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arXiv:cond-mat/0512520 · Applied Physics Letters

Sensing electric and magnetic fields with Bose-Einstein condensates

Stephan Wildermuth, Sebastian Hofferberth, Igor Lesanovsky, S. Groth, P. Krüger, Jörg Schmiedmayer, I. Bar‐Joseph

Published Jun 26, 2006• 103 citations
arXivHTMLPDF

Abstract

We experimentally demonstrate that one-dimensional Bose-Einstein condensates brought close to microfabricated wires on an atom chip are a very sensitive sensor for magnetic and electric fields reaching a sensitivity to potential variations of ∼10−14eV at 3μm spatial resolution. We measure a two-dimensional magnetic field map 10μm above a 100-μm-wide wire and show how the transverse current-density component inside the wire can be reconstructed. The relation between the field sensitivity and the spatial resolution is discussed and further improvements utilizing Feshbach-resonances are outlined.

DOI
10.1063/1.2216932

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We experimentally demonstrate that one-dimensional Bose-Einstein condensates brought close to microfabricated wires on an atom chip are a very sensitive sensor for magnetic and electric fields reaching a sensitivity to potential variations of ∼10−14eV at 3μm spatial resolution. We measure a two-dimensional magnetic field map 10μm above a 100-μm-wide wire and show how the transverse current-density component inside the wire can be reconstructed. The relation between the field sensitivity and the spatial resolution is discussed and further improvements utilizing Feshbach-resonances are outlined.
Microscopic atom optical devices integrated on atom chips allow to precisely control and manipulate ultra-cold ( T < 1 µK) neutral atoms and Bose-Einstein condensates (BECs) close to surfaces. The relevant energy scale of a BEC is extremely small (down to < 10 −11 eV). Consequently, BECs can be utilized as a sensor for variations of the potential energy of the atoms close to the surface. Here we describe how to use trapped atoms as a measurement device and analyze the performance and flexibility of the field sensor. We demonstrate microscopic magnetic imaging with simultaneous high spatial resolution (3 µm) and high field sensitivity (4 nT). With one dimensional BECs, we probe the magnetic field variations close to the surface at distances down to a few microns. Measurements of the magnetic field of a 100 µm wide current carrying wire imply that the magnetic field variations stem from residual variations of the current flow direction, resulting from local properties of the wire. These disorder potentials found near lithographically fabricated wires are two orders of magnitude smaller than those measured close to electroplated conductors.
Atom chips are devices used to magnetically trap and manipulate ultracold atoms and Bose-Einstein condensates near a surface. In particular, permanent magnetic film atom chips can allow very tight confinement and intricate magnetic field designs while circumventing technical current noise. Research described in this thesis is focused on the development of a magnetic film atom chip, the production of Bose-Einstein condensates near the film surface, the characterisation of the associated magnetic potentials using rf spectroscopy of ultracold atoms and the realisation of a precision sensor based on splitting Bose-Einstein condensates in a double-well potential. The atom chip itself combines the edge of a perpendicularly magnetised GdTbFeCo film with a machined silver wire structure. A mirror magneto-optical trap collects up to 5 x 108 87Rb atoms beneath the chip surface. The current-carrying wires are then used to transfer the cloud of atoms to the magnetic film microtrap and radio frequency evaporative cooling is applied to produce Bose-Einstein condensates consisting of 1 x 105 atoms. We have identified small spatial magnetic field variations near the film surface that fragment the ultracold atom cloud. These variations originate from inhomogeneity in the film magnetisation and are characterised using a novel technique based on spatially resolved radio frequency spectroscopy of the atoms to map the magnetic field landscape over a large area. The observations agree with an analytic model for the spatial decay of random magnetic fields from the film surface. Bose-Einstein condensates in our unique potential landscape have been used as a precision sensor for potential gradients. We transfer the atoms to the central region of the chip which produces a double-well potential. A single BEC is formed far from the surface and is then dynamically split in two by moving the trap closer to the surface. After splitting, the population of atoms in each well is extremely sensitive to the asymmetry of the potential and can be used to sense tiny magnetic field gradients or changes in gravity on a small spatial scale.
