►Coherent Stern-Gerlach splitting on an atom-chip

1. China, Sep 2013 Ben-Gurion University of the Negev ►Coherent Stern-Gerlach splitting on an atom-chip www.bgu.ac.il/atomchip Shimon Machluf S. Machluf, Y. Japha, R. FolmanNature Communications 4, 2424 (2013)

2. Views from the desert

3. Outline • Motivation for interferometry on a chip • Why Stern-Gerlach Interferometers should not work • Our two level system • Our Stern-Gerlach method • Results • Conclusions

4. What we want to do with chip interferometry State of the art: RF and MW double-well splitting I: Surface physics – use the atoms as a probe e.g. Mesoscopic transport, Johnson noise, shot noise of fractional charge Example: electron transport Non-interferometric atom-chip measurements BGU+HD, Science (2008)

5. II: Many body e.g. Squeezing, collisional dephasing, thermodynamics e.g. an example of recent work done on an atom chip (Science, 2012) PS single atom physics is also still interesting! (x3)

6. III: momentum splitting for metrology e.g. Large area and large effective area Ken Takase / Mark Kasevich 2008 Could be used for sensing technology or fundamental studies: e.g. Chu, Holger Muller, Mark Kasevich

7. Fundamental tests with matter-wave interferometers

8. State-of-the-art in momentum splitting Typically, accurate beam splitters are done with light: quantum accuracy (!) but hard to get large momentum Is there an alternative, and can classical systems also do the job?

9. A plaque at the Frankfurt institute commemorating the experiment Stern-Gerlach 1922 Otto Stern Nobel prize 1943 The differential force of the Stern-Gerlach experiment Stern-Gerlach in cold atoms @ BGU

10. Two reasons why a Stern-Gerlach Interferometer should not work • External noise couples differently to different spin states

11. 2. Is the wave packet like Humpty-Dumpty? Heisenberg (1930), Wigner (1963): separation of the partial beams will introduce a large dispersion of phases within the individual beams. Bohm (1951), Englert (1988), Schwinger (1988), Scully (1989): The required precision is very high.

12. Alkali vapor Color centers in diamond Quantum systems in our lab The Atom Chip Find papers on these 3 systems on our web site: www.bgu.ac.il/atomchip

13. Vapor work:

14. Diamond work: Archive 2013

15. Hyperfine structure of Rb 87 F=3 F=2F=1 F=0 5P3/2 Zeeman sub-levels 780nm -1 -2 0 1 2 F=2 6.8GHz 5S1/2 F=1 -1 0 1

16. Lifting the degeneracy of the Zeeman sub-levels F=3 F=2F=1 F=0 5P3/2 Same happens in the excited state Pieter Zeeman Nobel 1902 780nm F=2 -1 -2 0 1 2 6.8GHz 5S1/2 F=1 Stern-Gerlach in cold atoms @ BGU

17. Utilizing Rb as a 2-level system F=3 F=2F=1 F=0 5P3/2 Same happens in the excited state 780nm Second order Zeeeman F=2 -1 -2 0 1 2 6.8GHz 5S1/2 F=1

18. Two unique properties of the atom chip which we use here: high field gradients and accurate on/off Example: I=2A r=10microns => B=400G => B’=40kG/mm In addition, low inductance of wires enables quick on/off

19. Field gradient beam splitter (in our case: ) Isidor Isaac Rabi Nobel prize 1944 Norman F. Ramsey Nobel prize 1989 Part we work with Gradient may be applied parallel or perpendicular to motion

20. Z  Y  X Figure 1.1 – The Bloch sphere Simple kinematic view: differential acceleration Large distance (< 10^6 A/cm^2) 10^7 A/cm^2 F=μ B’ B[G]=2 I[A]/r[mm] Geometrical factor for finite size: (2z/D)*arctan(D/2z) Theory includes Breit-Rabi GP sim. Fourier transform view: varying Ramsey frequency Data from BGU A. Daniel et al., PRA (2013)

21. Experiment: free fall • Single MOT atom chip experiment with BEC of 10^4 Rb^87 atoms • atoms 100 μm from the surface of the chip • Zeeman splitting of 25MHz • Strong enough field to take the transition to the |2,0> out of resonance (250kHz) • Two π/2 pulses with Rabi frequency 20-25 kHz • Between the pulses, 2-3 A current in a 2x200 μm gold wire (< 10^6 A/cm^2) • Measure momentum separation

23. Characterizing the beam splitter Error bars are from different runs

24. The FGBS is very versatile • Large dynamic range • Can split in the direction, and perpendicular to the direction, of motion • Can work also in trapped mode for BEC or guided interferometry • Can work also with the mag. insensitive clock states |1,0> ►|2,0> for low noise: [ Hz ] [ T ] • If you put far away the second π/2, or two FGBS, you create a population interferometer

25. Choose your signal spatial population

26. Another example of versatility: trapped BEC • Single MOT atom chip experiment with BEC of 10^4 Rb^87 atoms • atoms 250 μm from the surface of the chip • Trap frequencies 2π x 100 Hz and 2π x 100/1.4 Hz • Zeeman splitting of 18MHz • Strong enough field to take the transition to the |2,0> out of resonance (100kHz) • Two π/2 pulses with Rabi frequency 5-10 kHz (pulses less accurate because of traps) • Between the pulses, no need for current in the chip wire as traps give acceleration • Measure momentum separation

