Tests of fundamental physics using atom interferometry

Transcription

1 Tests of fundamental physics using atom interferometry Leibniz Universität Hannover RTG 1729, Lecture 3 Jason Hogan Stanford University January 30, 2014

2 Large wavepacket separation Long interferometer time (>2 seconds) Large momentum transfer beam splitters (>10 hk) 4 cm

3 Testing fundamental physics with AI Some physics motivation for increasing sensitivity Testing general relativity Equivalence principle Short range gravity/fifth forces Post-Newtonian effects Gravitational wave astronomy Terrestrial and space detectors Tests of QED Photon recoil (alpha measurements) Tests of quantum mechanics Macroscopic superposition states Decay of coherence

4 Equivalence Principle

5 Equivalence Principle Test Bodies fall (locally) at the same rate, independent of composition Gravity = Geometry 85 Rb vs. 87 Rb predicted bounds Why test the EP? Foundation of General Relativity Quantum theory of gravity (?) Current Bounds Violations of EP due to fifth forces Yukawa type: EP test are sensitive to charge differences of new forces Analysis by P. Graham

6 Equivalence Principle Co-falling 85 Rb and 87 Rb ensembles Evaporatively cool to enforce tight control over kinematic degrees of freedom Statistical sensitivity dg ~ g with 1 month data collection (2 hk atom optics) Systematic uncertainty dg/g ~ limited by magnetic field inhomogeneities and gravity anomalies.

7 Three contributions: Semi-classical phase shift analysis Laser phase at each node Propagation phase along each path Separation phase at end of interferometer Include all relevant forces in the classical Lagrangian: Rotation of Earth Gravity gradients, etc. Magnetic field shifts

8 EP Systematic Analysis Use standard semi-classical methods to analyze spurious phase shifts from uncontrolled: Earth s Rotation Gravity anomalies/gradients Magnetic fields Proof-mass overlap Misalignments Finite pulse effects Known systematic effects appear controllable at the dg < g level. Common mode cancellation between species is critical

9 EP: Magnetic Field Control Three layer mu-metal magnetic shield Welded together and annealed Residual field < 1 mg rms Measured magnetic field Susannah Dickerson et al., Rev. Sci. Instrum. 83, (2012)

10 EP: Coriolis Compensation Coriolis force puts tight constraint on transverse velocity control Solution: Counter-rotate the reference mirror at Earth s rotation rate Piezo-actuated precision tip-tilt platform Required precision: Tip-tilt mirror platform

11 EP: Gravity Gradients Earth GG is ~10-16 g/nm Tight constraints on kinematics: <10 nm overlap ~ nm/s relative velocity Mitigation strategies: Measure and subtract Reduce GG with trim masses Higher order pulse sequences Symmetric 4 pulse Asymmetric 4 pulse Eliminates all T 2 terms Golden ratio diamonds: Eliminates all T 3 terms B. Dubetsky et al., PRA 74, (2006).

12 EP: Local gravity inhomogeneities Differential gravity response function for simultaneous 87 Rb and 85 Rb interferometers: Spatial averaging Common mode cancelation Assumes identical kinematics Peak response at scale of wavepacket separation Total phase error is sum over all spatial frequencies: Transfer function Gravity Fourier component

13 Tests of Quantum Mechanics

14 Theories of wavefunction collapse Does the universe allow massive particles to be in superposition states with macroscopic spatial separations? Standard Quantum Mechanics: Yes Introduce a mechanism to make macroscopic superposition states collapse towards localized states. Continuous spontaneous localization (CSL) Gravity-induced wavefunction collapse (e.g., Diosi model, Penrose model) Quantum foam (?) Experiments can put bounds on these theories by demonstrating more macroscopic superposition states

15 Macroscopicity: Comparing different experiments Macroscopicity Contrast Reduction

16 Maximal Definition of μ < 1 μk/s temp. inc. of Rb gas Talbot-Lau Au Cluster 10 5 amu 10 8 amu 2.3 ng micromirror Atom Interferometry Persistent Supercurrents Nimmrichter et al., PRL 110, (2013)

17 Constraints from 10 m AI Observation of 3 nk Rb clouds after 2.3 s TOF 10 5 amu 98%, 87 Rb, 2T = 2.3 s, 2 ħk 30%, 87 Rb, 2T = 2.3 s 12 ħk Nimmrichter et al., PRL 110, (2013)

18 General Relativistic Effects

19 GR Back of the Envelope With this much sensitivity, does relativity start to affect results? Gravitational red shift of light: 10 m/s 10m Special relativistic corrections:

20 General relativistic phase shifts Light-pulse interferometer phase shifts in GR: Geodesic propagation for atoms and light. laser Path integral formulation to obtain quantum phases. Atom-field interaction at intersection of laser and atom geodesics. atom Atom and photon 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.

