Telecom-Band Quantum Optics with Ytterbium Atoms and Silicon Nanophotonics

Wavelengths in the telecommunication window (approximately 1.25–1.65 $\mu \mathrm{m}$) are ideal for quantum communication due to low transmission loss in fiber networks. To realize quantum networks operating at these wavelengths, long-lived quantum memories that couple to telecom-band photons with high efficiency need to be developed. We propose coupling neutral ytterbium atoms, which have a strong telecom-wavelength transition, to a silicon photonic crystal cavity. Specifically, we consider the ${}^3{P}_0{\leftrightarrow }^3{D}_1$ transition in neutral ${}^{171}\mathrm{Yb}$ to interface its long-lived nuclear spin in the metastable ${}^3{P}_0$ “clock” state with a telecom-band photon at $1.4\mu \mathrm{m}$. We show that $\mathrm{Yb}$ atoms can be trapped using a short-wavelength (approximately $470$ nm) tweezer at a distance of 350 nm from the silicon photonic crystal cavity. At this distance, due to the slowly decaying evanescent cavity field at a longer wavelength, we obtain a single-photon Rabi frequency of $g/2\pi \approx 100$ MHz and a cooperativity of $C\approx 47$ while maintaining a high photon collection efficiency into a single mode fiber. The combination of high system efficiency, telecom-band operation, and long coherence times makes this platform well suited for quantum optics on a silicon chip and long-distance quantum communication.

Figure 1

Schematic overview. Silicon photonic crystal cavity with an ${}^{171}\mathrm{Yb}$ atom trapped nearby in an optical tweezer. The minimum atom-device separation $d_{\mathrm{twzr}}\approx 350$ nm allowed by our approach corresponds to an atom-cavity system on a strong telecom-band transition with vacuum Rabi frequency $g_0/2\pi \approx 100$ MHz and emission bandwidth of ${\mathrm{\Gamma }}_{1\mathrm{D}}/2\pi \approx 15$ MHz, for a partially open cavity with external coupling ${\kappa }_e/2\pi \approx 2.7$ GHz and atomic free-space linewidth of $\mathrm{\Gamma }/2\pi =0.32$ MHz. The nuclear spin projections $m_I$ are of the $I=1/2$ nuclear spin of ${}^{171}\mathrm{Yb}$. The photon in the cavity is coupled to an optical fiber with length $L\sim 100$ km. This system constitutes a node in a telecom quantum repeater in which entanglement between nodes is established by a Bell state measurement using a 50:50 beam splitter (BS) and single-photon detectors (PD).

Figure 2

Level diagram of the relevant states of ${}^{171}\mathrm{Yb}$. (a) Low-lying states of $\mathrm{Yb}$ in the singlet and triplet manifolds. The telecom transitions from the metastable $6s6p{}^3{P}_J$ states to the $5d6s{}^3{D}_1$ state are highlighted in the red box. (b) Enlargement of the highlighted transitions. The nuclear spin in ${}^{171}\mathrm{Yb}$ is $I=1/2$, so the hyperfine states are given by $F=1/2$ when $J=0$ and $F=\{J+1/2,J-1/2\}$ when $J\ge 1$. The lifetimes of the ${}^3{P}_J$ states, transition wavelengths, and transition linewidths, as well as the lifetime and hyperfine splitting of the ${}^3{D}_1$ state, are given. We employ the transition shown with the orange double arrow.

