# Presentation: 942142

## Atom Interferometry

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

## Outline

- de Broglie wave interferometry
- Current Generation Sensors
- 	(Mobile) Gravity Gradiometer
- 	Hybrid Navigation Sensor
- Sensors for Science
- 	Testing Newton’s inverse square law
- 	Equivalence principle
- 	Gravity beyond Newton
- 	Gravity wave detection
- 	Testing atomic charge neutrality
- Quantum Metrology

## 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.

## Example: Gyroscope

- East/west oriented propagation vectors k1, North/south atomic beam velocity v2, Earth radius R, horizontal Earth gravity gradient Txx, and Earth gravity g3 and interrogation time T:

## 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

## Measurement of Newton’s Constant

*Pb mass translated vertically along gradient measurement axis.*

- Yale, 2002 (Fixler PhD thesis)

*Characterization of source mass geometry and atom trajectories (with respect to source mass) allows for determination of Newton’s constant G.*
*Use gravity gradiometer to reject spurious technical vibrations. *

## Measure gravitational field from nearby mass

## Measurement of G

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

- Fixler, et al., Science, 2007, also Fixler PhD thesis, 2003.

## Current Generation Sensors

## Differential Accelerometer 

- Differential accelerometer, horizontal configuration

- ~ 1 m

## Gravity Gradiometer

- Demonstrated accelerometer resolution: ~6x10-12 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

## Mobile Gravity Gradient Survey

- Sensor mounted in truck on gyro-stabilized platform

## Hybrid Navigation Sensor

- Partial inertial measurement unit (IMU).

## Semi-classical model for light-pulse sensors

- Atom is in a near perfect inertial frame of reference (*no spurious forces*).
- Laser/atomic physics interactions determine the the relative motion between the inertial frame (*defined by the atom deBroglie waves*) and the sensor case (*defined by the laser beams*).
- Sensor accuracy derives from the use of optical wavefronts to determine this relative motion.
- Sensor is kinematic:  directly reads angular and linear displacements
- Semi-classical model valid** **at 10-10 level.

**v**

- Laser

## Gravity gradiometer

- 250 E/Hz1/2 noise during quiet periods.
- Signal has also been observed directly on individual accelerometers

## Gyroscope 

- Measured gyroscope output vs.orientation:

- Typical interference fringe record:

- Phase shift   = 6**k******(**g**x**** T3
- Inferred ARW:  ~100 deg/hr1/2
- 10 deg/s max input

## A quantum sensor .... coherence length

- Measurement of coherence length of laser cooled atomic source (~ 100 nm)

- Time-skewed pulse sequence to reject spurious mutli-path interferences

## Optimal Bayesian phase estimation

- Numerical simulation to compare performance of Bayesian vs. ellipse specific methods for white, non-common, phase noise (Stockton,  submitted).

- Bayesian error

- Bayesian noise

- Ellipse noise

- Ellipse error

*Currently investigating computationally efficient implementations.*
*Suppresses systematic offsets in phase determination *

## Moving mass phase shifts 

- Actuate test mass motion.
- Observe corrections to interferometer phase shift due to time-varying (over the course of the interferometer measurement sequence) gravitational potential.

## Sensors for Science

## Test Newton’s Inverse Square Law

- 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.

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

## 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 g limited by magnetic field inhomogeneities and gravity anomalies.

***10 m atom drop tower***

***Atomic source***

- 10 m drop tower

**Use atom interferometric differential accelerometer to test EP**

## Equivalence Principle Installation

- Long free-fall enables ground-based assessment of possible space-based sensor implementations.

## Error model

- Error model, including Newtonian gravity anomalies, magnetic field gradients, rotations, and       apparatus misaligments.
- Known systematic errors are controllable at the    < 10-15 g level.
*(Hogan, Johnson, Proc. Varenna School, 2007)*

## 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.

*Post-Newtonian trajectories for classical particle:*

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

## 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 (T. Kovachy)
- 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)

## Gravity wave primer

- Distance between objects modulates by *hL*, where* h *is strain of wave and *L* is their average separation.

- Interesting astrophysical objects (black hole binaries, white dwarf binaries) are sources of gravitational radiation in 0.01 – 10 Hz frequency band.

- LIGO is existing sensor utilizing long baseline optical interferometry.  Sensitive to sources at > 40 Hz.

