Atom Interferometry using Bose-Einstein Condensates Cass Sackett Research Talk 15 February 2008
Outline • Condensate interferometry • Making BEC • Our interferometer • Polarizability measurement
What is atom interferometry? Just like optical interferometry: path A Atom beam or laser beam Output 1 Output 2 grating 1 grating 2 grating 3 Gratings can split and recombine waves - whether from Maxwell or Schrodinger equations
Differences between atoms and light: Atoms (thermal beam): Light: • Hard to manipulate • Easy to manipulate - atoms in vacuum - beams in air - gratings - mirrors, beamsplitters - small deflection angles • High flux (10 16 photons/s) • High flux (10 photons/s) • Low flux (10 9 atoms/s)
Differences between atoms and light: Atoms (thermal beam): Light: • Hard to manipulate • Easy to manipulate - atoms in vacuum - beams in air - gratings - mirrors, beamsplitters - small deflection angles • High flux (10 16 photons/s) • High flux (10 photons/s) • Low flux (10 9 atoms/s) • Weak interactions with • Strong interactions with environment π 2 n environment φ = ∆ d t λ φ = ∆ E � - path length difference ∆ d - energy difference ∆ E - index of refraction n - interaction time t
Applications Can measure anything that changes energy of an atom: - All kinds of EM fields (external or collisions) - Gravity Also inertial effects: - Acceleration and rotation Light also sensitive to inertial effects Light also sensitive to inertial effects but atoms more sensitive by mc 2 / � ω ~ 10 10
Applications Can measure anything that changes energy of an atom: - All kinds of EM fields (external or collisions) - Gravity Also inertial effects: - Acceleration and rotation Light also sensitive to inertial effects Light also sensitive to inertial effects but atoms more sensitive by mc 2 / � ω ~ 10 10 Potential uses: • Fine-structure constant • Magnetometry • Atomic properties • Inertial navigation • Surface characterization • Geophysics • Quantum light detection • Oil exploration Many already realized with thermal atom interferometers
Making an interferometer First need to make a condensate! BEC happens when Λ ≈ � deBroglie wavelength ≈ interparticle spacing In air: Λ = 10 -11 m, � = 10 -9 m Λ ~ T -1/2 , so could cool air to 30 mK 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 ⇒ Get much colder
Making BEC Use 87 Rb atoms Aim for T ~ 100 nK, n ~ 10 13 cm -3 (about 10 -6 n air ) Achieve with 3 steps: 1. Laser cooling 2. Magnetic trapping 2. Magnetic trapping 3. Evaporative cooling Discuss briefly
Laser Cooling Laser beams Start with gas of rubidium atoms Glass cell: Shine lasers from all directions tuned below atomic resonance Rb vapor Doppler shift: - moving atoms scatter light - moving atoms scatter light from beam opposing motion Atoms slow down = cool Get sample of cold atoms: N ≈ 4 × 10 9 atoms T ≈ 250 µ K n ≈ 3×10 11 cm -3 n Λ 3 ≈ 5 × 10 -7 → Limited by opacity of cloud
Magnetic Trap Can’t get much colder or denser with laser cooling Transfer to magnetic trap: Rb atoms have one unpaired electron Get energy shift in field due to magnetic moment Get energy shift in field due to magnetic moment ⇒ Zeeman effect: V = 2 µ B Bm S µ B = Bohr magneton = 58 µ eV/T = 67 µ K/G m S = spin quantum number = ± ½ For m S = +½ state, have V = µ B B energy high when B high ⇒ atom attracted to region of low B
So atoms trapped near minimum in B Easy way to achieve: two opposed coils Get B = 0 in center Can’t get lower than that! Switch off lasers, turn on magnets Good isolation from environment: Good isolation from environment: - Lifetime about 100 s - Negligible heating V Gives linear potential (We actually make it harmonic) r
So atoms trapped near minimum in B Easy way to achieve: two opposed coils Get B = 0 in center Can’t get lower than that! Switch off lasers, turn on magnets Good isolation from environment: Good isolation from environment: - Lifetime about 100 s - Negligible heating V Gives linear potential (We actually make it harmonic) r
Evaporative Cooling How to get colder? Take away hot atoms m S = +½ Drive transition m S = +½ → -½ using rf field Only resonant if � ω rf = 2 µ B B Tune ω rf above trap bottom: only energetic atoms ejected only energetic atoms ejected � ω rf Take away more than average energy - remaining atoms colder Continue to BEC × 10 4 atoms → N ≈ 2 × × × T ≈ 200 nK m S = -½