Surface based geometries of microfabricated wires or patterned magnetic films can be used to magnetically trap and manipulate ultracold neutral atoms or Bose-Einstein condensates. We investigate the magnetic properties of such atom chips using a scanning magnetoresistive (MR) microscope with high spatial resolution and high field sensitivity. By comparing MR scans of a permanent magnetic atom chip to field profiles obtained using ultracold atoms, we show that MR sensors are ideally suited to observe small variations of the magnetic field caused by imperfections in the wires or magnetic materials which ultimately lead to fragmentation of ultracold atom clouds. Measurements are also provided for the magnetic field produced by a thin current-carrying wire with small geometric modulations along the edge. Comparisons of our measurements with a full numeric calculation of the current flow in the wire and the subsequent magnetic field show excellent agreement. Our results highlight the use of scanning MR microscopy as a convenient and powerful technique for precisely characterizing the magnetic fields produced near the surface of atom chips.
Ultracold gases provide micrometer size samples whose sensitivity to external fields may be exploited in sensor applications. Bose-Einstein condensates of atomic gases have been demonstrated to perform excellently as magnetic field sensors in atom chips. Here we propose that condensates of fermions can be used for noninvasive sensing of time-dependent and static magnetic and electric fields, by utilizing the tunable energy gap in the excitation spectrum as a frequency filter. Perturbations by the field create collective excitations and quasiparticles. The latter requires the frequency of the perturbation to exceed the gap. The frequencies of the field may be selectively monitored from the amount of quasiparticles which is measurable, e.g., by rf spectroscopy. We analyze the method by calculating the density-density susceptibility and discuss its sensitivity and spatial resolution.
Ultra-cold atoms have small kinetic energy and are therefore very sensitive to external fields that act on the atoms. By having fine control over the positioning of the ultra-cold atom cloud we can use the atom cloud as a sensor for magnetic fields. By imaging these atom clouds we can infer a spatial map of the magnetic field. This spatial map will have a resolution proportional to the distance between the source of the magnetic field and the atom cloud which can be on the order of 0:1 µm. In the first half of the thesis, we investigate the two colour magneto-optical trap. This is a simple technique that can lead to a multiplicative increase in the number of atoms in a magneto-optical trap with a simple change to the optical setup. Using the two colour magneto-optical trap we have observed an increase of 5 times in the number of trapped atoms. An increase in the number of atoms in a magneto-optical helps with later cooling processes that are not lossless such as evaporative cooling which in turn helps the realisation of the ultra-cold atom microscope. In the second half of the thesis, we demonstrate how a 2d current density can be recovered from a 2d magnetic field map generated by the ultra-cold atom microscope. We then go on to show the sensitivity and responsivity of a cold atom cloud and a Bose-Einstein condensate. We then use the results of the previous section to simulate the measurement of currents in a silver nanowire network. Properties of the silver nanowire network can be simulated and aid in showing the abilities and limitations of the ultra-cold atom microscope. We found that the ultra-cold atom microscope can directly measure currents in low-density silver nanowire networks. In a high-density silver nanowire network, the average distance between the wires becomes too small to resolve. Hot-spots, areas of high current density can still be identified using the ultra-cold atom microscope. The ultracold atom microscope could then be used as a tool to aid the research look to use silver nanowires in many industrial applications such as touch screens.
Magnetic field sensing utilizing Bose-condensed atomic gases can achieve both high sensitivity and spatial resolution. Employing two-photon transitions from F=1, mF=1→F=2, mF=-1 (F is the quantum number of total atomic angular momentum, mF is the magnetic quantum number of F level) of Bose-condensed 87Rb atomic gases in one-dimensional optical lattice, the precision magnetic field measurement with phase Ramsey interference has been demonstrated. Utilizing single-photon transitions from F=1, mF=1→F=2, mF=0 of Bose-condensed 87Rb atomic gases in a crossed optical dipole trap, we experimentally study frequency domain Ramsey interference, time domain Ramsey interference, and phase domain Ramsey interference. Based on phase Ramsey interference, the sensitivity and spatial resolution of static magnetic field measurement are evaluated. The comparison of these three typical Ramsey interferences reveals that phase Ramsey interference can effectively avoid the fringe distortion in frequency-domain interference and the decoherence effects in time-domain interference, thereby improving the sensitivity and accuracy of the static magnetic field measurement. Utilizing Bose-condensed 87Rb atomic gases with the volume of 1.31±0.03×10-9 cm3 in an unshielded environment, a sensitivity of 130 nT/Hz for static magnetic fields can be achieved. By reducing the preparation time of the atomic gases and increasing the signal interrogation time, the sensitivity has the potential to be further improved.