Interference with Bose-Einstein condensates on atom chips Sebastian Hofferberth, Igor Lesanovsky, Bettina Fischer, Thorsten Schumm, Jörg Schmiedmayer International workshop on „Advances in precision tests and experimental gravity in space“
Outline: A brief introduction to atom chips: magnetic wire traps A tunable double well potential based on RF adiabatic potentials A matter wave interferometer based on dynamic splitting of a BEC Further experiments and outlook
magnetic wire traps Use the interaction of the magnetic moment of an atom with an external field: r r r trap atoms at minimum of |B| = − µ ≈ µ V . B g m B F F B ( g F m F =1 for 87 Rb in m F =2 ) 3D trapping needed! x z B ext y h B wire I d
magnetic wire traps: the Z wire trap Use the interaction of the magnetic moment of an atom with an external field: r r r trap atoms at minimum of |B| = − µ ≈ µ V . B g m B F F B ( g F m F =1 for 87 Rb in m F =2 ) 3D trapping needed! B Zwire B Z provided by Z wire geometry I B Z I I B Zwire
magnetic wire traps: the Z wire trap Use the interaction of the magnetic moment of an atom with an external field: r r r trap atoms at minimum of |B| = − µ ≈ µ V . B g m B F F B ( g F m F =1 for 87 Rb in m F =2 ) 3D trapping needed! provided by Z wire geometry h I reducing wire size d , wire current I and atom–wire separation h I increases the atomic confinement miniaturization of atom chip structures I d
magnetic atom chip traps: miniaturization microfabricated microfabricated macroscopic wire structures wire structures wire structures (optical lithography) (double layer e-beam lithography) 10 µm 1997 2003 2006 millimeters 100 – 10 microns 1 micron miniaturizing wire sizes, reducing wire current, bringing atoms close to wire structures
Integrated atom optics with atom chips ? photon optics atom optics on chip BEC Lasers production monomode guiding, Fibers conveyor belts ? coherent Beam beam splitting splitters with BEC? goal: (portable?) interferometers on atom chips
an atom chip beam splitter: the two wire scheme r B ext I I 2d Calarco et al , PRA 61 , 22304 (2000) Zobay / Garraway Opt. Com. 178, 93 (2000) Hinds et al, PRL 86 , 1462 (2001)
an atom chip beam splitter: the two wire scheme r B ext I I 2d Calarco et al , PRA 61 , 22304 (2000) Zobay / Garraway Opt. Com. 178, 93 (2000) Hinds et al, PRL 86 , 1462 (2001)
an atom chip beam splitter: the two wire scheme r B ext I I 2d Calarco et al , PRA 61 , 22304 (2000) Zobay / Garraway Opt. Com. 178, 93 (2000) Hinds et al, PRL 86 , 1462 (2001)
an atom chip beam splitter: the two wire scheme r B ext I I 2d Calarco et al , PRA 61 , 22304 (2000) Zobay / Garraway Opt. Com. 178, 93 (2000) Hinds et al, PRL 86 , 1462 (2001)
an atom chip beam splitter: the two wire scheme r a single trap B of hexapolar coal geometry d I I 2d Calarco et al , PRA 61 , 22304 (2000) Zobay / Garraway Opt. Com. 178, 93 (2000) Hinds et al, PRL 86 , 1462 (2001)
an atom chip beam splitter: the two wire scheme two output ports r B ext g n i d t t i l p D s s I I s c e i c m o a r p n y two input ports d 2d The two wire scheme is extremely sensitive to fluctuations: • wire size approx. splitting distance (d > D, needs micron size wires) • atoms very close to surface (heating, fragmentation) • 10 -4 stability on external fields (needs magnetic shielding) coherent splitting using this scheme failed so far Y. Shin et al , PRA 72 , 21604 (2005)
an atom chip beam splitter: adiabatic dressed rf potentials Idea: combine static magnetic trap with RF fields to couple different magnetic states → adiabatic potentials bare states trapped state m F =+1/2 (low field seeker) untrapped state m F =-1/2 (high field seeker)
an atom chip beam splitter: adiabatic dressed rf potentials Idea: combine static magnetic trap with RF fields to couple different magnetic states → adiabatic potentials bare states v ω = h µ | B ( r ) | m F =+1/2 RF B trap ω h RF m F =-1/2 crossing position controlled by RF frequency
an atom chip beam splitter: adiabatic dressed rf potentials Idea: combine static magnetic trap with RF fields to couple different magnetic states → adiabatic potentials bare states dressed states ‘m F =+1/2 m F =+1/2 the crossing is at a position where v v µ B B | | ω h RF ω = h µ B | B ( r ) | RF ‘m F =-1/2 controlled by m F =-1/2 RF frequency crossing position controlled level repulsion controlled by RF frequency by RF amplitude Zobay / Garraway PRL 87 , 1195 (2001) Colombe et al, Europhys. Lett. 67 ,593 (2004)
