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Talbot interferometry with a point-like source:rationale, technology, & experiment
James BatemanM. Rashid, D. Hempston, J. Vovrosh
Group leader: Hendrik Ulbricht
Matterwave GroupPhysics & Astronomy
University of SouthamptonSouthampton, SO17 1BJ, UK
23rd March 2015
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Overview
1 Introduction
2 Theoretical description
3 Experimental & recent results
4 Squashing/squeezing
5 The source problem
6 Dark Matter
Near-field interferometry of a free-falling nanoparticle froma point-like source, Bateman, Nimmrichter, Hornberger, &
Ulbricht, Nature Communications 5:4788 (2014)
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Aims
Path separation exceeding particle size
As large a mass as possible
M ∼ 106uD ∼ 10nm
Optically resolvable fringes
∆ ∼ 150 nmSimilar to length-scale in GRW
(Large ‘macroscopicity’)
(Ground-based demonstrationof technique for MAQRO)
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
D
Λ
m~106u
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Macroscopicity: µ = 18
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Nimmrichter & Hornberger, PRL 110, 160403 (2013)
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Schematic
(a) Nanoparticle in dipole trap106 amu (10 nm sphere)localised to < 30 nm
(b) Phase grating177 nm periodns, mJ, trippled Nd:YAG
(c) Glass slideFixed fall time ≈ 300 msNear-field (Fresnel)Scaled Talbot effect
(d) Optical detectionHigh NA with fitting to PSF
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
g
I(x)
x
125mm
275mm
(a)
(b)
(c)
(d)
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Schematic
(a) Nanoparticle in dipole trap106 amu (10 nm sphere)localised to < 30 nm
(b) Phase grating177 nm periodns, mJ, trippled Nd:YAG
(c) Glass slideFixed fall time ≈ 300 msNear-field (Fresnel)Scaled Talbot effect
(d) Optical detectionHigh NA with fitting to PSF
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
g
I(x)
x
125mm
275mm
(a)
(b)
(c)
(d)
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Schematic
(a) Nanoparticle in dipole trap106 amu (10 nm sphere)localised to < 30 nm
(b) Phase grating177 nm periodns, mJ, trippled Nd:YAG
(c) Glass slideFixed fall time ≈ 300 msNear-field (Fresnel)Scaled Talbot effect
(d) Optical detectionHigh NA with fitting to PSF
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
g
I(x)
x
125mm
275mm
(a)
(b)
(c)
(d)
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Schematic
(a) Nanoparticle in dipole trap106 amu (10 nm sphere)localised to < 30 nm
(b) Phase grating177 nm periodns, mJ, trippled Nd:YAG
(c) Glass slideFixed fall time ≈ 300 msNear-field (Fresnel)Scaled Talbot effect
(d) Optical detectionHigh NA with fitting to PSF
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
g
I(x)
x
125mm
275mm
(a)
(b)
(c)
(d)
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
The Talbot effect
Classic wave phenomena
In near-field (Fresnel region)find Talbot self-image
Structure length-scale set bygrating, not wavelength
Usually ‘Talbot length’ LT = Λ2/λdB
We use ‘Talbot time’ τT = MΛ2/h
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Talbot effect illustration from Hornberger et al.,
Rev. Mod. Phys. 84, 157–173 (2012)
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Theoretical overview
Wigner function descriptionStart with small, thermal stateCan treat grating classically or QM→ Talbot coefficients
Characteristic functionFourier transform of WignerPhase grating is periodicEase of treating decoherence
Decoherence‘Smears out’ position informationConvolution (Wigner) becomes multiplication (Characteristic)Different decoherence mechanisms are separable
Free-evolution is a shearing(same as for classical phase-space distribution)
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
w(x , p) ∝ exp(− x2
2σ2x− p2
2σ2p
)
χ(s, q) = exp(−σ2
xq2+σ2
ps2
2~2
)
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Theoretical overview
Wigner function descriptionStart with small, thermal stateCan treat grating classically or QM→ Talbot coefficients
