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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Cold 87 Rb ensembles: non-Gaussian state detection and spin tomography

Morgan W. Mitchell, S.R. de Echaniz, Marcin Kubasik, Marco Koschorreck

Published Jun 1, 2007• 0 citations
Publisher

Abstract

Light interacting with atomic ensembles allows the possibility of strong, and thus deterministic, quantum interface processes. Recently demonstrated processes of interest for quantum networking include quantum memory for light and teleportation of a quantum state from light to matter. Many important results have been accomplished with room temperature ensembles, which has thus far limited the experiments to relatively long interaction times, ~ ms, large numbers of atoms ~1012, and far-detuned interactions. In contrast, a cold, trapped atomic ensemble can have the same optical depth with far fewer atoms ~106, simultaneous with faster ~mus interaction times. For a combination of technical and fundamental reasons, this allows for new types of experiments using light-ensemble interfaces. Here we describe methods to detect non-gaussian states and perform spin-state tomography.

DOI
10.1109/cleoe-iqec.2007.4386949

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Light interacting with atomic ensembles allows the possibility of strong, and thus deterministic, quantum interface processes. Recently demonstrated processes of interest for quantum networking include quantum memory for light and teleportation of a quantum state from light to matter. Many important results have been accomplished with room temperature ensembles, which has thus far limited the experiments to relatively long interaction times, ~ ms, large numbers of atoms ~1012, and far-detuned interactions. In contrast, a cold, trapped atomic ensemble can have the same optical depth with far fewer atoms ~106, simultaneous with faster ~mus interaction times. For a combination of technical and fundamental reasons, this allows for new types of experiments using light-ensemble interfaces. Here we describe methods to detect non-gaussian states and perform spin-state tomography.
Optically thick spin polarized atomic ensembles have emerged as a new medium optimal for the exotic quantum state engineering via quantum interface with light. The exciting feature of this medium is that quantum atom optics can be carried out with atoms in the range of temperatures from nano-Kelvin to room temperature. Recent theoretical and experimental developments, such as light-atoms entanglement, quantum memory, quantum teleportation, and quantum nondemolition detection of strongly correlated systems will be reviewed in this talk.
Atomic ensembles have gained a lot of interest in the last decade for their prospective use as quantum memories, in precision measurements and other applications in quantum information processing. The atomic part of the interface presented here is an all-optically trapped atomic ensemble of 87Rb at a temperature of 25 muK. The ensemble consists of 106atoms and has an elongated shape with an aspect ratio of about 250:1. The resonant optical depth is around 50. The light part is an off-resonant polarized laser beam which dispersively probes the atomic state. The detection is a shot-noise limited polarization measurement of light pulses of a few mus and 3 x 105photons.
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.
Summary form only given. A new approach to the problem of the quantum interface between light and atoms has been recently developed. The method utilizes free space dispersive interaction between pulses of light and spin polarized atomic ensembles. Entanglement between the polarization state of light and the collective spin state of atoms is established by measurement, more precisely by detection of light in a certain polarization basis. In the first demonstration of this approach we have generated a long-lived entangled state of two separate macroscopic atomic samples by a polarization measurement on light transmitted through the samples. We then have shown that this approach also works for mapping of a quantum state of light onto long-lived atomic spin state paving the road towards realization of the quantum memory for light. Recently we have also extended the free space light-atoms interface beyond the continuous variables in the proposal, where a coherent superposition "cat" state of an atomic ensemble is generated by a measurement sequence. Progress with other communication protocols such as atomic state teleportation and multiparty networks will be presented.