Low-Mass Dark Matter Searches Using Quantum Sensing and Readout - - PowerPoint PPT Presentation
Low-Mass Dark Matter Searches Using Quantum Sensing and Readout with MKIDs and Paramps Ritoban Basu Thakur on behalf of Golwala-group New Directions in the Search for Light Dark Matter Particles 2019/06/06 Overview Detector requirements
Ritoban Basu Thakur
New Directions in Searches for Light DM Basu Thakur/Golwala
Small detectors focused on energy resolution for low-mass reach (< GeV, << GeV) Large detectors focused on ER/NR rejection and position reconstruction for neutrino floor reach at 0.5-5 GeV
SuperCDMS Pyle, Zurek, Kurinsky, McKinsey et al
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New Directions in Searches for Light DM Basu Thakur/Golwala
Current technologies ~1 eV threshold
MeV thermal relics, eV dark photons
Need new technologies to access keV thermal relics, meV dark photons! Sharp targets due to simplicity:
same diagrams for annih. and scatt. no accidental cancellations
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103 102 101 100 101 102 103
mχ [MeV]
1045 1044 1043 1042 1041 1040 1039 1038 1037 1036 1035 1034 1033 1032
σe [cm2]
BBN Stellar bounds Freeze-in
SuperCDMS G2 DAMIC-1K LBECA SENSEI-100g ZrTe5 Al SC
Xenon10
Dark photon mediator mA0 ⌧ keV GaAs Al2O3 Al2O3 (mod) p h
s c i n t i l l a t
101 102 103
mX (keV)
10−43 10−42 10−41 10−40 10−39 10−38 10−37 10−36 10−35 10−34
σn (cm2)
H e ( m u l t i p h
)
Al2O3
ω > 1 meV ω > 25 meV ω > 50 meV ω > 75 meV
10−3 10−2 10−1 100 101 102
mA [eV]
10−18 10−16 10−14 10−12 10−10
κ
Stellar constraints
Al SC
e excitation
Ge
phonon excitation
S i
Dirac material M
e c u l e s
Direct detection constraints 1 kg-yr, Sapphire 1 kg-yr, GaAs
dark photon absorption DM-electron scattering (light mediator) DM-nucleon scattering
New Directions in Searches for Light DM Basu Thakur/Golwala
Superconductors have an AC inductance due to inertia of Cooper pairs
alternately, due to magnetic energy stored in screening supercurrent
Changes when Cooper pairs broken by energy, creating quasiparticles (qps) Sense the change by monitoring a resonant circuit Key point: superconductors provide very high Q (Qi > 107 achieved), so thousands of such resonators can be monitored with a single feedline
enormous cryogenic multiplex technology relative to existing ones very simple cryogenic readout components
Cryostat Frequency Synthesizers IQ Mixers I Q 5
Day Mazin
sub-meV pair- breaking energy
New Directions in Searches for Light DM Basu Thakur/Golwala
Superconductors have an AC inductance due to inertia of Cooper pairs
alternately, due to magnetic energy stored in screening supercurrent
Changes when Cooper pairs broken by energy, creating quasiparticles (qps) Sense the change by monitoring a resonant circuit Key point: superconductors provide very high Q (Qi > 107 achieved), so thousands of such resonators can be monitored with a single feedline
enormous cryogenic multiplex technology relative to existing ones very simple cryogenic readout components
Cryostat Frequency Synthesizers IQ Mixers I Q 6
Day Mazin
sub-meV pair- breaking energy
New Directions in Searches for Light DM Basu Thakur/Golwala
Quiescent nqp exponentially suppressed as T decreases*
* as long as no anomalous qp recombination physics * as long as no anomalous qp creation
Responsivity only weakly T
(not exponential!)
