Quantum mechanics, since its very beginning, has totally changed the way we understand nature. The past hundred years have seen great successes in the application of quantum physics, including atomic spectra, laser technology, condensed matter physics and the remarkable possibility for quantum computing, etc. This thesis is dedicated to a small regime of quantum physics. In the first part of the thesis, I present the studies of atomic quasi-stable states, which refer to those Rydberg states of an atom that are relatively stable in the presence of strong fields. Through spectrally probing the quasi-stable states, series of survival peaks are found. If the quasi-stable electrons were created by ultraviolet (UV) lasers with two different frequencies, the survival peaks could be modulated by continuously changing the phase difference between the UV and the IR laser. The quantum simulation, through directly solving the Schrödinger equation, matches the experimental results performed with microwave fields, and our studies should provide a guidance for future experiments. Despite the huge achievements in the application of quantum theory, there are still some fundamental problems that remain unresolved. One of them is the so-called quantum-to-classical transition, which refers to the expectation that the system behaves in a more classical manner when the system size increases. This basic question was not well answered until decoherence theory was proposed, which states that the coherence of a quantum system tends to be destroyed by environmental interruptions. Thus, if a system is well isolated from its environment, it is in principle possible to observe macroscopic quantum coherence. Quite recently, testing quantum principles in the macroscale has become a hot topic due to rapic technological developments. A very promising platform for testing macroscale quantum physics is a laser levitated nanoparticle, and cooling its mechanical motion to the ground state is the first step. In the second part of this thesis, we develop the theory of decoherence for a mesoscopic system's rotational degrees of freedom. Combining decoherence in the translational degrees of freedom, the system's shot noise heating is discussed. We then focus on cooling the nanoparticle in the laser-shot-noise-dominant regime using two different feedback cooling schemes: the force feedback cooling and the parametric feedback cooling. Both quantum and classical calculations are performed, and an exact match is observed. We also explore the parameters that could possibly affect the cooling trend, where we find that the cooling limit for both cooling schemes strongly depends on the position measurement efficiency, and it poses good questions for researchers interested in achieving ground state cooling: what is the best measurement efficiency for a given measurement setup and what can be done to get a better measurement efficiency?
Quantum mechanics, since its very beginning, has totally changed the way we understand nature. The past hundred years have seen great successes in the application of quantum physics, including atomic spectra, laser technology, condensed matter physics and the remarkable possibility for quantum computing, etc. This thesis is dedicated to a small regime of quantum physics. In the first part of the thesis, I present the studies of atomic quasi-stable states, which refer to those Rydberg states of an atom that are relatively stable in the presence of strong fields. Through spectrally probing the quasi-stable states, series of survival peaks are found. If the quasi-stable electrons were created by ultraviolet (UV) lasers with two different frequencies, the survival peaks could be modulated by continuously changing the phase difference between the UV and the IR laser. The quantum simulation, through directly solving the Schrödinger equation, matches the experimental results performed with microwave fields, and our studies should provide a guidance for future experiments. Despite the huge achievements in the application of quantum theory, there are still some fundamental problems that remain unresolved. One of them is the so-called quantum-to-classical transition, which refers to the expectation that the system behaves in a more classical manner when the system size increases. This basic question was not well answered until decoherence theory was proposed, which states that the coherence of a quantum system tends to be destroyed by environmental interruptions. Thus, if a system is well isolated from its environment, it is in principle possible to observe macroscopic quantum coherence. Quite recently, testing quantum principles in the macroscale has become a hot topic due to rapic technological developments. A very promising platform for testing macroscale quantum physics is a laser levitated nanoparticle, and cooling its mechanical motion to the ground state is the first step. In the second part of this thesis, we develop the theory of decoherence for a mesoscopic system's rotational degrees of freedom. Combining decoherence in the translational degrees of freedom, the system's shot noise heating is discussed. We then focus on cooling the nanoparticle in the laser-shot-noise-dominant regime using two different feedback cooling schemes: the force feedback cooling and the parametric feedback cooling. Both quantum and classical calculations are performed, and an exact match is observed. We also explore the parameters that could possibly affect the cooling trend, where we find that the cooling limit for both cooling schemes strongly depends on the position measurement efficiency, and it poses good questions for researchers interested in achieving ground state cooling: what is the best measurement efficiency for a given measurement setup and what can be done to get a better measurement efficiency?
In this thesis novel methods for the laser cooling of quantum systems are presented. The use of quantum interference allows for the tailored cancelation of heating processes, so that an approximation to a cooling operator is possible that does not rely on the rotating wave approximation. This makes these schemes considerably faster and more efficient than existing ground state cooling methods, and allow for a significant relaxation of current experimental constraints. Several approaches are investigated in different systems. On the one hand, a special laser configuration, applicable to trapped ions, atoms or cantilevers, generates a double dark state that eliminates both the blue sideband and the carrier transition. As a consequence, vanishing phonon occupation up to first order in the perturbative expansion is achieved. Underlying this scheme is a combined action of two cooling schemes which makes the proposal very stable under parameter fluctuations. Its suitability as a cooling scheme for several ions in a trap or for a cloud of atoms in a dipole trap is shown. On the other hand, a pulsed cooling scheme for optomechanical systems is presented. It can be implemented for both strongly and weakly coupled optomechanical systems in both weakly and highly dissipative cavities. Its underlying mechanism is based on interferometric control of optomechanical interactions, and its efficiency is demonstrated with pulse sequences that are obtained by using methods from optimal control. Finally, it is shown how this pulsed method can be combined with continuous measurement to drive mechanical oscillators to highly squeezed steady states. Its mechanism relies on the modification of the dissipation and measurement terms, which drive the system towards a specific quadrature eigenstate. The scheme is robust to measurement inefficiencies and works also with highly dissipative cavities, which makes it accessible to implementation with state of the art technology.
