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Frequency Multiplexing for Quasi-Deterministic Heralded Single-Photon Sources

Chaitali Joshi, Alessandro Farsi, Stéphane Clemmen, Sven Ramelow, Alexander L. Gaeta

arXiv:1707.00048v2quant-phphysics.optics

TL;DR

Parametric single-photon sources operate probabilistically because of multi-photon generation, and spatial or temporal multiplexing incurs increasing switching losses as modes are added. This paper uses Bragg scattering four-wave mixing for frequency multiplexing and demonstrates three modes, reporting 46 kHz generation and g(2)(0) of 0.07.

  • Problem

    Multi-photon generation makes parametric single-photon sources probabilistic, limiting their use for deterministic photon generation.

    Source: §I · p. 2

  • Method

    The paper uses Bragg scattering four-wave mixing for frequency translation and multiplexes photons across frequency modes with switching loss independent of mode count.

    Source: §I · p. 3, §V · p. 10

  • Results

    46 kHz multiplexed-photon generation was reported, with g(2)(0) of 0.07.

    Source: §I · p. 3

  • Takeaways & Limitations

    The three-mode demonstration shows frequency multiplexing with fixed loss as a route toward scaling to more frequency modes.

    Source: §V · p. 10

Abstract

from arXiv · show

Single-photon sources based on optical parametric processes have been used extensively for quantum information applications due to their flexibility, room-temperature operation and potential for photonic integration. However, the intrinsically probabilistic nature of these sources is a major limitation for realizing large-scale quantum networks. Active feedforward switching of photons from multiple probabilistic sources is a promising approach that can be used to build a deterministic source. However, previous implementations of this approach that utilize spatial and/or temporal multiplexing suffer from rapidly increasing switching losses when scaled to a large number of modes. Here, we break this limitation via frequency multiplexing in which the switching losses remain fixed irrespective of the number of modes. We use the third-order nonlinear process of Bragg scattering four-wave mixing as an efficient ultra-low noise frequency switch and demonstrate multiplexing of three frequency modes. We achieve a record generation rate of $4.6\times10^4$ multiplexed photons per second with an ultra-low $g^{2}(0)$ = 0.07, indicating high single-photon purity. Our scalable, all-fiber multiplexing system has a total loss of just 1.3 dB independent of the number of multiplexed modes, such that the 4.8 dB enhancement from multiplexing three frequency modes markedly overcomes switching loss. Our approach offers a highly promising path to creating a deterministic photon source that can be integrated on a chip-based platform.

I. INTRODUCTION

Parametric sources are limited by probabilistic multi-photon generation, while spatial and temporal multiplexing incur increasing switching losses as mode count grows. The introduction presents frequency multiplexing as a fixed-loss alternative and reports a three-mode demonstration.

I. INTRODUCTION

  • Parametric sources are fundamentally limited by multi-photon generation, making operation probabilistic and limiting a single source's maximum heralding efficiency to 25%.The introduction identifies increasing switching losses in spatial and temporal multiplexing as a further obstacle to scaling beyond a few modes.Source: §I · pp. 2–3
  • Frequency multiplexing keeps switching losses fixed as the number of modes increases, unlike spatial and temporal schemes whose losses rise with mode count.It performs multiple switching operations in one spatial mode, implementing an N × 1 switch in a fiber or waveguide.Source: §I · p. 3
  • Bragg scattering four-wave mixing provides tunable, close-to-unity-efficiency, ultra-low-noise quantum frequency translation for switching between frequency channels.The introduction reports tunable conversion over more than 1 THz, with a 100 GHz acceptance bandwidth and few-nanosecond pump pulses.Source: §I · pp. 3–4
  • The demonstration multiplexes three frequency modes in an all-fiber setup using low-loss off-the-shelf dense wavelength division multiplexing components.The paper also presents theoretical analysis of scaling performance for large mode counts.Source: §I · p. 3
  • 46 kHz multiplexed-photon generation was achieved, with a coincidences-to-accidentals ratio exceeding 100 and g(2)(0) of 0.07.The setup is described as low-loss and low-noise.Source: §I · p. 3

II. PRINCIPLE AND THEORY:

The scheme uses heralding information to frequency-convert signal photons from multiple channels to a common target, with BS-FWM providing a single-spatial-mode switch. Its fixed switching loss supports better modeled scaling than spatial and temporal switching networks as mode count grows.

