Quantum measurement is one of the most important features of quantum theory. Although mathematical predictions have been verified in great detail, practical implementation has lagged behind. Only recently have people begun to take advantage of quantum measurement properties to produce new technologies. This research helps fill that technological gap by experimental examination of a continuous, optical measurement for an ensemble of cold atomic spins. The essential physics reduces to the interaction between an atomic ensemble and a weak optical field, which has many well known results. While this work demonstrates many novel applications of the interaction, it also shows that the whole can be more than the sum of the individual parts. Starting with basic characterization of the measurement system using laser-cooled cæsium atoms, the mean value of a spin component is obtained in real time. In essence, the angular momentum of the atomic spins creates a Faraday-like rotation in the polarization of a laser probe beam. With slight modifications, additional spin components are also observed, and are shown to be in good agreement with predictions. In measuring spin dynamics, it is important to account for effects of the probe on the spin states as well. Capitalizing on this as a resource, the probe-induced ac-Stark shift is used to transform a quasi-classical spin-coherent state into a highly quantum Schrödinger cat type of superposition between two spin states. Finally, this work combines all the previous results to demonstrate how a continuous measurement of the spin with a carefully crafted evolution created in part by the probe, allows for nearly real-time determination of the complete spin density matrix. In a single 1.5 millisecond run, a spin density matrix is determined with fidelities ranging from about 85% to 90% across a wide spectrum of test states.
Quantum measurement is one of the most important features of quantum theory. Although mathematical predictions have been verified in great detail, practical implementation has lagged behind. Only recently have people begun to take advantage of quantum measurement properties to produce new technologies. This research helps fill that technological gap by experimental examination of a continuous, optical measurement for an ensemble of cold atomic spins. The essential physics reduces to the interaction between an atomic ensemble and a weak optical field, which has many well known results. While this work demonstrates many novel applications of the interaction, it also shows that the whole can be more than the sum of the individual parts. Starting with basic characterization of the measurement system using laser-cooled cæsium atoms, the mean value of a spin component is obtained in real time. In essence, the angular momentum of the atomic spins creates a Faraday-like rotation in the polarization of a laser probe beam. With slight modifications, additional spin components are also observed, and are shown to be in good agreement with predictions. In measuring spin dynamics, it is important to account for effects of the probe on the spin states as well. Capitalizing on this as a resource, the probe-induced ac-Stark shift is used to transform a quasi-classical spin-coherent state into a highly quantum Schrödinger cat type of superposition between two spin states. Finally, this work combines all the previous results to demonstrate how a continuous measurement of the spin with a carefully crafted evolution created in part by the probe, allows for nearly real-time determination of the complete spin density matrix. In a single 1.5 millisecond run, a spin density matrix is determined with fidelities ranging from about 85% to 90% across a wide spectrum of test states.
The field of quantum metrology concerns the physical measurement of sensors with a precision comparable to fundamental limits set by quantum mechanics. It is possible to outperform naive interpretations of these limits by using entangled states of the sensor system. One example is that of a spin-squeezed state, in which the uncertainty of one variable is decreased at the expense of another while still obeying Heisenberg's uncertainty principle, improving rotation sensitivity along a chosen axis. These states are potentially useful in devices including atomic clocks, inertial sensors, and magnetometers. Any model of a quantum metrology device must respect the fact that physical measurements are not passive, as imagined classically, but necessarily invasive. Far from being a negative feature, well-understood quantum measurement can conditionally drive a system into desirable entangled states, including spin-squeezed states. Furthermore, the fundamental randomness of this process can, in principle, be removed with real-time feedback control, motivating an adaptation of classical feedback concepts to the quantum realm. In this thesis, I describe these ideas in the context of one experimental example. A laser-cooled cloud of cesium spins is polarized along one axis via optical pumping and, subsequently, a linearly polarized far-off resonant probe beam traverses the sample. Due to the interaction Hamiltonian, the optical polarization rotates by an amount nominally proportional to one spin component of the collective spin state, enacting a weak, continuous, nondemolition measurement of that collective variable. This optical Faraday rotation is then measured with a polarimeter and the inherently noisy result used to condition the collective atomic state via a quantum filter, or stochastic master equation. Ideally, this process is capable of producing spin-squeezed states via the measurement itself. The details of this measurement are investigated in depth, including a derivation of the nonideal polarizability Hamiltonian, an analysis of the projection process with control, and a derivation of the magnetometry sensitivity. Experimentally, we demonstrate continuous measurement of the collective spin state with a large single-shot signal-to-noise ratio and verify many predictions of the model. Finally, we describe attempts to observe the atomic projection noise, which would infer the preparation of spin-squeezed states.
A weak continuous quantum measurement of an atomic spin ensemble can be implemented via Faraday rotation of an off-resonance probe beam, and may be used to create and probe nonclassical spin states and dynamics. We show that the probe light shift leads to nonlinearity in the spin dynamics and limits the useful Faraday measurement window. Removing the nonlinearity allows a nonperturbing measurement on the much longer time scale set by decoherence. The nonlinear spin Hamiltonian is of interest for studies of quantum chaos and real-time quantum state estimation.
