Three-Wave Mixing Kinetic Inductance Traveling-Wave Amplifier with Near-Quantum-Limited Noise Performance

We present a theoretical model and experimental characterization of a microwave kinetic inductance traveling-wave (KIT) amplifier, whose noise performance, measured by a shot-noise tunnel junction (SNTJ), approaches the quantum limit. Biased with a dc current, this amplifier operates in a three-wave mixing fashion, thereby reducing by several orders of magnitude the power of the microwave pump tone and associated parasitic heating compared to conventional four-wave mixing KIT amplifier devices. It consists of a $50\mathrm{\Omega }$ artificial transmission line whose dispersion allows for a controlled amplification bandwidth. We measure ${16.5}_{-1.3}^{+1}$ dB of gain across a 2 GHz bandwidth with an input 1 dB compression power of $-63$ dBm, in qualitative agreement with theory. Using a theoretical framework that accounts for the SNTJ-generated noise entering both the signal and idler ports of the KIT amplifier, we measure the system-added noise of an amplification chain that integrates the KIT amplifier as the first amplifier. This system-added noise, $3.1\pm 0.6$ quanta (equivalent to $0.66\pm 0.15$ K) between 3.5 and 5.5 GHz, is the one that a device replacing the SNTJ in that chain would see. This KIT amplifier is therefore suitable to read large arrays of microwave kinetic inductance detectors and promising for multiplexed superconducting qubit readout.

Popular Summary

The microwave range of the electromagnetic spectrum (1–20 GHz) contains signals ranging from cellular telephone communications to the faint electromagnetic waves used to control and measure superconducting qubits. Microwave amplifiers play a crucial role in all these technologies. Today’s semiconductor amplifiers provide gigahertz of bandwidth and high power handling, but their noise is determined by classical processes and is an important source of degradation when measuring faint signals. As a result, there is great interest in the development of alternative microwave amplifiers whose noise is set by the fundamental limits imposed by quantum mechanics. Up to now, achieving noise performance near the quantum limit has required sacrifices in bandwidth and power handling.

In this manuscript, we demonstrate a parametric amplifier based on a superconducting material with nonlinear microwave properties that is patterned into a weakly dispersive superconducting transmission line. This amplifier possesses all the properties desired for microwave signal amplification: noise near the quantum limit, 2 GHz of bandwidth, and sufficient power handling for the simultaneous measurement of 1000 or more independent signals. We combine experimental results with a theoretical model that qualitatively describes key features of the amplifier and provides important design guidance. Our parametric amplifier will provide a significant performance advantage over existing amplifiers for the measurement of microwave signals from large numbers of superconducting photon sensors and qubits. As a result, it is expected to impact diverse scientific fields ranging from searches for exoplanets in Earth-like orbits to the realization of a practical quantum computer.

Figure 1

Schematic of the KIT amplifier artificial transmission line. (a) Three cells in series (not to scale) are arranged in a CPW topology. The highly inductive central line (red) is flanked by IDC fingers, which match it to $50\mathrm{\Omega }$. Each finger constitutes a low-$Q$, quarter-wave resonator. (b) In the equivalent electrical circuit, each cell consists of a series inductance $L_d$ and two resonators with inductance $L_f$ and capacitance to ground $C/2$.

Figure 2

Influence of the phase matching on the gain profile. (a) The nonlinear wavenumber $k^{\ast }$ is calculated as a function of frequency for the transmission line represented in Fig. 1 (dashed), and for a similar line, periodically loaded at $80\mathrm{\Omega }$ (black). The nonlinear part of four triplets $\{k_s,k_i,k_p\}$ that satisfy the phase-matching condition [Eq. (2)] are indicated with colored circles: in purple ${\omega }_i-{\omega }_s=4$ GHz, green ${\omega }_i-{\omega }_s=3$ GHz, red ${\omega }_i-{\omega }_s=2$ GHz, and blue ${\omega }_i={\omega }_s$. Additionally, a gray line indicates a pump frequency for which phase matching is nowhere fulfilled. (b) Solving the CMEs [Eqs. (A5a)], the signal power gain profile is calculated [Eq. (A9)] for the related pump frequencies [the colors match with panel (a)]. The KIT amplifier length is $N_c=6.6\times {10}^4$ cells.

Figure 3

Micrographs of the KIT amplifier. (a) The transmission line (false color red) is periodically loaded with shorter IDC fingers. (b) Line and fingers are 1 $\mu \mathrm{m}$ wide, and each cell is 5 $\mu \mathrm{m}$ long. (c) The overall KIT amplifier is laid out in a spiral configuration on a $2\times 2$ cm chip, and clamped on a copper packaging.

Figure 4

Amplification properties of the KIT amplifier. (a) The power gain is measured with a vector network analyzer (VNA), when ${\omega }_p=2\pi \times 8.895$ GHz (blue), and ${\omega }_p=2\pi \times 8.931$ GHz (red). (b) The gain of a probe tone at 4.5 GHz compresses as the tone’s power increases. At $P_{-1\mathrm{dB}}=-63$ dBm, referred to the KIT amplifier’s input, the gain has lowered by 1 dB from its small signal value. It is measured for ${\omega }_p=2\pi \times 8.895$ GHz. (c) At the same pump frequency, a closeup on the small signal gain around 4.5 GHz shows ripples with 8 MHz characteristic frequency.