II. PRINCIPLE AND THEORY:

  • Heralding identifies the signal photon’s frequency, and tunable conversion routes it from its frequency bin to the common target channel.Source: §II · p. 4
  • BS-FWM uses two strong classical pumps and is theoretically noiseless, preserving translated photons’ quantum properties while allowing independent input and target frequency control.Auxiliary pumps are selectively activated to choose the target frequency.Source: §II · p. 4
  • Efficient conversion requires each channel bandwidth to be below the BS-FWM acceptance bandwidth; its repetition rate is limited by 1/∆νBS.Source: §II · p. 4
  • All frequency switching occurs in one spatial mode, and adding channels requires only additional BS-FWM pumps, introducing no scaling losses in the single-photon path.Source: §II · p. 5
  • Log-tree switching losses scale as ηs^⌈log2 N⌉ and multi-pass losses as ηs^N, while the fixed-loss scheme remains at ηs irrespective of N.The passage describes multi-pass scaling in the worst case and notes an optimized implementation.Source: §II · p. 5
  • At N = 10, fixed-loss switching gives a heralding probability of 0.60, while log-tree and multi-pass schemes peak at 0.41 and 0.50 and saturate below 10 modes.Source: §II · p. 5
  • At N = 40, fixed-loss switching achieves pmux(n = 1) = 0.75, compared with 0.89 for an ideal no-loss network.The ideal comparison is for a no-loss switching network.Source: §II · p. 5
  • At N = 30 and ηs = 0.75, single-photon probability is 0.65 for fixed-loss switching versus 0.21 for log-tree and 0.29 for multi-pass switching.The comparison is for a moderate increase in switching loss to 1.2 dB per switch.Source: §II · pp. 5–6

III. EXPERIMENTAL SETUP

The experiment uses a three-channel heralded source and a fiber-based BS-FWM setup to convert signal photons to a shared target frequency. Both measured conversion paths achieve 93% efficiency.

III. EXPERIMENTAL SETUP

  • Broadband SPDC in a PPLN crystal produces photon pairs at 940 nm and 1280 nm, with heralding photons separated into three 100-GHz channels.Source: §III · p. 6
  • The three signal frequencies enter a setup built around 100 m of nonlinear fiber, WDM couplers, and a pump filter, with 1.3 dB total multiplexing-system loss.A tunable grating selects the 100-GHz target channel for detection.Source: §III · pp. 6–7
  • Conversion efficiency is 93% for both ω1 → ωt and ω2 → ωt.Source: §III · p. 6

Heralded single-photon rate

Frequency multiplexing increases the heralded photon rate over the individual channels while retaining a reported generation rate of 46 kHz after detector-efficiency correction. The measured rate enhancement exceeds the multiplexing setup’s loss.

Heralded single-photon rate

  • The multiplexed source’s coincidence rate is enhanced by 4.8 dB over the mean individual-channel rate, yielding a net heralded single-photon rate enhancement of 3.5 dB (220%) after 1.3 dB setup loss.Source: Heralded single-photon rate · p. 7
  • At maximum SPDC pump power of 25 mW, the source has a 1 MHz heralding rate and 23 kHz detected coincidences per second.Source: Heralded single-photon rate · p. 7
  • 46 kHz is the estimated single-photon generation rate after correcting for detector efficiency, the highest reported rate for multiplexed photon sources to date.Source: Heralded single-photon rate · p. 7
  • Increasing SPDC pump power can raise a single source’s generation rate but also increases multiphoton generation.Source: Heralded single-photon rate · p. 7

Coincidences-to-accidentals ratio (CAR)

The multiplexed source has a higher coincidences-to-accidentals ratio (CAR) than the NoMUX source and maintains high CAR at its maximum count rate. The measurements are consistent with little spurious noise from the BS-FWM pumps.