## Gravity wave detection

- Metric:

- Differential accelerometer configuration for gravity wave detection.
- Atoms provide inertially decoupled references (analogous to mirrors in LIGO)
- Gravity wave phase shift through propagation of optical fields.

- Previous work: B. Lamine, et al., Eur. Phys. J. D **20**, (2002);  R. Chiao, et al., J. Mod. Opt. **51**, (2004);  S. Foffa, et al., Phys. Rev. D **73**, (2006); A. Roura, et al., Phys. Rev. D **73**, (2006); P. Delva, Phys. Lett. A **357 **(2006); G. Tino, et al., Class. Quant. Grav. **24 **(2007).

*h* is strain, *L* is separation, *T* is pulse separation time,  is frequency of wave

- Gravity wave induced phase shift:

## Proposed Terrestrial Detector Performance

- 1 km

*Pre-print available indicating analysis details.  *

## Terrestrial detector sensitivity to stochastic sources

## Atom charge neutrality (?)

- Apparatus will support >1 m wavepacket separation
- Enables ultra-sensitive search for atom charge neutrality through scalar Aharonov-Bohm effect.

***e/e* ~ 10-26 for mature experiment using scalar Aharonov-Bohm effect
- Current limit: *e/e* ~ 10-20        (Unnikrishnan e*t al*., Metrologia **41**,** **2004)
- Impact of a possible observed imbalance currently under investigation.

- Phase shift:

- Theory collaborators:                      A. Arvanitaki, S. Dimopoulos,   A. Geraci

## 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

**No detectable (linear H) local signatures for Hubble expansion**
**Future theory:  Consider phenomenology of exotic/speculative theories?**

- Giulini, gr-qc/0602098

- From MTW

## Quantum Metrology

## Quantum Metrology:  Sub-shot noise detection

**Atom shot noise limits sensor performance.**
**Recently evolving ideas in quantum information science have provided a road-map to exploit exotic quantum states to significantly enhance sensor performance.**
- Sensor noise scales as 1/N where N is the number of particles
- “Heisenberg” limit
- Shot-noise ~ 1/N1/2  limits existing sensors
**Challenges:**
- Demonstrate basic methods in laboratory
- Begin to address engineering tasks for realistic sensors

**Impact of successful implementation for practical position/time sensors could be substantial.  Possible 10x – 100x reduction in sensor noise. **
**Enables crucial trades for sensitivity, size and bandwidth.**

## Quantum non-demolition atom detection

- (Tuchman, et al. PRA, 2006, Long,  Opt. Lett., submitted)

- Dispersive cavity shift

- Rabi oscillations detected via cavity shift

## QND state evaluation

- Use QND probe to prepare squeezed state.
- Rotate state on Bloch sphere using a microwave pulse.
- Measure number fluctuations.
- 13 dB squeezing inferred, agrees with theory.

- Fluctuations (mV)

- Rotation angle (rad)

- Control

- Shot noise

**Next step: run interferometer pulse sequence**

## Measured squeezing factor vs. atom number

- Observed squeezing factor as a function of atom number
- Red line: theory based on cavity parameters and effective atom number

## Acknowledgements

- Grant Biedermann, PhD, Physics
- Ken Takase, PhD, Physics
- Romain Long, Post-doctoral fellow
- Olaf Mandel, Post-doctoral fellow
- John Stockton, Post-doctoral fellow
- Louis Delsauliers, Post-doctoral fellow
- Xinan Wu, Graduate student, Applied physics
- Jongmin Lee, Graduate student, Electrical engineering
- Chetan  Mahadeswaraswamy, Graduate student, Mechanical engineering
- David Johnson, Graduate student, Physics
- Alex Sugarbaker, Physics
- Geert Vrijsen, Graduate student, Applied physics
- Jason Hogan, Graduate student, Physics
- Sean Roy, Graduate student, Physics
- Tim Kovachy, Undergraduate
- Boris Dubestsky, Research Scientist
- Paul Bayer, Engineer
- + THEORY COLLABORATORS:
**	**S. Dimopolous, P. Graham, S. Rajendran, A. Arvanitaki, A. Geraci
- + AOSense team
-  	B. Young, T. Gustavson, J. Spilker, A. Black, F. Roller, T. Tran, M. Mathews, A.  Vitushkin.