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Practical Microwave Amplifiers with Superconductors Lafe Spietz Leonardo Ranzani Minhyea Lee Kent Irwin Norm Bergren José Aumentado Outline • Motivation • The NIST DC-SQUID microwave amp • Parametric amplifiers Motivation • Some qubit readouts are limited by amplifier • Improve the amplifer, improve the readout • Present state of the are amplifiers are transistor amplifiers which must be separated from the experiment • SQUIDs provide lower noise and can be closer to experiment than transistor amplfiers What is Noise Temperature*? Temperature of matched load which doubles noise at output *for T>>hf/k Better Amplifiers Provide Orders of Magnitude Speedup: • Dicke Radiometer Formula: • Thus • 40x lower TN gives 1600x speedup in measurement times! Comes from Poisson statistics! Microwave Quantum Circuits semiconductor amplifier superconductor amplifier Quantum Noise of a Resistor 7 GHz 170 mK n = ½Coth(hf/2kT) Quantum Limits to Amplifiers I f(t) = A Cos(wt + f) f(t) = X Cos(wt) + Y Sin(wt) Phase quadratures are conjugate variables, subject to an uncertainty principle DX·DY ≥ ½ Quantum Limits to Amplifiers II Amplified coherent state Quantum limit Coherent state Noise above quantum limit Present Commercial State of the Art Semiconducting Amplifier: HEMT Amps from Weinreb Group • 0.1-14 GHz • 35 dB gain • TN = 1.5-3 K (5- 40 photons added) • $5000 each • Typical system noise ~10-20 K DC Squids: Flux to Voltage Amplifier ∂V/∂F gives gain From power coupled to flux Statement of the Problem: DC Squids in the Microwave (Nomenclature Disaster) Stray capacitances shunt incoming microwave signal making it difficult to couple power in: Our Approach • Shrink the physical size of the SQUID until it can be treated as a lumped element component • Model and experimentally characterize input and output impedance • Design input and output impedance transformers • Design box/board infrastructure to make a usable “product” which can be easily disseminated NIST SQUID design • Kent Iriwin’s octopole gradiometer squid design Assembly Line Construction and Interchangeable Parts Assembly Line Construction and Interchangeable Parts Impedance Measurement and Matching • Measure S parameters at harmonics of a quarter wave resonator to learn about input impedance V(x) V(x) Chip Layout of Quarter Wave 8 mm Multiple Harmonics 3f0 =5.04 GHz f0 =1.68 GHz Impedance Measurement >95% power coupling to 0.18 W source Impedance Model • With physically small squids, we treat them as lumped elements with minimal stray reactances * Measured Real[Zin] Voltage [mV] Voltage [mV] Transfer Function Gain and Noise Measurement (or shot noise source) Typical Gain Curves Broadband Gain 1 GHz Noise Temperature Noise Temperature Gain Map (5.4 GHz) Gain Scan Zoom Extreme Zoom Steep Ridge Drift Test: Gain Dependence on Flux Overnight Gain Drift Dynamic Range Parametric Amplification Vary some parameter of an oscillator to pump energy into or out of the system Josephson Parametric Amplifiers signal pump • Use the nonlinearity of JJ circuits to modify some resonant frequency in a microwave circuit • No quantum limit • Usually reflection amplifiers • Can create “squeezed states” of microwave radiation Josephson Parametric Amplifiers Driven by needs of QC community Rapidly growing field! • Lehnert et al. at JILA (beat quantum limit in a practical experiment!) • Nakamura et al. at NEC • Aumentado et al. at NIST • Devoret et al. at Yale • Siddiqi et al. at Berkeley • Etc. Amplification: The Dream Amplifier Technologies HEMT SQUID Parametric System noise Power dissipation Bandwidth ~10 K ~1 K ~ 0.1 K ~10 mW ~ 1 mW < 1 pW >14 GHz 400 MHz 100 kHz Availability Commercial Beginning distribution Largely in-house SNR Improvement: Before 20 hours No SQUID SNR Improvement: After 5 hours SQUID amp Imaginary Component of Input Impedance DC IV Characteristics Output Matching 170 pH 700 pH 4 pF 0.9 pF Summary • Measured input impedance at a range of microwave frequencies • Demonstrated minimal stray reactance • Demonstrated useful gains and bandwidths in 4-8 GHz frequency range • Constructed system for easy production and deployment of SQUID amplifiers • Demonstrated extreme stability of SQUIDs over hours of measurement time Future Work • • • • • Improve ultra-broadband design Build amplifiers at several more frequencies Understand and improve noise Measure shot noise with amplifiers Distribute amplifiers to collaborators Output Matching Output Matching Broadband Design Target: High frequency, maximum bandwidth Multipole lumped-element transformers at input and output Broadband Test: First Attempt • Microwave design needs work!! • Gain bandwidth product is encouraging Parametric Amplification Vary some parameter of an oscillator to pump energy into or out of the system Bias Modulates Frequency DC SQUID/Parametric amp hybrid Parametric mode acts as preamp: Phase Dependent Added Gain Differential Resistance High Frequency: First Attempt • Shorter resonator • Matched input • Lower Q Transfer Function and Gain Gain Map: Resonances I-V Curves SNR Improvement 10x Faster Measurement at 7 GHz 7 GHz Gain 100 MHz Outline • • • • Motivation Our Approach Amplifier Characterization Milestones and future work Other Superconducting Efforts: A renaissance is in progress! • Yurke JPA work (1980’s) • Clarke group DC SQUID amps • Japanese DC SQUID amps and parametric amps(NEC) • Lehnert Group(NIST/JILA/CU) • Yale Quantronics Group J-Bridge amp • All-invited session at March Meeting and ASC on amplifiers! Motivation • • • • • • Radio Astronomy Quantum computing Noise studies Microwave quantum optics RF-SET readout Fundamental measurement science Superconducting Microwave Amplifiers at NIST Lafe Spietz José Aumentado Resonator Length Typical High-f Input Resonator