Dispersive Photon Blockade in a Superconducting Circuit

Mediated photon-photon interactions are realized in a superconducting coplanar waveguide cavity coupled to a superconducting charge qubit. These nonresonant interactions blockade the transmission of photons through the cavity. This so-called dispersive photon blockade is characterized by measuring the total transmitted power while varying the energy spectrum of the photons incident on the cavity. A staircase with four distinct steps is observed and can be understood in an analogy with electron transport and the Coulomb blockade in quantum dots. This work differs from previous efforts in that the cavity-qubit excitations retain a photonic nature rather than a hybridization of qubit and photon and provides the needed tolerance to disorder for future condensed matter experiments.

Figure 1

Energy diagrams for Coulomb and photon blockades, with grey rectangles representing the distribution of particle energies in the leads. (a) Schematic for electronic transport through a quantum dot. The gate voltage, $V_g$ controls the energy offset between states in the dot and electrons in the leads, while the source-drain voltage, $V_{\mathrm{sd}}$, sets the range of electron energies that participate in transport. The Coulomb blockade can be overcome by increasing $V_{\mathrm{sd}}$. (b) Schematic for transmission through a dispersively coupled cavity-qubit system in the photon blockade regime. The center frequency, ${\omega }_{\mathrm{rf}}$, can be changed to align the energy of incident photons with states of the cavity, much like $V_g$ in a quantum dot. The bandwidth of the incident photons, $\Delta \omega$, controls the energy range of the photons in the system and can be increased to overcome photon blockade.

Figure 2

Calculated number of photons $n$ versus incident photon bandwidth $\sigma$ and center frequency ${\omega }_L$ for an effective drive parameter $f/\kappa =10$ for the system parameters quoted in the text. The black line shows the photon staircase for fixed center frequency ${\omega }_L=6977\mathrm{MHz}$ as a function of bandwidth. The inset shows the number of photons as a function of effective drive $f/\kappa$ on the first three plateaus of the staircase function with center frequency ${\omega }_L=6977\mathrm{MHz}$ and bandwidths $\sigma =1.5\mathrm{MHz}$ (red [dark gray]), $\sigma =2.5\mathrm{MHz}$ (orange [medium gray]) and $\sigma =4\mathrm{MHz}$ (yellow [light gray]). The white dashed line corresponds to the values used in the main graph.

Figure 3

Incoherent and coherent cavity transmission. The blue dots show the measured power transmitted through the cavity-qubit system in a 8 MHz measurement window for different incident photon bandwidths. The data was oversampled in bandwidth and the noise was reduced by using a five-point smoothing function. Four steps in the transmission are evident and correspond to the transmission of an additional photon. The vertical dashed lines indicate step locations based on eigenstates obtained by diagonalizing the Jaynes-Cummings Hamiltonian. Rounding of the steps in the staircase is consistent with measured $Q$ of the cavity. The measurement error is about 5%. The solid black line shows the normalized transmission spectrum measured using a coherent tone at few-photon power levels.