Characteristic functionFourier transform of WignerPhase grating is periodicEase of treating decoherence
Decoherence‘Smears out’ position informationConvolution (Wigner) becomes multiplication (Characteristic)Different decoherence mechanisms are separable
Free-evolution is a shearing(same as for classical phase-space distribution)
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
w(x , p) ∝ exp(− x2
2σ2x− p2
2σ2p
)
χ(s, q) = exp(−σ2
xq2+σ2
ps2
2~2
)
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Theoretical overview
Wigner function descriptionStart with small, thermal stateCan treat grating classically or QM→ Talbot coefficients
Characteristic functionFourier transform of WignerPhase grating is periodicEase of treating decoherence
Decoherence‘Smears out’ position informationConvolution (Wigner) becomes multiplication (Characteristic)Different decoherence mechanisms are separable
Free-evolution is a shearing(same as for classical phase-space distribution)
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
w(x , p) ∝ exp(− x2
2σ2x− p2
2σ2p
)
χ(s, q) = exp(−σ2
xq2+σ2
ps2
2~2
)
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Theoretical overview
Wigner function descriptionStart with small, thermal stateCan treat grating classically or QM→ Talbot coefficients
Characteristic functionFourier transform of WignerPhase grating is periodicEase of treating decoherence
Decoherence‘Smears out’ position informationConvolution (Wigner) becomes multiplication (Characteristic)Different decoherence mechanisms are separable
Free-evolution is a shearing(same as for classical phase-space distribution)
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
w(x , p) ∝ exp(− x2
2σ2x− p2
2σ2p
)
χ(s, q) = exp(−σ2
xq2+σ2
ps2
2~2
)
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Decoherence mechanisms
Rayleigh scattering
Very high scattering rate!Particle must be infree-flight
Gas collisions
Require � one collisionP ∼ 10−10 mbar
Blackbody radiation
A few long wavelengthphotons → OKLots → problem!Croygenics?Material choice!
Blackbody considerations
kBT ∼ hc/λ=⇒ λ ∼ 10µm
Require high transparency5µm < λ < 100µm
Semiconductors!
Candidates
SiliconSapphireGermanium. . .(Bad choice: SiO2)
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Decoherence mechanisms
Rayleigh scattering
Very high scattering rate!Particle must be infree-flight
Gas collisions
Require � one collisionP ∼ 10−10 mbar
Blackbody radiation
A few long wavelengthphotons → OKLots → problem!Croygenics?Material choice!
Blackbody considerations
kBT ∼ hc/λ=⇒ λ ∼ 10µm
Require high transparency5µm < λ < 100µm
Semiconductors!
Candidates
SiliconSapphireGermanium. . .(Bad choice: SiO2)
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Decoherence mechanisms
Rayleigh scattering
Very high scattering rate!Particle must be infree-flight
Gas collisions
Require � one collisionP ∼ 10−10 mbar
Blackbody radiation
A few long wavelengthphotons → OKLots → problem!
Croygenics?Material choice!
Blackbody considerations
kBT ∼ hc/λ=⇒ λ ∼ 10µm
Require high transparency5µm < λ < 100µm
Semiconductors!
Candidates
SiliconSapphireGermanium. . .(Bad choice: SiO2)
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Decoherence mechanisms
Rayleigh scattering
Very high scattering rate!Particle must be infree-flight
Gas collisions
Require � one collisionP ∼ 10−10 mbar
Blackbody radiation
A few long wavelengthphotons → OKLots → problem!Croygenics?Material choice!
Blackbody considerations
kBT ∼ hc/λ=⇒ λ ∼ 10µm
Require high transparency5µm < λ < 100µm
Semiconductors!
Candidates
SiliconSapphireGermanium. . .(Bad choice: SiO2)
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Decoherence mechanisms
Rayleigh scattering
Very high scattering rate!Particle must be infree-flight
Gas collisions
Require � one collisionP ∼ 10−10 mbar
Blackbody radiation
A few long wavelengthphotons → OKLots → problem!Croygenics?Material choice!
Blackbody considerations
kBT ∼ hc/λ=⇒ λ ∼ 10µm
Require high transparency5µm < λ < 100µm
Semiconductors!
