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Coherent splitting of a BEC using dressed state potentials
Peter Krüger
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Atom chips: micro vs. macrotraps
Atom Chip
87Rb U-MOT
•Complex (=complicated) assemblies
•limited optical access
•frabrication process
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Microtraps close to surfaces
Fabrication imperfections lead to fragmentation
Limited trap lifetimes (coherence times) near the surface
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Microtraps: possibilities
Complex potentials
Micro scalesSubmicron structures (ebeam lithography)
Tight confinementLarge aspect ratios
100μm
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ApplicationsDynamics in low dimensional confinement
Surface probing
Interferometry
High sensitivity, high resolution magnetic field measurements
Wildermuth, Hofferberth, Lesanovsky, Haller, Andersson, Groth, Bar-Joseph, P. K., Schmiedmayer, Nature 2005
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Interferometry
Coherent splitting of BECs
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Beam splitters
Time dependent beam splitter
Interferometer potential
Electric beam splitter
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New type of beam splitter
mF=+1/2
mF=-1/2
resonance condition shifts potential
the crossing is at a position where
controlled by RF frequency
|)(| rBµB
mF=+1/2
mF=-1/2
Ioffe field
‘mF=+1/2
‘mF=-1/2
coupling term creates level repulsion
the levels are repelled bycreating an effectiveIoffe field, cntrolledby RF amplitude
,| |B RF perpµ B
Idea: use DC magnetic trap and couple different magnetic states with RF fields adiabatic potentials
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Radio frequency beam splitter
RF coupling term creates
level repulsion
Theory: Zobay, Garraway, PRL 2001 + Andersson, Schumm, Lesanovsky, Hofferberth, P. K., Schmiedmayer comment (submitted 2005) Experiments with thermal atoms: Colombe et al., Europhys. Lett. 2004
•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
2 2
F( ) ( ) ( ) / 2eff B F DC RF B F RFV r m g B r g B r
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Population of all minima
BECthermal
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Atom chip implementation
45°
RF
RFwire
trapwire
atom chip
gravity
100 µm Z wire
50 µm Z wire
10 µm RF antenna
I I 25 µm U wirestransverseimaging
longitudinalimaging
in situ absorption image
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BEC double wellsplitting condensates over 80 µmfor different traps by sweeping the RF
limit of optical detection
25µm
400µm
longitudi-nal image
transverseimage
split BEC
RF freq.
•BECs can be split in separated double well over wide range
•min. distance of wells given by trap ground state size (~3μm)
•structures can be much larger
•state dependent coupling
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BEC interference
Images taken after 14 ms potential free time-of-flight expansionSmaller double well
separation (3-6 micron)
Deviation is interaction effect (during expansion)
Schumm, Hofferberth, Andersson, Wildermuth, Groth, Bar-Joseph, Schmiedmayer, P. K., Nature Physics (online Sept. 2005, print Oct. 2005)
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Coherence of the splitting processRelative phase between the fully split (tunneling suppressed on exp. time scales) BECs in measured in interference experiment – multiple realizations
Result: Well defined phase (spread of distribution σ = 13 degrees)
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Phase evolution
Phase evolution during the splitting: As long as the two condensates are connected (tunneling is possible), the phase remains locked at zero (splitting speed 1.4 microns / ms)
Phase control: At lower splitting speed (0.6 microns / ms), the phase evolution reacts more sensitively to imbalances.
Phase spread At remains non-random even for larger splitting, but increases with hold time (1d phase diffusion ?)
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Advantages over DC wire splitters•Number of (tightly confining) quadrupole minima is limited by number of wires used (i.e. at least two) for splitting (DC case)
•Splitting region can only be formed by merging two minima to a (weakly confining) higher order minimum (DC case)
•Small scales and surface distances needed for good splitters for DC case
•RF splitter performance equal at larger surface distance (trap frequencies of individual wells at equal barrier height)
•Distance of minima increases as a linear function of control parameter in RF case, as a square root function in the DC case
Lesanovsky, Schumm, Hofferberth, Andersson, P. K., Schmiedmayer, arXiv physics/0510076
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Guided matter waver interferometer
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, arXiv physics/0510076
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Other applications
Ring potentials
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Ring traps: circular polarisation
Lesanovsky, Schumm, Hofferberth, Andersson, P. K., Schmiedmayer, arXiv physics/0510076
Rings can be obtained by adiabatically converting a double well by adjusting the relative phase between two orthogonal (linearly polarized) RF fields
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Permanent magnetic ring traps
Fernholz, Gerritsma, P.K., Spreeuw
Dressed state potentials in circular polarization basis
220( / ) / 2
Fm F B F F BE m g B g
Can be used to lift the zero in (perm. magnetic) quadrupole ring
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Potential minima on a torus surface
Applying cylindrically symmetric RF fields allows to form and control minima on torus
•circular polarization (in any ρz-plane) results in homogeneous 2d surface (triply connected)
•Elliptic polarization results in two rings (1d)•Phase tuning can be used to rotate minima poloidally
•Added linear field allows to individually form and control (rotate) dimples toroidally
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Ring applications
• 1d and 2d traps in multiply connected geometries• adiabatic transfer between regimes• induced rotations in toroidal and poloidal directions• two split rings -> Sagnac type interferometry• controlled independent movement on the ring possible• tunnelling junctions between rings (squids)• …
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Conclusion
•atom chips are versatile tools for matter wave (quantum gas) manipulation
•Coherent beam splitter demonstrated: door to quantum dynamics experiments
•Many more applications of RF potentials possible (examples: interferometers & rings)
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The team
Experiment:Sebastian HofferberthThorsten SchummStephan WildermuthJose Verdu
Jörg Schmiedmayer
Chips:Israel Bar-JosephSönke Groth
Review on atom chips: Folman, P. K., Schmiedmayer, Denschlag, Henkel, Adv. At. Mol. Opt. Phys. 48, 263 (2002)
Theory:Igor LesanovskyMauritz Andersson
Funding: EU, DFG