Adaptive-Optics-Enabled Quantum Communication: A Technique for Daytime Space-To-Earth Links

Previous demonstrations of free-space quantum communication in daylight have been touted as significant for the development of global-scale quantum networks. Until now, no one has carefully tuned their atmospheric channel to reproduce the daytime sky radiance and slant-path turbulence conditions as they exist between space and Earth. In this article we report a quantum communication field experiment under conditions representative of daytime downlinks from space. Higher-order adaptive optics increased quantum channel efficiencies far beyond those possible with tip-tilt correction alone while spatial filtering at the diffraction limit rejected optical noise without the need for an ultranarrow spectral filter. High signal-to-noise probabilities and low quantum-bit-error rates are demonstrated over a wide range of channel radiances and turbulence conditions associated with slant-path propagation in daytime. The benefits to satellite-based quantum key distribution are quantified and discussed.

Figure 1

Illustration showing photonic qubits propagating from a satellite through atmospheric turbulence to a ground terminal with sunlight scattering into the telescope’s FOV, ${\mathrm{\Omega }}_{\mathrm{FOV}}$.

Figure 2

Conceptual schematic of relevant elements in a quantum receiver illustrating (a) the spatial filtering of background noise by the FS and (b) the effects of turbulence-induced wavefront errors on qubit probability distributions at the FS.

Figure 3

Summary of theoretical calculations showing that the 1.6-km propagation path produces spatial turbulence characteristics representative of slant-path propagation, including (a) equivalent horizontal propagation distances required to produce comparable spatial coherence and scintillation to that introduced by slant-path propagation over a range of zenith angles, and (b) the Rytov variance versus zenith angle for three different strengths of turbulence with the red shaded region showing the onset of deep turbulence effects. Horizontal dashed lines indicate the Rytov variance for 1.6- and 3.2-km horizontal propagation distances. The 1.6-km horizontal path introduces scintillation effects commensurate with slant-path propagation over a wide range of zenith angles, but without entering the realm of deep turbulence typically not encountered in slant-path propagation.

Figure 4

Experimental confirmation that the 1.6-km propagation distance introduces turbulence characteristics relevant to slant-path propagation, including (a) an aerial photograph from Google Maps showing propagation from transmitter to receiver along the northwest horizontal path and (b) a plot of the measured turbulence parameters $[r_0,{\sigma }_I^2]$ in blue with corresponding equivalent zenith angles ${\epsilon }_{\mathrm{zentih}}$ in green. Blue dots with red inset indicate data acquired with a heat source under the propagation path near the transmitter. The solid (dashed) line shows the theoretical $1\times {\mathrm{HV}}_{5/7}$ ($2\times {\mathrm{HV}}_{5/7}$) turbulence profile representing a slant-path channel over the range of zenith angles.

Figure 5

Hemispherical plots showing sky angles for which daytime atmospheric channels are simulated in the field experiment. Color scale shows sky radiances for the winter solstice (top) and summer solstice (bottom) with the sun position obscured by a black circle subtending ${14}^{\circ }$. Experimental data sets with comparable atmospheric scintillation, spatial coherence, and background radiance are shown as white circles for both open-loop (open circles) and closed-loop (filled circles) cases for both $1\times {\mathrm{HV}}_{5/7}$ (left) and $2\times {\mathrm{HV}}_{5/7}$ (right) turbulence strengths.

Figure 6

Theoretical plots demonstrating the relevancy of the field-experiment AO system to actual slant-path turbulence compensation and satellite engagements. In (a),(b) the Greenwood frequency $f_G$ is calculated with and without slewing and plotted versus the zenith angle for two turbulence strengths. In (c), the normalized decoy-state QKD bit yield is plotted as a function of $f_G$ without the benefit of AO (red line) and for three AO control-loop bandwidths (black dashed and solid lines). This shows that any of these bandwidths could be enabling for satellite-to-Earth downlinks.

Figure 7

Partial schematic of quantum transmitter showing PBSs, a half-wave plate (HWP), and a 50:50 BS used to combine horizontal ($H$), vertical ($V$), positive ${45}^{\circ }$ ($P$), and negative ${45}^{\circ }$ ($N$) polarized signal pulses. Neutral density filters (Atten) reduce MPNs to less than unity. A vertically polarized AO beacon and horizontally polarized sync pulse are combined with a fiber-coupled PBS and combined with signal pulses at a dichroic BS. A white-light projector, located outside the receiver FOV, introduces incoherent background light into the channel via atmospheric scattering.

Figure 8

Schematic of the quantum receiver including a FSM and DM. A dichroic BS separates the quantum signal from the AO beacon and sync pulse. A PBS directs the sync pulse to a fast timing detector and a 90:10 BS directs beacon light to a SHWFS and scoring camera. The quantum signal is filtered through a 30-$\mu \mathrm{m}$ diameter FS and a 1-nm bandwidth QCSF before propagating to the standard arrangement for measuring polarization states in rectilinear and diagonal bases, including a HWP for ${45}^{\circ }$ polarization rotation. Detection events are registered by a time-correlated single-photon event counter (TCSPC).

Figure 9

Autoscaled scoring camera images demonstrating the benefit of AO to spatial filter size, showing focal-plane spot sizes in (a) an open-loop AO configuration and (b) a closed-loop AO configuration, resulting in a 15-fold increase in peak intensity.

Figure 10

Experimental results showing that AO can increase quantum channel efficiencies by more than 10 dB while spatially filtering sky noise at the diffraction limit. Channel attenuation is plotted in decibels versus system Strehl for (a) $1\times {\mathrm{HV}}_{5/7}$ turbulence data sets and (b) $2\times {\mathrm{HV}}_{5/7}$ data sets for open-loop (open circles) and closed-loop (filled circles) cases with $r_0$ and ${\sigma }_I^2$ represented by the circle size and color scale, respectively.

Figure 11

Plots of experimental results illustrating the benefit of AO to daytime quantum channel performance, including (a) measured $S/N$ probabilities, (b) measured QBERs, and (c) calculated QKD bit yields versus channel radiance $H_b$ under open-loop (red) and closed-loop (blue) conditions with $r_0$ represented by circle size.

Figure 12

Hemispherical plots, similar to Fig. 5 but retaining only sky angles for data sets that yield positive QKD bit-yield probabilities.

Figure 13

Plot of $[{\sigma }_I^2,r_0]$ pairs calculated for slant-path propagation with three strengths of turbulence and zenith angles ranging from $0^{\circ }$ to ${75}^{\circ }$.

Figure 14

Plot of the Greenwood frequency versus zenith angle calculated for (a) $1\times {\mathrm{HV}}_{5/7}$, (b) $2\times {\mathrm{HV}}_{5/7}$, and (c) $3\times {\mathrm{HV}}_{5/7}$ turbulence strengths. Black and red solid lines are calculated for 400- and 800-km circular orbits, respectively. The dashed lines are calculated without the effects of slewing. Horizontal lines indicate the 130-, 200-, and 500-Hz AO loop bandwidths considered.