Selective single- and double-mode quantum-limited amplifier

Abdul Mohamed, Elham Zohari, Jarryd J. Pla, Paul E. Barclay, and Shabir Barzanjeh

Phys. Rev. Applied 21, 064052 – Published 24 June 2024

Abstract

A quantum-limited amplifier enables the amplification of weak signals while introducing minimal noise dictated by the principles of quantum mechanics. Such amplifiers serve a broad spectrum of applications in quantum computing, including fast and accurate readout of superconducting qubits and spins, as well as various uses in quantum sensing and metrology. Parametric amplification, primarily developed with use of Josephson junctions, has evolved into the leading technology for highly effective microwave measurements within quantum circuits. Despite their significant contributions, these amplifiers face fundamental limitations, such as their inability to handle high powers, their sensitivity to parasitic magnetic fields, and particularly their limitation to operate only at millikelvin temperatures. To tackle these challenges, here we experimentally develop a novel quantum-limited amplifier based on superconducting kinetic inductance and present an extensive theoretical model to describe this nonlinear coupled-mode system. Our device surpasses the conventional constraints associated with Josephson-junction amplifiers by operating at much higher temperatures up to 4.5 K. With two distinct spectral modes and tunability through bias current, this amplifier can operate selectively in both the single-mode-amplification regime and the double-mode-amplification regime near the quantum noise limit. Using a nonlinear thin film exhibiting kinetic inductance, our device attains gain exceeding 50 dB in a single-mode configuration and 32 dB in a double-mode configuration, while adding 0.82 input-referred noise quanta. Importantly, this amplifier eliminates the need for Josephson junctions, resulting in the capability to handle significantly higher powers than Josephson junction–based amplifiers. It also demonstrates resilience in the presence of magnetic fields, offers a straightforward design, and increases reliability. This positions the amplifier as a versatile solution for quantum applications and facilitates its integration into future superconducting quantum computers.

Received 26 November 2023
Revised 4 March 2024
Accepted 29 May 2024

DOI:https://doi.org/10.1103/PhysRevApplied.21.064052

Physics Subject Headings (PhySH)

Circuit quantum electrodynamics Optoelectronics Quantum information with solid state qubits Superconducting quantum optics

Optical parametric oscillators & amplifiers Superconducting devices Thin films

Microwave techniques

Quantum Information, Science & TechnologyAtomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Abdul Mohamed ¹, Elham Zohari ^1,2, Jarryd J. Pla³, Paul E. Barclay¹, and Shabir Barzanjeh^1,*

¹Department of Physics and Astronomy, University of Calgary, Calgary, Alberta T2N 1N4, Canada
²Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
³School of Electrical Engineering and Telecommunications, UNSW Sydney, Sydney, New South Wales 2052, Australia

^*Contact author: shabir.barzanjeh@ucalgary.ca

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Vol. 21, Iss. 6 — June 2024

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Figure 1
Schematic representation of a coupled-resonator system exhibiting coupling rate $J$ . Here one resonator, with resonance frequency $ω_{a}$ and annihilation operator $a$ , is coupled to an auxiliary resonator having resonance frequency $ω_{b}$ and annihilation operator $b$ . Incorporating a nonlinear medium characterized by a $χ^{(2)}$ nonlinearity, resonator $a$ facilitates amplification via the 3WM process. The system’s operation mode, whether single-mode or double-mode amplification, can be selected by one properly pumping the system. (a) The single-mode-amplification scenario, characterized by a significant separation in resonance frequencies between the two resonators, expressed as $| ω_{a} - ω_{b} | ≫ 2 J$ . In this setup, the system can be effectively treated as a single mode by one disregarding the dynamics of the auxiliary resonator $b$ . Amplification of the single mode is achieved by application of a strong pump at $ω_{p} = 2 ω_{a}$ , resulting in a degenerate amplification in mode $a$ , as seen in the power spectral density (PSD) of the output field. (b) In contrast, by adjustment of the resonance frequencies of the two modes so that they are equal, i.e., $ω_{a} = ω_{b}$ , and by the pumping of the system at $ω_{p} = ω_{a} + ω_{b}$ , double-mode amplification is realized, with the two modes being spectrally separated by the coupling rate $J$ . Here $κ_{j}^{e (i)}$ is the extrinsic (intrinsic) damping rate of each resonator $j = a, b$ .
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Figure 2
(a) A ring resonator with a 1.3-mm diameter and a 2- $μ m$ pitch is connected capacitively to an auxiliary resonator. The system is probed through a transmission line connected capacitively to the left side of the ring. A separate line provides the pump and direct current from the device’s bottom, flowing through the ring. (b) Optical image of the KIPA involving a ring and L-shaped auxiliary resonators. The inset in (b) displays the L-shaped auxiliary resonator with a width of $160 μ m$ and a length of 4 mm. The design prohibits direct current from passing this resonator, effectively setting the 3WM nonlinearity to zero for the auxiliary resonator. (c) Resonance frequency of the ring resonator as a function of applied bias current. The resonance frequency shows a quadratic pattern with respect to the applied current $Δ ω = - (ω_{0} / 2) {(I_{dc} / I^{*})}^{2}$ . (d) Resonance frequency of the resonator at fixed current $I_{dc} = 1.575$ mA, corresponding to $ω_{0} / 2 π = 7.155$ GHz.
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Figure 3
(a) Appearance of the two modes and the anticrossing point as a function of the applied direct current. The two modes are separated by $2 J \approx 43$ MHz. (b) Signal amplification versus pump frequency and detuning from the center of the anticrossing. (c) Phase-insensitive gain for the two modes at various pump powers versus the detuning from the center of the anticrossing.
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Figure 4
(a) Single-mode phase-insensitive signal gain versus the frequency detuning from the resonator $ω = δ + (ω_{p} / 2)$ for different pump powers. The experimental results (dots) align well with the theoretical model (solid lines) outlined in the text. (b) Phase-sensitive gain as a function of the pump phase $ϕ_{p}$ . A coherent tone positioned at $δ = 0$ is measured while the pump phase is varied. The data are adjusted to align all dips at zero radians. The result is in good agreement with the theory. (c) The 1-dB compression point for a coherent tone at $δ = 1$ kHz from the amplification center frequency. Power is varied to determine the 1-dB compression points at different pump powers.
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Figure 5
(a) Noise-calibration setup. A 50- $Ω$ terminator, varied in temperature, acts as the known noise source. The generated noise is directed to the KIPA at various gains. By using the Bose-Einstein distribution to fit the noise spectrum, we extract the total gain and noise quanta added by the amplification chain. (b) Noise quanta added by the whole amplification chain versus the gain of the KIPA when it is operating in the single-mode regime. At zero gain ( $G_{k} = 0$ ), the noise of the classical amplification chain $n_{h}$ dominates the added noise. In contrast, at large gains ( $G_{k} ≫ 1$ ), the noise added by the KIPA becomes noticeable $n_{add} \approx (\bar{n} + \frac{1}{2} + n_{k})$ . Our fitting the data using the theoretical model results in $n_{k} \approx 0.82$ . (c) Comparison of the KIPA gain at different device temperatures (80 mK, 1 K, 4 K, and 4.5 K). Here, SA is spectrum analyzer.
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