Fundamental Physics with Optically Levitated Objects Asimina - - PowerPoint PPT Presentation

Fundamental Physics with Optically Levitated Objects

Asimina Arvanitaki Stanford University with Andrew Geraci (experiment) and Sergei Dubovsky (theory)

Optical Trapping of Dielectrics

Optical Trapping of Dielectrics

Force / rE2 ⌘ kx

Ashkin et al. (1970,1971,1976)

Optical Trapping of Dielectrics

• Quality factor, ωmech / Γloss, larger than 1012 even at room

temperature

• Internal modes decoupled from CM for small objects
• CM motion controlled by the intensity of light

Force / rE2 ⌘ kx

Ashkin et al. (1970,1971,1976)

Optical Trapping Applications

• Atom Interferometry (Nobel Prize 1997, 2001, 2005, 2012)
• Biology
• Quantum Computing

Towards the Quantum Regime

ECM = (nthermal + 1/2)ωCM

Towards the Quantum Regime

ECM = (nthermal + 1/2)ωCM 109 atoms in a quantum superposition of states

Optical Cooling

Doppler cooling For an atom

ωphoton < ωatom

vatom

ωphoton |g, vatomi |e, vinti |g, v0 atomi v0 atom < vatom

Optical Cooling

Doppler cooling For an atom

ωphoton < ωatom

vatom

ωphoton |g, vatomi |e, vinti |g, v0 atomi ωatom v0 atom

Spontaneous emission

v0 atom < vatom

Optical Cavity Cooling

For a trapped oscillating dielectric

ωphoton |g, nvibi |e, nvib 1i |g, nvib 1i

ωphoton < ωcavity

Optical Cavity Cooling

For a trapped oscillating dielectric

ωphoton |g, nvibi |e, nvib 1i |g, nvib 1i

ωphoton < ωcavity

ωcavity

Photon is re-emitted at the frequency of the cavity tuned laser

ωcavity

Outline

• Gravitational Wave Detection
• Sources of High-Frequency Gravitational Waves
• Short Distance Tests of Gravity
• Future Prospects

Gravitational Wave Detection

• Last piece of General Relativity
• Sources:
• Inspirals of astrophysical objects
• Inflation, Phase transitions, etc.

Gravitational Wave Detection

xs `m

• Fused silica sphere (r = 150 nm) or disk (d=500 nm, r=75 µm)

sensor in optical cavity of 10-100 m in size

• One laser to hold, one to cool and one to measure the position

AA and Geraci (2012)

∆X = 1 2(xs − `m)h Xmin = 1 2`mh

Gravitational Wave Detection

• Changes the physical position of the laser antinode:
• Changes the physical distance between the sensor and the mirror:
• Sensor position changes with respect to the trap minimum:

δXs = 1 2xsh

xs `m

ds2 = dt2 − (1 + h cos(ω(t − y)))dx2 − dy2 − (1 − h cos(ω(t − y)))dz2

∆X = 1 2(xs − `m)h Xmin = 1 2`mh

Gravitational Wave Detection

• Changes the physical position of the laser antinode:
• Changes the physical distance between the sensor and the mirror:
• Sensor position changes with respect to the trap minimum:

δXs = 1 2xsh

xs `m

Gravitational wave changes the physical distance between masses L=L0 (1+ h cosωt)

∆X = 1 2(xs − `m)h Xmin = 1 2`mh

Gravitational Wave Detection

• Changes the physical position of the laser antinode:
• Changes the physical distance between the sensor and the mirror:
• Sensor position changes with respect to the trap minimum:

δXs = 1 2xsh

xs `m

Gravitational wave changes the physical distance between masses L=L0 (1+ h cosωt)

∆X = 1 2(xs − `m)h Xmin = 1 2`mh

Gravitational Wave Detection

• Changes the physical position of the laser antinode:
• Changes the physical distance between the sensor and the mirror:
• Sensor position changes with respect to the trap minimum:

δXs = 1 2xsh

xs `m

Gravitational wave changes the physical distance between masses L=L0 (1+ h cosωt)

