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arXiv:1801.10582 · Scientific Reports

Atomic-state diagnostics and optimization in cold-atom experiments

Krystian Sycz, Adam M. Wojciechowski, Wojciech Gawlik

Published Feb 6, 2018• 9 citations
arXivHTMLPDF

Abstract

We report on the creation, observation and optimization of superposition states of cold atoms. In our experiments, rubidium atoms are prepared in a magneto-optical trap and later, after switching off the trapping fields, Faraday rotation of a weak probe beam is used to characterize atomic states prepared by application of appropriate light pulses and external magnetic fields. We discuss the signatures of polarization and alignment of atomic spin states and identify main factors responsible for deterioration of the atomic number and their coherence and present means for their optimization, like relaxation in the dark with the strobed probing. These results may be used for controlled preparation of cold atom samples and in situ magnetometry of static and transient fields.

DOI
10.1038/s41598-018-20522-x

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Physical Review A•Apr 22, 2005•3 citations
We report on the creation, observation and optimization of superposition states of cold atoms. In our experiments, rubidium atoms are prepared in a magneto-optical trap and later, after switching off the trapping fields, Faraday rotation of a weak probe beam is used to characterize atomic states prepared by application of appropriate light pulses and external magnetic fields. We discuss the signatures of polarization and alignment of atomic spin states and identify main factors responsible for deterioration of the atomic number and their coherence and present means for their optimization, like relaxation in the dark with the strobed probing. These results may be used for controlled preparation of cold atom samples and in situ magnetometry of static and transient fields.
We report on the observation of nonlinear Faraday rotation with cold atoms at a temperature of  100~100 100 $\ensuremath{\mu}$K. The observed nonlinear rotation of the light polarization plane is up to 0.10.10.1 rad over the 111-mm-size atomic cloud in approximately 101010-mG magnetic field. The nonlinearity of rotation results from long-lived coherence of ground-state Zeeman sublevels created by a near-resonant light. The method allows for creation, detection, and control of atomic superposition states. It also allows applications for precision magnetometry with high spatial and temporal resolution.
We report on our experiments on nonlinear magneto-optical effects in laser-cooled, near-degenerate rubidium samples. Atoms are laser-cooled and subsequently transferred to the crossed-beam optical dipole trap (ODT), formed by a tight focusing of 1560-nm laser beams. The trap not only provides long relaxation time but also allows us to investigate the quantum degeneracy regime. Moreover, the tight confinement of atoms enables magnetic field probing with a high spatial resolution of a few tens of micrometers.
The subject of this thesis is the construction and characterization of an experimental setup for studying the interaction of an ensemble of 10^5 - 10^6 cold 87 Rb atoms held in a far off-resonance optical dipole trap with a probe detuned by about 100 natural line widths, a regime in which refractive effects are resonantly enhanced but absorption is small. An important feature of this type of atom-light interface is that it facilitates quantum non-demolition measurements which in turn have numerous applications in quantum information technology, as well as in the field of ultra-precise metrology where they allow the measurements to overcome the so-called standard quantum limit. The use of a dipole trap has several advantages over more conventional approaches in which vapor cells or magneto-optical traps (MOT) have been used. Most importantly interaction strength of comparable magnitude can be achieved with a far lower number of atoms and with longer coherence times. The elongated geometry that can be realized in a dipole trap maximizes the interaction strength. One of the complications that arise is that the achievable interaction strength is highly sensitive to the mode-matching between the trapped ensemble and the probe beam. The theoretical description of the interaction between a trapped ensemble and a freely-propagating probe beam is provided in the framework of continuous variables. The relevant quantities are a pseudo-spin, defined for an ensemble of atoms in their ground state, and the Stokes vector that characterizes the polarization state of light. In practice the experiment consists of four main blocks: the atom traps, the optical pumping