The Microstrip SQUID Amplifier in ADMX 21 August 2018 Sean O’Kelley Clarke group, Berkeley CA
Outline • Motivations from the Axion search • Principle of SQUIDs as microwave amplifiers • Practical MSA design and performance
Motivations from the Axion search The Invisible Universe • Ordinary Matter Astronomical observations indicate that baryonic matter accounts for only 4% of the mass-energy of the universe. • Dark Matter Orbital kinematics of stars in galaxies, galaxies in clusters, and observations of gravitational lensing all point towards the presence of about 5 times more mass than can be accounted for by stars, gas, and other ordinary matter. • Dark Energy The observation that our universe is not just expanding, but accelerating indicates that the universe’s total mass -energy is dominated by the cosmological constant, quintessence, or other dark energy.
Motivations from the Axion search The Invisible Universe Credit to: xkcd.com (Aug. 20, 2018) “ A webcomic of romance, sarcasm, math, and language .”
Motivations from the Axion search The Invisible Universe Credit to: xkcd.com (Aug. 20,2018) “ A webcomic of romance, sarcasm, math, and language .” • The axion was originally proposed in 1977 by Peccei and Quinn (before the idea of dark matter) as a solution that “cleans up” the problem of extremely high symmetry observed in the strong force. • If axions exist, they would have been produced in the big bang, and are an excellent dark matter candidate because they are cold (non-relativistic) and interact with ordinary light and matter very weakly.
Motivations from the Axion search The Axion: a Candidate for DM • The Axion has been observed at UC Berkeley, among a disused lab sink deep in the second basement of Birge hall! • Initial data suggests a non-virialized velocity distribution and highly non- homogenous density, so universal abundance remains an open question and no competing DM candidates have yet been excluded. • Even 10 years after the expiration date, Axion remains an excellent degreaser.
Motivations from the Axion search The Axion Search Space 3 orders of magnitude in mass/frequency to search
Motivations from the Axion search How to Find an Axion Expected Signal 6 ~ 10 Power Primakoff Conversion to Amplifier Magnet Frequency Need to scan frequency Cavity Need low noise floor Pierre Sikivie (1983)
The Axion Dark Matter Candidate What Sets the Noise Floor? Power Total Noise Power = Thermal Noise + Extra Noise from Amplifier Frequency amplifier G x signal noise signal thermal noise + = + = G IN OUT
The Axion Dark Matter Candidate What Sets the Noise Floor? Power Total Noise Power = Thermal Noise + Extra Noise from Amplifier Frequency amplifier G x signal noise signal thermal noise + = + = G IN OUT amplifier G x signal signal thermal noise noise + + = G
The Axion Dark Matter Candidate What Sets the Noise Floor? Power Total Noise Power = Thermal Noise + Extra Noise from Amplifier Frequency amplifier G x signal noise signal thermal noise + = + = G IN OUT amplifier G x signal signal thermal noise noise + + = G Thermal Noise Power at Input = 𝑙 𝐶 𝑈∆𝑔 Amp. Noise Power at Input = 𝑙 𝐶 𝑼 𝑶 ∆𝑔
The Axion Dark Matter Candidate Noise Temperature T N Resonat ator MSA MSA HEMT Si Si G 3 G 2 G 1 𝑡𝑧𝑡 = 𝑈 𝑞ℎ𝑧𝑡 + 𝑈 𝑂 𝑁𝑇𝐵 + 1 1 𝑇𝑧𝑡𝑢𝑓𝑛 𝑂𝑝𝑗𝑡𝑓 𝑈𝑓𝑛𝑞𝑓𝑠𝑏𝑢𝑣𝑠𝑓 𝑈 𝐻 1 𝑈 𝑂 𝐼𝐹𝑁𝑈 + 𝐻 1 𝐻 2 𝑈 𝑂 𝑇𝑗 + … Amplifier Technology T T N Conventional Si Microwave Amp. 300 K 50 K Cryogenic HEMT Amp. 4.2 K 2 K T N ≈ max(T/2, T Q ) MSA 4.2 K to 50 mK Standard Quantum Limit T Q -- hf/k B (48mK @ 1GHz) For a small T S : • Need a T N MSA on par or small relative to T Q and T • Need a G 1 large or on par with T N HEMT /T N MSA
Motivations from the Axion search The Importance of Noise Temperature • Original system noise temperature: T S = T + T N = 3.2 K Cavity temperature: T = 1.5 K (pumped He 4 ) Amplifier noise temperature: T N = 1.7 K (HEMT) • Time* to scan the frequency range from f 1 = 0.24 to f 2 = 0.48 GHz: t ( f 1 , f 2 ) = 4 x 10 17 (3.2K/1 K) 2 (1/ f 1 – 1/ f 2 ) sec ≈ 270 years *Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) theory