The linear Faraday effect is used to implement a continuous measurement of the spin of a sample of laser-cooled atoms trapped in an optical lattice. One of the optical lattice beams serves also as a probe beam, thereby allowing one to monitor the atomic dynamics in real time and with minimal perturbation. A simple theory is developed to predict the measurement sensitivity and associated cost in terms of decoherence caused by the scattering of probe photons. Calculated signal-to-noise ratios in measurements of Larmor precession are found to agree with experimental data for a wide range of lattice intensity and detuning. Finally, quantum back-action is estimated by comparing the measurement sensitivity to spin projection noise, and shown to be insignificant in the current experiment. A continuous quantum measurement based on Faraday spectroscopy in optical lattices may open up new possibilities for the study of quantum feedback and classically chaotic quantum systems.
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.
This dissertation studies the statistics and modeling of a quantum system probed by a coherent laser field. We focus on an ensemble of qubits dispersively coupled to a traveling wave light field. The first research topic explores the quantum measurement statistics of a quasi-monochromatic laser probe. We identify the shortest timescale that successive measurements approximately commute. Our model predicts that for a probe in the near infrared, noncommuting measurement effects are apparent for subpicosecond times. The second dissertation topic attempts to find an approximation to a conditional master equation, which maps identical product states to identical product states. Through a technique known as projection filtering, we find such a equation for an ensemble of qubits experiencing a diffusive measurement of a collective angular momentum projection, and global rotations. We then test the quality of the approximation through numerical simulations. In the presence of strong randomized rotations, the approximation reproduces the exact expectation values to within 95%. The final topic applies the projection filter to the problem of state reconstruction. We find an initial state estimate based on a single continuous measurement of an identically prepared atomic ensemble. Given the ability to make a continuous collective measurement and simultaneously applying time varying controls, it is possible to find an accurate estimate given based upon a single measurement realization. Here we explore the fundamental limits of this protocol by studying an idealized model for pure qubits, which is limited only by measurement backaction. Using the exact dynamics to produce simulated measurements, we then numerically search for a maximum likelihood estimate based on the approximate expression. Our estimation technique nearly achieves an average fidelity bound set by an optimum POVM.
At the beginning of the 20th century measurement precision was related exclusively to the capabilities of the experimenter and the apparatus. Any imprecision was attributed to imperfect devices for the measurement. Later on, when the quantumness of objects like photons, electrons, or atoms, was recognized, it became clear that the measurement and the object to be measured could no longer be separated. Both follow the laws of quantum physics which impose limits on the accuracy of any measurement. In the last three decades, a lot of research has been dedicated to find strategies to overcome these limitations. This new field of quantum metrology is where this work is placed.
This thesis describes the generation of interparticle entanglement in form of a squeezed spin state in a cloud of cold 87Rb atoms by performing nondestructive spin measurements. Towards this goal, we have implemented a shot-noise limited polarization probing and detection system, atom counting by means of absorption imaging, spin state preparation via optical pumping and nondestructive spin state detection. The quantum noise limited spin readout with polarized light is characterized in two complementary ways in terms of sensitivity and all possible quantum and classical noise sources are measured.
To address the rich opportunities provided in the multilevel structure of 87Rb with dispersive probing, we have developed and implemented a frequency offsetlock which allows a large tuning range of several GHz for the dispersive probing.
Working with a magnetically sensitive atomic system triggered the development of a magnetic field imaging technique. This applies the elongated atomic sample and internal atomic states as a way of measuring magnetic fields over several millimeters with micrometer resolution and sensitivities down to a few tens of pT/ Hz.
We developed a new method for tomographic measurements of the atomic density matrix. Based on our ability of shot noise limited detection of polarization rotations we can in principle, characterize the whole atomic spin state.
First, measurements are shown and possible improvements are discussed.
An in depth characterization of the light-atom interaction between polarized pulses of light and collective atomic states are the basis for measurements at the quantum level. On one side, we apply classical measurements of spin polarized atoms to measure the strength of the lightatom interaction. On the other side, we use quantum measurements of unpolarized atomic states to characterize all noise sources both technical and quantum.
One of the major results of this thesis is the realization of quantum nondemolition measurements in a largespin system. We realized limitations to the performance of the QND measurement implied by higher order light shifts in multilevel atoms, which are often neglected for these kind of systems. We develop a technique which suppresses the detrimental effects of higher order light shifts and recovers an ideal QND measurement.
The thesis culminates in the demonstration of spin squeezing in the magnetically sensitive ground state of 87Rb. We achieve a quantum noise reduction by 3 dB, where metrological sensitivity is improved by 2 dB beyond the standard quantum limit of a coherent spin state with the same spin polarization.
We address the question how spatial and temporal inhomogeneities both in light and atoms influence the preparation of nonclassical states. An existing covariance matrix approach is extended and we apply it to study effects of detector time resolution, spatial inhomogeneities and atomic motion.