21 General Relativity Effects High precision motivates GR phase shift calculation Consider Schwarzschild metric in the PPN expansion: ( ) (can only measure changes on the interferometer s scale)

22 Measurement Strategies Can these effects be distinguished from backgrounds? 1. Velocity dependent gravity (Kinetic Energy Gravitates) Phase shift ~~~~~~ has unique scaling with, Compare simultaneous interferometers with different v_l 2. Non-linear gravity (Gravity Gravitates) Newtonian mass density Gravitational field energy! Divergence: So, in GR in vacuum: Can discriminate from Newtonian gravity using three axis measurement

23 Tests of General Relativity Schwarzschild metric, PPN expansion: Corresponding AI phase shifts: Projected experimental limits: (Dimopoulos, et al., PRL 2007; PRD 2008)

24 Single photon vs. two photon AI Breakdown the origin of various phase terms in the relativistic calculation (for Raman transitions) GR calculation gives terms arising from change of rest mass in different atomic states. In the case of a single photon interferometer, this is the dominate effect. Phase shift comes from propagation phase, not laser phase. Single photon AI phase shift does not depend on the laser wavevector. Non-relativistic single photon calculation incorrectly predicts kgt 2

25 Gravitational Wave Detection

26 Gravitational Wave Detection frequency Megaparsecs L (1 + h sin(ωt )) strain Why study gravitational waves? New carrier for astronomy: Generated by moving mass instead of electric charge Tests of gravity: Extreme systems (e.g., black hole binaries) test general relativity Cosmology: Can see to the earliest times in the universe But, they are incredibly weak! Strain oscillation: Amplitude of motion depends on separation Example: 1000 km baseline, oscillation amplitude is only 10 fm

27 Gravitational Wave Detection Why consider atoms? Neutral atoms are excellent test particles (follow geodesics) Atom interferometry provides exquisite measurement of geodesic w.r.t. laser ruler (LMT phase amplification) Flexible operation modes (broadband, resonant detection) Single baseline configuration possible (e.g., only two satellites)

28 Gravitational Wave Phase Shift Signal Laser ranging an atom (or mirror) that is a distance L away: Position Acceleration Phase Shift: Relativistic Calculation:

29 Vibrations and Seismic Noise Atom test mass is inertially decoupled (freely falling); insensitive to vibration Atoms analogous to LIGOs mirrors However, the lasers vibrate Laser has phase noise Laser vibration and intrinsic phase noise are transferred to the atom s phase via the light pulses.

30 Differential Measurement Differential phase retains the GW single and suppresses many sources of noise. Two-photon transitions: Light from the second laser is not exactly common. Light travel time delay is a source of noise susceptibility

31 Terrestrial Configuration Run two, widely separated interferometers using common lasers Measure the differential phase shift Benefits: 1. Signal scales with length L ~ 1 km between interferometers (easily increased) 2. Common-mode rejection of seismic & phase noise Allows for a free fall time T ~ 1 s. (Maximally sensitive in the ~1 Hz band) (e.g., vertical mine shaft)

32 Gravity Gradient Noise Limit Seismic noise induced strain analysis for LIGO (Thorne and Hughes, PRD 58). Seismic fluctuations give rise to Newtonian gravity gradients which can not be shielded. Could allow for terrestrial gravitational wave detection down to ~ 0.3 Hz

33 Projected Terrestrial GW Sensitivity

34 Satellite GW Antenna Atoms Common interferometer laser Atoms L ~ km Avoid Earth gravity gradient noise Allows detection in the mhz band Baseline can be made very large Some practical considerations: Solar radiation shields Space vacuum, satellite outgassing Magnetic fields

35 Potential Strain Sensitivity J. Hogan, et al., GRG 43, 7 (2011).

36 Stochastic GW Sensitivity AGIS Requires correlation among multiple independent baselines

37 Technology development for GW detectors 1) Large wavepacket separation (meter scale) 2) Ultra-cold atom temperatures (picokelvin) 3) Spatial wavefront noise characterization 4) Laser frequency noise mitigation strategies No Lens With Lens 4 cm

38 Two-photon vs. single photon configurations 2-photon transitions 1 photon transitions Rb Sr GW signal from relative positions of atom ensembles with respect to optical phase fronts. GW signal from light propagation time between atom ensembles.

39 Laser frequency noise insensitive detector Long-lived single photon transitions (e.g. clock transition in Sr, Ca, Yb, Hg, etc.). Excited state Atoms act as clocks, measuring the light travel time across the baseline. Laser noise is common GWs modulate the laser ranging distance. Graham, et al., arxiv: , PRL (2013)

40 Laser frequency noise insensitive detector Example LMT beamsplitter (N = 3) Long-lived single photon transitions (e.g. clock transition in Sr, Ca, Yb, Hg, etc.). Atoms act as clocks, measuring the light travel time across the baseline. GWs modulate the laser ranging distance. Graham, et al., arxiv: , PRL (2013)

41 Kinematic noise sensitivity Laser noise cancels. What are the remaining sources of noise? Relative velocity Δv between the interferometers changes the time spent in the excited state, leading to a differential phase shift. Leading order kinematic noise sources: 1. Platform acceleration noise da 2. Pulse timing jitter dt 3. Finite duration Dt of laser pulses 4. Laser frequency jitter dk Most severe constraint on laser frequency noise is that laser needs to be resonant with the transition (linewidth < transition Rabi freq.)

42 Sr compact optical clock 6 liter physics package. Contains all lasers, Sr source, 2D MOT, Zeeman slower, spectrometer, pumps, and 3 W Sr oven; 4e10 cold atoms/sec. As built view with front panel removed in order to view interior. AOSense AOSense.com 42 Sunnyvale, CA

43 Collaborators Stanford Mark Kasevich (PI) Susannah Dickerson Alex Sugarbaker Sheng-wey Chiow Tim Kovachy NASA GSFC Babak Saif Bernard D. Seery Lee Feinberg Ritva Keski-Kuha Theory: Peter Graham Savas Dimopoulos Surjeet Rajendran AOSense Brent Young (CEO) Former members: David Johnson Visitors: Philippe Bouyer (CNRS) Jan Rudolph (Hannover)