Candidates
SiliconSapphireGermanium. . .(Bad choice: SiO2)
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Decoherence mechanisms
Rayleigh scattering
Very high scattering rate!Particle must be infree-flight
Gas collisions
Require � one collisionP ∼ 10−10 mbar
Blackbody radiation
A few long wavelengthphotons → OKLots → problem!Croygenics?Material choice!
Blackbody considerations
kBT ∼ hc/λ=⇒ λ ∼ 10µm
Require high transparency5µm < λ < 100µm
Semiconductors!
Candidates
SiliconSapphireGermanium. . .
(Bad choice: SiO2)
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Decoherence mechanisms
Rayleigh scattering
Very high scattering rate!Particle must be infree-flight
Gas collisions
Require � one collisionP ∼ 10−10 mbar
Blackbody radiation
A few long wavelengthphotons → OKLots → problem!Croygenics?Material choice!
Blackbody considerations
kBT ∼ hc/λ=⇒ λ ∼ 10µm
Require high transparency5µm < λ < 100µm
Semiconductors!
Candidates
SiliconSapphireGermanium. . .(Bad choice: SiO2)
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Blackbody emmissivity: compare Si and SiO2
Typical blackbody wavelength: & 10µm
Glass (dashed) absorbs; silicon (solid) is highly transparent
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
10−1 100 101 102
0
1
2
3
4
5
6
Wavelength/µm
Ref
ract
ive
index
10−1 100 101 10210−9
10−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
100101
Wavelength/µm
Exti
nct
ion
coeffi
cien
t
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Decoherence via Blackbody radiation
Reduction in fringe visibility vs time & particle initial temperature
Cooling into 300K environment
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Silicon Glass
0 200 400 600 800 1,000300
600
900
1,200
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Time/ms
Tint/K
(a)
0 200 400 600 800 1,000300
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900
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Tint/K
(b)
0.0
0.2
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0.6
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1.0
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Predicted Talbot carpets (below phase grating)
Strong decoherence would ‘smear’ distributions
Here, quantum and classical predictions differ
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Quantum Classical
−1 −0.5 0 0.5 1
0
100
200
Position/µm
Tim
et 2/m
s
(a)
−1 −0.5 0 0.5 1
0
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200
Position/µm
Tim
et 2/m
s
(b)
0.0
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sity/a
rb.units
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Dipole Trapping at 1550nm
Refracting optics: aspherics/objectives
Designed for visible (λ . 1 µm)
Significant aberrations at 1.5µm
Reflecting optics: parabolic mirror
Inherently achromatic
Single-point diamond turning
15nm roughness (λ/100)
< 1µm form accuracy
NA = 0.995
Working distance = 900µm
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Dipole Trapping at 1550nm
Refracting optics: aspherics/objectives
Designed for visible (λ . 1 µm)
Significant aberrations at 1.5µm
Reflecting optics: parabolic mirror
Inherently achromatic
Single-point diamond turning
15nm roughness (λ/100)
< 1µm form accuracy
NA = 0.995
Working distance = 900µm
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Position detection
Sense position and apply feedback [1,2]
Centre-of-mass cooling to ∼ 10mK for ∼ 100nm particle [2]
Transmission imaging
∂xφ ∼ 1/f
∂zφ ∼ 1/zR
Reflection imaging
∂xφ ∼ 1/f
∂zφ = 4π/λ
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Input light
Reflected light
Rayleigh scattering
Input light
[1] Li, Kheifets, Raizen, Nat. Phys. 7 527 (2011)
[2] Gieseler, Deutsch, Quidant, Novotny, PRL 109 103602 (2012)
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Position detection
Sense position and apply feedback [1,2]
Centre-of-mass cooling to ∼ 10mK for ∼ 100nm particle [2]
Transmission imaging
∂xφ ∼ 1/f
∂zφ ∼ 1/zR
Reflection imaging
∂xφ ∼ 1/f
∂zφ = 4π/λ
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Input light
Reflected light
Rayleigh scattering
Input light
[1] Li, Kheifets, Raizen, Nat. Phys. 7 527 (2011)
[2] Gieseler, Deutsch, Quidant, Novotny, PRL 109 103602 (2012)
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Position detection
Sense position and apply feedback [1,2]
Centre-of-mass cooling to ∼ 10mK for ∼ 100nm particle [2]
Transmission imaging
∂xφ ∼ 1/f
∂zφ ∼ 1/zR
Reflection imaging
∂xφ ∼ 1/f
∂zφ = 4π/λ
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Input light
Reflected light
Rayleigh scattering
Input light
[1] Li, Kheifets, Raizen, Nat. Phys. 7 527 (2011)
[2] Gieseler, Deutsch, Quidant, Novotny, PRL 109 103602 (2012)
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Recent results
Photodiode signal ∝ position
Fourier transform & average ≈ PSD
PSD(ω) = kBTπm
Γ
(ω20−ω2)
2+ω2Γ2
Γ ∝ Pressure
Reduce pressure =⇒ melt particle!
