Generation and efficient measurement of single photons from fixed-frequency superconducting qubits

We demonstrate and evaluate an on-demand source of single itinerant microwave photons. Photons are generated using a highly coherent, fixed-frequency qubit-cavity system, and a protocol where the microwave control field is far detuned from the photon emission frequency. By using a Josephson parametric amplifier (JPA), we perform efficient single-quadrature detection of the state emerging from the cavity. We characterize the imperfections of the photon generation and detection, including detection inefficiency and state infidelity caused by measurement back-action over a range of JPA gains from 17 to 33 dB. We observe that both detection efficiency and undesirable back-action increase with JPA gain. We find that the density matrix has its maximum single-photon component ${\rho }_{11}=0.36\pm 0.01$ at 29 dB JPA gain. At this gain, back-action of the JPA creates cavity photon number fluctuations that we model as a thermal distribution with an average photon number $\overline{n}=0.041\pm 0.003$.

Figure 1

Simplified schematic and energy-level diagram for photon generation. (a) The drive and measurement microwave generators couple to the input of the qubit cavity system where the measurement tone excites the cavity in order to infer the qubit state, and the drive tone manipulates the state of the qubit-cavity system. A switch can connect the amplifier chain to a thermal noise source allowing for an independent characterization of the measurement efficiency. (b) Starting with the qubit in the ground state and zero photons in the cavity, a two-photon blue sideband pulse (blue double arrow) excites the qubit and creates one photon. The photon then decays out of the system, creating a propagating photon in the microwave lines. We compare this process with a control, where a qubit pulse (green arrow) directly excites the qubit and no photon is created.

Figure 2

Time-domain depiction of photon generation and detection. (a) A timing diagram for the photon creation and measurement sequence. The drive tone (black) either creates a photon or excites the qubit for the vacuum calibration. Qubit readout tones (red) are used before and after the drive. (b) The mean voltage $\langle V_m\rangle \left(t\right)$ measured from 7000 individual time traces with the drive at the blue-sideband frequency (solid blue) or at the qubit's frequency (dashed green). (c) The variance of the individual measurements $\mathrm{var}\left(V_m\right)\left(t\right)$ with the drive at the blue sideband frequency (solid blue) and at the qubit frequency (dashed green). In blue, the photon power can be seen following the blue sideband pulse at $t=0 \mu s$. For the control in green, no such signal is seen. (d) The mode matching function $f\left(t\right)$ is applied to each individual voltage trace, $V_m\left(t\right)$, to extract the quadrature measurement for the propagation state exciting the cavity.

Figure 3

Photon state tomography. (a) Histogram of a quadrature measurement set of single photons (narrow blue bars) and the no-photon control (wide green bars) with the JPA gain at 27 dB. The histograms are plotted as a probability density (bars) and are fit by the expected distribution for a diagonal density matrix with a three-photon Fock basis (solid lines). (b) Diagonal density matrix elements determined from fitting the quadrature histogram over a range of JPA gains from 17 to 33 dB. The error bars are determined from the standard deviation of the mean using eight sets of the quadrature measurements at each gain (only four sets are used at 17 and 33 dB). The systemic uncertainties are indicated with dashed lines.

Figure 4

Characterizing and correcting for imperfections in generation and detection. (a) The qubit dephasing rate ($\mathrm{\Gamma }=1/T_2^{*}$) is shown (points) over a range of JPA gains along with a fit (line) to Eq. (2) over the range of JPA gains (main text). (b) The solid line shows the best estimate of the average photon number in the cavity, $\overline{n}$ (uncertainty in dashed lines), due to the JPA at each gain used in the experiment. (c) The measurement efficiency ${\eta }_m$ is determined from a thermal sweep at three JPA gains (circles). This quantity is interpolated over the range of JPA gains by fitting the data points to Eq. (C4) (Appendix pp3) with the uncertainty in dashed lines. (d) The plots show the fidelity of the measured density matrix with respect to an ideal single photon (blue squares), and the density matrix we expect to measure given pure photon generation in the cavity (black points). Here, the statistical one-standard-deviation uncertainties are plotted as errors bars. The systematic error plotted in dashed lines is calculated from both the systematic uncertainty in ${\eta }_m$ and in the density matrix elements.

Figure 5

The microwave schematic for the experiment.

Figure 6

Thermal sweep data for the JPA operated at 20-dB (green squares), 25-dB (blue circles), and 30-dB (red crosses) gains. The data are fit to Eq. (C1) (solid lines). The input noise source used in the thermal sweep is a 50-$\mathrm{\Omega }$ resister whose temperature is adjusted from 79 to 900 mK. This thermal noise power is expressed in units of quanta at 5.8 GHz on the $x$ axis.