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arXiv:cond-mat/0302568 · Physical Review A

Nondestructive dynamic detectors for Bose-Einstein condensates

Jessica Lye, J. J. Hope, J. D. Close

Published Apr 22, 2003• 53 citations
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Abstract

We propose and analyze a series of nondestructive dynamic detectors for Bose-Einstein condensates based on photodetectors operating at the shot-noise limit. These detectors are compatible with real-time feedback to the condensate. The signal-to-noise ratio of different detection schemes are compared subject to the constraint of minimal heating due to photon absorption and spontaneous emission. This constraint leads to different optimal operating points for interference-based schemes. We find the somewhat counterintuitive result that without the presence of a cavity, interferometry causes as much destruction as absorption for optically thin clouds. For optically thick clouds, cavity-free interferometry is superior to absorption, but it still cannot be made arbitrarily nondestructive. We propose a cavity-based measurement of atomic density which can in principle be made arbitrarily nondestructive for a given signal-to-noise ratio.

DOI
10.1103/physreva.67.043609

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We propose and analyze a series of nondestructive dynamic detectors for Bose-Einstein condensates based on photodetectors operating at the shot-noise limit. These detectors are compatible with real-time feedback to the condensate. The signal-to-noise ratio of different detection schemes are compared subject to the constraint of minimal heating due to photon absorption and spontaneous emission. This constraint leads to different optimal operating points for interference-based schemes. We find the somewhat counterintuitive result that without the presence of a cavity, interferometry causes as much destruction as absorption for optically thin clouds. For optically thick clouds, cavity-free interferometry is superior to absorption, but it still cannot be made arbitrarily nondestructive. We propose a cavity-based measurement of atomic density which can in principle be made arbitrarily nondestructive for a given signal-to-noise ratio.
We present the first detector that is capable of recording high-bandwidth atom number density measurements of a Bose-Einstein condensate, with a readout of the data in real time. It is based on a shot-noise-limited unbalanced Mach-Zehnder interferometer designed for a minimally destructive measurement of the atom column density of a Bose-Einstein condensate. The shot-noise limit is reached by phase modulating the laser in one arm and phase locking the interferometer with a second-color laser. The detector is characterized, and its sensitivity for a fractional change in the column density of a Bose-Einstein condensate is calculated. With this detection system it may be possible to implement feedback to stabilize a Bose-Einstein condensate or an atom laser.
All optical techniques used to probe the properties of Bose-Einstein condensates have been based on dispersion and absorption that can be described by a two-level atom. Both phenomena lead to spontaneous emission that is destructive at the low energies involved with ultracold atomic systems. Recently, both were shown to lead to the same limit to the signal to noise ratio for a given destruction. We develop a new method for calculating the phase shift of a laser beam and show that no single-pass optical technique using classical light and a three-level atom can exceed this limit. This puts significant restrictions on potential nondestructive measurement schemes.
We present a minimally destructive interferometric measurement of the column density of cold atoms with a passively stabilized separated beam path interferometer. We achieve a heating rate of 4 (photons/sec)/atom. The interferometer employed in these measurements utilizes a photodiode rather than a charge-coupled device camera and is suitable for the measurement of fast dynamics in Bose-Einstein condensates and real-time feedback with atom lasers. The technique is compatible with modulation techniques employing squeezed light as the probe beam for sub-shot-noise-limited measurements.
This thesis presents theoretical principles on laser cooling and trapping as well as magnetic trapping and evaporative cooling, methods necessary for Bose-Einstein condensation.It presents the construction of a very dependable BEC machine.We demonstrate a novel class of trapping potentials, time-averaged adiabatic potentials (TAAP) which allows the generation of a large variety of traps and waveguides for ultracold atoms.The ring-geometry is of particular interest for guided matter-wave interferometry as it provides a perfectly smooth waveguide of controllable diameter, and thus a tunable sensitivity of the interferometer.In addition we report the experimental realization of double-well traps based on TAAP traps.Quantum degenerate Fermi gases and Bose-Einstein condensates give access to a vast new class of quantum states.The resulting multi-particle correlations places extreme demands on the detection schemes.Here we introduce diffractive darkground imaging as a novel ultra-sensitive imaging technique.We detect clouds with less than 30 atoms with near atom shot-noise limited signal to noise ratio.This presents an improvement of about one order of magnitude when compared to our standard absorption imaging.We also examine the optimal conditions for absorption imaging including saturation and fluorescence contributions.
We present a Ramsey-type atom interferometer operating with an optically trapped sample of 10 6 Bose-condensed 87 Rb atoms. We investigate this interferometer experimentally and theoretically with an eye to the construction of future high precision atomic sensors. Our results indicate that, with further experimental refinements, it will be possible to produce and measure the output of a sub-shot-noise-limited, large atom number BEC-based interferometer. The optical trap allows us to couple the | F =1, m F =0⟩→| F =2, m F =0⟩ clock states using a single photon 6.8 GHz microwave transition, while state selective readout is achieved with absorption imaging. We analyse the process of absorption imaging and show that it is possible to observe atom number variance directly, with a signal-to-noise ratio ten times better than the atomic projection noise limit on 10 6 condensate atoms. We discuss the technical and fundamental noise sources that limit our current system, and present theoretical and experimental results on interferometer contrast, de-phasing and miscibility.
Bose-Einstein condensates are coherent matter waves, produced by cooling gaseous atomic clouds to ultra-low temperatures. For applications in atom interferometry and precision measurements, Bose-condensed sources present an intriguing alternative to thermal atoms. Although the current sensitivity achievable with interferometers using coherent atoms is not comparable to thermal beam machines (mainly due to the lower flux), there are promising ways to utilise the potential of Bose-condensed sources for atom interferometry. Among those is the low momentum width of Bose-Einstein condensates, which can generally be well controlled and is advantageous for increased interferometric sensitivities by implementing large momentum transfer beam splitters. As part of this thesis, experimental and theoretical investigations are presented to investigate the potential of Bose-Einstein condensates for such applications. We shall present the quantum projection noise limited performance of a Ramsey interferometer operating on the atomic clock transition of a freely expanding cloud of Bose-condensed rubidium 87 atoms. The results include Ramsey fringes of high visibility, not measurably affected by atomic interaction-induced dephasing effects. The achievement and detection of the quantum projection noise limit rely critically on the precision and accuracy of both the imaging setup and the coupling scheme in the interferometric beam splitters. The stabilisation of the beam splitters via an optical Sagnac interferometer is the basis for the quantum projection noise limited performance of the interferometer presented. For an increase of bandwidth and flux in atom interferometric measurements, it is advantageous to use a continuous atomic beam. A truly continuous coherent atom source has not been realised to date, and we present results on a pumping mechanism in this thesis, as a decisive step towards a continuous atom laser. By the investigation of different momentum resonances, we find that the pumping scheme relies on a Raman superradiance-like process. Finally, the thesis demonstrates two interaction measurements in rubidium. The strong mean field interactions due to the high densities in Bose-Einstein condensates are used to probe the potential of a rubidium 87 condensate with an atom laser. The measurement allows a determination of the scattering length between the two atomic states involved. In addition to this two-body scattering scheme, we present a measurement of three-body loss coefficients, extracted from loss curves in rubidium 85 Bose-Einstein condensates. The measurement provides new upper bounds on the three-body loss coefficients at the scattering lengths considered.