Coincidences-to-accidentals ratio (CAR)

Single-photon purity (g(2)(0))

The three-mode frequency-multiplexed source combines a 46 kHz generation rate with low measured g^2(0), while its low-loss switch supports a 2.2 multiplexing enhancement. The section also reports heralding efficiency, pump-power, and switching-speed measurements that qualify the source's performance.

Single-photon purity (g(2)(0))

  • At a 2.5 kHz heralded photon rate, the multiplexed and NoMUX sources have g^2(0) values of 0.015 ± 0.002 and 0.056 ± 0.005, respectively.At the maximum heralded photon rate, the multiplexed source has g^2(0)=0.07 ± 0.005.Source: Single-photon purity (g(2)(0)) · p. 8
  • The average SPDC pump power required for the same photon rate is a factor of 3 lower for the multiplexed source than for the NoMUX source.Source: Single-photon purity (g(2)(0)) · p. 8
  • 46 kHz generation rate with g^2(0)=0.07 versus 19.3 kHz and 0.48, alongside a 2.2 enhancement using three frequency modes and 1.3 dB switching loss.The reported rates and correlation values compare this source with the temporal-multiplexing result in.Source: Single-photon purity (g(2)(0)) · p. 8
  • 2.3% raw and 4.6% detector-corrected heralding efficiencies are reported, the latter highest among demonstrated fiber-based and integrated multiplexed systems.Source: Single-photon purity (g(2)(0)) · p. 8
  • The 4.6% heralding efficiency is mainly limited by fiber-collection and spectral-filtering losses at the SPDC source, independently of frequency switching.Collection efficiencies as high as 90% are described as achievable with reduced transmission and filtering losses and careful mode-matching.Source: Single-photon purity (g(2)(0)) · p. 9
  • The switch's conversion rate could in principle approach the inverse of its 100 GHz acceptance bandwidth, while the current system supports 5 MHz and is limited by BS-FWM pump amplification.The amplification requirement could be reduced by increasing interaction length or using highly nonlinear fibers, enabling higher repetition rates.Source: Single-photon purity (g(2)(0)) · p. 9

Pulsed operation and scaling

Pulsed operation is necessary to obtain photons in well-defined temporal modes. The paper reports that frequency-switch efficiency and projected scaling depend on triggering and pump-amplification constraints.

Pulsed operation and scaling

  • Pulsed operation is necessary to obtain photons in well-defined temporal modes, and cavity-based sources with matched pump and cavity linewidths can generate discrete uncorrelated joint spectral amplitudes.The system is described as capable of approaching deterministic generation in pure spectral and temporal modes.Source: Pulsed operation and scaling · p. 9
  • 93% frequency-switch efficiency is partly limited by BS-FWM pump-power fluctuations from randomized triggering under CW source operation, while periodic pump triggering yields up to 97%.Source: Pulsed operation and scaling · p. 9
  • With 10 frequency modes, the system is projected to exceed 50% single-photon heralding probability per input pump pulse at a 2.5 MHz generation rate.The existing fiber setup can incorporate up to 10 modes without decreased frequency-conversion efficiency.Source: Pulsed operation and scaling · p. 9

V. DISCUSSION

The demonstrated three-mode source uses low-noise frequency translation in a single spatial mode, keeping losses independent of the number of modes. The discussion points to fiber and integrated implementations as routes for scaling frequency multiplexing.

