Charge-Noise Insensitive Chiral Photonic Interface for Waveguide Circuit QED

A chiral photonic interface is a quantum system that has different probabilities for emitting photons to the left and right. An on-chip compatible chiral interface is attractive for both fundamental studies of light-matter interactions and applications to quantum information processing. We propose such a chiral interface based on superconducting circuits, which has wide bandwidth, rich tunability, and high tolerance to fabrication variations. The proposed interface consists of a core that uses Cooper-pair boxes (CPBs) to break time-reversal symmetry, and two superconducting transmons that connect the core to a waveguide in the manner reminiscent of a “giant atom.” The transmons form a state decoupled from the core, akin to dark states of atomic physics, rendering the whole interface insensitive to the CPB charge noise. The proposed interface can be extended to realize a broadband fully passive on-chip circulator for microwave photons.

Figure 1

Proposal for realizing the on-chip compatible charge-noise insensitive chiral photonic interface. (a) Circuit of the chiral interface consisting of two CPBs (green boxes) coupled to a waveguide (top) through two tunable transmons (blue boxes) connecting to the waveguide at positions $x_l$ and $x_r$. $C_J$ and $E_J$ denote the capacitance and Josephson energy of the CPBs, $C_{ab}$ and $E_{J,ab}$ are those of the junction connecting CPB-$a$ and CPB-$b$, ${\phi }_{\mathrm{ext}}$ is the dimensionless external flux, $C_g$ is the gate capacitance, $C_q$ couples the CPB and transmons, $C_t$ and $E_{J_t}$ are the total capacitance and (tunable) Josephson energy of the transmons and $C_c$ couples the transmons to the transmission line. (b) Circuit model of the capacitive coupling between a transmon and the transmission line. (c) A circulator based on chiral interface (right-hand chirality) and Mach-Zehnder interferometer. “BS” denotes $50:50$ beam splitters. Input from port 1 goes to port 3 while input from port 3 goes to port 2.

Figure 2

Fidelity of circulator $F_L(\omega )$ against the detuning to the first excited state for direct coupling between the waveguide and the bi-CPB core. The device parameters are $c{\delta }_z=C_q=C_{\mathrm{\Sigma }}=C_{ab}=1\mathrm{fF}$, $E_J=5.5h\mathrm{GHz}$, and (a) ${\phi }_{\mathrm{ext}}=0.5\pi$ and various values of $E_{J,ab}(h\mathrm{GHz})$; (b) $E_{J,ab}=5.5h\mathrm{GHz}$ and the external flux ${\phi }_{\mathrm{ext}}$ varying from 0 to $\pi$.

Figure 3

Energy levels and performance of the full system. (a) Fidelity of circulator as a function of the detuning from ${\omega }_{01}$ and ${\omega }_{02}$ with device parameters in (c). (b) Values (in unit of $h\mathrm{GHz}$) of ${\omega }_{01}$ and ${\omega }_{02}$ of the full device as a function of $n_{g,a/b}$, using parameters listed in (c), where units for capacitances and Josephson energies are fF and $h\mathrm{GHz}$, respectively.

Figure 4

Tunability of the chiral interface. (a) 150 realizations of the chiral interfaces with device parameters randomly sampled to represent fabrication variations (see text for details). The marker shows peak fidelity for a given realization, error bar indicates the $F_R>0.9$ bandwidth. The gray points show results obtained when $n_{g,a/b}$ and ${\phi }_{\mathrm{ext}}$ are optimized for the ideal parameters listed in Fig. 3. Red points show fidelities obtained when $n_{g,a/b}$ and ${\phi }_{\mathrm{ext}}$ are optimized for each realization. (b) Upper panel: Peak fidelities as a function of photon frequency, for the chiral interface with parameters given in Fig. 3 and 100 samples of transmon Josephson energy $E_{Jt}$ between $6\sim 22h\mathrm{GHz}$. For each red dot thereof, the vertically aligned markers in the lower panel shows the adaptively optimized $n_{g,a/b}$ and ${\phi }_{\mathrm{ext}}$.