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
0 50 100 150 200 250 300Frequency [kHz]
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0.5
1.0
log 1
0(PSD
) [ar
b.]
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Recent results: cleaner particles
Photodiode signal ∝ position
Fourier transform & average ≈ PSD
PSD(ω) = kBTπm
Γ
(ω20−ω2)
2+ω2Γ2
Γ ∝ Pressure
Reduce pressure =⇒ melt particle!
=⇒ Use cleaner particles
Time domain: beautiful sinewave
Q factor limited by intensity stability
Demonstrated P . 10−5 mbar
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
0.4 0.2 0.0 0.2 0.4Time/ms
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Pow
er
Spect
ral D
ensi
ty (
dB
/kH
z)
z
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Recent results: cleaner particles
Photodiode signal ∝ position
Fourier transform & average ≈ PSD
PSD(ω) = kBTπm
Γ
(ω20−ω2)
2+ω2Γ2
Γ ∝ Pressure
Reduce pressure =⇒ melt particle!
=⇒ Use cleaner particles
Time domain: beautiful sinewave
Q factor limited by intensity stability
Demonstrated P . 10−5 mbar
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
0.4 0.2 0.0 0.2 0.4Time/ms
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2
1
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nal/arb
0 50 100 150 200Frequency (kHz)
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er
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ral D
ensi
ty (
dB
/kH
z)
z
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Recent results: cooling
Feedback position to intensity→ Parametric feedback
Position resolution limitsachievable temperature
Demonstrated in 1D;need 3D to achieve UHV
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Recent results: cooling
Feedback position to intensity→ Parametric feedback
Position resolution limitsachievable temperature
Demonstrated in 1D;need 3D to achieve UHV
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Recent results: cooling
Feedback position to intensity→ Parametric feedback
Position resolution limitsachievable temperature
Demonstrated in 1D;need 3D to achieve UHV
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Recent results: cooling
Feedback position to intensity→ Parametric feedback
Position resolution limitsachievable temperature
Demonstrated in 1D;need 3D to achieve UHV
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Recent results: cooling
Feedback position to intensity→ Parametric feedback
Position resolution limitsachievable temperature
Demonstrated in 1D;need 3D to achieve UHV
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Recent results: cooling
Feedback position to intensity→ Parametric feedback
Position resolution limitsachievable temperature
Demonstrated in 1D;need 3D to achieve UHV
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Recent results: cooling
Feedback position to intensity→ Parametric feedback
Position resolution limitsachievable temperature
Demonstrated in 1D;need 3D to achieve UHV
High mechanical Q=⇒ sensitive detector
(gravity, rotation, magnetic fields. . . )
Need cooling, control,and passive stability
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
65 66 67 68 69 70 71 72Frequency (kHz)
0.000
0.005
0.010
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Pow
er
Spect
ral D
ensi
ty (
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1)
ref-0.4-0.6-0.8
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1
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-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4
Norm
alis
ed a
rea u
nder
peak
Phase/pi
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Recent results: cooling
Feedback position to intensity→ Parametric feedback
Position resolution limitsachievable temperature
