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A magnetic lattice and macroscopic entanglement of a BEC on an atom chip

Mandip Singh

Published Jan 1, 2008• 2 citations
Publisher

Abstract

Atom chips provide a convenient platform to study ultracold quantum gases and their interactions with electromagnetic fields, surfaces, micro-magnetic structures, superconducting circuits and nanomechanical systems. The research work presented in this thesis is classified in two major categories. The first part is focused on the development and construction of a permanent magnetic lattice on an atom chip and the study of trapped atoms in the permanent magnetic lattice potential. In the second part, a new experiment is proposed to create a macroscopic entanglement between the flux state of a superconducting loop and a Bose-Einstein condensate (BEC) on a superconducting atom chip. The permanent magnetic lattice potential is produced by applying a uniform bias magnetic field to a grooved silicon structure coated with a permanent magnetic film. The magnetic film consists of a multilayer structure of GdTbFeCo with perpendicular intrinsic magnetization. The permanent magnetic structure is mounted beneath a current carrying wire structure glued to a ceramic insulator. The current carrying wires assist in the preparation of the ultracold atoms and for loading into the magnetic lattice. In addition, the current carrying wires are used to produce a BEC in a Z- wire magnetic trap. The magnetic lattice potential is produced by a one-dimensional array of highly anisotropic and extremely tight magnetic microtraps of period 10 ¹m. A detailed study of the reflection dynamics of atoms in the magnetic lattice potential is presented along with numerical simulations. Finally, the trapping of atoms in the permanent magnetic lattice at a distance less than 5 ¹m from the surface of the atom chip is described. The properties of the trapped atoms including lifetime, temperature and trap frequency are discussed. A maximum radial trap frequency of about 90 kHz is measured in the magnetic lattice potential with no confinement applied along the axial direction. A new experiment which combines the quantum coherent dynamics in superconducting circuits and BEC manipulation on a superconducting atom chip is proposed and investigated. It is shown how a macroscopic entanglement can be produced between the flux state of a superconducting loop and the state of a BEC trapped in a magnetic trap. In addition, the detection of the macroscopic entanglement based on a quantum eraser and an entangled BEC interference is discussed. Thus, this proposal provides a platform to realise interferometry with an entangled BEC and to explore the quantum-classical interface.