Figure 3

Spin-photon entanglement scheme and quantum repeater operation. (a) The relevant (irrelevant) hyperfine states are shown in solid (semitransparent) colors. The cavity-enhanced transition wavelength is ${\lambda }_{\mathrm{cavity}}$. (b) A single trapped ${}^{171}\mathrm{Yb}$ atom in a cavity is represented by a green dot inside two curved semicircles. Local node pairs are shown in the dashed box. Node pairs are separated by $L_0$. BS denotes the beam splitter and PD the single-photon detector. (c) The entanglement distribution rate versus total distance via direct communication at 10 GHz for 1550 nm (solid blue curve) and 1390 nm (large-dashed orange) and via a quantum repeater with $2^4$ nodes with (without) local deterministic entanglement, shown as a solid red (short-dashed green) curve. Note that a 10-GHz rate for the direct transmission scheme [62] can be interpreted as an information-theoretic bound for information distribution without quantum repeaters if an ideal single-photon source with a $10/1.44=6.9$-GHz repetition rate is employed [63]. (d) The entanglement distribution rate over 600 km versus the number of nodes via direct communication at 10 GHz for 1550 nm (solid blue) and 1390 nm (large-dashed orange, not visible) and via a quantum repeater with (without) local deterministic entanglement, shown as a solid red (short-dashed green) curve.

Figure 4

Design and characterization of the $\mathrm{Si}$ cavity. (a) Schematic of the photonic crystal cavity. The different colors show the different sections of the cavity. (b) An enlargement of the first mirror section of the photonic cavity. (c) The TE mode band structure of the air (green) and dielectric (blue) mode. The red dashed line is the atomic resonance and the shaded gray region is outside the light cone. (d) The coherent coupling rate $g_0$ shown on a color map as a function of distance in the $y$ and $z$ directions from the center antinode of the photonic cavity ($x=0$) in the bottom image, and the profile along the $x$ direction across the center tooth in the top image. The red ellipse and circle show the size of the atomic motional wave function (see Sec. 5). (e) The blue left vertical scale shows the line cut of the coherent coupling rate for $x=z=0$ versus the distance from the surface. The dashed line represents the value of $g_0$ for which $C_0=1$. The green right vertical scale shows the surface force from the photonic crystal on the atom. The curve is meant to show the qualitative scaling only. The dashed line shows the maximum restoring force from an optical tweezer of depth 1 mK and waist of approximately $330$ nm. The vertical red line shows the proposed position of the atom at $d_{\mathrm{twzr}}=350$ nm.

Figure 5

Coupling an $\mathrm{Yb}$ atom to a silicon photonic crystal cavity via an optical tweezer trap. (a) An enlargement illustrating the atom in a tweezer near the device at a distance $d_{\mathrm{twzr}}$. (b) The electic field magnitude of the tweezer trap in arbitrary units at a distance of $d_{\mathrm{twzr}}=350$ nm from the edge of the device. (c) Schematic of the silicon chip. The silicon top layer is brown and the insulator layer below is orange. The blue microstrips on the chip are used for Ohmic temperature control and applying rf magnetic fields. The lensed fiber on the right can be coupled to any cavity using a three-dimensional (3D) translation stage. Wavy white lines indicate cuts to show the entire chip. The green circle on the left is the $\mathrm{Yb}$ MOT. Atoms can be shuffled between it and the device using optical tweezers. This architecture allows simultaneous operation of multiple $\mathrm{Yb}$-cavity nodes on a single device.

Figure 6

Tweezer trapping in a fiber Fabry-Perot cavity. (a) The geometry of the fiber FP cavity and the tweezer trap at the center. (b) An enlargement of the center $\pm 2\mu \mathrm{m}$ of the cavity mode. The black ellipse shows a liberal estimate of the atomic wave function in a tweezer trap as described in Sec. 5. (c) The efficiencies associated with the fiber cavity vs ${\mathit{F}}_e$ (see text). $P_{\mathrm{cavity}}$ (orange long-dashed line), ${\eta }_{\mathrm{coll}}$ (green short-dashed), and their product ${\eta }_{\mathrm{ext}}$ (blue).

Figure 7

${\mathrm{Yb}}^{+}$ level structure, and excitation scheme for ${}^{171}{\mathrm{Yb}}^{+}$. (a) The relavent levels of ${\mathrm{Yb}}^{+}$, showing their wavelengths and linewidths. The thick red line shows the proposed telecom transition. (b) Three-level scheme by which quantum information in the ground state can be entangled with a telecom photon via the proposed telecom transition resonant with the cavity mode.