setup, the probe laser setup, and the photodetection. Before loading into the dipole trap, atoms are cooled in a MOT. An existing MOT setup has been improved by implementing a new, more powerful laser system. A dedicated dipole trap, which had been constructed in collaboration with another project, has been thoroughly characterized and the results are presented in this thesis. Setups for optical pumping and for the probe have been built, characterized and incorporated into the apparatus. Several experimental techniques have been developed and tested in order to optimize the alignment of the probe with the trapped ensemble. The effect of the geometrical overlap on the achievable signal to noise ratio is discussed and illustrated using simple, intuitive models. Photo-detection is a critical part of the setup. In order to facilitate detection of non-classical (squeezed) states of the atomic (pseudo-) spin, the detection system must be shot-noise limited within the range of photon numbers used in the experiments. Such a system has been constructed and tested, and is described in detail. It employs a charge-sensitive amplifier (CSA) but, unlike earlier implementations, it does not use a pulse-shaping stage. Instead, an algorithm has been devised and implemented that derives the quantities of interest directly from the output signal of the CSA. This novel approach avoids the technical problems that arise in systems using hardware-based pulse shaping. It also makes the detector more flexible in terms of the shape and timing of the probe pulses that can be used. The atomic states produced in the setup are intrinsically sensitive to stray magnetic fields. Therefore an efficient cancellation of stray fields is essential. On the other hand having the possibility to apply a fully controlled, external magnetic field makes the experimental setup more versatile. Both goals can be achieved with a magnetic field control unit that has been built during this project. It facilitates active cancellation of stray magnetic fields at the frequency of the mains and in addition allows to apply an arbitrary waveform magnetic fields along all three axes. One of the main results reported in this thesis is the observation of polarization rotation caused by population imbalance created in the process of optical pumping and, in a separate series of measurements, due to an applied magnetic field. These measurements have allowed us to assess the strength of the atom-light interaction available in the current setup. They indicate that with the necessary modifications to the optical pumping scheme the system should prove successful in implementing quantum information protocols, in particular quantum memory for light. An interesting off-shoot has been the spectroscopic characterization of the atomic state in the dipole trap. In these measurements Doppler free spectra are recorded in a very simple setup without the need to use nonlinear techniques. Apart from providing a method to characterize the efficiency of the optical pumping into the hyperfine level of interest, the acquired spectra are a very direct illustration of the power of the laser cooling techniques developed in the recent years and without which this work would not have been possible.
We report our study of the magneto-optical effect in a strictly linear regime on spin-polarized cold cesium atoms. Due to the low intensity and the short illumination period of the probe beam, less than 7.5% of the sample atoms change their states by absorbing probe photons. We produce a medium of atoms at rest in either the 6S1∕2,F=3,mF=06{S}_{1∕2},F=3,{m}_{F}=06S1∕2​,F=3,mF​=0 or 6S1∕2,F=3,mF=36{S}_{1∕2},F=3,{m}_{F}=36S1∕2​,F=3,mF​=3 state by optically pumping atoms trapped in a magneto-optical trap. We use the D1D1D1 resonance with large lower and upper state hyperfine splittings as a probe transition to avoid hyperfine mixing from the Zeeman interaction. Under this idealized situation we measure the Stokes parameters in order to find the polarization rotation and circular dichroism experienced by the probe light. We find that there are qualitative differences between the results for the mF=0{m}_{F}=0mF​=0 and mF=3{m}_{F}=3mF​=3 cases. While dispersion and consequent Faraday rotation play a dominant role when the atoms are in the mF=0{m}_{F}=0mF​=0 state, it is dissipation and circular dichroism that are important when they are in the mF=3{m}_{F}=3mF​=3 state. Similarly, while the size of the Faraday rotation and the circular dichroism for the mF=0{m}_{F}=0mF​=0 case scales linearly with the applied magnetic field, for the mF=3{m}_{F}=3mF​=3 case it is the shift of the probe polarization change versus frequency that is linearly proportional to the magnetic field strength.