Demonstrated in 1D;need 3D to achieve UHV
High mechanical Q=⇒ sensitive detector
(gravity, rotation, magnetic fields. . . )
Need cooling, control,and passive stability
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
65 66 67 68 69 70 71 72Frequency (kHz)
0.000
0.005
0.010
0.015
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Pow
er
Spect
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ensi
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1)
ref-0.4-0.6-0.8
0.1
1
10
100
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Norm
alis
ed a
rea u
nder
peak
Phase/pi
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Recent results: cooling
Feedback position to intensity→ Parametric feedback
Position resolution limitsachievable temperature
Demonstrated in 1D;need 3D to achieve UHV
High mechanical Q=⇒ sensitive detector
(gravity, rotation, magnetic fields. . . )
Need cooling, control,and passive stability
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
65 66 67 68 69 70 71 72Frequency (kHz)
0.000
0.005
0.010
0.015
0.020
0.025
Pow
er
Spect
ral D
ensi
ty (
kHz−
1)
ref-0.4-0.6-0.8
0.1
1
10
100
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4
Norm
alis
ed a
rea u
nder
peak
Phase/pi
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Squashing/squeezing
Reduce σx (or σv )
Evolution in HO is rigid-bodyrotation in x–v/ω plane
Protocol:
Thermal state with frequency ωChange trap frequency to ω′
Quarter-cycle rotation at ω′
Return trap frequency to ω
Experiment:
Debug with hot stateApply to cooled state×103 better localisation?Squeezing? σx < groundstate?
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
x
v/ω
x
v/ω'1) 2)
x
v/ω'
x
v/ω 3)4)
After (4), non-thermal state;expect xRMS =
√〈x2〉 to
oscillate at 2ω.
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Squashing/squeezing
Reduce σx (or σv )
Evolution in HO is rigid-bodyrotation in x–v/ω plane
Protocol:
Thermal state with frequency ωChange trap frequency to ω′
Quarter-cycle rotation at ω′
Return trap frequency to ω
Experiment:
Debug with hot stateApply to cooled state×103 better localisation?Squeezing? σx < groundstate?
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
x
v/ω
x
v/ω'1) 2)
x
v/ω'
x
v/ω 3)4)
After (4), non-thermal state;expect xRMS =
√〈x2〉 to
oscillate at 2ω.
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Squashing/squeezing
Reduce σx (or σv )
Evolution in HO is rigid-bodyrotation in x–v/ω plane
Protocol:
Thermal state with frequency ωChange trap frequency to ω′
Quarter-cycle rotation at ω′
Return trap frequency to ω
Experiment:
Debug with hot stateApply to cooled state×103 better localisation?Squeezing? σx < groundstate?
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
x
v/ω
x
v/ω'1) 2)
x
v/ω'
x
v/ω 3)4)
After (4), non-thermal state;expect xRMS =
√〈x2〉 to
oscillate at 2ω.
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Squashing/squeezing experiments
Desired peak 25dBabove background
Extract x and v
Histogram of revealsthermal state
Time-domain plots
Reduce laser powerfor ∼ 10µs
〈x〉 ≈ constant
xRMS oscillatesat 2ω
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
0 50 100 150 200 250 300Frequency/kHz
50
45
40
35
30
25
20
15
10
Spect
ral densi
ty/d
B
01.200VSpectrum of recorded voltage
Unfiltered
3 2 1 0 1 2 3x/x0
3
2
1
0
1
2
3
v/(ωx
0)
01.200V2D histogram of position, velocity
4 2 0 2 4 6 8 10Time/Periods
1.0
0.5
0.0
0.5
1.0
<x>/x
0
01.200V<x>(t) with pulse marked with black lines
4 2 0 2 4 6 8 10Time/Periods
0.0
0.5
1.0
1.5
2.0
xR
MS/x
0
01.200VxRMS(t) with pulse marked with black lines
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Squashing/squeezing experiments
Desired peak 25dBabove background
Extract x and v
Histogram of revealsthermal state