DOI
10.25916/sut.26263460

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Atom chips provide a convenient platform to study ultracold quantum gases and their interactions with electromagnetic fields, surfaces, micro-magnetic structures, superconducting circuits and nanomechanical systems. The research work presented in this thesis is classified in two major categories. The first part is focused on the development and construction of a permanent magnetic lattice on an atom chip and the study of trapped atoms in the permanent magnetic lattice potential. In the second part, a new experiment is proposed to create a macroscopic entanglement between the flux state of a superconducting loop and a Bose-Einstein condensate (BEC) on a superconducting atom chip. The permanent magnetic lattice potential is produced by applying a uniform bias magnetic field to a grooved silicon structure coated with a permanent magnetic film. The magnetic film consists of a multilayer structure of GdTbFeCo with perpendicular intrinsic magnetization. The permanent magnetic structure is mounted beneath a current carrying wire structure glued to a ceramic insulator. The current carrying wires assist in the preparation of the ultracold atoms and for loading into the magnetic lattice. In addition, the current carrying wires are used to produce a BEC in a Z- wire magnetic trap. The magnetic lattice potential is produced by a one-dimensional array of highly anisotropic and extremely tight magnetic microtraps of period 10 ¹m. A detailed study of the reflection dynamics of atoms in the magnetic lattice potential is presented along with numerical simulations. Finally, the trapping of atoms in the permanent magnetic lattice at a distance less than 5 ¹m from the surface of the atom chip is described. The properties of the trapped atoms including lifetime, temperature and trap frequency are discussed. A maximum radial trap frequency of about 90 kHz is measured in the magnetic lattice potential with no confinement applied along the axial direction. A new experiment which combines the quantum coherent dynamics in superconducting circuits and BEC manipulation on a superconducting atom chip is proposed and investigated. It is shown how a macroscopic entanglement can be produced between the flux state of a superconducting loop and the state of a BEC trapped in a magnetic trap. In addition, the detection of the macroscopic entanglement based on a quantum eraser and an entangled BEC interference is discussed. Thus, this proposal provides a platform to realise interferometry with an entangled BEC and to explore the quantum-classical interface.
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.
We report on the loading and trapping of ultracold atoms in a one-dimensional permanent magnetic lattice of period 10 µm produced on an atom chip. The grooved structure which generates the magnetic lattice potential is fabricated on a silicon substrate and coated with a perpendicularly magnetized multilayered TbGdFeCo/Cr film of effective thickness 960 nm. Ultracold atoms are evaporatively cooled in a Z-wire magnetic trap and then adiabatically transferred to the magnetic lattice potential by applying an appropriate bias field. Under our experimental conditions trap frequencies of up to 90 kHz in the magnetic lattice are measured and the atoms are trapped at a distance of less than 5 µm from the surface with a measured lifetime of about 450 ms. These results are important in the context of studies of quantum coherence of neutral atoms in periodic magnetic potentials on an atom chip.
We report the loading of a 1D permanent magnetic lattice with ultracold atoms on an atom chip. Our magnetic lattice is produced by a perpendicularly magnetised film of Gd10Tb6Fe80Co4 deposited on a 10 μm period grooved structure. A BEC is created in a Z-wire trap about 300 μm from the surface of the chip. An atom cloud at about 5 μK is moved adiabatically towards the lattice by an appropriate bias field. We estimate that about one hundred lattice sites are loaded with atoms about 7 μm from the chip surface at a temperature of about 10 μK.
We present a practically implementable scheme to realise macroscopic entanglement of a Bose-Einstein condensate on a superconducting atom chip. Our proposal combines the two emerging fields of micro-manipulation of a Bose-Einstein condensate on an atom chip and quantum coherent dynamics in superconducting circuits. Our idea is based on coupling a superconductor flux loop to a Bose-Einstein condensate in a magnetic trap on an atom chip. We treat the superconductor flux loop in quantum superposition of two flux states. Our scheme also provides a platform to realise entangled atoms interferometry through a Bose-Einstein condensate on an atom chip.
In this thesis I discuss work that has been carried out on the dynamics of a Bose Einstein condensate of Rb 87 produced near an atom chip. A Bose Einstein Condensate (BEC) is a quantum state of matter where a single quantum state becomes occupied by a macroscopic number of identical Bosons. In our case this is achieved by cooling a system of trapped identical rubidium 87 atoms to its ground state. To reach temperatures of condensation we initially laser cool atoms from room temperature, before loading them into a magnetic trap. The magnetic trap is produced through a combination of uniform magnetic fields from coils outside our vacuum chamber and currents running through wires on an atom chip. The atom chip is a microfabricated device, produced by a coating a silicon chip with a thin layer of gold and etching wires into it. Together, these fields create a magnetic field minimum 120μm from the surface of the chip which can be used to confine low field seeking hyperfine states of the atom in an elongated harmonic trap. Once the atoms are confined in the magnetic trap we used force evaporative cooling out to reach the phase space densities required for Bose Einstein condensation. The BEC is used to investigate the relative dynamics between the fraction of the atoms in the condensate to those not in the condensate. Our atom chip provided a suitable environment to investigate this due to fragmentation of the magnetic potential close to the chip. Small imperfections in the wires on our atom chip mean that the trapping potential isn’t smooth. Small regions of higher trapping frequency - or fragments - are formed. Due to the small size of these fragments it is possible to find a position where a condensate can form in the fragment, and see a potential of high frequency, whereas a non-condensed atom will see a lower frequency potential. We exploit this to set the condensed fraction moving relative to the non condensed part and investigate the subsequent damping of their motion relative to each other.
Atom chips are an excellent tool for studying ultracold degenerate quantum gases, due to the high degree of controllability afforded by the precise potentials generated from the current-carrying microfabricated wires on the chip surface. The geometries of the trapping potentials are inherently capable of realising extreme aspect ratios, and therefore creating model systems with effectively reduced dimensionality, particularly the theoretically-tractable one-dimensional Bose gas. In addition, the temporal tunability makes it possible to impart non-adiabatic changes on the trapping potentials, allowing experimental investigation of samples which have been brought out of equilibrium - a situation which is not fully theoretically understood. This thesis describes the implementation, development and characterisation of an experimental system for producing the first Bose-Einstein condensates of atomic rubidium 87 gas trapped on the surface of an atom chip in Nottingham. Such an apparatus is very complex and requires careful characterisation in order to run in a stable and reliable way. Details of the experimental setup are thoroughly outlined, including the vacuum system, lasers, electronics, computer control and timing, and the optical imaging system. A newly installed compact two-dimensional magneto-optical trap provides an loading rate of 5e7 atoms per second for loading a three-dimensional mirror-magneto-optical trap with 1.5e8 atoms, at a temperature of 300uK within 10s. The cloud is then sub-Doppler cooled to 50uK, and spin-polarised with 96% purity into the |F=2,mF=+2> ground state within 5ms, in preparation for loading a purely magnetic trap. A millimeter sized copper Z-shaped conductor located beneath the atom chip surface creates a Ioffe-Pritchard magnetic trap, into which the laser cooled cloud is loaded with 70% efficiency, and can be held with a vacuum-limited lifetime of 40s. Evaporative cooling then pre-cools the sample to below 20uK within 10s, to allow the subsequent loading into potentials created by the atom chip with 100% efficiency. A final evaporation stage then cools the cloud below the phase transition temperature of 800nK, resulting finally in pure BECs with 10510^5105 atoms confined using the atom chip. Key measurements of various properties of the trapped condensates are presented, which are important in order to characterise the system fully, and to compare with theoretical expectations. In particular, included are the variation of condensate fraction with temperature, the BEC expansion dynamics, and the condensate lifetime in the trap, for example. Finally, it is demonstrated how BECs can be produced on the atom chip without the use of external macroscopic coils, achieved by using novel, integrated sheet structures located beneath the chip surface - unique to this experimental system - to create the necessary bias fields.