Motivations from the Axion search The Importance of Noise Temperature • Original system noise temperature: T S = T + T N = 3.2 K Cavity temperature: T = 1.5 K (pumped He 4 ) Amplifier noise temperature: T N = 1.7 K (HEMT) • Time* to scan the frequency range from f 1 = 0.24 to f 2 = 0.48 GHz: t ( f 1 , f 2 ) = 4 x 10 17 (3.2K/1 K) 2 (1/ f 1 – 1/ f 2 ) sec ≈ 270 years • Next generation: Cavity temperature: T = 50 mK (He 3 dilution unit) Amplifier noise temperature: T N = 50 mK (MSA) • Time* to scan the frequency range from f 1 = 0.24 to f 2 = 0.48 GHz: t ( f 1 , f 2 ) = 4 x 10 17 (0.1K/1 K) 2 (1/ f 1 – 1/ f 2 ) sec ≈ 100 days *Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) theory
Motivations from the Axion search ADMX at UW
Outline • Motivations from the Axion search • Principle of SQUIDs as microwave amplifiers • Practical MSA design and performance
Principle of SQUIDs as microwave amplifiers The Microstrip SQUID Amplifier I B I B V d V d Φ Φ Φ 0 0 1 2 Microstrip SQUID Amplifier (MSA): 20 Nb 15 Nb coil, washer Gain (dB) isolated from (ground) 10 washer (input) 5 Nb Counter electrode 0 (output) -5 Nb-AlOx-Nb 400 600 800 1000 junctions Resistive shunts Frequency (MHz)
Principle of SQUIDs as microwave amplifiers Superconductivity Flux Quantization • At low temperatures in a SC metal, ½-spin • ψ must be continuous, so on trips around a SC electrons (fermions) bind into 0-spin Cooper ring, θ may “advance” only in intervals of 2π . pairs (bosons). • Momentum (current) is determined by del θ . • • Cooper pairs are the charge-carrying unit in Total flux is (I x L) constrained to integer superconductors. multiples of h /2 e. • As cold Bosons, the Cooper pairs almost all = n 0 condense to the ground state (Bose-Einstein condensate) resulting in a macroscopically coherent quantum state . J • All the magic is possible due to this large- scale quantum coherence! • Coherence length in θ can range from 100’s = n 0 (n = 0, ±1, ±2, ...) of nm to several m! (Typical device size is 1 mm) Φ 0 = h /2 e ≈ 2.07 10 -15 Wb (also, current can flow without dissipation)
Principle of SQUIDs as microwave amplifiers Superconductivity • At low temperatures in a SC metal, ½-spin Josephson Tunneling electrons (fermions) bind into 0-spin Cooper insulating pairs (bosons). barrier i i e e 1 2 1 2 • Cooper pairs are the charge-carrying unit in superconductor superconductor superconductors. I I • As cold Bosons, the Cooper pairs almost all condense to the ground state (Bose-Einstein ~ 20 Å condensate) resulting in a macroscopically d coherent quantum state . 1 2 Overlap interaction of the wavefunctions in the “classically forbidden” insulator leads to the • All the magic is possible due to this large- Josephson relations: scale quantum coherence! • Coherence length in θ can range from 100’s V= 𝐽 = 𝐽 0 sin 𝜀 𝜀𝛸 0 /2 π of nm to several m! (Typical device size is 1 mm) (also, current can flow without dissipation)
Principle of SQUIDs as microwave amplifiers The RCSJ Model substituting the 2 nd Josephson relation: A Josephson junction is two conductors separated 𝐽 − 𝐽 0 sin 𝜀 = Φ 0 1 𝜀 + Φ 0 2𝜌 𝐷 𝜀 by an insulator, so there is a capacitance. A 2𝜌 𝑆 resistance may also exist due to an imperfect insulating layer or a resistance added by design. or − 2𝜌 𝜖𝑉 𝜖𝜀 − Φ 0 1 𝜀 = Φ 0 2𝜌 𝐷 𝜀 Φ 0 2𝜌 𝑆 with 𝑉 = Φ 0 2𝜌 𝐽 0 1 − cos 𝜀 − 𝐽𝜀 “phase” particle on a tilted washboard: From Kirchhoff’s laws: 𝐽 = 𝐽 0 sin 𝜀 + 𝑊 𝑆 + 𝐷 𝑊 Josephson relations: V= 𝐽 = 𝐽 0 sin 𝜀 𝜀𝛸 0 /2 π − 𝜖𝑉 𝜖𝑦 − ξ 𝑦 = 𝑛 𝑦
Principle of SQUIDs as microwave amplifiers The RCSJ Model Insight from tilted washboard potential: • V=0 for any I < I 0 (starting flat, at rest) • As soon as I > I 0 , V > 0 (particle rolls downhill) • For small damping terms, V may remain non-zero, even if I < I 0 2𝜌 Φ 0 I 0 𝑆 2 𝐷 Critical damping parameter β 𝑑 = • “phase” particle on a tilted washboard: determines if V 0 for I < I 0 regardless of tilt 𝑉 = Φ 0 2𝜌 𝐽 0 1 − cos 𝜀 − 𝐽𝜀 tilt I position δ velocity V mass C damping 1/R This is why we add parallel resistance
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