Time-domain plots
Reduce laser powerfor ∼ 10µs
〈x〉 ≈ constant
xRMS oscillatesat 2ω
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
0 50 100 150 200 250 300Frequency/kHz
50
45
40
35
30
25
20
15
10
Spect
ral densi
ty/d
B
01.200VSpectrum of recorded voltage
Unfiltered
3 2 1 0 1 2 3x/x0
3
2
1
0
1
2
3
v/(ωx
0)
01.200V2D histogram of position, velocity
4 2 0 2 4 6 8 10Time/Periods
1.0
0.5
0.0
0.5
1.0
<x>/x
0
01.200V<x>(t) with pulse marked with black lines
4 2 0 2 4 6 8 10Time/Periods
0.0
0.5
1.0
1.5
2.0
xR
MS/x
0
01.200VxRMS(t) with pulse marked with black lines
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Squashing/squeezing experiments
Desired peak 25dBabove background
Extract x and v
Histogram of revealsthermal state
Time-domain plots
Reduce laser powerfor ∼ 10µs
〈x〉 ≈ constant
xRMS oscillatesat 2ω
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
0 50 100 150 200 250 300Frequency/kHz
50
45
40
35
30
25
20
15
10
Spect
ral densi
ty/d
B
01.200VSpectrum of recorded voltage
Unfiltered
3 2 1 0 1 2 3x/x0
3
2
1
0
1
2
3
v/(ωx
0)
01.200V2D histogram of position, velocity
4 2 0 2 4 6 8 10Time/Periods
1.0
0.5
0.0
0.5
1.0
<x>/x
0
01.200V<x>(t) with pulse marked with black lines
4 2 0 2 4 6 8 10Time/Periods
0.0
0.5
1.0
1.5
2.0
xR
MS/x
0
01.200VxRMS(t) with pulse marked with black lines
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
The Source Problem: Ultrasonic source
Nanoparticles are stickyvan der Waals ∝ r2
& inertial ∝ r3
=⇒ high acceleration
r ∼ 1µm → use piezo transducer
r . 100nm → use high-power ultrasound
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
40kHz, 50W
Focus powerwith waveguide
MHz? GHz?
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
The Source Problem: Ultrasonic source
Nanoparticles are stickyvan der Waals ∝ r2
& inertial ∝ r3
=⇒ high acceleration
r ∼ 1µm → use piezo transducer
r . 100nm → use high-power ultrasound
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
40kHz, 50W
Focus powerwith waveguide
MHz? GHz?
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
The Source Problem: Ultrasonic source
Nanoparticles are stickyvan der Waals ∝ r2
& inertial ∝ r3
=⇒ high acceleration
r ∼ 1µm → use piezo transducer
r . 100nm → use high-power ultrasound
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
40kHz, 50W
Focus powerwith waveguide
MHz? GHz?
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
The Source Problem: Ultrasonic source
Nanoparticles are stickyvan der Waals ∝ r2
& inertial ∝ r3
=⇒ high acceleration
r ∼ 1µm → use piezo transducer
r . 100nm → use high-power ultrasound
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
40kHz, 50W
Focus powerwith waveguide
MHz? GHz?
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
The Source Problem: Ultrasonic source
Nanoparticles are stickyvan der Waals ∝ r2
& inertial ∝ r3
=⇒ high acceleration
r ∼ 1µm → use piezo transducer
r . 100nm → use high-power ultrasound
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
40kHz, 50W
Focus powerwith waveguide
MHz? GHz?
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Dark matter?
Bateman, McHardy, Merle, Morris, & Ulbricht, Sci. Rep. 5 8058 (2015)
Generic candidate; surprisingly light!
Annihilation cross-section tied to scattering cross-section
Interacts coherently, like UCN
Mass-density known from CMB(WMAP & Planck)
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
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u, d
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u, d
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u, d
u, d
u, d
Γ
Γ
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Dark matter?
Bateman, McHardy, Merle, Morris, & Ulbricht, Sci. Rep. 5 8058 (2015)
Generic candidate; surprisingly light!