an atom chip beam splitter: adiabatic dressed RF potentials A single trap can be deformed to a double well potential by controlling RF frequency and amplitude : bare states dressed states start RF frequency m F =+1/2 m‘ F =+1/2 below trap bottom ω h adiabaticly deform RF trapping potential by ramping up m F =-1/2 m‘ F =-1/2 frequency
an atom chip beam splitter: adiabatic dressed RF potentials A single trap can be deformed to a double well potential by controlling RF frequency and amplitude : bare states dressed states m F =+1/2 m‘ F =+1/2 m F =-1/2 m‘ F =-1/2 1-100 µm
an atom chip beam splitter: adiabatic dressed RF potentials A single trap can be deformed to a double well potential by controlling RF frequency and amplitude : bare states dressed states m F =+1/2 m‘ F =+1/2 g n i t t i l p s s s e c c i m o r m F =-1/2 m‘ F =-1/2 a p n y d 1-100 µm The RF scheme realizes a true 1 to 2 beam splitter: • robust against magnetic field fluctuations (10 -2 stability on external fields) • can be performed with large wire structures (d > 100D) far from the chip surface
adiabatic dressed RF potentials: realization on an atom chip side view top view atom chip 50 µm Z wire y x I RF Z wire wire z B ext 10 µm RF wire
adiabatic dressed RF potentials: realization on an atom chip side view top view atom chip 50 µm Z wire y x I RF 45° Z wire wire z 80 µm RF I B ext 10 µm RF wire
adiabatic dressed RF potentials: realization on an atom chip side view top view atom chip 50 µm Z wire y x I RF 45° Z wire wire z 80 µm RF I B ext 10 µm RF wire
adiabatic dressed RF potentials: realization on an atom chip side view top view atom chip 50 µm Z wire y x I RF 45° Z wire wire z 80 µm RF I 10 µm in situ RF wire absorption image longitudinal imaging (BEC) 30 µm
adiabatic dressed RF potentials: dynamic splitting of a BEC in situ f 2 h = RF r absorption 0 µ B ' B images f=1.7 MHz f=2.0 MHz limit of optical resolution f=2.3 MHz f=2.6 MHz ( ω L =2 π · 750 kHz) • controlled dynamic splitting BECs up to 80 µm
adiabatic dressed RF potentials: matter wave interference
adiabatic dressed RF potentials: matter wave interference 14 ms time- taking into account of-flight atom-atom interactions absorption images r 0 =2.9 µm r 0 =3.8 µm simple double slit formula extract fringe spacing ∆ z r 0 =4.7 µm r 0 =5.5 µm • split BECs show interference when recombined in expansion • atom interactions have to be considered to understand interference patterns
adiabatic dressed RF potentials: coherent beam splitter for BEC The relative phase between two fully split BECs is measured in many realizations (40) of an interference experiment: 90° 135° 45° measurements 2 σ =28 ° 0° ±180° -45° -135° 90° relative condensate phase obtained relative phases obtained relative phases is extracted from each fit in a polar diagram in a histogram Result: a phase preserving beam splitter for BEC Schumm et al , Nature Physics 1 , 57 (2005)
adiabatic dressed RF potentials: evolution of the relative phase Phase evolution can be controlled by deliberately tilting the double well potential. For connected condensates, the relative phase is locked to zero Phase spread remains non-random even for larger splitting, but increases with split time (1d phase diffusion!)
adiabatic dressed RF potentials: arbitrary RF polarization Two perpendicular RF fields give additional parameters: • phase shift δ between RF sources • ratio of amplitudes of AC currents allows the realization of any RF polarization: sigma minus linear +45° sigma plus linear -45° state dependent potentials! Lesanovsky et al , PRA 73 , 033619 (2006)
linear RF polarization: turning the double well Hofferberth et al , quant-ph/0608228
circular RF polarization: a ring potential (current project) phase shift δ = π /2 Numeric wavepacket propagation ⇒ circular polarization ground state in IP trap Parameters G=20 T/m ω =2 π x 500 kHz B I = 0.75 Gauss δ = π /2 work in progress…
Interferometry with BEC on atom chips Conclusions: • Coherent beamsplitting of BEC using dressed adiabatic potentials • Some control over the evolution of the relative phase • Need to characterize the BEC: • Phase coherence of the initial (1D) BEC • Role of interactions (phase evolution, expansion) • Phase diffusion (Fermions?) • More complex adiabatic potentials using arbitrary polarization of the RF field (ring potential) • portable devices…?
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