Entangling Two Individual Atoms of Different Isotopes via Rydberg Blockade

We report on the first experimental realization of the controlled-not (cnot) quantum gate and entanglement for two individual atoms of different isotopes and demonstrate a negligible cross talk between two atom qubits. The experiment is based on a strong Rydberg blockade for ${}^{87}\mathrm{Rb}$ and ${}^{85}\mathrm{Rb}$ atoms confined in two single-atom optical traps separated by $3.8\mu \mathrm{m}$. The raw fidelities of the cnot gate and entanglement are $0.73\pm 0.01$ and $0.59\pm 0.03$, respectively, without any corrections for atom loss or trace loss. Our work has applications for simulations of many-body systems with multispecies interactions, for quantum computing, and for quantum metrology.

Figure 1

Experimental setup. (a) Energy levels and lasers for ${}^{87}\mathrm{Rb}$ and ${}^{85}\mathrm{Rb}$. Atoms are excited to Rydberg states through Raman transitions using 480 (${}^{\mathrm{Ryd}}480$) and 780 nm (${}^{\mathrm{Ryd}}780$) ${\sigma }^{+}$-polarized lasers. The laser ${}^{\mathrm{Ryd}}480$ is blue detuned by 4.8 GHz from the intermediate state, and its waist $12.8\mu \mathrm{m}$ covers both atoms. The lasers ${}^{\mathrm{Ryd}}780-87$ and ${}^{\mathrm{Ryd}}780-85$, whose frequencies differ by 1.13 GHz, address ${}^{87}\mathrm{Rb}$ and ${}^{85}\mathrm{Rb}$. The degeneracy of the Rydberg states $|79D_{5/2},m_j⟩$ is lifted by the static magnetic field $B=3\mathrm{G}$ along the quantization axis $y$, and the laser frequencies are resonant with the $m_j=5/2$ state. Single qubit operations are performed through Raman transitions using the 795 nm lasers ${}^{\mathrm{Ram}}85$ and ${\mathrm{Ram}}_{87}$, which are red detuned by 50 GHz from the $5S_{1/2}\to 5P_{1/2}$ transition. (b) Experimental geometry. Two 830 nm lasers have the beam waist $2.1\mu \mathrm{m}$ to form two dipole traps separated by $3.8\mu \mathrm{m}$ along the $z$ direction.

Figure 2

Cross talk between ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$. (a) Rabi oscillations between the ${}^{87}\mathrm{Rb}$ $|\uparrow ⟩$ and $|\downarrow ⟩$ states of ${}^{87}\mathrm{Rb}$ (black squares). The red circles show the experimental data obtained when using the ${}^{85}\mathrm{Rb}$ blow away laser before measuring the state of ${}^{87}\mathrm{Rb}$. The solid curves are damped sinusoidal fits $P=P_0+A{e}^{-t/t_0}\cos [2\pi f(t-t_c)]$, with $A=0.49\pm 0.01$, $f=0.625\pm 0.002\mathrm{MHz}$, and $t_0=28\pm 7\mu \mathrm{s}$ for black squares and $A=0.50\pm 0.02$, $f=0.625\pm 0.003\mathrm{MHz}$, $t_0=27\pm 15\mu \mathrm{s}$ for red circles. (b) The ${}^{87}\mathrm{Rb}$ Rydberg excitation laser covers both ${}^{87}\mathrm{Rb}$ in trap 1 (black squares) and ${}^{85}\mathrm{Rb}$ in trap 2 (red circles). The ${}^{87}\mathrm{Rb}$ atom shows coherent Rabi oscillations between the $|\uparrow ⟩$ and $|r⟩$ states. The solid curves are damped sinusoidal fits with $A=0.41\pm 0.01$, $f=0.685\pm 0.008\mathrm{MHz}$, and $t_0=19\pm 5\mu \mathrm{s}$. The ${}^{85}\mathrm{Rb}$ atom is almost unaffected, which shows a negligible cross talk.

Figure 3

Heteronuclear Rydberg blockade. (a) Time sequence. (b) Rabi oscillations between the ${}^{85}\mathrm{Rb}$ $|\Uparrow ⟩$ and $|r⟩$ states. The experimental data are shown both in the absence (black squares) and in the presence (red circles) of ${}^{87}\mathrm{Rb}$ in trap 1. The solid curves are damped sinusoidal fittings with $P=P_0+A{e}^{-t/t_0}\cos [2\pi f(t-t_c)]$. The fitting parameters are $A=0.455\pm 0.008$, $f=0.600\pm 0.003\mathrm{MHz}$, $t_0=10\pm 1\mu \mathrm{s}$ for black squares. We preset $f=0.6\mathrm{MHz}$, $t_0=10\mu \mathrm{s}$ for red circles to get $A=0.017\pm 0.006$. Each data point is an average value of 150 measurements.

Figure 4

Heteronuclear cnot gate. (a) Experimental time sequence. (b) Output states as a function of the relative phase between the Raman $\pi /2$ pulses, for the initial states $|\downarrow \Uparrow ⟩$ (black squares) and $|\uparrow \Uparrow ⟩$ (red circles). The solid curves are sinusoidal fits yielding the phase difference of $(0.94\pm 0.01)\pi$ between the two signals. (c) Measured truth table matrix $U_{\mathrm{CNOT}}$ for the cnot gate with the relative phase between the $\pi /2$ pulses set to 0.

Figure 5

Entanglement of two heteronuclear atoms. (a) Time sequence. (b) Measured probabilities for the entangled state. (c) The parity signal $P$. The solid curve is a sinusoidal fit with $P=2\mathrm{Re}(C_2)-2|C_1|\cos (2{\varphi }_1+\xi )$, where $\mathrm{Re}(C_2)=0.02\pm 0.02$, $|C_1|=0.16\pm 0.01$.