Annihilation cross-section tied to scattering cross-section
Interacts coherently, like UCN
Mass-density known from CMB(WMAP & Planck)
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
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Χ
u, d
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u, d
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u, d
u, d
u, d
Γ
Γ
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Dark matter? Detect with MAQRO http://maqro-mission.org
Bateman, McHardy, Merle, Morris, & Ulbricht, Sci. Rep. 5 8058 (2015)
Mass & cross-section well-constrained
Detection with free-floating particle
Weak potential→ same field across particle→ Born approximation→ N2 scaling for small particles
Partial-waves series for larger
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
a
b
c
Sun Earth L2
Objective lens Particle Lens PDs
Incident χ
Scattered χ
Particle recoil
10−9 10−8 10−7 10−6 10−5 10−4
10−11
10−9
10−7
10−5
10−3
10−9 10−8 10−7 10−6 10−5 10−4
10−11
10−9
10−7
10−5
10−3
Born Intermediate Geometric
Target particle radius, r [m]
Acceleration,a[m
/s2]
a ∝ N
a ∝ N−1/3
Full solution
104 105 106 107 108 1090
0.2
0.4
0.6
0.8
1
C60fullerenes
State-of-the-art
ProposedEarth-based
‘MAQRO’proposal
Nucleons in target particle, N
Relativesinusoidalvisibility,
R 1 keV
100 eV
10 eV
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Dark matter? Detect with MAQRO http://maqro-mission.org
Bateman, McHardy, Merle, Morris, & Ulbricht, Sci. Rep. 5 8058 (2015)
Mass & cross-section well-constrained
Detection with free-floating particle
Weak potential→ same field across particle→ Born approximation→ N2 scaling for small particles
Partial-waves series for larger
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
a
b
c
Sun Earth L2
Objective lens Particle Lens PDs
Incident χ
Scattered χ
Particle recoil
10−9 10−8 10−7 10−6 10−5 10−4
10−11
10−9
10−7
10−5
10−3
10−9 10−8 10−7 10−6 10−5 10−4
10−11
10−9
10−7
10−5
10−3
Born Intermediate Geometric
Target particle radius, r [m]
Acceleration,a[m
/s2]
a ∝ N
a ∝ N−1/3
Full solution
104 105 106 107 108 1090
0.2
0.4
0.6
0.8
1
C60fullerenes
State-of-the-art
ProposedEarth-based
‘MAQRO’proposal
Nucleons in target particle, N
Relativesinusoidalvisibility,
R 1 keV
100 eV
10 eV
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Dark matter? Detect with MAQRO http://maqro-mission.org
Bateman, McHardy, Merle, Morris, & Ulbricht, Sci. Rep. 5 8058 (2015)
Mass & cross-section well-constrained
Detection with free-floating particle
Weak potential→ same field across particle→ Born approximation→ N2 scaling for small particles
Partial-waves series for larger
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
a
b
c
Sun Earth L2
Objective lens Particle Lens PDs
Incident χ
Scattered χ
Particle recoil
10−9 10−8 10−7 10−6 10−5 10−4
10−11
10−9
10−7
10−5
10−3
10−9 10−8 10−7 10−6 10−5 10−4
10−11
10−9
10−7
10−5
10−3
Born Intermediate Geometric
Target particle radius, r [m]
Acceleration,a[m
/s2]
a ∝ N
a ∝ N−1/3
Full solution
104 105 106 107 108 1090
0.2
0.4
0.6
0.8
1
C60fullerenes
State-of-the-art
ProposedEarth-based
‘MAQRO’proposal
Nucleons in target particle, N
Relative
sinusoidal
visibility,
R 1 keV
100 eV
10 eV
Introduction Theoretical description Experimental & recent results Squashing/squeezing The source problem Dark Matter
Summary & outlook
So far
Nanoparticles in vacuum
Feedback cooling in 1D
Next steps
3D feedback and UHV
Smaller particles→ UHV nano-particle source
UV Grating (similar to OTIMA)
∼ 10nm position detection
High throughput; long-term stability
James Bateman: [email protected] University of Southampton
Talbot interferometry with a point-like source: rationale, technology, & experiment
0 50 100 150 200Frequency (kHz)
100
90
80
70
60
50
40
30
20
10
Pow
er
Spect
ral D
ensi
ty (
dB
/kH
z)
z
65 66 67 68 69 70 71 72Frequency (kHz)
0.000
0.005
0.010
0.015
0.020
0.025
Pow
er
Spect
ral D
ensi
ty (
kHz−
1)
ref-0.4-0.6-0.8