1. Peter Krüger University of Nottingham
Atom chips
Peter Krüger
University of Nottingham

2. Atom chips: concept Microfabrication Quantum optics Atom chip
Neutral atoms:
weak interaction with the environment
internal structure provides handles for manipulation
standard industrial process
integration of different and complex components possible
Atom chip
Integrated matter wave device for the control & manipulation of complex quantum systems

3. Atom chips: miniaturized atom optics
Degenerate quantum gases in low dimensions
Surface probes/atom-surface interaction
robust complex structures
steep trapping potentials at low currents & voltages
high trap gradients & frequencies
high aspect ratios (reduced dimensions)
non-trivial topologies
high tailoring resolution at low atom-surface distances
Precision measure-ments: interferometry
Quantum dynamics: single/few atoms, QIP

4. Outline Atom chips: A toolbox for complex matter wave manipulation
Surface effects: coupling cold atoms – hot surfaces, rough potentials
Application: Chip based atom interferometry
Current routes: hybrid systems, low dimensional quantum gases in complex geometries

5. Manipulating potentials
Tools & Techniques
Manipulating potentials

6. Microscopic potentials
Magnetic interaction
current carrying wires: very versatile
micro magnets: strong quiet field
tight confinement
Electric interaction
additional degree of freedom
together with magnetic traps:
state dependent
Light fields
state independent guides and traps,
modified by electric and magnetic
fields from the microstructures
Integration with other techniques
cavity QED
nano-optics, nano electronics, MEMs

7. Basic magnetic traps U-trap: U-MOT Z-trap: Ev. cooling, BEC
Superimpose field of current carrying wire with homogeneous bias field gives guiding potential + =
U-trap:
Quadrupole
minimum
Bmin=0
U-MOT
Ioffe-Pritchard
minimum
(harmonic bottom)
Bmin>0
Z-trap:
Ev. cooling, BEC

8. Scaling laws
Trap position
(μm, G, mA)
Confinement (gradient) w h
wire
Tolerated diss. heat
Heat sink (substrate)
Values of j (>107 A/cm2) possible for chip based wires, like superconductors

9. duration of sequence: 250ms
Magnetic fields
Side guide
Folman, P. K., Cassettari, Hessmo, Maier, Schmiedmayer, PRL 2000
5mm
duration of sequence: 250ms
Omni directional guide
Luo, P. K., et al. Opt. Lett. 2004

10. Electric fields Combined electric & magnetic interaction
U(r) = gF mF µB B(r) – ½ a E(r)2
Electrostatic interaction
does not depend on mF
always attractive
Typical orders of magnitude (7Li)
UB [µK]  67 B [G]
UE [µK]  98 E2 [V/µm] + HV
electrodes
side guide wire +
Magnetic side guide (1.6A / 44G) is modulated along axis of free movement by means of electric fields (300V)
Periodic potentials (λ<1μm possible)
P. K. et al., PRL 2003

11. Optical fields
Arrays of microtraps: lattice with individual site addressability
Birkl et al.
Standing wave formed by near-resonant red detuned (2-3nm) beam impinging the surface at an angle close to vertical
High transverse frequencies (>100 kHz) possible, single well loadable
2d thermal gases and 2d BEC possible

12. Surface effects
Problem or virtue ?

13. Setup Atom Chip 87Rb U-MOT Cu-”U” replaces quadrupole coils for MOT:
Iw = 55 A, Bb = 8 G
>3 108 atoms in ~ 15s
> 105 atoms in BEC in various traps
BEC may be transferred or formed on site
‘H’: U/Z
Broad U
Wildermuth, P. K., Becker, Brajdic, Haupt, Kasper, Folman, Schmiedmayer, PRA (R) 2004

14. Surface effects: technical current noise
Coupling between hot surface (300K) and cold atoms (nK) via noisy currents
at Larmor frequency (spin flip losses)
trap frequency (heating)
Over-exponential rapid decay for small h (attractive surface pot.)
See also Lin et al., PRL 2004
theory (bulk)
theory (layer)
Theory by C. Henkel, predicts losses due to thermal current noise as a function of distance
data taken near flat current carrying wire
Lifetimes longer than predicted for bulk
Shorter than expected for layer
Residual technical noise

15. Thermal current noise
Johnson noise in conductors leads to magnetic near field fluctuations
Rotation of bias field allows to place clouds close to conducting layer (z), but far from current carrying structure (d)
Separation between technical and thermal noise possible (in principle)
Large d result in low trapping frequencies, surface induced evaporation kicks in at higher z

16. Fragmented clouds near surfaces
Tübingen (Cu)
Sussex/London (Al)
Jones et al., PRL 2003
Orsay (Au)
Fortagh et al., PRA (R) 2002
MIT (Cu)
Experiment: Estève et al., PRA 2004
Theory: Wang et al., PRL 2004
Leanhardt et al., PRL 2002

