Resonant absorption of dark matter in molecules Ken Van Tilburg - - PowerPoint PPT Presentation

▶
resonant absorption of dark matter in molecules
SMART_READER_LITE
LIVE PREVIEW

Resonant absorption of dark matter in molecules Ken Van Tilburg - - PowerPoint PPT Presentation

Sep 20, 2023 158 likes •618 views

Resonant absorption of dark matter in molecules Ken Van Tilburg (NYU & IAS) arXiv:1709.05354, Phys. Rev. X 8 , 041001 with Asimina Arvanitaki (Perimeter), Savas Dimopoulos (Stanford) Karl Berggren (MIT), Ilya Charaev (MIT), Jeff Chiles

slide-1
SLIDE 1

Resonant absorption of dark matter in molecules

arXiv:1709.05354, Phys. Rev. X 8, 041001

with Asimina Arvanitaki (Perimeter), Savas Dimopoulos (Stanford)

Ken Van Tilburg (NYU & IAS)

Light Dark Matter Workshop, KICP/Fermilab, 2019/06/06

in progress with Karl Berggren (MIT), Ilya Charaev (MIT), Jeff Chiles (NIST), Marco Colangelo (MIT), Andrew Dane (MIT), SaeWoo Nam (NIST), Varun Verma (NIST) Masha Baryakhtar (NYU), Junwu Huang (Perimeter), Robert Lasenby (Stanford) DOE QuantiSED grant, DE-SC0019129

slide-2
SLIDE 2

Outline

(1) Dark matter fields can resonantly excite a molecular system

bosonic DM couplings | two-level system dynamics | molecular levels

(2) Experimental setup

configurations | photon detection | backgrounds | discrimination 0.2 eV < m < 20 eV

(3) Dark matter sensitivity

hidden vectors | moduli | axions

slide-3
SLIDE 3

Outline

(1) Dark matter fields can resonantly excite a molecular system

bosonic DM couplings | two-level system dynamics | molecular levels

(2) Experimental setup

configurations | photon detection | backgrounds | discrimination 0.2 eV < m < 20 eV

(3) Dark matter sensitivity

hidden vectors | moduli | axions

Why is a molecular gas a good dark matter detector?

signal rate backgrounds calculable discrimination power selection rules control variables: P, T, E, B energy resolution: ∆ω/ω ⌧ 10−6 ∆θ/θ . 10−6 directional focusing:

slide-4
SLIDE 4

Outline

(1) Dark matter fields can resonantly excite a molecular system

bosonic DM couplings | two-level system dynamics | molecular levels

(2) Experimental setup

configurations | photon detection | backgrounds | discrimination 0.2 eV < m < 20 eV

(3) Dark matter sensitivity

hidden vectors | moduli | axions

Why is a molecular gas a good dark matter detector?

signal rate backgrounds calculable discrimination power selection rules control variables: P, T, E, B energy resolution: ∆ω/ω ⌧ 10−6 ∆θ/θ . 10−6 directional focusing:

slide-5
SLIDE 5

Bosonic dark matter couplings

EFT of DM bosons coupled to electrons, quarks, photons, gluons ✏A0

µJµ EM

gA0

µJµ BL

spin-1 spin-0

parity-even parity-odd

φ¯ ee aF ˜ F φF 2 φG2 φ¯ qq (∂µa)¯ eγµγ5e (∂µa)¯ qγµγ5q aG ˜ G

kinetic mixing B-L charge

inflationary production misalignment mechanism

slide-6
SLIDE 6

DM-induced transitions

slide-7
SLIDE 7

Resonant excitation of a two-level system

h1|δH|0i ⇠ Ω cos(ωt) ω Ω ω0 |0i |1i γ0

slide-8
SLIDE 8

Resonant excitation of a two-level system

DM photon k = mv ω = m k = m h1|δH|0i ⇠ Ω cos(ωt) ω Ω ω0 |0i |1i γ0

slide-9
SLIDE 9

Resonant excitation of a two-level system

DM photon k = mv ω = m k = m h1|δH|0i ⇠ Ω cos(ωt) ω Ω ω0 |0i |1i γ0

Γabs = nV |Ω|2 γ 1 1 + 4(ω0−ω)2

γ2

# molecules

|Ω|2

}

  • n-resonance

absorption rate per molecule lineshape

nV

}

γ = γrad + 2γcol + ∆ω π ∆ω γrad 2γcol γcol = nσcolvmol ∆ωDoppler negligible γrad ' ¯ rγ0 + X

