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Bulletin of the American Physical Society

Interference and Coherence in 1-d Bose-Einstein-Condensates

Jörg Schmiedmayer

Published Jun 6, 2007• 0 citations
OpenAlex

Abstract

Atom chips promise manipulation of matter waves with high precision. Our exceptionally smooth atom chips potentials allow to experiment with continuous 1 mm long 1d condensates at strong transversal confinement (>10kHz) and extreme aspect ratio up to 10000. In these atom chip traps we employ RF induced adiabatic potentials to split a 1d condensate along its long axis. Bringing the two split clouds together we observe interference between the two ensembles. The RF potentials allow unprecedented precise control enabling a coherent splitting process as demonstrated by the deterministic and stable phase of the interference. The interference pattern itself is sensitive probe of the order parameter in the 1d quantum gas:

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Atom chips promise manipulation of matter waves with high precision. Our exceptionally smooth atom chips potentials allow to experiment with continuous 1 mm long 1d condensates at strong transversal confinement (>10kHz) and extreme aspect ratio up to 10000. In these atom chip traps we employ RF induced adiabatic potentials to split a 1d condensate along its long axis. Bringing the two split clouds together we observe interference between the two ensembles. The RF potentials allow unprecedented precise control enabling a coherent splitting process as demonstrated by the deterministic and stable phase of the interference. The interference pattern itself is sensitive probe of the order parameter in the 1d quantum gas:
We have used a microfabricated atom chip to split a single Bose-Einstein condensate of sodium atoms into two spatially separated condensates. Dynamical splitting was achieved by deforming the trap along the tightly confining direction into a purely magnetic double-well potential. We observed the matter wave interference pattern formed upon releasing the condensates from the microtraps. The intrinsic features of the quartic potential at the merge point, such as zero trap frequency and extremely high field-sensitivity, caused random variations of the relative phase between the two split condensates. Moreover, the perturbation from the abrupt change of the trapping potential during the splitting was observed to induce vortices.
We have used a microfabricated atom chip to split a single Bose-Einstein condensate of sodium atoms into two spatially separated condensates. Dynamical splitting was achieved by deforming the trap along the tightly confining direction into a purely magnetic double-well potential. We observed the matter wave interference pattern formed upon releasing the condensates from the microtraps. The intrinsic features of the quartic potential at the merge point, such as zero trap frequency and extremely high field-sensitivity, caused random variations of the relative phase between the two split condensates. Moreover, the perturbation from the abrupt change of the trapping potential during the splitting was observed to induce vortices.
We report on progress for a couple of experiments on manipulating cold atoms on a chip for quantum sensing. The first experiments are directed towards developing a compact atom interferometer on an atom chip using a double-well potential. The interferometer uses 87Rb atoms magnetically confined in an atomic waveguide produced by wires on the surface of a lithographically patterned chip. Finite element modeling of combinations of different current configurations with various external bias fields indicated a means of coherently splitting the atomic cloud through dynamically adjusting the currents and bias fields. In these experiments we investigate real-time transformations between different double-well configurations adiabatically and non-adiabatically, and study their effects on the initially trapped atoms. Coherence properties of the two atomic wavepackets are examined. In another set of experiments we investigate the properties of bosons confined to (quasi) one dimension in our magnetic waveguide. When the atom-atom repulsive interaction becomes much larger than the kinetic energy, bosons confined in one dimension can enter a new state of matter, the Tonks-Girardeau gas, in which they behave like non-interacting fermions. However, the bosons can still occupy the same momentum state and therefore the gas cannot be fully described by either Bose-Einstein or Fermi-Dirac statistics. This transition has been observed in optical lattices but not in magnetic atom chip waveguides. We discuss the conditions for obtaining a Tonks-Girardeau gas with 87Rb atoms in our atom chip waveguide as well as a novel signature for observing the transition in our system.
During this thesis a novel trapping and manipulation technique for neutral atoms on atom chips has been developed and experimentally implemented. Radio-frequency (rf) coupling of internal states of magnetically trapped atoms results in versatile microscopic potentials, which overcome various limitations of static magnetic traps. An extensive experimental analysis of this new technique has been carried out, exploring the state-dependency of the rf potentials and the possible realization of non-trivial trapping geometries. Based on these results, the first coherent matter wave beam splitter on an atom chip has been realized, demonstrating for the first time the all-magnetic coherent splitting of a condensate. This new atom optical tool has then been applied to investigate the phase-properties of one-dimensional Bose-Einstein condensates. The potential configuration developed during this thesis provides direct access to the phase fluctuations in the system and has allowed the first time-resolved study of equilibrium properties and non-equilibrium dynamics in a one-dimensional Bose gas.
We measure the relative phase of two Bose-Einstein condensates confined in a radio frequency induced double-well potential on an atom chip. We observe phase coherence between the separated condensates for times up to approximately 200 ms after splitting, a factor of 10 longer than the phase diffusion time expected for a coherent state for our experimental conditions. The enhanced coherence time is attributed to number squeezing of the initial state by a factor of 10. In addition, we demonstrate a rotationally sensitive (Sagnac) geometry for a guided atom interferometer by propagating the split condensates.
Atom chips are a great tool for creation of low dimensional magnetic trapping geometries via micro-structures on the chip surface. Such structures allow the creation of time-dependent magnetic and electric potentials with highly accurate spatial and temporal dependency. As part of this thesis we have investigated the coherence dynamics in one-dimensional Bose-Einstein condensate while creating a sudden change in the atomic trapping potential. Such sudden changes create phase perturbations of the wave function, which leads to density perturbations. Analyzing these changes enables studies of the evolution of the coherence in a one-dimensional Bose gas with dynamically changing boundary conditions. Of particular interest is the study of prethermalization which can be understood in an integrable systems as so-called generalized Gibbs state. This state does not decay, but in case that there are perturbations that break integrability, this state relaxes further to a thermal state. To get a good understanding of such 1D systems we first investigated the transition from 3D to 1D Bose gas by observing both in situ and time of flight density profiles and analyzing the spatial variations in atom number as a function of temperature, geometry, and atomic density. High quality imaging is essential in these types of atomic physics experiments, and therefore a whole chapter is devoted to a new optimization method of absorption imaging. In this method we have taken into account the quantum nature of both the atomic medium and imaging light. Last, we have outlined an experiment that utilizes one-dimensional Bose-Einstein condensate as an analogue model of quantum field theory, in particular the dynamical Casimir effect and Hawking radiation. We do so by dynamically splitting a condensate along its long axis to a Y-like shape and measure the differential phase between the branches.