Figure 5

Schematic of the noise measurement setup. Each component is labeled with its gain or transmission efficiency, and with its input-referred added noise. Calibrated noise $N_{\mathrm{in}}^s$ ($N_{\mathrm{in}}^i$) is generated by the SNTJ at the signal (idler) frequency. It is routed to the KIT amplifier with transmission efficiency ${\eta }_1^s$ (${\eta }_1^i$), i.e., it undergoes a beamsplitter interaction and part of it is replaced with vacuum noise whose value $N_f=0.5$ quanta. At the KIT amplifier’s input, the noise is $N_1^j$, $j\in \{s,i\}$. On the signal-to-signal path, the KIT amplifier then adds $N_{\mathrm{ex}}^s$ quanta of excess noise and has a gain $G$; on the idler-to-signal path, the KIT amplifier adds $N_{\mathrm{ex}}^i$ quanta of excess noise and has a gain $G-1$. Noise $N_2^s$ at the KIT amplifier’s output is then routed with efficiency ${\eta }_2$ to the HEMT (input noise $N_3^s$). With gain $G_H$ and added noise $N_H$, it further directs the noise $N_4^s$ to room-temperature components. Amplification and loss at room temperature are excluded from our schematic but not our analysis. The noise reaching the spectrum analyzer (SA) is $N_o^s$. The full setup is described in Appendix pp5.

Figure 6

System-added noise measurement of a microwave amplification chain with a KIT amplifier as the first amplifier. (a) The gain’s frequency dependence is measured with a VNA (with a 1 kHz intermediate frequency bandwidth). (b) The output noise $N_o^s$ is measured with a SA (5 MHz resolution bandwidth, comparable to a typical resonant amplifier’s bandwidth), while varying the SNTJ dc voltage bias $V$. Fitting the whole output noise response, we obtain the frequency-dependent system-added noise $N_{\mathrm{\Sigma }}$ and the chain’s signal-to-signal gain $G_c^{\mathrm{ss}}$. We divide $N_o^s$ by $G_c^{\mathrm{ss}}$ to refer it to the KIT amplifier input, and subtract the zero bias noise value $N_f=0.5$, so that $N_{\mathrm{\Sigma }}$ [panel (c)] visually matches the zero bias value of $N_o^s$ (see Appendix 17). Three colored curves indicate output noises at 4, 5, and 6 GHz, with fits superimposed in black lines. (c) Data from the output noise spectra are compiled to form $N_{\mathrm{\Sigma }}$. Uncertainties are indicated by the gray area surrounding the black line. They predominantly come from the fit of the curves in (b). The quantum limit (QL) on amplifier-added noise is indicated by the dashed black line.

Figure 7

Theory of KIT amplifier saturation, calculated by solving the full CMEs, Eqs. (A5a). (a) Distortion of the gain profile, at four different input signals: $I_{s0}=I_{p0}/100$ (blue curve), corresponding to a small signal regime, $I_{s0}=I_{p0}/12$ (red curve), $I_{s0}=I_{p0}/8$ (green curve), and $I_{s0}=I_{p0}/6$ (purple curve). The KIT amplifier length is $N_c=6.6\times {10}^4$ cells. Vertical lines indicate three frequencies: 3.4406 GHz (long dashed), 4.4406 GHz (solid), equal to the half pump frequency, and 5.4406 GHz (short dashed). (b) The gain of a probe tone is calculated at these three frequencies, as a function of the probe tone power. (c) The 1 dB compression power is shown as a function of frequency.

Figure 8

KIT amplifier packaging. (a) The amplifier is clamped on a gold plated copper box and wire bonded to PCBs and to the box itself. Although not very sensitive to the magnetic field, the KIT amplifier is shielded with aluminum and A4K cryogenic shielding. Two SMA connectors protrude on both sides of the packaging. (b) A closeup on the central region of the amplifier shows the periodically loaded transmission line, with gold strips deposited between its spiral arms. (c) The top copper lid contains spring-loaded pogo pins inserted halfway into the box. They are arranged to contact the chip between the KIT amplifier trace. (d) A closeup on the pins shows their top thinner part, which can retract inside the body of the pin. They are fixed on the copper lid with dried silver paint.

Figure 9

Full schematic of the noise measurement experimental setup. The KIT amplifier is represented by a spiral, enclosed in a square. A permanent magnet suppresses the Josephson effect in the SNTJ. A magnetic shield protects other microwave components from the effect of this magnet. The 4–12 GHz isolator is from Quinstar technology, model CWJ1015-K13B. The dashed purple line represents the bypass.

Figure 10

System-added noise measurement of a microwave amplification chain with the HEMT as the first amplifier. (a) The transmission through the whole noise setup (KIT amplifier unpumped), when the SNTJ has been replaced by a transmission line capacitively coupled to an array of resonators (not used in the present experiment). It is performed in two situations: without (black curve) and with (purple curve) the bypass. (b) Examples of $T_o^{s^{\prime }}=N_o^{s^{\prime }}\hslash \omega /k_B$ are shown for the SA centered at 4, 5, and 6 GHz, with fits superimposed in black lines. The SA RBW is 5 MHz. (c) From the fits, we extract the system-added noise temperature $T_{\mathrm{\Sigma }}^{\prime }=N_{\mathrm{\Sigma }}^{\prime }\hslash \omega /k_B$ as a function of frequency without (black curve) and with (purple curve) the bypass. Uncertainties are indicated by the gray area surrounding the lines.

Figure 11

Insertion loss from the microwave components used in the noise measurement setup (see Fig. 9). The ILs (a) are measured at 4 K: the bias tee, Anritsu K250 (red curve), the low-pass filter, Pasternack PE87FL1015 (green curve), the directional coupler, Pasternack PE2204-20 (blue curve), and the isolator, Quinstar CWJ1015-K13B (purple curve). (b) Combining the IL from the components before and after the KIT amplifier, we estimate the transmission efficiencies ${\eta }_1^s$ (black curve) and ${\eta }_2$ (purple curve).