Condensate Production Just before condensation: evaporate to 2.95MHz Initiate condensate formation: evaporate to 2.90MHz Mostly condensate: Mostly condensate: evaporate to 2.77MHz Absorption images: Shine laser on atoms, observe shadow
Interferometry So we got a condensate… yay! Want to make an interferometer: Split wave function apart and later recombine Hard to do in trap: - packets can’t move very far apart - packets can’t move very far apart But if we turn off trap, atoms fall in gravity - hard to deal with Our solution: put atoms in magnetic waveguide
Atom Guide Two dimensional trap - like optical fiber for atoms Send atoms wherever we want Basic design: Current four wire, linear quadrupole Line with B = 0 at center of rods Confines atoms to axis Again gives linear potential… use tricks to make harmonic
Waveguide Construction Copper rods provide fields Rod spacing ~ 1 cm All inside vacuum chamber at P ~ 10 -11 torr Make BEC inside guide structure
Interferometry reflect split split Basic scheme: guide axis - Split into two packets - Packets fly apart - Turn around via reflection - Packets come back together - Apply splitting operation again - Apply splitting operation again time time
Interferometry reflect split split Basic scheme: guide axis - Split into two packets - Packets fly apart - Turn around via reflection - Packets come back together - Apply splitting operation again - Apply splitting operation again time time Quantum operations are reversible: - If ψ unchanged, atoms brought back to rest But if packets have phase shift e i φ , ψ is not the same - Atoms keep moving Probability to come to rest ~ cos 2 φ
Splitting laser Implement with standing wave laser beam Intensity: Laser tuned far from resonance atoms - no absorption But do get energy shift ∝ intensity But do get energy shift ∝ intensity V laser = β cos 2 ( kz ) mirror (atoms are dielectrics: field induces dipole moment p ∝ E , get energy pE ∝ E 2 ∝ I )
Two pictures: 1) Atom wave diffracts from light potential just like light diffracts from grating ± 1 diffraction orders move at v 0 = 2 � k/M = 1.2 cm/s (from grating spacing λ/2 ) excited 2) Atoms absorb photon from state one beam, emit into other Net momentum transfer 2 � k Reverse process gives -2 � k p = 0 p = 2 � k p = -2 � k
Interferometer experiment Atoms make full oscillation: split reflect reflect split time T (Trap gradients cancel out in 2 nd half)
Pictures N 1 ( ( ) ) = = + + φ φ 0 0 1 1 cos cos N 2 ������� π �������� π �����
Interference! 1.0 0.8 0.6 N 0 /N 0.4 0.4 0.2 0.0 Applied Phase
Interferometer visibility 1.0 data 0.8 model Visibility 0.6 Vis 0.4 0.4 0.2 0.0 0 20 40 60 80 100 120 Total interferometer time [ms]
Arm Separation Get interferometer time ~80 ms … competitive with non-condensate techniques Have record for arm separation ~0.4 mm - Useful for putting different arms in different environments - Allows measurement of more different phenomena Example: interactions with surface - need one packet to hit surface, other not - easier if packets well separated Also, neat to make “macroscopic” quantum states
Our atoms separate for time T /4 = 18 ms Picture of split packets: Separation = 0.42 mm = 4 sheets of paper In most other experiments, separation ~ 10 µ m, if at all Get literal picture of distinct atomic waves that are quantum coherent
Applied interferometer to first measurement: Electric Polarizability � 1 = − α α defined by U E 2 2 Related to: • Index of refraction • Index of refraction • Electron and ion scattering • Van der Waals interactions • Rayleigh scattering • Casimir-Polder effect Proof of importance: it’s in the CRC
Measure at optical frequencies: imaging lens waveguide structure standing- wave laser aperture Stark beam Apply intensity I for time τ Measure phase φ ∝ α I τ
Polarizability Results 1.0 1.0 ������ ������ 0.8 0.8 0.6 0.6 N 0 / N N 0 / N 0.4 0.4 0.2 0.2 0.0 0.0 0 2 4 6 0 2000 4000 6000 8000 I·t [mW ms cm -2 ] I·t [mW ms cm -2 ] ( ) ( ) − − − − α = ± × α = ± × 25 3 28 3 8 . 37 0 . 24 10 m 9 . 48 0 . 25 10 m exp exp − − − − α = × α = × 25 3 28 3 8 . 67 10 m 9 . 14 10 m th th Most accurate measurement to date
Polarizability for resonant light: 0.2 0.1 φ/2π 0.0 -0.1 -0.1 -0.2 -15 -10 -5 0 5 10 15 Detuning [MHz] Get dispersion shape, like index of refraction
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