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Mattis-Bardeen Relations
10-20 10-15 10-10 10-5 100 nqp/(2N0Δ) 10-20 10-15 10-10 10-5 100 [σ-σ(0)]/|σ(0)|
real part Recall σ(0) = jσn(πΔ/hν)
0.1 T/Tc 1 2 3 4 5 [2N0Δ/nqp] [σ-σ(0)]/|σ(0)| = [2N0Δ] ∂(σ/|σ(0)|)/∂nqp
real part
| | σ1 |σ(0)| = 4 π nqp 2N0∆ 1 ⌦ 2π kT
∆
sinh ⇥ ¯ hω 2kT ⇤ K0 ⇥ ¯ hω 2kT ⇤ σ2 |σ(0)| = 1 − nqp 2N0∆ ⌅ 1 + ↵ 2∆ πkT exp ⇥ − ¯ hω 2kT ⇤ I0 ⇥ ¯ hω 2kT ⇤⇧ (0) )
∆ 4 1 ⇥ ¯ ⇤ ⇥ ¯ ⇤ | | 2N0∆ ∂(σ1/|σ(0)|) ∂nqp
= 2N0∆ nqp σ1 |σ(0)| = 4 π 2N0∆ ∂(σ2/|σ(0)|) ∂nqp
= 2N0∆ nqp σ2 − σ2(0) |σ(0)| =
conductivity fully inductive at T = 0
weak T
thermally generated quasiparticle density quiescent fractional conductivity deviation from T=0 value fractional responsivity
New Directions in Searches for Light DM Basu Thakur/Golwala
≥ δ devel τ τ §4.2.2
Noroozian Lifetime (msec)
Quasiparticle response governed by quasiparticle lifetime, observed to follow where n∗ may be a limiting qp density Frequently written as with the recombination constant Sets bandwidth over which noise integrated: larger 𝜐qp is better Many ms lifetimes achievable but perhaps only at low readout powers Need to make conservative assumptions about 𝜐qp to avoid optimistic predictions
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τqp = τmax 1 + nqp/n∗
102 103 102 101 101
100 1,000 750 500 250
Al flms BCS theory Ta flms
75 50 25 0 0 0.05 0.10 0.15 0.20 0.25
100 0.03 0.3
Ta relaxation time (µs)
Ta relaxation time (µs)
Reduced temperature (T/Tc)
T/Tc
Al relaxation time (µs)
Al relaxation time (µs)
Barends et al PRL (2008) as reproduced in Zmuidzinas, ARCMP (2012) asymptotic regime; limiting excess qp density n∗, or something else? related to disorder? (Barends et al implantation experiment)
1 τqp = 2 R nqp + 1 τmax R = (2 n∗ τmax)−1
New Directions in Searches for Light DM Basu Thakur/Golwala
Goal: detection of sub-eV energies from:
Dark phonon absorption, DM-e scattering, scalar-mediated nucleon scattering at very low recoil energies, directly producing phonons w/o e-h pairs
Methods:
Detection of qp creation in superconducting target via phonon or qp collection (Hochberg, Zhao, Zurek, arXiv:1504.07237)
Phonons appropriate when 2∆substrate > hνphonon: phonons propagate quasi-ballistically with long decay times (100 µs - ms: SuperCDMS, Gaitskell thesis w/high RRR Nb) Quasiparticles appropriate when 2∆substrate < hνphonon: phonons cannot propagate, but qp’s can, w/long decay times (e.g.: probably Al, other low T superconductors: untested!)
Detection of optical phonon production in polar materials:
GaAs (Knapen, Lin, Pyle, Zurek, arXiv:1712.06598) Al2O3 (Griffin, Knapen, Lin, Zurek, arXiv:1807.10291)
Architecture:
Single mm-scale KID on gm-scale, few-mm target substrate
Lower-gap superconductor for KID (e.g., AlMn) and/or better amplifiers promise meV-scale resolution
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KID insulating crystal DM-produced phonon
no quasiparticle trapping!*
insulator KID superconducting crystal DM-produced qp quiescent qp phonon insulator KID qp trap
*of the conventional kind with collector >> KID
b)
2 cm 1 g
New Directions in Searches for Light DM Basu Thakur/Golwala
Assume
delta-function-like energy deposition qp population dominated by readout power generation dissipation readout (no TLS noise) amplifier noise dominant over g-r noise (T ~ 0.1 Tc required) quasiparticle lifetime >> phonon absorption time, τqp >> τph,abs ~ 100 µs
Reduce ∆, TN to get well below eV resolution
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quality factor due to quasiparticles 1 mm2 x 10 nm resonator effective volume (weighted by current2) superconductivity factor
r χc = 4 Q2
r
Qi Qc 1
fraction of inductance due to KI ~ aluminum gap amplifier noise temperature “efficiency factors” all assumed to be unity by design (optimistic) efficiency for converting phonons to qps probability for phonon to enter KID per try superconducting gap energy efficiency of qp creation by readout power
χqp = Qi Qi,qp 1 χBW = τqp τabs + τqp 1
normal state single-spin density of states
no quasiparticle trapping!
