A cloud of ultracold atoms trapped within the confines of a high-finesse optical cavity shakes from the pressure of the light that probes it. This form of measurement backaction, a central component of quantum measurement theory, is the subject of this dissertation. Enlisting the collective motion of ultracold atoms as the mechanical degree of freedom in a cavity optomechanical system, we reach settings cold and quiet enough to allow for the effects of measurement backaction to manifest. We report predictions for and experimental observa- tions of the Standard Quantum Limit for force sensitivity, optical ponderomotive squeezing, and the possibility of complex squeezing through generalized optical correlations.
A cloud of ultracold atoms trapped within the confines of a high-finesse optical cavity shakes from the pressure of the light that probes it. This form of measurement backaction, a central component of quantum measurement theory, is the subject of this dissertation. Enlisting the collective motion of ultracold atoms as the mechanical degree of freedom in a cavity optomechanical system, we reach settings cold and quiet enough to allow for the effects of measurement backaction to manifest. We report predictions for and experimental observa- tions of the Standard Quantum Limit for force sensitivity, optical ponderomotive squeezing, and the possibility of complex squeezing through generalized optical correlations.
An exciting scientific goal, common to many fields of research, is the development of ever-larger physical systems operating in the quantum regime. Relevant to this dissertation is the objective of preparing and observing a mechanical object in its motional quantum ground state. In order to sense the object's zero-point motion, the probe itself must have quantum-limited sensitivity. Cavity optomechanics, the interactions between light and a mechanical object inside an optical cavity, provides an elegant means to achieve the quantum regime. In this dissertation, I provide context to the successful cavity-based optical detection of the quantum-ground-state motion of atoms-based mechanical elements; mechanical elements, consisting of the collective center-of-mass (CM) motion of ultracold atomic ensembles and prepared inside a high-finesse Fabry-P'erot cavity, were dispersively probed with an average intracavity photon number as small as 0.1. I first show that cavity optomechanics emerges from the theory of cavity quantum electrodynamics when one takes into account the CM motion of one or many atoms within the cavity, and provide a simple theoretical framework to model optomechanical interactions. I then outline details regarding the apparatus and the experimental methods employed, highlighting certain fundamental aspects of optical detection along the way. Finally, I describe background information, both theoretical and experimental, to two published results on quantum cavity optomechanics that form the backbone of this dissertation. The first publication shows the observation of zero-point collective motion of several thousand atoms and quantum-limited measurement backaction on that observed motion. The second publication demonstrates that an array of near-ground-state collective atomic oscillators can be simultaneously prepared and probed, and that the motional state of one oscillator can be selectively addressed while preserving the near-zero-point motion of neighboring oscillators.
Cavity Optomechanics, that is the study of the interaction between an optical cavity mode and a mechanical degree of freedom, has known impressive evolution over the past decade, to become a new field at the union of condensed matter physics and optics. One of the major goals of this discipline is to test and study quantum mechanics using macroscopic systems. Among the most fundamental problems the community aims to address is the question of the quantum limits in position measurement. Quantum mechanics predicts that any measurement comes along with a backaction, which perturbs the state of the measured system. Moreover, it is expected to be conjugated with the quantum noise of the measurement apparatus (called measurement noise) used to probe the system. The optimal sensitivity is reached whenever both the measurement and the backaction noise are identical, a situation which can be assimilated to the acceptance of Heisenberg's inequality for the measurement apparatus. In cavity optomechanics, the mode of an optical cavity is used as a measurement apparatus of the position of a mechanical resonator which is expected to be responsible for the backaction imprecision. However, this so-called radiation pressure quantum backaction has never been observed to date, while it remains a decisive step towards understanding quantum measurement processes. We describe in this manuscript the study of radiation pressure effects in cavity optomechanics. We introduce the optomechanical system we have developed, which consists in a cm-scale ultra high Q (~ 1 000 000) plano-convex mechanical resonator incorporated into a ultra-high finesse (~ 300 000) Fabry-Prot cavity. We present two important results we obtained with this system. First, we were able to report the first direct observation of radiation pressure in real-time, based on establishing pump-probe correlations. We were also able to demonstrate for the first time nonlinear backaction effects related to substantial improvement of position measurement sensitivity. We explain why demonstrating quantum backaction requires ultra-high stability of the optical mode. We present important changes made to the previous experimental setup, notably on the laser source, on the detection and the stabilization of the experiment. We then describe a new optomechanical detection technique providing an independent measurement of the cavity detuning. Finally, we present a proof-of-principle experiment allowing to extract quantum optomechanical correlations at room temperature.
The quantum nature of light makes it a basic component for models of quantum measurement and information exchange between disparate quantum modes, pioneered in the field of cavity quantum electrodynamics. The interaction of atomic ensembles with the mode of an optical cavity provides a flexible platform for exploring the coherent interaction of light with diverse macroscopic dynamics, such as collective motion and spin. This dissertation presents experimental results and theoretical models for continuous measurement and control of the center of mass motion and collective spin precession of an atomic ensemble, mediated by coupling to a high-finesse optical cavity. First, the theory of dispersive coupling between the cavity mode and the collective motion and spin of an atomic ensemble is derived, and then a general time-domain formalism is developed for theoretical analysis of multi-mode optodynamical systems. Single-mode optodynamical effects are introduced through experimental demonstrations of measurement and control of the collective atomic spin, providing a close analogy to cavity optomechanics.Next, multiple collective atomic modes are considered within a single cavity, in order to assemble optically mediated interactions within multi-mode optodynamical systems. A demonstration of optodynamical interactions between the center of mass motion of two atomic ensembles is presented, coupled through an optical spring mediated by the cavity mode. Then simultaneous coupling of the center of mass motion and total spin precession of a single ensemble of atoms is described, yielding an experimental realization of a negative-mass instability, facilitated by the novel resource of the spin ensembles inverted state. A theoretical analysis of the negative-mass instability is presented, which indicates the possibility of generating two-mode squeezed states in the absence of excess incoherent noise. Finally, linear state retrodiction from the optodynamical signals is discussed, providing background and supplemental material for a forthcoming manuscript.
