Frequency-Time Multiplexing for Near-Deterministic Generation of n-Photon Frequency-Bin States

Abstract

One of the primary challenges of photonic quantum information processing is the on-demand preparation of multiple single-photon-level quantum states from probabilistic photon pair sources. Motivated by recent developments in frequency-bin-encoded photonic quantum information processing, here we consider active time multiplexing to generate n-photon states, where n single photons with n distinct frequencies occupy the same spatiotemporal mode. We devise an approach that uses optical quantum memories to manipulate the temporal mode of heralded single photons and an array of fiber Bragg grating reflectors to jointly manipulate the frequency and temporal modes of the photons, overlapping n photons in n separate frequency bins into a single spatiotemporal mode. We calculate multiphoton state generation rates that, accounting for loss, are realistically achievable with commercially available hardware. Using only a single free-space switchable delay loop for an optical quantum memory, this scheme could feasibly produce 8-photon states at an average rate of 1 kHz.

Figures (4)

• Figure 1: Schematic of our multiplexing scheme. A photon pair source (PPS) pumped with a pulsed laser produces signal-idler photon pairs in discrete frequency and time bins. Time bins have length $t$. Measuring the signal photons heralds the existence of idler photons in known, random frequency and time bins. An example frequency and time diagram is shown in (a). Bold lines delineate batches of $m$ time bins. The optical quantum memory is shown here as a switchable free-space optical delay. A free-space loop defined by mirrors (M) gets light switched in and out of it with polarizing beamsplitters (PBS) and a Pockels Cell (PC). It delays selected photons such that each batch, corresponding to one frequency bin, has a photon in the last time bin of the batch [see (b)]. Fiber Bragg grating (FBG) reflectors spaced by $T/2=mt/2$ align photons in each frequency bin into the same time bin [see (c)]. A circulator (C) redirects the photons reflected from the FBGs to an output port.
• Figure 2: $n$-photon generation rates. (a) $n$-photon generation rates, with (dashed) and without (solid) loss, with and without (dotted) multiplexing. We show both dimensionless rates that are the expected number of multiphoton events per time bin (left axis), and dimensionful rates that assume a 10 ns time bin length (right axis). (b) Maximum $n$-photon generation rates, with and without accounting for loss, with and without multiplexing, as a function of number of photons to generate.
• Figure 3: Ratio of $n$-photon generation rates with our multiplexing scheme versus without multiplexing. Here we assume 100-, 10-, and 1-timestep length storage loops, to enable storing light for hundreds of timesteps without high loss. For each photon number $n\in\{4,6,8\}$, we show the ratio of the rate at the choice of number of time bins per batch $m$ with maximal rate, to the rate without multiplexing $p^n$, as a function of the probability of generating a photon per frequency-time bin $p$.
• Figure 4: Multiphoton state generation rate for the $n$-photon, $2n$ frequency bins setting, and for the standard $n$-photon, $n$ frequency bins setting.