Measurement of the He-McKellar-Wilkens and Aharonov-Casher phases by atom interferometry

Transcription

1 Measurement of the He-McKellar-Wilkens and Aharonov-Casher phases by atom interferometry J. Gillot, S. Lepoutre, A. Gauguet, M.Büchner, G. Trénec and J. Vigué LCAR/IRSAMC Université de Toulouse UPS et CNRS UMR 5589, Toulouse

2 Summary Our separated-arm atom interferometer Measurement of lithium electric polarizability Topological phases: the Aharonov-Bohm, Aharonov-Casher and He-McKellar Wilkens phases Simultaneous measurements of the He-McKellar Wilkens and Aharonov-Casher phases Conclusion

3 Our atom interferometer

4 Principle of our lithium atom interferometer Thermal lithium with velocity near 1000 m/s de Broglie wavelength 55 pm Laser diffraction Bragg regime λ L = 671 nm 1st order diffraction angle 160 microradian X Highly collimated atomic beam Atom diffraction by 3 laser standing waves (λ L = 671 nm) M1 M2 M3 Outpu t beam 2 Output beam 1 Atom detector signal Observation of interference fringes ϕ d = diffraction phase sensitive to the mirror x- positions

5 Measurement of a perturbation U perturbation U Outpu t beam 2 M1 M2 M3 Output beam m 0.6 m Diffraction angle close to 160 microradian Distance between laser standing waves 0.6 m the maximum distance between interferometer arms is 100 micrometers. Each atom goes from the source to the detector by the black and violet paths! Signal with the perturbation phase ϕ p

6 Some experimental details Atomic beam: supersonic expansion of lithium with a noble gas -Narrow velocity distribution v/v 10% -Tunable mean velocity v 1/ M (M noble gas atomic mass) -Langmuir-Taylor (hot-wire) detector -Isotopic selection 7 Li only : natural abundance (92.5%) and laser diffraction

7 Measurement of lithium electric polarizability

8 Measurement of lithium electric polarizability α An electric field E on one interferometer arm only perturbation U =-2πε 0 αe 2 induced phase shift ϕ pol M1 M2 M3 ϕ pol is a dynamical phase shift Electric field V=0 V=V 0 V=0 50 mm V=0 V=0 The interferometer arms are 30 micrometer wide, 100 micrometers apart «Septum» : thin foil (6 to 20 micrometers thick ) well stretched and placed between the two interferometer arms

9 Phase shift induced by the electric field Signal (c/s) 180k 160k 140k 120k Capacitor voltage V= 0 Volt, fringe visibility 62 % 100k 80k 60k 40k 20k h l b Capacitor voltage V= 260Volts fringe visibility 43 % Phase shift 3π Best measurement of lithium polarizability: α= ± 1.1 u.a., in agreement with the best theoretical value α = ± u.a. M. Puchalski (Phys RevA 2012) Limits on precision: ϕ pol proportional to 1/v accuracy on the mean velocity value

10 Topological phases : the Aharonov-Bohm, the Aharonov-Casher and the He-McKellar Wilkens phases

11 The Aharonov-Bohm topological phase (1959) I The magnetic field vanishes on the ABF and ACF paths followed by the electron: no force but the waves suffer a phase shift ϕ The Aharonov-Bohm phase ϕ is a topological (or geometric) phase: - it can be detected only by interferometry - it is independent of the particle velocity - it changes sign with its direction of propagation

12 Experimental study of Aharonov-Bohm phase Chambers in 1960; Tonomura et al. in 1986 phase shift exactly equal to π (or nπ) due to the magnetic flux quantization in the niobium supraconducting ring

13 Aharonov-Casher phase (1984) Aharonov-Bohm effect with the solenoid replaced by a line of magnetic dipoles Aharonov-Casher phase: exchange the role of the charge and of the magnetic dipole µ µ µ µ E e e e e µ E e µ Topological phase shift:

14 Experimental studies of Aharonov-Casher phase First test with a neutron interferometer by Cimmino et al. in Following experiments with Ramsey or Ramsey-Bordé interferometers with TlF (research group of Ed Hinds in ) with Rb (research group of A. Weis in 1995) with Ca (research group of J. Helmcke in 1995)

15 Further generalizations of Aharonov-Bohm topological phase e Aharonov-Bohm(1959) µ µ µ dual of Aharonov-Bohm phase g d d d µ d Aharonov-Casher (1984) µ d E e e e e µ dual of Aharonov-Casher phase He-McKellar-Wilkens (1993) B g g g g d E B Maxwell duality E B e g exchange electric and magnetic charges µ d exchange electric and magnetic dipoles

16 Heuristic explanation of Aharonov-Casher by motional field A.G. Klein (1986) Same argument for the He-McKellar Wilkens phase

17 Connection between the Aharonov-Bohm phase and the He-McKellar Wilkens phase Wei et al. (1995), the HMW phase is equal to the algebraic sum of the Aharonov-Bohm phases calculated for the positive and negative charges forming the dipole, interacting with a uniform magnetic field B.

