Switchable detector array scheme to reduce the effect of single-photon detector’s deadtime in a multi-bit/photon quantum link

Abstract

We explore the use of a switchable single-photon detector (SPD) array scheme to reduce the effect of a detector’s deadtime for a multi-bit/photon quantum link. The case of data encoding using $\mathrm{M}$ possible orbital-angular-momentum (OAM) states is specifically studied in this paper. Our method uses $N$ SPDs with a controllable $M\times N$ optical switch and we use a Monte Carlo-based method to simulate the quantum detection process. The simulation results show that with the use of the switchable SPD array, the detection system can allow a higher incident photon rate than what might otherwise be limited by detectors’ deadtime. For the case of $M=4$, $N=20$, a 50-ns deadtime for the individual SPDs, an average photon number per pulse of 0.1, and under the limit that at most 10 % of the photon-containing pulses are missed, the switchable SPD array will allow an incident photon rate of 2250 million counts/s (Mcts/s). This is 25 times the 90 Mcts/s incident photon rate that a non-switchable, 4-SPD array will allow. The increase in incident photon rate is more than the 5 times increase, which is the simple increase in the number of SPDs and the number of OAM encoding states (e.g., $N∕M=20∕4$).

Introduction

Quantum information systems have the ability to protect the information channels against eavesdropping [1], [2]. This security is derived from the quantum non-cloning theorem that any eavesdropping made by a third party would inevitably leads to errors that can be detected by the sending and receiving parties [3], [4]. Typical qubits encoding on photon’s two polarizations can provide one bit/photon of information [5], [6]. However, since each photon has only two orthogonal polarizations, quantum system capacity might be increased if a basis set having more than two orthogonal states is used for data encoding. One example may be through the use of a set of orthogonal spatial modes, for which the photon can occupy one of the many states at a given time [7]. A potential spatial basis set that has recently received increasing interest is the orbital-angular-momentum (OAM) mode set, which is a subset of Laguerre Gaussian (LG) modes [8], [9], [10], [11], [12], [13], [14].

A light beam’s phasefront that has an azimuthal ($\varphi$) dependence of $exp\left(i\mathcal{l}\varphi \right)$ will “twist” in a helical fashion as it propagates. Such a beam carries OAM corresponding to $\mathcal{l}\hslash$ per photon, in which the OAM charge $\mathcal{l}$ represents the number of $2\pi$ phase shifts in the azimuthal direction. An OAM beam will be orthogonal to other OAM beams depending on its $\mathcal{l}$ value. Since a single photon can carry a distinct OAM charge, photons can be encoded on more orthogonal OAM states than those provided by polarization states [15], [16], [17], [18]. Typically, a quantum system encoded in $M$ OAM states $(M=1,2,3,\dots )$ of photons could transmit up to ${log}_{2}M$ quantum bits per photon [14].

A key limitation for the incident photon rate in a quantum system is the deadtime of a single photon detector (SPD). This deadtime is defined as the length of time that the detector must recover after “firing” from one detected photon before it is ready to detect and accurately register another incoming photon. This limitation on incident photon rate would be present to a larger or smaller extent depending on the deadtime of different SPDs. In typical avalanche photodiode (APD) based SPDs, the deadtime ranges from $\sim$50 ns for actively quenched APDs to $\sim$ $10\mathrm{\mu }\mathrm{s}$ for passively quenched ones [19]. Gated APD based SPDs have the potential to be operated at higher incident photon rate because their deadtimes only exist in some of the clock cycles [20]. Some free-running superconducting single-photon detectors could also achieve a shorter deadtime (about tens of picosecond) with a reduced dark count rate than the APD-based SPDs [21], [22], [23].

For two-polarization-state quantum encoding systems, the deadtime limitation on the incident photon rate of SPDs could be reduced by using a switchable detection scheme [19], [24]. In this approach, more SPDs are used in the receiver than are strictly necessary, and a controllable optical switch routes an incoming photon away from an SPD that is still within its deadtime to a “fresh” SPD.

Previous reports have shown that a switchable SPD array with $N$ SPDs can potentially operate at more than $N$ times the incident photon rate that a single SPD can achieve for a single quantum channel [19], [24]; we note that this result was for a goal of missing no more than 10% of photon-containing incident pulses, which could be considered as a limit for some quantum detection applications. In addition, they show that a switchable $N$-SPD array can potentially operate at a higher incident photon rate than that of a single SPD that has a deadtime reduced to $1∕N$.

In this paper, we extend the previous work using SPD arrays in polarization-encoded quantum systems to investigate the use of a switchable SPD array in a multi-bit/photon quantum link where bits are encoded on $M$ OAM states. Our method uses $N$ SPDs with a controllable $M\times N$ optical switch to route the incoming photon from an SPD within its deadtime to a fresh active SPD awaiting a new photon. Our Monte Carlo-based simulation results show that the switchable SPD array scheme with $N$ SPDs could operate at an increased incident photon rate under the same deadtime when the same detection limitation is applied. For the case of $M=4$, $N=20$, the SPDs’ individual deadtime of 50 ns, an average photon number per pulse of 0.1, and under the limitation that missing at most 10% of the photon-containing pulses, the switchable SPD array can operate at an incident photon rate of 2250 million counts/s (Mcts/s). This is 25 times the 90 Mcts/s incident photon rate that a non-switchable, 4-SPD array will allow. The increase in incident photon rate is more than the 5 times, which is the simple increase in the number of SPDs ($N$) over the number of OAM encoding states ($M$).