On-Demand Microwave Generator of Shaped Single Photons

We demonstrate the full functionality of a circuit that generates single microwave photons on demand, with a wave packet that can be modulated with a near-arbitrary shape. We achieve such a high tunability by coupling a superconducting qubit near the end of a semi-infinite transmission line. A dc superconducting quantum interference device shunts the line to ground and is employed to modify the spatial dependence of the electromagnetic mode structure in the transmission line. This control allows us to couple and decouple the qubit from the line, shaping its emission rate on fast time scales. Our decoupling scheme is applicable to all types of superconducting qubits and other solid-state systems and can be generalized to multiple qubits as well as to resonators.

Figure 1

(a) Sketch of the device operating principle. A dc SQUID shunts the line to ground and a flux threading it controls the profile of the rms amplitude of the vacuum fluctuations. The field offset at $\mathrm{\Phi }=0$ is due to the finite SQUID impedance. We plot a single mode for clarity, but the effect is broadband. A qubit of frequency ${\omega }_{01}=2\pi v/{\lambda }_{01}$ is positioned near an odd number of quarter wavelengths, $L=(2n+1){\lambda }_{01}/4$. At $\mathrm{\Phi }=0$, depicted in red, the qubit is maximally coupled to the line, even though the field offset lowers the maximum coupling as a function of the qubit wavelength. At a particular decoupling flux $\mathrm{\Phi }={\mathrm{\Phi }}_{\mathrm{dec}}$, depicted in blue, the qubit is decoupled from the line. (b) Optical image of a device similar to the one used in the experiment and the circuit schematic. The output from the source line is amplified at different stages and digitized at room temperature. (c) Optical image of the single-junction transmon qubit capacitively coupled to the transmission line. The excitation line has a weak, fixed coupling to the qubit, allowing its state to be controlled irrespective of the coupling strength to the source line. (d) Optical image of the SQUID shunting the source line to ground. The current line connecting from the left is used to tune the SQUID flux ${\mathrm{\Phi }}_{\mathrm{SQ}}$ in real time.

Figure 2

Extracted qubit decay rates. The qubit emission rate into the source line, ${\mathrm{\Gamma }}_1$ (the black squares), and the total decoherence rate, ${\mathrm{\Gamma }}_2$ (the red circles), are obtained from Eq. (5). The pure dephasing rate ${\mathrm{\Gamma }}_{\varphi }$ is calculated as ${\mathrm{\Gamma }}_{\varphi }={\mathrm{\Gamma }}_2-{\mathrm{\Gamma }}_1/2$. All three rates tune with flux, showing a clear modulation of the qubit–source line coupling strength. The blue trace is a fit using Eqs. (1), (4), and (6), including SQUID junction asymmetry.

Figure 3

Qubit dynamics at two operating flux bias points with higher (red) and lower (blue) qubit–source line coupling rate. (a) Rabi oscillations. The Rabi decay times, $T_R$, differ by a factor of 4.3. The upper axis indicates the angle of the qubit-state rotation on the Bloch sphere. (b) Free induction decay of the qubit state after a $\pi /2$ pulse. The decay rate is enhanced 4.6 times between the two bias points. The enhanced coupling of the qubit into the line is further evidenced by a larger qubit signal for the shortest-lived traces, for both the free decay and the Rabi oscillations.

Figure 4

Power and quadrature oscillations of emitted radiation from the driven qubit. Black circles represent the measured $I$ quadrature amplitude, while red circles correspond to the second moment of the emission, the emitted power $⟨P⟩=⟨(I^2+Q^2)⟩$. The solid curves are sinusoidal fits to the data. The two curves are offset by $(0.58\pm 0.08)\pi$, which rules out a coherent state and provides strong evidence for single-photon emission. The upper axis indicates the angle of the qubit-state rotation on the Bloch sphere.

Figure 5

On-demand single-photon generation. The pulse sequence begins by bringing the qubit to the decoupling point by pulsing current through the SQUID and then exciting the qubit with a $\pi /2$ pulse. The qubit emission is triggered by ending the current pulse through the SQUID, bringing the qubit back to a strongly coupled point. The peak registered near $0.5\mu \mathrm{s}$ is the excitation pulse partially leaking into the measurement chain circuit.

Figure 6

Shaped-photon generation. (a)–(c) Emission of the source given differing current modulations $f(t)$, sketched with the black traces above the data. The solid blue lines represent the targeted waveforms. (a) Emitted qubit voltage with a sharp falling edge. The qubit emission is clearly exponential. (b) Same as (a) but using a falling exponential edge. The qubit emission looks to be nearly symmetric. (c) The falling edge of the SQUID current pulse is an inverted cubic exponential. The qubit emission in this case approaches the time reverse of the emission in (a). The signal recorded $1\mu \mathrm{s}$ prior to the qubit emission corresponds to the excitation pulse.

Figure 7

Intrinsic qubit coherence properties. (a) The intrinsic relaxation time $T_{1,i}$ and (b) the free induction decay time $T_{2,i}^{*}$ of the qubit are measured at the decoupling point following the pulse sequence indicated in the figure. (a) In order to measure $T_{1,i}$, a resonant $\pi$ pulse is delayed from a $\pi /2$ pulse that projects the qubit state onto the equatorial plane at the end of the sequence [32]. When the SQUID current pulse ends, the qubit spontaneously emits and its coherence properties are translated into the field quadrature amplitudes $I$ and $Q$. (b) The sequence to measure $T_{2,i}^{*}$ requires only a $\pi /2$ pulse that excites the qubit in a superposition state at the decoupling point followed by a time delay from the end of the SQUID current pulse which enables the qubit emission. The fact that $T_{2,i}^{*}<2T_{1,i}$ indicates the presence of a significant amount of intrinsic pure dephasing ${\mathrm{\Gamma }}_{\varphi ,i}=(1/2.49)\mu {\mathrm{s}}^{-1}$.