Simultaneous Excitation of Two Noninteracting Atoms with Time-Frequency Correlated Photon Pairs in a Superconducting Circuit

We report the first observation of simultaneous excitation of two noninteracting atoms by a pair of time-frequency correlated photons in a superconducting circuit. The strong coupling regime of this process enables the synthesis of a three-body interaction Hamiltonian, which allows the generation of the tripartite Greenberger-Horne-Zeilinger state in a single step with a fidelity as high as 0.95. We further demonstrate the inhibition of the simultaneous two-atom excitation by continuously measuring whether the first photon is emitted. This work provides a new route in synthesizing many-body interaction Hamiltonian and coherent control of entanglement.

Figure 1

Simultaneous excitation of two noninteracting qubits. (a) The quantum paths for $A_1$ and $A_2$ in Eq. (1). The pathways with the same color (blue or red) in $A_1$ and $A_2$ cancel each other, evident from their opposite values of the detunings from the atomic levels. (b) Sketch of part of the multiqubit superconducting circuit. Four qubits, labeled $Q_1$, $Q_2$, $Q_3$, and $Q_4$, are used in this experiment. Each qubit has its own flux bias line (blue) for fast frequency tuning and microwave line (green) for SU(2) spin rotations. For qubit readout, each qubit is capacitively coupled to its own readout resonator which is coupled to one of the two common transmission lines (pink). (c) The single-qubit probabilities of finding $Q_1$ (blue) and $Q_2$ (red) in their excited states when they are simultaneously driven by correlated photon pairs (circles) and uncorrelated classical microwaves (triangles) as functions of the interaction time $\tau$. The joint probability of finding $Q_1$ and $Q_2$ in $|e_1,e_2⟩$ by absorbing the correlated photon pairs is denoted by the filled yellow circles, which almost overlap with the empty blue and red circles. The simultaneous excitation of the two qubits is in conformity with the prediction of Ref. [10].

Figure 2

Generating the GHZ state with the three-body interaction Hamiltonian. (a) Illustrative pulse sequence drawn in the frequency versus time frame. After initializing $Q_1\text{−}{Q}_2\text{−}{Q}_3$ in $|g_1,g_2,g_3⟩$ at their respective idle frequencies, we prepare the state $|g_1,g_2,f_3⟩$ by successively applying to $Q_3$ an $X_{\pi }$ rotation (a $\pi$ rotation around $X$ axis transferring $|g_3⟩$ to $|e_3⟩$, red sinusoid) and an $X_{\pi }^f$ rotation (transferring $|e_3⟩$ to $|f_3⟩$, light red sinusoid), following which we apply square pulses to tune the qubit frequencies, so that Eq. (1) is satisfied, for a dynamical evolution with a variable time $\tau$. Finally we bring the qubits back to their idle frequencies for simultaneous readout: The same pulse sequence is repeated 1500 times to count the 12 probabilities $\{P_{ggg},P_{gge},P_{ggf}\cdots P_{gef},P_{eef}\}$. The tomographic pulses in the shaded box is only inserted for QST of the GHZ state, $|{\psi }_{\mathrm{GHZ}}⟩$, where the $X_{\pi }^f$ rotation transforms $|{\psi }_{\mathrm{GHZ}}⟩$ to its equivalent $|{\psi }_{\mathrm{GHZ}}^{\prime }⟩=(|g_1,g_2,e_3⟩+e^{i\varphi }|e_1,e_2,g_3⟩)/\sqrt{2}$, followed by null or $\pi /2$ rotations running through the Pauli set $\{I,X_{\pi /2},Y_{\pi /2}\}$ for all three qubits. (b) The dominant occupational probabilities $|c_1(\tau ){|}^2$ for $|g_1,g_2,f_3⟩$ ($P_{ggf}$, orange circles) and $|c_2(\tau ){|}^2$ for $|e_1,e_2,g_3⟩$ ($P_{eeg}$, blue circles) measured as functions of the interaction time $\tau$, in comparison with the numerical simulation (lines). (c) QST of the experimental $|{\psi }_{\mathrm{GHZ}}^{\prime }⟩$ at $\tau \approx 88\mathrm{ns}$. Shown is the real part of the three-qubit density matrix, $\rho$, after a numerical rotation to remove the phase $\varphi$ in $|{\psi }_{\mathrm{GHZ}}^{\prime }⟩$.

Figure 3

The quantum Zeno effect of inhibiting the simultaneous two-atom excitation by continuous observation. (a) Illustrative pulse sequence drawn in the frequency versus time frame. Starting from all four qubits in their ground state, we first apply two $X_{\pi }$ rotations to $Q_3$ and $Q_4$ (red and orange sinusoids). Then, we tune the frequencies of the four qubits into two-photon resonance, i.e., ${\omega }_1+{\omega }_2={\omega }_3+{\omega }_4$ where ${\omega }_3={\nu }_2$ and ${\omega }_4={\nu }_1$, by applying square pulses to the qubit flux bias lines. At $\tau <500\mathrm{ns}$, $Q_4$ is continuously measuring the state of $Q_3$. At $\tau \approx 500\mathrm{ns}$ when $Q_3$ is in state $|f_3⟩$, we tune $Q_4$ to its idle frequency by applying a rectangle pulse. (b) The probabilities of finding the qubits in the state $|g_1,g_2,e_3,e_4⟩$ (green circles), $|g_1,g_2,f_3,g_4⟩$ (red circles), and $|e_1,e_2,g_3,g_4⟩$ (blue circles) as functions of the interaction time $\tau$, in comparison with the numerical simulation (lines). At $\tau <500\mathrm{ns}$, we observe the Rabi oscillation between $|g_1,g_2,e_3,e_4⟩$ and $|g_1,g_2,f_3,g_4⟩$, without the state $|e_1,e_2,g_3,g_4⟩$ being noticeably excited due to the constant observation of $Q_3$ by $Q_4$. At $\tau >500\mathrm{ns}$ when $Q_4$ is tuned off-resonant with $Q_3$, we observe the simultaneous excitation of $Q_1$ and $Q_2$ by the two cascade photons from $Q_3$.