σE = 2 ∆ ηph r ηread αχcχqp s N0Vr γsS1(fr, Tqp, ∆) Qi,qp s kBTN χBW σE = (0.9 eV) ✓ 0.3 ηph rηread pt 0.1 α ◆ ✓ ∆ 200 µeV ◆ s 106 Qi,qp s Vr 104 (µm)3 TN 5 K 1.6 S1(fr, Tqp, ∆)
New Directions in Searches for Light DM Basu Thakur/Golwala
Assume (conservatively):
qp population dominated by readout power generation dissipation readout (no TLS noise) amplifier noise dominant over g-r noise (T ~ 0.1 Tc required) quasiparticle lifetime in KID << phonon absorption timescale (τqp << τph,abs ~ 100 µs; conservative) Reduce ∆, TN, increase τqp to get well below eV resolution
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superconducting gap energy efficiency for converting phonons to qps fraction of inductance due to KI probability for phonon to enter KID per try efficiency of qp creation by readout power amplifier noise temperature normal state single-spin density of states superconductivity factor quasiparticle lifetime
no quasiparticle trapping!
~ aluminum gap
σE = 2 ∆ ηph rηread αpt s 1 χcχqp s N0 γsS1(fr, Tqp, ∆) s 1 Qi,qp s kBTN τqp r Vabsλpb cs = (7 eV) ✓ 0.3 ηph rηread pt 0.1 α ◆ ✓ ∆ 200 µeV ◆ s 106 Qi,qp s Msub 1 gm λpb 1 µm 7 km/s cs 100 µs τqp TN 5 K 1.6 S1(fr, Tqp, ∆)
pair-breaking length in KID film substrate volume sound speed substrate mass (assuming silicon) quality factor due to quasiparticles
r χc = 4 Q2
r
Qi Qc 1
“efficiency factors” 𝜓c, 𝜓qp assumed to be unity by design, 𝜓BW << 1 (conservative)
χqp = Qi Qi,qp 1 χBW = τqp τabs + τqp 1
New Directions in Searches for Light DM Basu Thakur/Golwala
SuperCDMS 0.5-5 GeV search limited by:
Bulk cosmogenics producing electron recoils Surface background rejection
Requirements:
ER/NR rejection using spectral information and e/h quantization Position-based rejection
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Germanium Raw background spectra expected for SuperCDMS SNOLAB dominated by :
New Directions in Searches for Light DM Basu Thakur/Golwala
Goal:
traditional nuclear recoil search at very low recoil energies (10 eVr)
Method:
10 eV resolution + Neganov-Trofimov-Luke phonon production by drifting e-h pairs in large electric field for single e-h pair detection Or, 0.25-eV resolution and no NTL
Architecture:
~100 KIDs on 10-cm-scale substrate Energy resolution provides ER/NR discrimination Fine pixelation yields surface bgnd rejection via fiducialization Also provides pos’n correction for energy
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Recoil phonons Drift phonons Charge propagation Recoil phonons
~100V 10 cm 100-1000 g
no quasiparticle trapping! Surface event: Bulk event:
Energy (eV) Energy (eV) SuperCDMS PRL 121: 051301 (2018)
New Directions in Searches for Light DM Basu Thakur/Golwala
Assume (conservatively):
qp population dominated by readout power generation dissipation readout (no TLS noise) amplifier noise dominant over g-r noise (T ~ 0.1 Tc required) resonator is coupling dominated (Qi >> Qc = 10k-50k) so τr < τph,r quasiparticle lifetime in KID << phonon absorption timescale (τqp << τph,abs ~ ms; conservative) Reduce ∆, TN, increase τqp to reach eV resolution
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superconducting gap energy efficiency for converting phonons to qps fraction of inductance due to KI probability for phonon to enter KID per try area of substrate (including sidewalls) efficiency of qp creation by readout power pair-breaking length in KID film KID resonant frequency amplifier noise temperature normal state single-spin density of states superconductivity factor quasiparticle lifetime
no quasiparticle trapping!