Nanoscale systems represent a frontier in contemporary physics, where classical physics intersects with quantum mechanics, resulting in unique physical properties and phenomena. These properties not only deepen our understanding of fundamental physical principles but also enable the development of novel technological applications. Precise control over the state of systems at the nanoscale is essential for understanding and leveraging their full potential. The main objective of this thesis is to propose novel methods for the control of classical and quantum nanoscale systems, focusing both on theoretical understanding and practical implementation. In the first part of the thesis, we address the tayloring of pulse propagation inside waveguides, with applications for classical information processing and quantum technologies. The confinement of light fields to nanoscale sizes allows for exotic properties such as frequency dependent group velocity, discretization of the frequency spectrum and unconventional pulse propagation. This confinement also leads to an enhanced interaction with quantum emitters and results in interesting properties of light-matter interaction. In Chapter 2, we introduce a family of chirped pulses that dynamically self-compress during their evolution in a generic medium with a quadratic dispersion relation. We propose to use these pulses to remotely addresss individual quantum emitters embedded in the medium. In Chapter 3, we present an experimental demonstration of the proposal introduced in Chapter 2, performed in collaboration with the group of Prof. Kirchmair at IQOQI and the University of Innsbruck. We show self-compression of pulses inside a rectangular microwave waveguide and spatial addressing of two superconducting qubits separated by a sub-wavelength distance. In Chapter 4, we turn our attention to spin-wave pulses, namely excitations of the magnetization that propagate in a magnetic material. We provide a method based on inverse design to generate spin-wave pulses in magnonic waveguides with a desired spatial-temporal profile. In the second part of the thesis, we focus on the quantum control of the motional state of a levitated nanoparticle. This system presents a promising experimental platform for the exploration of quantum mechanics with mesoscopic objects, as they could allow for the observation of macroscopic quantum superposition states and matter-wave interferometry, and have applications as ultraprecise sensors. In Chapter 5, we introduce an optimization method to determine optimal static potentials for the generation of largely delocalized and non-Gaussian quantum states of levitated nanoparticles under decoherence.
The building blocks of Nature, namely atoms and elementary particles, are described by quantum mechanics. This fundamental theory is the ground on which physicists have built their major mathematical models [1]. Today, the unique features of quantum objects have led to the advent of promising quantum technologies [2, 3]. However, the macroscopic world is manifestly classical, and the nature of the quantum-to-classical crossover remains one of the most challenging open question of Science to date. In this respect, moving objects play a specific role [4, 5]. Pioneering experiments over the last few years have begun exploring quantum behaviour of micron-sized mechanical systems, adapting laser cooling techniques developed in atomic physics to cool specific modes far below the temperature of their surroundings [6-11]. Here instead we describe a very different approach, passive cooling of a micromechanical system down to 500 microK, reducing the average number of quanta in the fundamental vibrational mode to just 0.3; the challenge being to be still able to detect the motion without disturbing the system noticeably. With such an approach higher harmonics and the surrounding environment are also cooled, leading to potentially much longer mechanical coherence times, and enabling experiments questioning mechanical wave-function collapse [12], potentially from the gravitational background [13, 14], and quantum thermodynamics [15]. Beyond the average behaviour, here we also report on the fluctuations of the fundamental vibrational mode of the device in-equilibrium with the cryostat. These reveal a surprisingly complex interplay with the local environment and allow characteristics of two distinct thermodynamic baths to be probed.