i

γi

slide-10
SLIDE 10

Resonant excitation of a two-level system

DM photon k = mv ω = m k = m h1|δH|0i ⇠ Ω cos(ωt) ω Ω ω0 |0i |1i γ0

Γabs = nV |Ω|2 γ 1 1 + 4(ω0−ω)2

γ2

# molecules

|Ω|2

}

  • n-resonance

absorption rate per molecule lineshape

nV

}

γ = γrad + 2γcol + ∆ω π ∆ω γrad 2γcol γcol = nσcolvmol ∆ωDoppler negligible γrad ' ¯ rγ0 + X

i

γi |Ψ(t)0i = ei

R t

0 δHdt0|00i ' |00i i

2Ωei(ω0ω)t 1 i(ω0 ω) |10i Ω ω0 ω

slide-11
SLIDE 11

Molecular levels and transitions

discretuum of transition energies = multimode resonator

ωvib ∼ α2me ⇣me M ⌘1/2 ωrot ∼ α2me ⇣me M ⌘ ωel ∼ α2me

solid diatomic molecule atom DM

slide-12
SLIDE 12

DM absorption rate

V = 300 cm3 T = 100 K P = 5 bar ✏ = 10−12

  • ω []

Γ [] =〉 → =〉 =→

  • =→

=→

hidden photon DM

slide-13
SLIDE 13

DM absorption rate

V = 300 cm3 T = 100 K P = 5 bar P = 0.05 bar ✏ = 10−12

  • ω []

Γ [] =〉 → =〉 =→

  • =→

=→

  • ω []

Γ [] =〉 → =〉 =→

  • =→

=→

hidden photon DM

slide-14
SLIDE 14

Outline

(1) Dark matter fields can resonantly excite a molecular system

bosonic DM couplings | two-level system dynamics | molecular levels

(2) Experimental setup

configurations | photon detection | backgrounds | discrimination 0.2 eV < m < 20 eV

(3) Dark matter sensitivity

hidden vectors | moduli | axions

Why is a molecular gas a good dark matter detector?

signal rate backgrounds calculable discrimination power selection rules control variables: P, T, E, B energy resolution: ∆ω/ω ⌧ 10−6 ∆θ/θ . 10−6 directional focusing:

slide-15
SLIDE 15

Bulk configuration

Phase I Phase II

V = (0.3 m)3 T = 300 K DCR = 1 Hz V = (2 m)3 T = 100 K DCR = 10−3 Hz

slide-16
SLIDE 16

Bulk configuration

Phase I Phase II

V = (0.3 m)3 T = 300 K DCR = 1 Hz V = (2 m)3 T = 100 K DCR = 10−3 Hz reflective coating fluorescence photon photodetector absorption event molecules

slide-17
SLIDE 17

Cooperative radiation

coherence length: f(v) ∝ exp  −(v − vlab)2 v2

  • typical deBroglie wavelength:

λcoh = 2 mv0 λdB ∼ 2π mvlab λγ = 2π m photon wavelength: λγ λcoh |0i + εe−i[mt+ϕ(x)]|1i

slide-18
SLIDE 18

Cooperative radiation

coherence length: f(v) ∝ exp  −(v − vlab)2 v2

  • typical deBroglie wavelength:

λcoh = 2 mv0 λdB ∼ 2π mvlab λγ = 2π m photon wavelength: λγ λcoh |0i + εe−i[mt+ϕ(x)]|1i

slide-19
SLIDE 19

Cooperative radiation

coherence length: f(v) ∝ exp  −(v − vlab)2 v2

  • typical deBroglie wavelength:

λcoh = 2 mv0 λdB ∼ 2π mvlab λγ = 2π m photon wavelength: λγ λcoh |0i + εe−i[mt+ϕ(x)]|1i

slide-20
SLIDE 20

Cooperative radiation

coherence length: f(v) ∝ exp  −(v − vlab)2 v2

  • typical deBroglie wavelength:

