# Presentation: 942141

## Gravitational Physics                   using Atom Interferometry

- Prof. Mark Kasevich
- Dept. of Physics and Applied Physics
- Stanford University, Stanford  CA

## Young’s double slit with atoms

*Young’s 2 slit with Helium atoms*

*Slits*

*Interference fringes*

*One of the first experiments to demonstrate de Broglie wave interference with atoms, 1991 (Mlynek, PRL, 1991)*

## (Light-pulse) atom interferometry

- Resonant traveling wave optical excitation, (wavelength )

- 2-level atom

**|**2****

**|**1****

**Resonant optical interaction**

**Recoil diagram**

- Momentum conservation between atom and laser light field (recoil effects) leads to spatial separation of atomic wavepackets.

## Laser cooling

*Laser cooling techniques are used to achieve the required velocity (wavelength) control for the atom source.*

**Laser cooling:** Laser light is used to cool atomic vapors to temperatures of ~10-6 deg K.

*Image source:www.nobel.se/physics*

## Semi-classical approximation

**Three contributions to interferometer phase shift:**

- Propagation    shift:

- Laser fields        (Raman interaction):

- Wavepacket separation at detection:

- See Bongs, et al., quant-ph/0204102 (April 2002) also App. Phys. B, 2006.

## Laboratory gyroscope

*AI gyroscope*

- Noise:		3 deg/hr1/2
- Bias stability: 	< 60 deg/hr
- Scale factor: 	< 5 ppm

- Gyroscope interference fringes:

- Sensor noise

- Atom shot noise

- Lab technical noise

- Gustavson, et al., PRL, 1997, Durfee, et al., PRL, 2006

## Compact gyroscope/accelerometer

- Multi-function sensor measures rotations and linear accelerations along a single input axis.

- Interior view

- Interference fringes are recorded by measuring number of atoms in each quantum state

- F=3

- F=4

## Measurement of Newton’s Constant

*Pb mass translated vertically along gradient measurement axis.*

- Yale, 2002 (Fixler PhD thesis)

## Measurement of G

*Systematic error sources dominated by initial position/velocity of atomic clouds.*
***G/G ~ 0.3%*

- Fixler, et al., Science, 2007

## Next generation experiment (in progress)

- Using new sensors, we anticipate G/G ~ 10-5.
- This will also test for deviations from the inverse square law at distances from   ~ 1 mm to 10 cm.

*Sensors in use for next generation G measurements.*

- Theory in collaboration with S. Dimopoulos, P. Graham,  J. Wacker.

## Experiment in progress

- Currently achieved statistical sensitivity at ~2x10-4 G.

## Airborne Gravity Gradiometer

*AI sensors potentially offer 10 x – 100 x improvement in detection sensitivity at reduced instrument costs.*

- Land: 3 wks.

- Air: 3 min.

- LM Niagra Instrument

- Sanders Geophysics

- Kimberlite

- Existing technology

## Equivalence Principle

- Co-falling 85Rb and 87Rb ensembles
- 	Evaporatively cool to < 1 K  to enforce tight control over kinematic degrees of freedom
- Statistical sensitivity
- g  ~ 10-15 g with 1 month data collection
- Systematic uncertainty
- 	 g  ~ 10-16 limited by magnetic field inhomogeneities and gravity anomalies.
- Also, new tests of General Relativity

***10 m atom drop tower***

***Atomic source***

- 10 m drop tower

## Post-Newtonian Gravitation

- Light-pulse interferometer phase shifts for Schwarzchild metric:
- Geodesic propagation for atoms and light.
- Path integral formulation to obtain quantum phases.
- Atom-field interaction at intersection of laser and atom geodesics.

- Prior work, de Broglie interferometry: Post-Newtonian effects of gravity on quantum interferometry, Shigeru Wajima, Masumi Kasai, Toshifumi Futamase, Phys. Rev. D, 55, 1997; Bordé, et al.

- From Weinberg, Eq. 9.2.1

*Post-Newtonian trajectories for classical particle:*

**Collaborators:  Savas Dimopoulos, Peter Graham, Jason Hogan.**

## Post-Newtonian Gravitation

- Light-pulse interferometer phase shifts for Schwarzchild metric:
- Geodesic propagation for atoms and light.
- Path integral formulation to obtain quantum phases.
- Atom-field interaction at intersection of laser and atom geodesics.

- Prior work, de Broglie interferometry: Post-Newtonian effects of gravity on quantum interferometry, Shigeru Wajima, Masumi Kasai, Toshifumi Futamase, Phys. Rev. D, 55, 1997; Bordé, et al.

- From Weinberg, Eq. 9.2.1

*Post-Newtonian trajectories for classical particle:*

**Collaborators:  Savas Dimopoulos, Peter Graham, Jason Hogan.**

## Theory

**Initial **
- Define metric
- Calculate geodesic equations for photons and atoms
**Atom interferometer phase shift**
- Initial coordinates for optical pulses, atom trajectories
- Find intersection coordinates for atom and photon geodesics           (2 photons for Raman transitions)
- Evaluate scalar propagation phase
- Coordinate transformation to local Lorentz frame at each atom/photon intersection (Equivalence Principle) to for atom/photon interaction (eg. apply Sch. Eq.).
- Coordinate transformation to local Lorentz frame at final interferometer pulse to evaluate separation phase

## Parameterized Post-Newtonian (PPN) analysis

- Schwazchild metric, PPN expansion:

- Corresponding AI phase shifts:

- Projected experimental limits:

- Steady path of apparatus improvements include:
- Improved atom optics
- Taller apparatus
- Sub-shot noise interference read-out
- In-line, accelerometer, configuration (milliarcsec link to external frame NOT req’d).

- (Dimopoulos, *et al., *PRL 2007)

## Equivalence Principle Installation

## Cosmology

- Are there (local) observable phase shifts of cosmological origin?
- Analysis has been limited to simple metrics:
- FRW:     *ds**2** = dt**2** – a(t)**2**(dx**2**+dy**2**+dz**2**)*
- McVittie:  ~Schwarzchild + FRW
- Gravity waves

**Work in progress ...**
**Future theory:  Consider phenomenology of exotic/speculative theories (after validating methodology)**

- Giulini, gr-qc/0602098

- From MTW

## Acknowledgements

- Todd Gustavson, Research Scientist
- Boris Dubetsky, Research Scientist
- Todd Kawakami, Post-doctoral fellow
- Romain Long, Post-doctoral fellow
- Olaf Mandel, Post-doctoral fellow
- Peter Hommelhoff, Post-doctoral fellow
- Ari Tuchman, Research scientist
- Catherine Kealhoffer, Graduate student, Physics
- Wei Li, Graduate student, Physics
- Hui-Chun Chen, Graduate student, Applied Physics
- Ruquan Wang, Graduate student, Physics
- Mingchang Liu, Graduate student, Physics
- Ken Takase, Graduate student, Physics
- Grant Biedermann, Graduate student, Physics
- Xinan Wu, Graduate student, Applied physics
- Jongmin Lee, Graduate student, Electrical engineering
- Chetan  Mahadeswaraswamy, Graduate student, Mechanical engineering
- David Johnson, Graduate student, Aero/Astro engineering
- Geert Vrijsen, Graduate student, Applied physics
- Jason Hogan, Graduate student, Physics
- Nick Ciczek, Graduate student, Applied Physics
- Mike Minar, Graduate student, Applied Physics
- Sean Roy, Graduate student, Physics
- Larry Novak, Senior assembly technician
- Paul Bayer, Optomechanical engineer
**+ THEORY COLLABORATORS!**