17. Chip surfaces and fragmentation
Wire imperfections cause non-straight current flow and potential roughness
200nm
100nm
Groth, P. K. et al., APL 2004

18. Potential roughness characterization
Distance from wire (microns)
1d limit
TOF
in spite of roughness, cloud stays continuous over 1 millimeter (width ~ 100 nm), aspect ratio ~10 000
P. K et al., PRA 2007

19. 1d BEC as sensitive surface probe
Two dimensional map of local disorder fields measured with BECs near a broad wire

20. Field maps & current reconstruction
100μm wide wire
wire-atom distance 10μm (determines spatial resolution), may be smaller
parallel disorder field components corresponding to current density components perpendicular to wire direction
sensitivity ΔB/B ~ 10-6 (10-13 eV)
reconstruction of high resolution current density map in conductors

21. Magnetic imaging: comparison
Magnetic Field sensitivity: ΔB = γ ΔN / (ρ02z0)
γ = 9.29·10-29 Tm3 For 87Rb atoms in the |F=2,mF=2> state
ρ0=z0 =1μm a sensitivity of ΔB = 1nT is possible.
By changing to a different atom with higher mass and/or by tuning the scattering length ascat to close to zero using a Feshbach resonance a significant increase in sensitivity can be achieved.
Wildermuth, Hofferberth, Lesanovsky, Haller, Andersson, Groth, Bar-Joseph, P. K., Schmiedmayer, Nature 2005

22. Coherent manipulation
measuring phases and phase correlations interferometrically

23. Beam splitters Interferometer potential Time dependent beam splitter
Electric beam splitter

24. New type of beam splitter
Idea: use DC magnetic trap and couple different magnetic states with RF fields  adiabatic potentials
mF=+1/2
mF=-1/2
mF=+1/2
mF=-1/2
Ioffe field
resonance condition
shifts potential
the crossing is at
a position where
controlled by
RF frequency
‘mF=+1/2
‘mF=-1/2
coupling term creates
level repulsion
the levels are
repelled by
creating an effective
Ioffe field, controlled
by RF amplitude

25. Radio frequency beam splitter
RF coupling term creates
level repulsion
BECs can be split in separated double well over wide range (2-80 μm)
min. distance of wells given by trap ground state size
structures can be much larger
state dependent coupling
Zobay, Garraway, PRL 2001
Experiments with thermal atoms: Colombe et al., Europhys. Lett. 2004
Relevance of polarization: Schumm et al., Nature Physics 2005

26. Fringes and coherence
split BECs expand and fall under gravity after trapping potential is turned off
information on contrast and phase of interference patterns
multiple realizations show constant phase relation of completely split (no tunneling) BECs
Schumm, Hofferberth, Andersson, Wildermuth, Groth, Bar-Joseph, Schmiedmayer, P.K., Nature Physics 2005

27. Low dimensional gases and hybrid systems
Current routes
Low dimensional gases and hybrid systems

28. 1d Bose gases
Transverse confinement strong enough, so that
for 87Rb

29. One dimensional gases on atom chips
100 µm Z wire
50 µm Z wire
10 µm RF
antenna I
25 µm U wires
transverse
imaging
longitudinal
At ~50 microns from the wire very elongated (aspect ratios > 1000) smooth BECs can be formed
100μm
1d: μ  ω

30. Momentum distribution: TOF
Momentum distribution of the ground state ?
μ  ω
Experiment: Measure density dependence of transverse cloud width after TOF expansion
Fragmented cloud gives (almost) single shot measurement of large density span

31. 1d time of flight: widths
F. Gerbier, EPL 2005
Even in purely 1d, there is a mean field correction

32. Finite T: bimodal 1d clouds
If the expansion for both a quasi-BEC and a thermal cloud is gaussian, how can they be distinguished (kT ~ ω) ?
Discern the interferable fraction !
cold
hot
Fourier transform

33. 1d gases at finite temperature

34. Time evolution coupled uncoupled Schumm et al., Nature Physics 2005
t=0ms
t=4ms
t=8ms
coupled
uncoupled
Schumm et al., Nature Physics 2005
Hofferberth et al., Nature 2008

35. Interferometers and rings
Fully integrated wave guide interferometer:
RF amplitude controls splitting distance
A single RF current can provide varying RF amplitude if its width is adjusted
Lesanovsky, Schumm, Hofferberth, Andersson, P. K., Schmiedmayer, PRA 2006
Ring and torus geometries:
Static magnetic (quadrupole) rings can be modified with RF fields
Possibilities include homogeneous 2d torus surfaces, 1d rings, toroidal and poloidal stirring, 2 (coupled) rings, …
Fernholz, Gerritsma, P.K., Spreeuw, PRA 2007

36. New group & experiments at Nottingham
Non-trivial potentials, topologies
Surface probes, atom-surface interaction/coupling
Hybrid atom-semiconductor chips
Chip based atom-light interfaces