18 Simultaneous measurements of the He-McKellar Wilkens phase and of the Aharonov-Casher phase

19 Our goal: detection of the He-McKellar-Wilkens phase d d B g g g g d B B d E Interferometer arms I d E Interferometer arms 48 mm Electric field E (V/m ) = 900 V (V in V) B (T) = I (I in A) ϕ HMW (rad) = VI

20 Maximum applied voltage V max = 800 V Maximum coil current I max = 40 A ϕ HMW 40mrad Phase drifts 100 mrad in 10 minutes and not exactly linear in time Simultaneous measurements of different field configurations during a 20 second long fringe scan (0,0) Uncertainty on 10 5 (V,0) about 30 mrad after a single fringe scan atom counts (V,I) (0,I) about 3 mrad after averaging 100 scans i.e s of data collection 10 5 (-V,I) Optical Michelson's phase (rad) (-V,0)

21 First experiment without optical pumping of lithium Large stray phase shifts due to several small experimental defects Zeeman phase shifts (small field difference on the two arms) Dispersion of polarizability phase shift (geometric defects of the capacitors) Most defects induce phase shifts which are even functions of the magnetic field cancellation by using results with opposite current values Measured slope ϕ final (V,I) /VI = -(1.68±0.07) 10-6 rad/va Predicted slope ϕ HMW (V,I) /VI = -(1.28±0.03) 10-6 rad/va

22 Optical pumping of the lithium beam in F=2, m F = +2 (or -2) Pumping on the D1 line with two laser beams m F = +2 m F = -2 Test of the pumping efficiency on atom interferometry signals no pumping perfect pumping

23 Experiment with optical pumping of the lithium beam in the F=2, m F = +2 or -2 sublevel As previously, we define: Now, two measurements for m F = +2 or -2 ϕ EB (V,I,m F ) ϕ EB (V,I,m F ) is sensitive to the Aharonov-Casher phase ϕ HMW (V,I,m F ) is independent of m F while ϕ AC (V,I,m F ) changes sign with m F

24 Observation of a stray phase shift of unknown origin Different offsets for opposite voltage values Already observed in our first measurement of the HMW phase It does not modify the variation of this phase with the magnetic field For each series with a given voltage, we subtract the offset.

25 ϕ HMW (V,I) as a function of the product VI Lithium beam mean velocity v m = 1062±20 m/s (carrier gas argon) Measured slope ϕ HMW (V,I) /VI = -(1.315±0.071) 10-6 rad/va Predicted slope ϕ HMW (V,I) /VI = -(1.28±0.03) 10-6 rad/va

26 Topological character of the He-McKellar-Wilkens phase 3 measurements for v m = 744 m/s, v m = 1062 m/s and v m = 1520 m/s variations if ϕ HMW 1/v α α= 1 : dynamical phase α= 2 : inertial phase

27 Measurement of the Aharonov-Casher phase ϕ EB (V,I,m F ) for m F = +2 or -2 is sensitive to the Aharonov-Casher phase ϕ AC (V,I,m F ) proportional to m F When the coil current I=0, the lab field is not vanishing and only the component of B mot along the lab field contributes to ϕ AC (V,I=0,m F ). separate measurement of ϕ AC (V,I=0,m F ) from the phases in electric field only

28 Measured values of the Aharonov-Casher phase Lithium beam in argon: mean velocity v= 1062 m/s

29 Velocity dependence of the Aharonov-Casher phase ϕ AC /V (10-4 rad/v)

30 Conclusion First successful test of the He-McKellar-Wilkens phase 20 years after its theoretical prediction. Separated-arm atom interferometers. Topological/geometric phases: a quantum curiosity... but they are very interesting because these phases are non-dispersive. A new interferometer under construction for the following experiments Test of the electric neutrality of lithium atom with Aharonov-Bohm scalar phase Measurement of the electric polarizability of lithium with a topological phase