Demonstration of a Quantum Gate Using Electromagnetically Induced Transparency

We demonstrate a native $\mathrm{CNOT}$ gate between two individually addressed neutral atoms based on electromagnetically induced transparency. This protocol utilizes the strong long-range interactions of Rydberg states to enable conditional state transfer on the target qubit when operated in the blockade regime. An advantage of this scheme is it enables implementation of multiqubit ${\mathrm{CNOT}}^k$ gates using a pulse sequence independent of qubit number, providing a simple gate for efficient implementation of digital quantum algorithms and stabilizer measurements for quantum error correction. We achieve a loss corrected gate fidelity of ${\mathcal{F}}_{\mathrm{CNOT}}^{\mathrm{cor}}=0.82(6)$, and prepare an entangled Bell state with ${\mathcal{F}}_{\text{Bell}}^{\mathrm{cor}}=0.66(5)$, limited at present by laser power. We present a number of technical improvements to advance this to a level required for fault-tolerant scaling.

Figure 1

EIT gate protocol. (a) A single control and target atom trapped in two optical dipole traps separated by distance $R$. (b) $\mathrm{CNOT}$ pulse sequence. (c) If the control atom is in $|0{⟩}_c$ during the smooth pulse the target qubit adiabatically follows the EIT dark state $|0{⟩}_t\to |0{⟩}_t$ leaving its state unchanged. (d) If the control atom is initially in $|1{⟩}_c$ then strong dipole-dipole interactions $V(R)$ detune the target qubit Rydberg state, breaking the EIT resonance and enabling resonant transfer $|0{⟩}_t\to |1{⟩}_t$.

Figure 2

Experiment setup. (a) Schematic showing single atoms trapped in microscopic tweezer traps, overlapped with the Rydberg laser on a dichroic mirror (DM) and circularly polarized using a quarter wave plate (QWP). The Raman and qubit lasers are combined on a polarizing beam splitter (PBS) and counterpropagate with the Rydberg and trapping lasers. (b) Qubit level scheme with $|1⟩=|6S_{1/2},F=4,m_F=0⟩$, $|0⟩=|6S_{1/2},F=3,m_F=0⟩$, and $|r⟩=|81D_{5/2},m_j=5/2⟩$. The qubit (red) and Rydberg (green) lasers drive a two-photon transition from $|1⟩\to |r⟩$ detuned by $\mathrm{\Delta }$ from the intermediate state $|e⟩$. The Raman laser ${\mathrm{\Omega }}_p$ (brown) drives transitions between $|1⟩\to |0⟩$, and is phase locked to ${\mathrm{\Omega }}_a$.

Figure 3

Pulse optimization. (a) Target atom qubit excitation scheme, showing all the hyperfine levels of the intermediate state $6P_{3/2}$. (b) Smooth-pulse optimization with ${\mathrm{\Omega }}_c=0$ to maximize transfer $|1⟩\to |0⟩$ as a function of two-photon detuning $\delta$ and (c) relative pulse power $P_{\mathrm{rel}}$ for $\tau =2\mathrm{\mu }\mathrm{s}$. (d)–(f) EIT optimization vs coupling laser detuning for $\tau =1.5,2,3\mathrm{\mu }\mathrm{s}$ to find EIT resonance where state transfer is suppressed due to adiabatic following of the dark state $|1⟩\to |1⟩$. Data are overlaid with theoretical model (gray line) [50].

Figure 4

Gate measurement. (a) Raw and (b) loss-corrected CNOT gate data with fidelities of ${\mathcal{F}}_{\mathrm{CNOT}}=0.55(3)$ and ${\mathcal{F}}_{\mathrm{CNOT}}^{\mathrm{cor}}=0.82(6)$.

Figure 5

Bell state preparation. (a) Gate sequence applied for Bell state preparation and analysis. (b) Measured Bell state populations. (c) Parity oscillation with amplitude $|c|=0.17(1)$.