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arXiv:0805.3801 · Physical Review A

Photodetection using Bose-Einstein-condensed atoms in a microtrap

Sascha Wallentowitz, A. B. Klimov

Published Oct 24, 2008• 0 citations
arXivHTMLPDF

Abstract

A model of photodetection using a Bose-Einstein condensate in an atom-chip-based microtrap is analyzed. Atoms absorb photons from the incident light field, receive part of the photon momentum, and leave the trap potential. Upon counting escaped atoms within predetermined time intervals, the photon statistics of the incident light is mapped onto the atom-count statistics. Whereas traditional photodetection theory treats the emission centers of photoelectrons as distinguishable, here the centers of escaping atoms are condensed and thus indistinguishable atoms. From this, an enhancement of the photon-number resolution as compared to the commonly known counting formula is derived for the case of low saturation.

DOI
10.1103/physreva.78.043822

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A model of photodetection using a Bose-Einstein condensate in an atom-chip-based microtrap is analyzed. Atoms absorb photons from the incident light field, receive part of the photon momentum, and leave the trap potential. Upon counting escaped atoms within predetermined time intervals, the photon statistics of the incident light is mapped onto the atom-count statistics. Whereas traditional photodetection theory treats the emission centers of photoelectrons as distinguishable, here the centers of escaping atoms are condensed and thus indistinguishable atoms. From this, an enhancement of the photon-number resolution as compared to the commonly known counting formula is derived for the case of low saturation.
We propose a measurement scheme that allows determination of even moments of a Bose-Einstein condensate (BEC) atom number, in a ring cavity, by continuous photodetection of an off-resonant quantized optical field. A fast cavity photocounting process limits the heating of atomic samples with a relatively small number of atoms, being convenient for BECs on microchip scale applications. The measurement back-action introduces a counting-conditioned phase damping, suppressing the condensate typical collapse and revival dynamics.
We describe a novel method of fabricating atom chips that are well suited to the production and manipulation of atomic Bose–Einstein condensates. Our chip was created using a silver foil and simple micro-cutting techniques without the need for photolithography. It can sustain larger currents than conventional chips, and is compatible with the patterning of complex trapping potentials. A near pure Bose–Einstein condensate of 4 × 10 4 87 Rb atoms has been created in a magnetic microtrap formed by currents through wires on the chip. We have observed the fragmentation of atom clouds in close proximity to the silver conductors. The fragmentation has different characteristic features to those seen with copper conductors.
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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.
The counting statistics give insight into the properties of quantum states of light and other quantum states of matter such as ultracold atoms or electrons. The theoretical description of photon counting was derived in the 1960s and was extended to massive particles more recently. Typically, the interaction between each particle and the detector is assumed to be limited to short time intervals, and the probability of counting particles in one interval is independent of the measurements in previous intervals. There has been some effort to describe particle counting as a continuous measurement, where the detector and the field to be counted interact continuously. However, the formalism based on continuous measurements does not provide a formula applicable to general time- and space-dependent fields. In our work, we derive a fully time- and space-dependent description of the counting process for linear quantum many-body systems, taking into account the back-action of the detector on the field. We apply our formalism to an expanding Bose-Einstein condensate of ultracold atoms, and show that it describes the process correctly, whereas the standard approach gives unphysical results in some limits. The example illustrates that, in certain situations, the back-action of the detector cannot be neglected and has to be included in the description.
In the presented work, we report about the successful creation of a Rubidium Bose-Einstein condensate. We use so called magnetic wire traps, which are especially simple, as they consist out of a wire and a homogeneous bias field. These wire traps are especially suited for Bose-Einstein condensation. Furthermore complex trapping potentials to manipulate a Bose-Einstein condensate can be realized. We combine 'large' and small scale wire traps. The 'large' scale is realized with a massive copper structure, while for the small wire traps we use the so called atom chip. This combination is promising, because it allowed us to develop a condensation process in the copper structure, which is independent of the structures on the atom chip, and thus the exchange of the 'physics' area. First experiments with the Bose-Einstein condensate are presented and discussed in detail.