∆X = 1 2(xs − `m)h Xmin = 1 2`mh

Gravitational Wave Detection

• Changes the physical position of the laser antinode:
• Changes the physical distance between the sensor and the mirror:
• Sensor position changes with respect to the trap minimum:

δXs = 1 2xsh

xs `m

Gravitational wave changes the physical distance between masses L=L0 (1+ h cosωt)

Gravitational Wave Detection

• Laser intensity changes resonant frequency of the sensor:

Tunable resonant GW detector

• For a 100 m cavity h ~10-22 Hz-1/2 sensitivity and increases

linearly with the cavity size

• Main background: Thermal motion in the trap

xs `m

∆X = 1 2(xs − `m)h

h = 1 ωGW L s 4T ωGW mQ ∼ 10−22 √ Hz

for a disk in a 100 m cavity

GW sensitivity

GW sensitivity

150 nm sphere

GW sensitivity

150 nm sphere 500 nm × (75 µm)2 disk

Radical change in sensitivity between the two geometries due to difference in mass and in light scattering properties

GW sensitivity compared to LIGO

Current and Advanced LIGO

GW sensitivity compared to LIGO

Current and Advanced LIGO LIGO: 4 km cavity

GW sensitivity compared to LIGO

Current and Advanced LIGO Current setup: 100 m cavity LIGO: 4 km cavity

GW Sources in the High Frequency Regime

• Astrophysical Sources:
• Beyond-the-Standard Model Sources:

Natural upper bound on GW frequency Black Hole Super-radiance

AA and Dubovsky (2010)

1 Minimum Black Hole Size ∼ 30 kHz

Black Hole Superradiance

Ergoregion Rotating Black Hole

Ergoregion: Region where even light has to be rotating Penrose Process

Black Hole Superradiance

Extracts angular momentum and mass from a spinning black hole

Ergoregion Rotating Black Hole

Penrose Process

Black Hole Bomb

Photons reflected back and forth from the black hole and through the ergoregion

Press & Teukolsky 1972

Black Hole Bomb

Photons reflected back and forth from the black hole and through the ergoregion

Press & Teukolsky 1972

Superradiance for a Massive Boson

Particle Compton Wavelength comparable to the size of the Black Hole Penrose Process

Damour et al; Zouros & Eardley; Detweiler; Gaina

Superradiance for a Massive Boson

Particle Compton Wavelength comparable to the size of the Black Hole Penrose Process

Damour et al; Zouros & Eardley; Detweiler; Gaina

Superradiance for a Massive Boson

Penrose Process

Damour et al; Zouros & Eardley; Detweiler; Gaina

Gravitational Atom in the Sky

The Strong CP Problem

Experimental bound: θQCD < 10-10 Non-zero electric dipole moment for the neutron

LSM ⊃ g2

s

32π2 θQCDGa ˜ Ga

Solution: θQCD is a dynamical field, an axion Axion mass from QCD: fa : axion decay constant µa ∼ 6 × 10−11 eV 1017 GeV fa ∼ (3 km)−1 1017 GeV fa

Evolution of Superradiance for an Axion

Superradiance instability time (100 sec minimum)

Evolution of Superradiance for an Axion

Superradiance instability time (100 sec minimum) Black Hole Accretion τaccretion ~ 108 years

Evolution of Superradiance for an Axion

Superradiance instability time (100 sec minimum) Axion self-interactions Black Hole Accretion τaccretion ~ 108 years

Evolution of Superradiance for an Axion

Superradiance instability time (100 sec minimum) Gravity wave transitions of axions between levels Axion self-interactions Black Hole Accretion τaccretion ~ 108 years

Evolution of Superradiance for an Axion

Superradiance instability time (100 sec minimum) Gravity wave transitions of axions between levels Gravity wave emission through axion annihilations Axion self-interactions Black Hole Accretion τaccretion ~ 108 years

Spin Gap for the QCD Axion

2 4 6 8 10 12 14 0.0 0.2 0.4 0.6 0.8 1.0 Black Hole Mass in units of Msolar Black Hole Spin a

µa ≈ 3 · 10−11 eV (fa ≈ 2 · 1017 GeV)