28. Error bars are from different runs with different Rabi frequencies and different TOF. vr GP simulation with no free parameters

29. Non deterministic fringes 1D BEC @ BGU: phase fluctuations – Self-induced interference pattern Bringing the wave packets together • For the freely falling atoms, a second gradient is applied • For trapped atoms, an oscillation time is added All periodicities fit well with the known estimate: ht/md

30. Coherence = deterministic fringes 29 runs (1/2 an hour of data) So why do we see coherence: • Wave packets very small • Different spin for very short time • And we are lucky that the initial position does not matter

31. Outlook: ultimate phase stability Single shot: Calculate C(t). For BEC C(t)=1 so visibility should be 100% pending purity, population imbalance, imaging resolution, etc. Shot-to-Shot: General FGBS: Our FGBS: δΦ/ΔΦ , δp/Δp ~ δI/I, δT/T, δz/z δp in our interferometer is canceled by the second pulse and is dependent on Δp which goes to zero. δΦ within our FGBS: If you plug in our 2A 5μs pulse, 100μm distance, δI/I=10^-3, you get δΦ=1 rad δz/z may be made negligible e.g. in a 3 wire configuration where the trap position is independent of current, but in any case as shown it affects only the c.m. degree of freedom.

32. Comment on trapped BEC δp/Δp: 10^-7 and beyond.

33. Side remark: A separate project by Shuyu Zhou Quantum coherence in a collision between a BEC and a snake shaped wire Shuyu explaining his experiment to Peter Zoller and Ignacio Cirac

34. Very preliminary results of phase imprint Average of 30 images

35. Humpty-Dumpty is slowly recovering Shimon Machluf To conclude: • The field gradient beam splitter is fast, allows large momentum, is very versatile, and requires no light • Atom Chips enable the strong pulsed gradients this beam splitter requires • Applications range from many body, to surface\material science, and metrology. • We have seen first signs of coherence. We are still very far from shot noise so there is much to improve. • It seems that for high momentum transfer, the SG beam-splitter may even have better accuracy than light beam-splitters, but its still very early to tell…

36. My latest anti-gravity experiment…. Thanks for your attention

38. Pieter Zeeman Nobel 1902 first and second orders A field gradient will produce a force on any magnetic moment

40. No two separate wave packets

41. Additional tools we will use: 0  Z 2  Y  X Figure 2.1 – Rabi oscillations Figure 1.1 – The Bloch sphere Rabi Oscillations in a 2-level system: Isidor Isaac Rabi Nobel prize 1944 Bloch sphere π/2 pulse Examples: Cold atoms @ BGU Room temperature atoms in a solid (!) @ BGU

42. Norman F. Ramsey Nobel prize 1989 Z  Y  X Figure 1.1 – The Bloch sphere Ramsey fringes Bloch sphere Ramsey Oscillations @ BGU

43. Norman Ramsey (Nobel 1989, passed away 2011) and Dan Kleppner - 2005

44. A quick reminder of what the atom chip is: “where material engineering meets quantum optics” Atom chip review article: RF et al. Adv. At. Mol. Opt. Phys. 48, 263 (2002) One of the humble beginnings: RF et al. PRL 84, 4749 (2000) Applications: clocks, acceleration sensors, gravitational sensors, magnetic sensors, quantum memory and communications, quantum computing Drawing from paper by Jakob Reichel; conveyer belt – invention by Ted Haensch Fundamental science: Decoherence, interferometry, many body, atomic physics, low dimensional systems, atom-surface physics, surface physics, symmetries and fundamental constants

45. The Atom Chip definition is broadening The atom chip technology is advancing very rapidly so that eventually, all the different particles such as Rydberg, molecules, atom-like (NV), ions, cold electrons, etc. may be put on the chip, including entanglement to a quantum surface. Atom Chips: From 3 in 2000 to ~30 today, The monolithic integration dream Ion and permanent magnet chips @ BGU for Mainz and Amsterdam + near field optics, plasmonics, etc. More information on the atom chip in: • new book on atom chips, RF, Philipp Treutlein and Joerg Schmiedmayer, (Eds: Jakob Reichel and Vladan Vuletic) • special issue on QIP (Journal of Quantum Information Processing Editors :Howard Brandt & RF ) Highest temperature gradient known to mankind

46. A Bose-Einstein Condensation 3D BEC @ BGU 1D BEC @ BGU: phase fluctuations – Self-induced interference pattern

48. Phase Imprint What is phase imprint?

49. The Process of Phase Imprint Icu_Z =32.3A Isnake1 =30mA Ucu_Z + Usnake1 Isnake2 =5mA Iy_bias =84.7A Ix_bias =0A About 38um We suddenly reduced the snake current from 30mA to 5mA. The BEC approached the chip surface and came back. After 6ms, about one oscillation cycle, we turned off all currents and released the BEC. After about 9-13ms we probe the density distribution by absorption imaging. Ucu_Z + Usnake2 About 5um

50. Experiment result of phase imprint __single shot