The motion of sub-atomic particles is characteristically quantum mechanical in nature. In contrast, quantum aspects of the motion of massive, many-atom objects are typically obscured by high phonon occupation and thermal noise. This contrast is now diminishing, owing to research efforts to bring the control and measurement of macroscopic motion fully into the quantum regime, using objects with masses from attograms to kilograms. This achievement will be critical for constructing force detectors sensitive to gravitational waves, verifying the correspondence principle at macroscopic scales, and realizing protocols that mechanically store and exchange quantum information. Here, we directly observe the quantization of the collective motion of an ultracold atomic ensemble by measuring the inability of a 0.6 attogram centre-of-mass mode to emit energy from its ground state. Moreover, the optical output of our strongly coupled cavity-optomechanical system contains a spectroscopic record of the energy exchanged between light and motion, directly quantifying the heat deposited by a quantum position measurement's backaction. These results, in addition to providing a method for calibrating the motion of low-occupation mechanical systems, offer new possibilities for investigating collective modes of degenerate gases and for diagnosing optomechanical measurement backaction.
Cavity optomechanics originated from the research of interferometric detection of gravitational waves, and later became a fast-growing area of techniques and approaches ranging from the fields of atomic, molecular, and optical physics to nano-science and condensed matter physics as well. Recently, it focused on the exploration of operating mechanical oscillators deep in the quantum regime, with an interest ranging from quantum-classical interface tests to high-precision quantum metrology. In this paper, recent theoretical work of our group in the field of quantum measurement with cavity optomechanical systems is reviewed. We explore the quantum measurement theory and its applications with several unconventional cavity optomechanical schemes working in the quantum regime. This review covers the basics of quantum noises in the cavity optomechanical setups and the resulting standard quantum limit of precision displacement and force measurement. Three novel quantum measurement proposals based on the hybrid optomechanical system are introduced. First, we describe a quantum back-action insulated weak force sensor. It is realized by forming a quantum-mechanics-free subsystem with two optomechanical oscillators of reversed effective mass. Then we introduce a role-reversed atomic optomechanical system which enables the preparation and the quantum tomography of a variety of non-classical states of atoms. In this system, the cavity field acts as a mechanical oscillator driven by the radiation pressure force from an ultracold atomic field. In the end, we recommend a multimode optomechanical transducer that can detect intensities significantly below the single-photon level via adiabatic transfer of the microwave signal to the optical frequency domain. These proposals demonstrate the possible applications of optomechanical devices in understanding of quantum-classical crossover and in achieving quantum measurement limit.
Why are classical theories often sufficient to describe the physics of our world even though everything around us is entirely composed of microscopic quantum systems? The boundary between these two fundamentally dissimilar theories remains an unsolved problem in modern physics. Position measurements of small objects allow us to probe the area where the classical approximation breaks down. In quantum mechanics, Heisenbergâ s uncertainty principle dictates that any measurement of the position must be accompanied by measurement induced back-action---in this case manifested as an uncertainty in the momentum. In recent years, cavity optomechanics has become a powerful tool to perform precise position measurements and investigate their fundamental limitations. The utilization of optical micro-cavities greatly enhances the interaction between light and state-of-the-art nanomechanical oscillators. Therefore, quantum mechanical phenomena have been successfully observed in systems far beyond the microscopic world. In such a cavity optomechanical system, the fluctuations in the position of the oscillator are transduced onto the phase of the light, while fluctuations in the amplitude of the light disturb the momentum of the oscillator during the measurement. As a consequence, correlations are established between the amplitude and phase quadrature of the probe light. However, so far, observation of quantum effects has been limited exclusively to cryogenic experiments, and access to the quantum regime at room temperature has remained an elusive goal because the overwhelming amount of thermal motion masks the weak quantum effects. This thesis describes the engineering of a high-performance cavity optomechanical device and presents experimental results showing, for the first time, the broadband effects of quantum back-action at room temperature. The device strongly couples mechanical and optical modes of exceptionally high quality factors to provide a measurement sensitivity ∼104 times below the requirement to resolve the zero-point fluctuations of the mechanical oscillator. The quantum back-action is then observed through the correlations created between the probe light and the motion of the nanomechanical oscillator. A so-called â variational measurementâ , which detects the transmitted light in a homodyne detector tuned close to the amplitude quadrature, resolves the quantum noise due to these correlations at the level of 10\% of the thermal noise over more than an octave of Fourier frequencies around mechanical resonance. Moreover, building on this result, an additional experiment demonstrates the ability to achieve quantum enhanced metrology. In this case, the generated quantum correlations are used to cancel quantum noise in the measurement record, which then leads to an improved relative signal-to-noise ratio in measurements of an external force. In conclusion, the successful observation of broadband quantum behavior on a macroscopic object at room temperature is an important milestone in the field of cavity optomechanics. Specifically, this result heralds the rise of optomechanical systems as a platform for quantum physics at room temperature and shows promise for generation of ponderomotive squeezing in room-temperature interferometers.