Spin Gap for the QCD Axion

2 4 6 8 10 12 14 0.0 0.2 0.4 0.6 0.8 1.0 Black Hole Mass in units of Msolar Black Hole Spin a

µa ≈ 3 · 10−11 eV

2 4 6 8 10 12 14 0.0 0.2 0.4 0.6 0.8 1.0 Black Hole Mass in units of Msolar Black Hole Spin a

(fa ≈ 2 · 1017 GeV)

Spin Gap for the QCD Axion

2 4 6 8 10 12 14 0.0 0.2 0.4 0.6 0.8 1.0 Black Hole Mass in units of Msolar Black Hole Spin a

µa ≈ 3 · 10−11 eV

2 4 6 8 10 12 14 0.0 0.2 0.4 0.6 0.8 1.0 Black Hole Mass in units of Msolar Black Hole Spin a

(fa ≈ 2 · 1017 GeV)

Possible to probe the QCD axion down to fa ~few × 1016 GeV

Signals from annihilations

BH Gravitational field ωgraviton = 2 maxion

signal duration > years and ε ~10-3

h ∼ 10−19 ⇣↵ ` ⌘7 ✏ ✓10 kpc r ◆ ✓ MBH 2 × MJ ◆

GWs from the QCD axion at high frequencies

QCD axion superradiance

Distance to the source: 10 kpc

GUT scale axion

Prospects of GW detection with optically trapped sensors

• Sensitivity better than 10-21 1/Hz1/2 above ~30 kHz
• Relatively small size enables GW array antenna design
• Improved GW sensitivity in new regime for GW astronomy

Outline

• Gravitational Wave Detection
• Sources of High-Frequency Gravitational Waves
• Future Prospects: Towards an interferometer of macroscopic
• bjects

Towards the Schroedinger Cat State

• Feasible goal: Ground state cooling of the CM motion of 108-9

atoms

• Can we put the wave-function of 109 atoms in a superposition of

spatially separated states?

Towards the Schroedinger Cat State

• Feasible goal: Ground state cooling of the CM motion of 108-9

atoms

• Can we put the wave-function of 109 atoms in a superposition of

spatially separated states?

Sources of Decoherence

• Black Body radiation emission
• Collisions with gas molecules
• Interaction with diffraction grating, holding light, etc.

Sources of Decoherence

• Black Body radiation emission
• Collisions with gas molecules
• Interaction with diffraction grating, holding light, etc.

λBB >> δx

Decoherence from BB emission

λBB >> δx For a 50 nm sphere with 0.1 nm separation

Romero-Isart (2011)

Decoherence from BB emission

λBB >> δx For a 50 nm sphere with 0.1 nm separation 100 ms is a long time There may be a setup that actually works...

Romero-Isart (2011)

Conclusions

• Optical trapping and cooling provides new precision tool
• Short distance tests of gravity
• GW detection in the high frequency regime
• Quantum Mechanics pushed to a new regime

Gravity Wave Transitions

QCD axion observable at high frequency gravity wave detectors

Super-Radiant Mode (n+1, l, m) Super-Radiant Mode (n, l, m) Gravitons

signal duration ~ 1 day-1 year

Einstein Telescope Advanced LIGO AGIS LISA

10-27 10-26 10-25 10-24 10-23 10-22 10-21 10-20 10-19 10-18

• 18
• 16
• 14
• 12
• 10

0.6 0.8 1.0 1.2 1.4 1.6 1.8 8 6 4 2 Axion mass in Log10 ma eV ma¥ rg Black Hole Mass in Log10 MBH Msolar for ma¥ rg=1

Gravity Wave Transitions

Distance to the source: 20 Mpc

6g level ⟶ 5g level

Einstein Telescope Advanced LIGO AGIS LISA

10-32 10-31 10-30 10-29 10-28 10-27 10-26 10-25 10-24 10-23 10-22 10-21 10-20 10-19

• 20
• 18
• 16
• 14
• 12
• 10

0.20 0.25 0.30 0.35 0.40 0.45 0.50 10 8 6 4 2 Axion mass in Log10 ma eV ma¥ rg Black Hole Mass in Log10 MBH Msolar for ma¥ rg=1

Signals from annihilations

Distance to the source: 20 Mpc

2p level