Quantum metrology uses quantum features such as entanglement and squeezing to improve the sensitivity of quantum-limited measurements. Long established as a valuable technique in optical measurements such as gravitational-wave detection, quantum metrology is increasingly being applied to atomic instruments such as matter-wave interferometers, atomic clocks, and atomic magnetometers. Several of these new applications involve dual optical/atomic quantum systems, presenting both new challenges and new opportunities. Here we describe an optical magnetometry system that achieves both shot-noise-limited and projection-noise-limited performance, allowing study of optical magnetometry in a fully-quantum regime [1]. By near-resonant Faraday rotation probing, we demonstrate measurement-based spin squeezing in a magnetically-sensitive atomic ensemble [2-4]. The versatility of this system allows us also to design metrologically-relevant optical nonlinearities, and to perform quantum-noise-limited measurements with interacting photons. As a first interaction-based measurement [5], we implement a non-linear metrology scheme proposed by Boixo et al. with the surprising feature of precision scaling better than the 1/N “Heisenberg limit” [6].
Quantum metrology uses quantum features such as entanglement and squeezing to improve the sensitivity of quantum-limited measurements. Long established as a valuable technique in optical measurements such as gravitational-wave detection, quantum metrology is increasingly being applied to atomic instruments such as matter-wave interferometers, atomic clocks, and atomic magnetometers. Several of these new applications involve dual optical/atomic quantum systems, presenting both new challenges and new opportunities. Here we describe an optical magnetometry system that achieves both shot-noise-limited and projection-noise-limited performance, allowing study of optical magnetometry in a fully-quantum regime [1]. By near-resonant Faraday rotation probing, we demonstrate measurement-based spin squeezing in a magnetically-sensitive atomic ensemble [2-4]. The versatility of this system allows us also to design metrologically-relevant optical nonlinearities, and to perform quantum-noise-limited measurements with interacting photons. As a first interaction-based measurement [5], we implement a non-linear metrology scheme proposed by Boixo et al. with the surprising feature of precision scaling better than the 1/N “Heisenberg limit” [6].
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.
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.
Measurements with quantum limited resolution have important applications in metrology and sensing, including atomic clocks, atom interferometry, and magnetometry. We perform a quantum-non-demolition measurement on a collective angular momentum of a million spin-4 Cs atoms with high optical depth in our work. Quantum mechanics limits the measurement's resolution to what is known as the standard quantum limit (SQL) when there is no entanglement between the individual atoms. We can generate entanglement between atoms to create spin squeezed states through quantum backaction, improving the measurement sensitivity by 5.5 dB relative to the SQL. We have recently rebuilt the entire experiment inside a state-of-the-art magnetic shield of mu-metal and aluminum. This upgrade has drastically mitigated classical control errors in the spin squeezing experiment. Furthermore, the ensemble's sensitivity to magnetic fields allows us to make precise measurements of the magnetic field environment. Using closed-loop feedback, we use our atomic magnetometer to measure magnetic fields 4.3 dB below the SQL. The shielded environment will allow us to optimize the magnetometer and sets the stage for future experiments to use the closed-loop control to explore more complicated quantum dynamics.
We consider the limitations due to noise (e.g., quantum projection noise and photon shot-noise) on the sensitivity of an idealized atomic magnetometer that utilizes spin squeezing induced by a continuous quantum nondemolition measurement. Such a magnetometer measures spin precession of N atomic spins by detecting optical rotation of far-detuned light. We show that for very short measurement times, the optimal sensitivity scales as ${N}^{\ensuremath{-}3/4}$; if strongly squeezed probe light is used, the Heisenberg limit of ${N}^{\ensuremath{-}1}$ scaling can be achieved. However, if the measurement time exceeds ${\ensuremath{\tau}}_{\mathrm{r}\mathrm{e}\mathrm{l}}/{N}^{1/2}$ in the former case, or ${\ensuremath{\tau}}_{\mathrm{r}\mathrm{e}\mathrm{l}}/N$ in the latter, where ${\ensuremath{\tau}}_{\mathrm{r}\mathrm{e}\mathrm{l}}$ is the spin relaxation time, the scaling becomes ${N}^{\ensuremath{-}1/2}$, as for a standard shot-noise-limited magnetometer.
We consider the limitations due to noise (e.g., quantum projection noise and photon shot-noise) on the sensitivity of an idealized atomic magnetometer that utilizes spin squeezing induced by a continuous quantum nondemolition measurement. Such a magnetometer measures spin precession of N atomic spins by detecting optical rotation of far-detuned light. We show that for very short measurement times, the optimal sensitivity scales as N-3/4; if strongly squeezed probe light is used, the Heisenberg limit of N-1 scaling can be achieved. However, if the measurement time exceeds tau(rel)/N-1/2 in the former case, or tau(rel)/N in the latter, where tau(rel) is the spin relaxation time, the scaling becomes N-1/2, as for a standard shot-noise-limited magnetometer.