Precision Interferometry with a Bose-Einstein Condensate. Cass Sackett. Research Talk 17 October 2008

Transcription

1 Precision Interferometry with a Bose-Einstein Condensate Cass Sackett Research Talk 17 October 2008

2 Outline Atom interferometry Bose condensates Our interferometer One application

3 What is atom interferometry? Just like optical interferometry: Atom beam or laser beam path A Output 1 grating 1 grating 2 grating 3 Output 2 Output depends on phase difference - whether for Maxwell or Schrodinger waves

4 For atoms, measure phase Applications t φ = E h Anything that changes energy of an atom: - All kinds of EM fields (external or atomic) - Gravity - Acceleration and rotation Potential uses: Fine-structure constant Atomic properties Surface characterization Quantum light detection Magnetometry Inertial navigation Geophysics Oil exploration

5 Atom interferometry works with thermal atoms Manipulate each atoms ψ Works better with Bose-Einstein condensate: Many atoms all in same quantum state condensate : thermal atoms as laser : light bulb Interferometry cleaner, more flexible But, requires a condensate

6 Making a condensate BEC happens when Λ l debroglie wavelength interparticle spacing In air: Λ m, l 10-9 m Λ ~ T -1/2, so could cool air to 30 mk - but gases freeze first Need to use dilute gas to avoid making solid or liquid n ~ cm -3 ~ 10-9 n air l ~ 10-6 m T ~ 100 nk Use 87 Rb atoms

7 How to get so cold? Three techniques: 1. Laser cooling 2. Magnetic trapping 3. Evaporative cooling Summarize briefly

8 Laser Cooling Photon carries momentum hk Scatter photons = force Cool by applying F -v Trick: Shine lasers from all directions tuned below atomic resonance Glass cell: Rb vapor Laser beams Doppler shift: Moving atoms scatter light from beam opposing motion Cool down to T 200 µk ( atoms) Then transfer to magnetic trap

9 Magnetic Trap Rb atoms have one unpaired electron Energy shift due to magnetic moment Zeeman effect: V = 2µ B Bm S µ B = Bohr magneton m S = spin quantum number = ±½ For m S = +½ state, have V = µ B B atom attracted to low B Magnetic trap = field with minimum in free space Make quadratic minimum harmonic trap B B + b x + b y + b z min x y z

10 Evaporative Cooling Only m S = +½ atoms trapped Drive +½ -½ using rf field Resonant if hω rf = 2µ B B m S = +½ Tune ω rf above trap bottom: only energetic atoms ejected Take away more than average energy - remaining atoms colder hω rf Continue to BEC N atoms T 200 nk m S = -½

11 Condensation T > T c T ~ T c T < T c Reach BEC, get macroscopic fraction in trap ground state Pictures from absorption imaging - destroys condensate

12 Interferometry So we got a condensate yay! Want to make an interferometer: Split wave function apart and later recombine reflect Basic scheme: split scheme: hbasic - Split into two packets - Packets fly apart - Turn around via reflection - Packets come back together - Apply splitting operation again time split horizontal

13 Recombination Split drives: 0 ( + v + v ) 1 Reversible: ( v v ) Phase shift gives orthogonal state: 1 + v v 1 + v v 2 2 ( ) ( ) General state ( 2iφ + v ) 0 + e v0 2 gives fraction So get φ by measuring N 0 /N 0 N 0 = cos 2 φ N

14 Splitting laser atoms mirror Implement with standing wave laser beam Laser tuned far from resonance - no direct absorption Virtual absorption OK -photon immediately emitted excited state Absorb from one direction, emit to other: Momentum transfer 2hk v 0 = 2hk/M = 12 mm/s p = -2hk p = 0 p = 2hk

15 Interferometer experiment Reflect pulse drives transition + 2hk 2hk Similar to split split reflect split Take picture of final state time T Vary phase by shifting standing wave before final split

16 Pictures N 0 = cos 2 N φ 0 phase π/4 phase π/2 phase

17 Interference! N 0 /N Applied Phase (arb) Visibility about 0.9

18 Visibility vs time Visibility Time [ms] Get about 80 ms before coherence lost

19 Arm Separation Max distance between packets = 0.5 mm - Record separation Literal picture of distinct atomic waves that are quantum coherent Macroscopic quantum state! Also useful: Put packets in different environments, measure phase

20 Application: Electric Polarizability Put atom in electric field E Energy shift U 1 = α E 2 α = polarizability Related to: Index of refraction Electron and ion scattering Van der Waals interactions Rayleigh scattering Casimir-Polder effect 2

21 We measured at optical frequencies: imaging lens waveguide structure standingwave laser aperture Stark beam Apply intensity I ~ E 2 for time τ Measure phase φ αiτ

22 Polarizability Results N 0 /N nm α α exp th = ( 8.37 ± 0.24) = m m I t [mw ms cm -2 ] Most accurate measurement technique to date Limited by uniformity, calibration of laser beam

23 Next big measurement: Measure dc polarizability Apply static field instead of laser E V Should work much better: Laser beams noisy, hard to calibrate With dc measurement, hope to get 10-3, 10-4 precision Sensitive test of atomic structure theories, atomic clock effects

24 Conclusions Condensate interferometry has good prospects for precision measurements - Demonstrated 80 ms coherence time and 0.5 mm arm separation - Used to measure ac polarizability Setting up experiment for dc measurement Other projects: bouncing interferometer, atom gyroscope, collective light scattering