The three experiments described in this thesis investigate fundamental properties of ultracold atoms. Using laser cooling and evaporative cooling, a dilute gas of sodium atoms is cooled to ~100 nK. Under these circumstances a Bose-Einstein condensate (BEC) forms, where millions of atoms collapse into the lowest energy state of the system and share a macroscopic wavefunction. The experiments are done in an ultrahigh vacuum and the atoms are manipulated remotely using laser beams, magnetic fields, and RF-fields. Using ultracold atoms allows unprecedented control over the internal and external degrees of freedom of the system, making it very suitable for precision measurements. Ultracold atoms also serve as a model system for more complicated or remote fields such as solid-state physics and cosmology. In the first experiment the refractive index of an ultracold bosonic gas is studied. The atomic clouds are analyzed for temperature and number of particles using nearly non-destructive phase-contrast imaging. After each pulse of probe light a small fraction of the atoms is lost, while the cloud is simultaneously slightly heated. This makes it possible to study the scattering rate as a function of temperature using only a single sample. It is observed that the scattering rate increases below the critical temperature for BEC by more than a factor of 3 compared to the classical value. This enhancement is in good agreement with the predictions by theoretical work that takes two-body correlation and the Lorentz-Lorenz correction into account. The method is also used to perform calorimetry on the Bose gas and directly measure the heat capacity of the BEC. The second chapter deals with magnetism in ultracold gases. When cooling an ultracold gas containing different spin components below the critical temperature for BEC, stable magnetic domains form. The appearance of these domains and the dynamics of the domain walls are studied. The spin mixture is prepared by performing an RF-sweep on ground state atoms in the presence of a magnetic field. Spin dynamics are induced by applying magnetic gradients. Spin drag, which is the transport coefficient responsible for damping spin currents, was measured in a two-component system. Furthermore a new method for spin resolved phase contrast imaging is presented, which is used to study time evolution in situ non-destructively. The last experiment focuses on spontaneous symmetry breaking. When passing a continuous phase transition, spontaneous symmetry breaking causes the development of domains with an independently chosen order parameter. The domains are separated by boundary defects. In this experiment the spontaneous creation of solitons was observed, which are boundary defects in the phase of the condensate, as well as magnetic domain walls, which are the boundary defects in the magnetization. Through the Kibble-Zurek mechanism it is possible to determine the critical exponents that characterize the phase transition. The critical exponents are predicted to be universal, i.e. do not depend on the microphysics of the system, so the results from our ultracold atoms lab can help answer universal questions for example from cosmology and from the early universe.
This thesis presents several experiments investigating the regimes of behaviour of a proto-typical open quantum many-body system far away from equilibrium. The experimental platform is based on ultracold atoms laser-excited to Rydberg states, which we engineer to emulate a strongly interacting, driven-dissipative quantum spin system. The high degree of control over the relevant microscopic processes and their parameters, as well as the ability to widely tune interaction and driving strengths provides the means to address fundamental questions on how different regimes of dynamical behaviour emerge in complex open quantum systems and how they can be characterised. \n \nIn the first part, we discuss how control over the relevant properties of Rydberg spin systems, like temperature, density, long evolution times, strong interactions, tunable driving, and dissipation can be achieved. We introduce the new experimental apparatus developed during this thesis, which combines both single-photon and two-photon Rydberg excitation schemes with high atom densities and long excitation times using an optical dipole trap. Additionally, we investigate theoretically how long coherence times exceeding motional timescales combined with strong many-body interactions can be achieved in such a system. We identify an optimal parameter regime for two-photon excitation where such conditions can be generated with coherence times and interaction strengths comparable to what is achievable for single-photon excitation. \n \nIn the second part we explore the macroscopic non-equilibrium behaviour of our system and devise suitable observables for characterising different regimes of behaviour. We discover that the slow atom loss inherent to our system provides a convenient observable for the many-body state of the system. Focussing on evolution times where the effect of the atom loss on the evolution is small, we discover that the rate of atom loss exhibits powerlaw scaling with the driving strength over several orders of magnitude. The measured scaling exponents reveal the non-equilibrium phase structure of the many-body system and allow us to distinguish dissipation-dominated, paramagnetic and critical regimes, as well as an instability. In the observed critical regime, collectively enhanced driving dominates over dissipation, leading to scaling associated to the critical point of the non-dissipative equilibrium Rydberg spin system. Based on the known microscopic processes of our system, we perform classical many-body rate equation simulations, which agree well with the observed phase structure as well as the position and associated scaling exponents of the individual regimes. These findings open up new means to study and classify out of equilibrium systems based on slow particle loss and powerlaw scaling. \n \nIn the last part of this thesis we reveal a second type of criticality in our system, which is genuinely non-equilibrium in character and arises from an absorbing state phase transition. The critical state of this phase transition dominates the system evolution at late times where particle loss is no longer negligible. We identify self-organisation as the mechanism driving the system to this critical state, which we observe through powerlaw scaling of the non-equilibrium steady-state. These experiments establish Rydberg atoms as a well controlled platform for implementing and exploring models of absorbing state phase transitions and self-organised criticality with unprecedented access to the underlying microscopic properties of the system.
State purity is a key resource for experimental tests of quantum mechanics with massive objects. Cavity cooling of a levitated nanoparticle via coherent scattering stands out as a strategy to prepare highly pure states of its roto-translational motion. In several cases, though, the performance of cooling by coherent scattering is limited by the classical fluctuations of the laser field. Here we present a quantum theory of coherent-scattering experiments which includes the effect of the laser amplitude and phase noise. We derive a master equation for the noise-averaged particle's dynamics, valid for both center-of-mass and rotational degrees of freedom, and quantify the cooling performance for different levels of noise in state-of-the-art experiments. We compute approximate analytical expressions for the laser-noise-induced heating rates and excess phonon number in both regimes of weak and strong optomechanical coupling. Moreover, our model can be applied to laser noise processes with generic power spectral densities and finite correlation times. This work offers a toolbox to quantify and optimize the state purity in coherent-scattering experiments, and opens new avenues towards the preparation of quantum states with levitated systems.