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The Application of Four-Wave Mixing to Cold and Ultra-Cold Atom Imaging

Francesca M. Fornasini

Published May 12, 2010• 0 citations
OpenAlex

Abstract

In this project, I investigated a new imaging technique for cold and ultra-cold atoms based on the four-wave mixing (FWM) process. In theory, this technique will provide more precise measurements of the number and spatial density distribution of cold atoms than fluorescence or absorption imaging. Since FWM is usually studied in high optical depth vapor cells but cold atoms have low optical depths, I first studied the dependence of FWM on optical depth. Results showed that Stokes field emission due to FWM decreases exponentially with decreasing optical depth, and that it can still be observed at optical depths of approximately 1. After determining the optimal conditions for Stokes field emission, I tried observing FWM with cold atoms. Absorption and emission-like features were observed on the probe and Stokes fields which depended on the interaction of the control field, the probe field, and the trapped atoms. There is significant reason to believe that these features are associated with the FWM process, although further studies need to be undertaken to determine more definitively the nature of these features, how they depend on various parameters of the experimental setup, and how they may be related to the number and density of the cold atoms.

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European Quantum Electronics Conference (EQEC)•Jan 18, 2006•0 citations
In this project, I investigated a new imaging technique for cold and ultra-cold atoms based on the four-wave mixing (FWM) process. In theory, this technique will provide more precise measurements of the number and spatial density distribution of cold atoms than fluorescence or absorption imaging. Since FWM is usually studied in high optical depth vapor cells but cold atoms have low optical depths, I first studied the dependence of FWM on optical depth. Results showed that Stokes field emission due to FWM decreases exponentially with decreasing optical depth, and that it can still be observed at optical depths of approximately 1. After determining the optimal conditions for Stokes field emission, I tried observing FWM with cold atoms. Absorption and emission-like features were observed on the probe and Stokes fields which depended on the interaction of the control field, the probe field, and the trapped atoms. There is significant reason to believe that these features are associated with the FWM process, although further studies need to be undertaken to determine more definitively the nature of these features, how they depend on various parameters of the experimental setup, and how they may be related to the number and density of the cold atoms.
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.
The goal of the project is to produce a pair of intensity-squeezed light fields using Four-Wave Mixing (FWM) in hot Rubidium vapor. In this process, interaction of atoms with near-resonant strong control optical field results in strong amplification of a weak probe optical field and in generation of a quantum correlated conjugate Stokes optical field. In order to establish the quantum correlation between the Stokes and probe fields, we measured the differential intensity noise between the Stokes and probe fields. If the noise falls below the quantum noise limit, then two-mode intensity squeezing has been achieved, as a first step toward realization of the polarization Bell states. We also examine the conservation of orbital angular momentum (OAM) in the FWM process with OAM-bearing input fields.
This thesis covers experimental work conducted within two distinct fields of cold-atom physics. The first part describes an experiment capable of spatially-selective dispersive measurements of a cold-atomic system in part or in whole, by virtue of a digital micromirror device (DMD). Atom clouds are trapped in optical tweezers made and controlled by an acousto-optical deflector. Two types of high-precision magnetometers are realised. One is vectorial and reaches a single-shot precision of dB = (100, 200) µG for the field components parallel and transversal to the probe light, exceeding a previous realisation by two orders of magnitude. The other is a scalar magnetometer based on Larmor precession and reaches dB = 30 µG, putting it on equal footing with other state-of-the-art cold-atom magnetometers. The second part is devoted to the characterisation and the first results of a new quantum gas microscope experiment. It features a 0.69 NA microscope objective for high-resolution fluorescence imaging of individual atoms trapped in deep optical lattices. The imaging system is shown to perform near the diffraction limit. By means of DMD-generated off-resonant tight optical tweezers, projected through the high-resolution optics, we can load only a few planes of a co-propagating 1D lattice. In a single realisation of the experiment we acquire multiple fluorescence images, where the objective is translated between images, bringing different planes of the optical lattices in focus. In this way we can tomographically reconstruct the atom distribution in 3D.
The goal of the project is to produce a pair of polarization-entangled light fields using four-wave mixing in hot Rb vapor. In this process, interaction of atoms with near-resonant strong control optical field results in strong amplification of a nearly-collinear probe optical field and in generation of a quantum correlated conjugate Stokes optical field. In order to establish the quantum correlation between the Stokes and probe fields, we have adopted a homodyne detection scheme. If the differential noise between the Stokes and probe fields is below the quantum noise limit, then intensity fluctuation entanglement has been achieved, and it is possible to produce the polarization Bell states.
We propose a scheme to transfer the spatial intensity as well as phase information encoded initially in the spatial profile of a weak probe field onto a newly generated Stokes field in a nonlinear process of four-wave mixing (FWM). The FWM process is explored in a gaseous medium consisting of atoms modeled as a three-level system in the $\mathrm{\ensuremath{\Lambda}}$ configuration. We found that different orders of Hermite-Gaussian and Laguerre-Gaussian modes carried by a probe beam are effectively transferred to a Stokes beam. Interestingly, the transferred intensity of the Stokes beam is a clone of the probe beam, whereas the phase profile is conjugate to the probe. The phase distribution of the transmitted modes at the exit of the medium is explored by superimposing them on a copropagating plane wave. Moreover, the parametric amplification due to the nonlinear process of FWM prevents any information loss due to linear absorption and permits us to work at high optical depths. We found a structural similarity between transferred images of about 9999%99, which provides clear evidence for the successful transfer of information in the FWM process.