Detecting Axion Dark Matter with Superconducting Qubits Akash Dixit, Ankur Agrawal, Srivatsan Chakram, Ravi Naik, Jonah Kudler-Flam, Aaron Chou, David Schuster University of Chicago avdixit@uchicago.edu 1
Outline of Talk • Moving from phase preserving measurement to photon counting • Designing a single photon counter • Experimental protocol to determine cavity photon occupation • Overcoming background sources and dark rates in new detection scheme 2
Photon Rates of Signal and Backgrounds DFSZ, 0.3 GeV/cc, 14T, C=1/2, Q=5x10 4 @1GHz, 1 ! 3 , crit.coup. 5 10 dN/dt [Hz] • Signal Rate decreases d g k b L Q S 4 10 with cavity volume. 2 3 5 Error prob. for 10 m K Potential b l n-qubit a <<1 photon per cavity c 2 A k 10 x b background i o o n d s coincidence y i g n a l reduction 10 measurement counting = (10 -2 ) n 1 4 qubit dark rate -1 10 • Quantum limited noise -2 4 qubit 3σ sensitivity 10 Signal shot noise limit 3σ, t=10 4 s from linear amplifier = 5 qubit 3σ sensitivity -3 10 5 qubit dark rate 1 photon/ -4 10 measurement -5 10 1 10 f [GHz] 20 GHz = 80 " eV itivity is only limited by signal shot noise. Signal rate can be increased 3
How to Bridge the Gap between Signal and Background • Signal Rate decreases with cavity volume. <<1 photon per cavity measurement • Quantum limited noise from linear amplifier = 1 photon/measurement 4
Advantages and Challenges of Counting • Circumvent quantum limited phase preserving amplifier • False positives dominate background • cavity thermal occupation • detector dark rate 5
Harmonic Oscillator + Two Level System H = ω c a † a + ω q σ z + 2 χ a † a σ z 6
Microwave Cavity Designed to Maximize Axion Conversion H = ω c a † a + ω q σ z + 2 χ a † a σ z Maximize overlap between L ∼ ga E · B cavity mode E and external B 7
Superconducting Qubit Functions as Two-Level System H = ω c a † a + ω q σ z + 2 χ a † a σ z 253 nm ↵ | e 260 nm ↵ | g Josephson ω q = E 1 − E 0 Junction Harmonic Oscillator (LC) + Customize transition frequency nonlinearity (Josephson Junction) 8 8
Designing Qubit-Cavity Interaction H = ω c a † a + ω q σ z + 2 χ a † a σ z g 2 χ = ∆ ( ∆ + α ) α 9
Designing Qubit-Cavity Interaction H = ω c a † a + ω q σ z + 2 χ a † a σ z r ~ ω d · E = q ∆ s V g 2 χ = ∆ ( ∆ + α ) α 10
Designing Qubit-Cavity Interaction H = ω c a † a + ω q σ z + 2 χ a † a σ z r ~ ω d · E = q ∆ s V g 2 χ = ∆ ( ∆ + α ) α ∆ = ω q − ω c 11
Designing Qubit-Cavity Interaction H = ω c a † a + ω q σ z + 2 χ a † a σ z r ~ ω ↵ d · E = q ∆ s | f V ↵ | e ↵ | g g 2 χ = ∆ ( ∆ + α ) α 20µm × 20µm 1mm ∆ = ω q − ω c 12
Axion Deposits Single Photon in Cavity H = ω c a † a + ( ω q + 2 χ a † a ) σ z Axion induced current pumps cavity with photon 13
Cavity Occupation Imprinted on Qubit H = ω c a † a + ( ω q + 2 χ a † a ) σ z ω q ω q − χ | n = 0 i | n = 1 i Cavity occupation shifts ω q − 2 χ qubit transition χ ∼ 15 MHz | n = 2 i 14
Qubit Interrogation H = ω c a † a + ( ω q + 2 χ a † a ) σ z ω q ω q − χ | n = 0 i | n = 1 i ω q − 2 χ χ ∼ 15 MHz | n = 2 i Excite qubit at shifted π frequency 15
False Positives from Backgrounds and Detector Dark Rate Cavity Photon Population Qubit Excited State Population 4 . 66 × 10 − 5 < ¯ n cav < 4 . 47 × 10 − 4 P e = 0 . 014 T cav = 55 . 13 +4 . 52 T qubit = 82 mK − 9 . 01 mK Residual photons in the cavity are Spurious population in the qubit excited state mimics a successful qubit flip indistinguishable from signal photons 16
Reducing Cavity Thermal Occupation • Reduce photons from higher temperature stages with line attenuation • Are circulators and isolators cold? • attenuators? Custom atten courtesy of B. Palmer: Journal of Applied Physics 121, 224501 (2017) 17
Active Cooling of Qubit Population Active sideband ↵ | f ↵ cooling with higher | e qubit levels ↵ | g ↵ ↵ | f 0 → | g 1 ω sb = ω ge q + ω ef q − ω cav π ef ω sb τ
Reduce effective dark rate by combining qubit measurements • Sample the same qubit N times • requires N times as much time to complete experiment • photon decays quickly (1us) • Sample N different qubits with error rate alpha P Nerrors = ( α ) N 19
4-Qubit Cavity Design 20
Conclusions • Employ quantum computing techniques/devices for dark matter cosmology experiment • Shift penalties of standard quantum limit by dispersively counting photons • Build superconducting detectors with customizable interactions with an EM environment • Use Qubit-Cavity interactions to store & process quantum information 21
Qubit Fabrication Fluorine Etcher Electron Beam Lithography Not pictured: -Double Angle Evap -Thermal Evap -Dicing Saw Optical Direct Writer -SEM -Sputter Coater 22
Dispersive Coupling of the Cavity and Qubit H int = 2 χ a † a σ z Interaction set by: • dipole arm geometry • qubit location in cavity • qubit-cavity frequency detuning • qubit anharmonicity 20µm × 20µm 1mm 23
Qubit Characterization Qubit Decoherence Qubit Energy Relaxation Ramsey Experiment T1 = 48us T2 = 44.5us 24
Number Splitting 25
Dephasing with Cavity Drive 26
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