σE = ∆ ηph rηread αpt s AsubλpbN0 γsS1(fr, Tqp, ∆) s kBTN 2πfrτqp (2) = (330 eV) ✓ 0.3 ηph rηread pt 0.1 α ◆ ✓ ∆ 200 µeV ◆ s Asub 100 cm2 λpb 1 µm 3 GHz fr 100 µs τqp TN 5 K 1.6 S1(fr, Tqp, ∆)
~ aluminum gap
Reasonable yield Qi’s spread from 104 - few 106
Fab goal is a cluster > 105
Formal noise limit being studied:
GR or TLS, no evidence of TLS yet
Proper responsibly calibrations
Sub-mm community has standard techniques
New Directions in Searches for Light DM Basu Thakur/Golwala
Calibration of KID response with readout power pulsing
Apply a 10 µs readout power pulse to one KID (red),
Quasiparticle recombination visible in pulsed KID
1/(pulse amplitude) shows linear relationship with time as expected for pair recombination
Phonon-mediated signal seen in other KIDs (blue)
Quasiparticle decay creates phonons Phonons propagate in substrate to other KID and create quasiparticles there (with rise time) Those quasiparticles decay (exp. decay because δnqp/nqp small)
Calibrate position information with many localized sources!
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pulse amplitude (A.U) 1/(pulse amplitude) (A.U) log(pulse amplitude) (A.U.)
New Directions in Searches for Light DM Basu Thakur/Golwala
Colleagues at JPL (P . Day et al) are developing a quantum-limited amplifier based on:
Nonlinearity due to kinetic inductance 3-wave mixing (DC + pump)
Broadband gain and quantum-limited performance demonstrated
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Transmission line: df ∝du ∝d𝛴 (phase) u(I) = 1/ q C (Lg + Lk,0 (1 + (I/I∗)2))
∂2I ∂z2 ∂ ∂t L(I)C ∂I ∂t
Transmission line traveling wave eq. Sum of currents: pump, weak-signal, idler
I = 1 2 X
n
An(z)ei(knz−ωnt) + c.c. !
3-current (nonlinear) mixing
New Directions in Searches for Light DM Basu Thakur/Golwala
Colleagues at JPL (P . Day et al) are developing a quantum-limited amplifier based on:
Nonlinearity due to kinetic inductance 3-wave mixing (DC + pump) (really 4 wave, but pumps are degenerate)
Broadband gain and quantum-limited performance demonstrated
22
Transmission line: df ∝du ∝d𝛴 (phase) u(I) = 1/ q C (Lg + Lk,0 (1 + (I/I∗)2))
∂2I ∂z2 ∂ ∂t L(I)C ∂I ∂t
Transmission line traveling wave eq. Sum of currents: pump, weak-signal, idler
I = 1 2 X
n
An(z)ei(knz−ωnt) + c.c. !
3-current (nonlinear) mixing
photon absorption is described by terms that contain
1+ 3.
In order to understand the four-wave mixing process, a closer examination of the third order nonlinear polarization must be made. The general form of the polarization may be written as shown in (3). P r E E E i k k k r i t
i ijkl j k l
( , ) ( , , , ) ( ) ( ) ( ) exp[ ( ) ]
( ) *
ω χ ω ω ω ω ω ω ω ω
4 1 2 3 4 1 2 3 1 2 3 1 2 3 4
! ! ! ! ! = − − − + ⋅ − + c.c. (3)
ω ω ω ω2 (SRS, RIKES) 2ω ω ω ω1-ω ω ω ω2 (CARS) 2ω ω ω ω2-ω ω ω ω1 (CSRS) Laser at ω ω ω ω1
Laser at
ω ω ω ω2 χ χ χ χ(3) Material ω ω ω ω1 (TIRES)
4-wave mixing (any nonlinear optics text book)
New Directions in Searches for Light DM Basu Thakur/Golwala
Colleagues at JPL (P . Day et al) are developing a quantum-limited amplifier based on:
Nonlinearity due to kinetic inductance 3-wave mixing (DC + pump)
Broadband gain and quantum-limited performance demonstrated
23
Transmission line: df ∝du ∝d𝛴 (phase) u(I) = 1/ q C (Lg + Lk,0 (1 + (I/I∗)2))
∂2I ∂z2 ∂ ∂t L(I)C ∂I ∂t
Transmission line traveling wave eq. Sum of currents: pump, weak-signal, idler
I = 1 2 X
n
An(z)ei(knz−ωnt) + c.c. !
