Optimally extracting information from measurements performed on a physical system requires an accurate model of the measurement interaction. Continuously probing the collective spin of an alkali-metal atom cloud via its interaction with an off-resonant optical probe is an important example of such a measurement where realistic modeling at the quantum level is possible using standard techniques from atomic physics. Typically, however, tutorial descriptions of this technique have neglected the multilevel structure of realistic atoms for the sake of simplification. We account for the full multilevel structure of alkali-metal atoms and derive the irreducible form of the polarizability Hamiltonian describing a typical dispersive quantum measurement. For a specific set of parameters, we then show that semiclassical predictions of the theory are consistent with our experimental observations of polarization scattering by a polarized cloud of laser-cooled cesium atoms. We also derive the signal-to-noise ratio under a single-measurement trial and use this to predict the rate of spin squeezing with multilevel alkali-metal atoms for arbitrary detuning of the probe beam.
Optimally extracting information from measurements performed on a physical system requires an accurate model of the measurement interaction. Continuously probing the collective spin of an alkali-metal atom cloud via its interaction with an off-resonant optical probe is an important example of such a measurement where realistic modeling at the quantum level is possible using standard techniques from atomic physics. Typically, however, tutorial descriptions of this technique have neglected the multilevel structure of realistic atoms for the sake of simplification. We account for the full multilevel structure of alkali-metal atoms and derive the irreducible form of the polarizability Hamiltonian describing a typical dispersive quantum measurement. For a specific set of parameters, we then show that semiclassical predictions of the theory are consistent with our experimental observations of polarization scattering by a polarized cloud of laser-cooled cesium atoms. We also derive the signal-to-noise ratio under a single-measurement trial and use this to predict the rate of spin squeezing with multilevel alkali-metal atoms for arbitrary detuning of the probe beam.
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.
Abstract Spin-polarized atomic ensembles probed by light based on the Faraday interaction are a versatile platform for numerous applications in quantum metrology and quantum information processing. Here we consider an ensemble of Alkali atoms that are continuously optically pumped and probed. Due to the collective scattering of photons at large optical depth, the steady state of atoms does not correspond to an uncorrelated tensor-product state, as is usually assumed. We introduce a self-consistent method to approximate the steady state including the pair correlations, taking into account the multilevel structure of atoms. We find and characterize regimes of Raman lasing, akin to the model of a superradiant laser. We determine the spectrum of the collectively scattered photons, which also characterizes the coherence time of the collective spin excitations on top of the stationary correlated mean-field state, as relevant for applications in metrology and quantum information.
Squeezing of collective atomic spins has been shown to improve the sensitivity of atomic clocks and magnetometers to levels significantly below the standard quantum limit. In most cases the requisite atom-atom entanglement has been generated by dispersive interaction with a quantized probe field or by state-dependent collisions in a quantum gas. Such experiments typically use complex multilevel atoms like Rb or Cs, with the relevant interactions designed so that atoms behave like pseudospin-21 particles. We demonstrate the viability of spin squeezing for collective spins composed of the physical angular momenta of 106 Cs atoms, each in an internal spin-4 hyperfine state. A peak metrological squeezing of at least 5dB is generated by quantum backaction from a dispersive quantum nondemolition (QND) measurement, implemented using a two-color optical probe that minimizes tensor light shifts without sacrificing measurement strength. Other significant developments include the successful application of composite pulse techniques for accurate dynamical control of the collective spin, enabled by broadband suppression of background magnetic fields inside a state-of-the-art magnetic shield. The absence of classical noise allows us to compare the observed quantum projection noise and squeezing to a theoretical model that properly accounts for both the relevant atomic physics and the spatial mode of the collective spin, finding good quantitative agreement and thereby validating its use in other contexts. Our work sets the stage for experiments on quantum feedback, deterministic squeezing, and closed-loop magnetometry. The implementation of real-time feedback may also create an opportunity for new types of quantum simulation, wherein the evolution of a quantum system is conditioned on the outcome of a time-continuous QND measurement. Such a scheme has the potential to access new regimes near the quantum-classical boundary, with opportunities to study long-standing issues related to quantum-classical correspondence in chaotic systems.
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.
Spin-polarised atomic ensembles probed by light based on the Faraday interaction are a versatile platform for numerous applications in quantum metrology and quantum information processing. Here we consider an ensemble of Alkali atoms that are continuously optically pumped and probed. Due to the collective scattering of photons at large optical depth, the steady state of atoms does not correspond to an uncorrelated tensor-product state, as is usually assumed. We introduce a self-consistent method to approximate the steady state including the pair correlations, taking into account the multilevel structure of atoms. We find and characterize regimes of Raman lasing, akin to the model of a superradiant laser. We determine the spectrum of the collectively scattered photons, which also characterises the coherence time of the collective spin excitations on top of the stationary correlated mean-field state, as relevant for applications in metrology and quantum information.
We investigate theoretically and experimentally a nondestructive interferometric measurement of the state population of an ensemble of laser-cooled and trapped atoms. This study is a step toward generation of (pseudo)spin squeezing of cold atoms targeted at the improvement of the cesium clock performance beyond the limit set by the quantum projection noise of atoms. We calculate the phase shift and the quantum noise of a near-resonant optical probe pulse propagating through a cloud of cold 133Cs atoms. We analyze the figure of merit for a quantum nondemolition (QND) measurement of the collective pseudospin and show that it can be expressed simply as a product of the ensemble optical density and the pulse-integrated rate of the spontaneous emission caused by the off-resonant probe light. Based on this, we propose a protocol for the sequence of operations required to generate and utilize spin squeezing for the improved atomic clock performance via a QND measurement on the probe light. In the experimental part we demonstrate that the interferometric measurement of the atomic population can reach a sensitivity of the order of Nat in a cloud of Nat cold atoms, which is an important benchmark toward the experimental realization of the theoretically analyzed protocol.