shape without constraints (f₃) and with a constraint hindering the convergence to pulses with a low overlap with the original Gaussian (\bar{f}₃). The bar on the left of each triplet (dark blue) corresponds to the Gaussian case, the central bar (dark green) to \bar{f}₃ , the bar on the right (light green) to f₃ . The horizontal lines show the average squeezing in each case (The Gaussian case, f₃ and \bar{f}₃ correspond to the top, middle and bottom lines, respectively). The pump profiles optimizing f₃ and \bar{f}₃ are shown in (b) and (c) respectively. The scale on the left refers to amplitude, the right one to phase.

[1] F. Arzani et al, PhysicalReviewA 97, 033808 (2018)

[2] J. Nokkala et al, NewJournalOfPhysics 20 (5), 053024 (2018)