3-current (nonlinear) mixing
Gs = |As(L)|2 |As(0)|2
0.5 1 1.5 2 5 10 15 20
fsignal / fpump Gain (dB)
Δθ = 1 radian 3 10
New Directions in Searches for Light DM Basu Thakur/Golwala
0.32, 0.25 um
PD
Colleagues at JPL (P . Day et al) are developing a quantum-limited amplifier based on:
Nonlinearity due to kinetic inductance 3-wave mixing (DC + pump)
Broadband gain and quantum-limited performance demonstrated
Devices low yield due to fine features
Applied to UV/O/IR MKIDs to obtain 10x lower TN
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2 4 6 8 10 12
5 10 15 20 25
Parametric Gain (dB)
High kinetic inductance thin films requires carful engineering of transmission lines
High Lk materials for higher gains Phase mismatch for varying frequencies for large BW Transmission / reflection optimized for large BW
New Directions in Searches for Light DM Basu Thakur/Golwala
Colleagues at JPL (P . Day et al) are developing a quantum-limited amplifier based on:
Nonlinearity due to kinetic inductance 3-wave mixing (DC + pump)
Broadband gain and quantum-limited performance demonstrated
Devices low yield due to fine features
New version made showing higher Gain! Y-factor noise measurement done! New low-loss a-Si:H dielectric enables higher-yield version: gain demonstrated, TN = 4 x QL at 3 GHz, likely to improve to QL
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5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10
frequency (GHz)
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
added noise (photons)
noise, 40mK, 14.747 GHz pump Quantum Limit
35 30 25 20 15 10 5 1 2 3 4 5 6 7 Frequency [GHz]
Gain [dB]
New Directions in Searches for Light DM Basu Thakur/Golwala
Near-term
Using KID pulsing scheme and 55Fe/129I x-rays to measure baseline σE; position-correct also
Mid-term
Provide position reconstruction and NR discrimination to reach neutrino floor > 1 GeV
Provide NR discrimination via e-h spectral peaks to reject dominant tritium and 32Si backgrounds Provide position reconstruction to reject non-cosmogenic surface bgnds (210Pb betas and 206Pb nuclei) Large-detector track 1: σ ~ 5-10 eV + HV: QL paramp + 1 ms qp lifetime Large-detector track 2: σ ~ 0.25 eV at 0V: QL paramp + 1 ms qp lifetime + lower ∆ + higher KI fraction
Small-detector track
Reoptimize design purely for energy resolution and small target size; σ ~ 0.15 eV possible with Al
Threshold, not position information
Continue using phonon absorption on semiconducting substrates. but begin to consider polar substrates
Start with Al2O3, try out GaAs for better mass reach.
Long-term
Revisit design for superconducting substrates, σ ~ 1 meV
Use quasiparticles or phonons? Phonon propagation challenging in superconductors (check Gaitskell). Find a configuration that works. Hybrid CPW-lumped element? Microstripline?
Other efforts? Not many!
CALDER = effort to deploy KIDs for photodetection in CUORE follow-on 0νββ expt CUPID
No scintillation in TeO2, but betas Cherenkov radiate. Separate dominant alpha background from betas by requiring Cherenkov signal. Need σ ~ 20 eV to see 100 eV signal → simpler needs.
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New Directions in Searches for Light DM Basu Thakur/Golwala
Small-detector architectures have potential to reach thermal relic mass limit via DM-e scattering and to probe boson DM in the meV - keV mass range inaccessible to coherent techniques Large-detector architectures have potential for background rejection needed to reach neutrino floor
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