λcoh = 2 mv0 λdB ∼ 2π mvlab λγ = 2π m photon wavelength: λγ λcoh |0i + εe−i[mt+ϕ(x)]|1i ¯ r ' 1 + 8πn m4Rz ⇡ 1 + 5 ⇥ 106 mRz ✓1 eV m ◆3 ✓ n n0 ◆

slide-21
SLIDE 21

Stack configuration

λγ

Phase I Phase II

A = π(0.3 m)3 D = 1 mm DCR = 10−5 Hz A = π(2 m)3 D = 100 mm DCR = 10−7 Hz T = 100 K

slide-22
SLIDE 22

Stack configuration

λγ

Phase I Phase II

A = π(0.3 m)3 D = 1 mm DCR = 10−5 Hz A = π(2 m)3 D = 100 mm DCR = 10−7 Hz T = 100 K transparent dielectric molecules

slide-23
SLIDE 23

Stack configuration

λγ

Phase I Phase II

A = π(0.3 m)3 D = 1 mm DCR = 10−5 Hz A = π(2 m)3 D = 100 mm DCR = 10−7 Hz T = 100 K transparent dielectric molecules lens cooperatively emitted photon photodetector

slide-24
SLIDE 24

Stack configuration

λγ

Phase I Phase II

A = π(0.3 m)3 D = 1 mm DCR = 10−5 Hz A = π(2 m)3 D = 100 mm DCR = 10−7 Hz T = 100 K transparent dielectric molecules lens cooperatively emitted photon photodetector

ηcoh ' (¯ r 1)γ0 ¯ rγ0 + 2γcol

slide-25
SLIDE 25

Absorption + Cooperative emission

✏ = 10−12 hidden photon DM

  • ω []

Γ [] =〉 → =〉 @ = = Γ Γ

  • =→

=←

  • =→

=→

V = π(30 cm)2(1 mm)

slide-26
SLIDE 26

Key considerations

frequency coverage radiative efficiency

Stark tuning (electric field) Zeeman tuning (magnetic field) molecular species

  • r isotope shift

collisional broadening Stack:

  • fluorescence

before quenching cooperative emission before Bulk: decoherence

slide-27
SLIDE 27

Backgrounds

thermal occupation / BBR: natural/cosmogenic radioactivity: cosmic rays: dark count rate (DCR): high-reflectivity coatings cryogenic photodetectors: SNSPD, MKID, TES underground and/or muon scintillator (99.9%) veto trigger: timing + fast relaxation many, high-E particles high-purity shield + components ionized electrons

{

10-12 mass fraction 238U for meter-scale volume ΓRD ∼ 10−2 Hz Stack configuration: 84% of signal in 10-7 solid angle nV e− ω0

T ⌧ 1

slide-28
SLIDE 28

Signal discrimination

collisional broadening: frequency shifts: selection rules:

DM radioactivity cosmic rays

Stark Zeeman species allowed forbidden + allowed directional emission: solid angle ∼ 10−6 solid angle ∼ 4π

  • ∝ n1 or ∝ n0
  • broadband

isotope

slide-29
SLIDE 29

Outline

(1) Dark matter fields can resonantly excite a molecular system

bosonic DM couplings | two-level system dynamics | molecular levels

(2) Experimental setup

configurations | photon detection | backgrounds | discrimination 0.2 eV < m < 20 eV

(3) Dark matter sensitivity

hidden vectors | moduli | axions

Why is a molecular gas a good dark matter detector?

signal rate backgrounds calculable discrimination power selection rules control variables: P, T, E, B energy resolution: ∆ω/ω ⌧ 10−6 ∆θ/θ . 10−6 directional focusing:

slide-30
SLIDE 30

Kinematically mixed photon

  • γ []

ϵ λγ [μ]

[] [] [Δ=] [] [Δ=]

slide-31
SLIDE 31

B-L gauge boson

  • γ []
  • λγ [μ]
  • α=
  • Γνν=
slide-32
SLIDE 32

Modulus: electron coupling

  • ϕ []

λγ [μ]

slide-33
SLIDE 33

Modulus: photon, quark, gluon

  • ϕ []

λγ [μ]

  • ϕ []

λγ [μ]

  • ϕ []

λγ [μ]

slide-34
SLIDE 34

Axion: nuclear coupling

  • []

λγ [μ]

slide-35
SLIDE 35

Axion: electron coupling

  • []

λγ [μ]

  • ()

()

slide-36
SLIDE 36

Conclusions

(1) Dark matter fields can resonantly excite a molecular system (2) Experimental setup (3) Dark matter sensitivity