V. DISCUSSION

  • The three-mode frequency-multiplexed source uses highly efficient, low-noise quantum frequency translation, with added channels increasing BS-FWM pump-configuration complexity but not adding components to the single-photon path.This keeps losses independent of the number of multiplexed modes.Source: §V · p. 10
  • Single-spatial-mode frequency switching maintains relative polarization stability across channels, rendering photons indistinguishable after frequency translation.Source: §V · p. 10
  • The scheme is adaptable to CMOS-compatible integrated platforms; integrated comb sources could remove filtering needs while generating spectrally pure photons.BS-FWM in nanophotonic waveguides could significantly reduce pump-power and amplification requirements.Source: §V · p. 10
  • Frequency multiplexing can harness fiber and integrated technologies optimized for classical applications to address scalability challenges in quantum technologies.The discussion also notes potential value for all-photonic quantum repeaters using active feed-forward heralding signals.Source: §V · p. 10

I. BRAGG SCATTERING FOUR-WAVE MIXING

This section characterizes BS-FWM as a tunable frequency converter and examines frequency-multiplexed source performance, including channel scalability and system efficiency.

I. BRAGG SCATTERING FOUR-WAVE MIXING

  • 93% conversion efficiency was measured, rising to 97% with a fixed periodic trigger, alongside background of 3 × 10^-3 photons per pump-pulse duration.With random triggering, pump-power fluctuations limit conversion efficiency; the target-channel filter bandwidth is 100 GHz, below the 160 GHz process acceptance bandwidth.Source: §I · p. 19

II. THEORY OF MULTIPLEXED SOURCES

  • As multiplexed-source number N increases, the optimized mean photon number falls and the corresponding multiphoton noise decreases for large N.The analysis optimizes mean photon number for each N and uses the same optimized value across schemes.Source: §II · p. 22

III. SOURCE CHARACTERIZATION

  • Heralding photons were characterized with a single-photon spectrometer and filtered into 100 GHz channels using reflecting Bragg gratings.The highlighted spectral regions correspond to the heralded channels.Source: §III · p. 22

IV. CHARACTERIZATION OF SYSTEM EFFICIENCY

  • 2.3% raw heralding efficiency versus 3% without multiplexing corresponds to 1.3 dB loss in the BS-FWM setup.After accounting for detection loss, the inferred heralding probability is 4.6%.Source: §IV · p. 23

PHOTON SOURCES

  • The system’s maximum switching speed is limited by amplification required for the BS-FWM pumps; in principle, operation can reach a repetition rate of 1/∆νBS.The current BS-FWM acceptance bandwidth is 100 GHz.Source: PHOTON SOURCES · p. 23

VI. FREQUENCY MULTIPLEXING SCALING

  • A 50% single-photon heralding probability is reported with just 10 multiplexed modes, while BS-FWM frequency multiplexing supports many channels without a drop in conversion efficiency.The analysis adds up to 10 additional channels separated by 100 GHz, maintaining maximum conversion efficiency across all 10.Source: §VI · pp. 23–24
  • 93% conversion efficiency was measured by signal depletion and was limited by pump-power fluctuations.With perfect phase matching, complete conversion occurs at interaction strength 2γP = π/2.Source: §VI · p. 25
  • 2.3% heralding efficiency with multiplexing, versus 3% without, corresponds to an estimated 1.3 dB transmission loss through the BS-FWM setup.Heralding efficiency is determined from heralding rate versus heralded-photon coincidence rate.Source: §VI · p. 27
  • 50% heralding efficiency is projected for 10 multiplexed modes, assuming 90% combined detection and fiber-collection efficiency.The scaling analysis considers multiplexing-system efficiencies of 0.75, 0.80, and 0.85.Source: Figure S5 · p. 28, §VI · p. 28
  • For BS-FWM, conversion efficiency is maintained across 10 channels separated by 100 GHz, while acceptance bandwidth is reduced by a factor of 2.One pump is fixed while the other is detuned so the pump separation matches the input-to-target frequency separation.Source: Figure S5 · p. 28, §VI · p. 28
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