0.2 eV < m < 20 eV dark matter absorption = weak, monochromatic signal gas of small molecules = multimode resonator with large signal rate low background rates tunable frequency response: superb discrimination power established field with photodetector technology advancements cooperative focusing effects: directional isolation and information spin-1: mixed photon, B-L gauge boson, … spin-0, parity-even: moduli fields for electron, quark, photon, gluon, … spin-0, parity-odd: axion coupling to electrons, nucleons, photons, … m < 0.2 eV | m > 20 eV | other use? | map out molecular forest

Future:

Phase I prototypes Phase II R&D: stack manufacturing | optimize photodetectors

slide-37
SLIDE 37

Bosonic dark matter couplings

φ dme p 4πGNme ¯ ψeψe EFT of DM bosons coupled to electrons, quarks, photons, gluons φ de p 4πGN 1 4FµνF µν φ dmq p 4πGNmq ¯ ψqψq φ dg p 4πGN β3 2g3 GµνGµν ✏A0

µJµ EM

gA0

µJµ BL

Gaqq(∂µa) ¯ ψqγµγ5ψq Gaee(∂µa) ¯ ψeγµγ5ψe Gaγγa1 4Fµν ˜ F µν α3 8π a fa Gµν ˜ Gµν

spin-1 spin-0

parity-even parity-odd

slide-38
SLIDE 38

Bosonic dark matter fields and interactions

|A0| φ a } ' p2ρDM ω cos(ωt) vector scalar pseudoscalar dρ dω m m(1 + v2

esc)

ω L = ✏AµJµ

EM

H = ✏E0 · µe

e.g. hidden photon: production:{

inflationary perturbations (spin-1) misalignment mechanism (spin-0) 3 kV/m ω ∆ω |A0|

slide-39
SLIDE 39

Bosonic dark matter fields and interactions

|A0| φ a } ' p2ρDM ω cos(ωt) vector scalar pseudoscalar dρ dω m m(1 + v2

esc)

ω L = ✏AµJµ

EM

H = ✏E0 · µe µe = e X

ψ

qψrψ

e.g. hidden photon: production:{

inflationary perturbations (spin-1) misalignment mechanism (spin-0) 3 kV/m ω ∆ω |A0|

slide-40
SLIDE 40

Bosonic dark matter fields and interactions

|A0| φ a } ' p2ρDM ω cos(ωt) vector scalar pseudoscalar dρ dω m m(1 + v2

esc)

ω L = ✏AµJµ

EM

H = ✏E0 · µe µe = e X

ψ

qψrψ

e.g. hidden photon: production:{

inflationary perturbations (spin-1) misalignment mechanism (spin-0) 3 kV/m equivalent to shining 20kW laser in a 1m2 beam waist area ω ∆ω |A0|

slide-41
SLIDE 41

Electronic states of a diatomic molecule

  • /

() []

0 1 2 3 4 5 6

  • Σ

+

  • Σ

+

  • Σ

+

  • Σ

+

  • Π
slide-42
SLIDE 42

Molecular info

slide-43
SLIDE 43

Configuration summary

slide-44
SLIDE 44

A(t, x, x0) = q 4π|x − x0| cos [ω (t − |x − x0|) + αv − mv · x0]

hAtot(t, x)2iv,α = D⇣ X

x0

A(t, x, x0) ⌘⇣ X

y0

A(t, x, y0) ⌘E

v,α

= X

x0

D A(t, x, x0)2E

v,α +

X

x0

X

y06=x0

D A(t, x, x0)A(t, x, y0) E

v,α

' Z

V

d3x0n(x0) q2 2(4π)2L2 + ZZ

V

d3x0d3y0n(x0)n(y0) q2 2(4π)2L2 Z d3vf(v) cos [m(ˆ x v) · (x0 y0)] ⌘ q2 2(4π)2L2 nV r(ˆ x)

Cooperation number

¯ r ' 1 + 8πn m4Rz ⇡ 1 + 5 ⇥ 106 mRz ✓1 eV m ◆3 ✓ n n0 ◆

slide-45
SLIDE 45

Key considerations

frequency coverage radiative efficiency

  • []

[] = =〉 → = =〉

  • γ

(-)γ η(-)γ γ Γ γ

  • =

=

  • μ/

ω

/

=→ =→ =→± =→ =→ =→ =±→ =→ =→

— Stark tuning: — Zeeman tuning — molecular species/isotope — collisional broadening — Bulk: γquench γ0 + X

i

γi — Stack: (¯ r − 1)γ0 γcol ∼ &