This thesis presents theoretical research on microscopic measuring devices and thermal machines constructed from single trapped atoms. We study several variants on this theme, with a particular emphasis on their application to ultracold atom physics. The first part of the thesis is about quantum refrigerators powered by thermal absorption rather than by external work. We propose and detail how such a machine may be practically constructed with a trapped atom placed inside an optical cavity, and employed to cool the atom close to absolute zero temperature using only collimated sunlight as an energy source. We then show that quantum absorption refrigerators in the strong-coupling regime exhibit coherent oscillations, thus enabling one to outperform a typical classical refrigerator by reaching lower temperatures than the steady state in a finite time using quantum coherence. The second part of the thesis studies the use of impurity atoms as probes of ultracold atomic gases. We discuss two different thermometry methods using impurities which are sensitive to temperature differences on the order of nanokelvin or less. We characterise the precision of the proposed thermometers by explicit calculations in the context of both weakly and strongly interacting atomic Bose gases. Finally, we study impurities immersed in a cold atomic Fermi gas realising a superfluid. We show that the impurities' energy dissipation rate probes the spectrum of density fluctuations in the gas, providing nondestructive access to various properties of the superfluid order parameter along the crossover from a Bardeen-Cooper-Schrieffer (BCS) state to a Bose-Einstein condensate (BEC).
This thesis presents theoretical research on microscopic measuring devices and thermal machines constructed from single trapped atoms. We study several variants on this theme, with a particular emphasis on their application to ultracold atom physics. The first part of the thesis is about quantum refrigerators powered by thermal absorption rather than by external work. We propose and detail how such a machine may be practically constructed with a trapped atom placed inside an optical cavity, and employed to cool the atom close to absolute zero temperature using only collimated sunlight as an energy source. We then show that quantum absorption refrigerators in the strong-coupling regime exhibit coherent oscillations, thus enabling one to outperform a typical classical refrigerator by reaching lower temperatures than the steady state in a finite time using quantum coherence. The second part of the thesis studies the use of impurity atoms as probes of ultracold atomic gases. We discuss two different thermometry methods using impurities which are sensitive to temperature differences on the order of nanokelvin or less. We characterise the precision of the proposed thermometers by explicit calculations in the context of both weakly and strongly interacting atomic Bose gases. Finally, we study impurities immersed in a cold atomic Fermi gas realising a superfluid. We show that the impurities' energy dissipation rate probes the spectrum of density fluctuations in the gas, providing nondestructive access to various properties of the superfluid order parameter along the crossover from a Bardeen-Cooper-Schrieffer (BCS) state to a Bose-Einstein condensate (BEC).
In this habilitation-thesis a collection of 14 experiments is presented. In these experiments we have developed and used novel techniques to control ultracold gases on the quantum level. In brief, Bose-Einstein condensates (BEC) and degenerate Fermi gases of laser-cooled alkali atoms are subjected to specially designed optical and magnetic fields. The fields influence in a coherent way the behavior, properties and dynamics of the gases. On this basis we developed tools to prepare, coherently manipulate, and analyze pre-defined quantum states. With this high level of control, it was possible to investigate interesting physics phenomena, and we were able to achieve several breakthroughs in the field of ultracold atoms. Highlights of our experimental results include the demonstration of phase engineering of a BEC wavefunction where we created solitons in a BEC and studied their propagation. In another experiment we constructed a spatially resolved matter wave interferometer with which we mapped out the phase distribution on a condensate. Illuminating the BEC with a periodic pattern, i.e. an optical lattice, allowed us to study solid states physics phenomena. In a second set of experiments we demonstrated optically tuning of the interaction between atoms with optical Feshbach resonances. Employing either magnetically tunable Feshbach resonances or laser radiation, we were able to produce ground state molecules in well defined quantum states. This led to the production of the first molecular BEC. By tuning the coupling of atom pairs in a Fermi gas of atoms, we could for the first time investigate the so-called BEC-BCS crossover which describes the continuous change from a BEC superfluid to a Bardeen-Cooper Schrieffer (BCS) superfluid. Due to the excellent control on the quantum level, the developed cold atom techniques open up intriguing prospects for future applications and experiments. They represent a general tool box to investigate fundamental physical phenomena in a pure and undisturbed environment. In the future, cold atoms might serve as a testing ground for fundamental theories or as quantum simulators for complex systems.
The quantum many-body problem is at the heart of some of the most formidable open problems in modern physics, such as high-Tc superconductivity or the behaviour of neutron stars. Ultracold atomic systems can now be used to simulate model Hamiltonians of condensed matter or nuclear physics, in very well-controlled environnement. In this thesis, we have developed a general method to probe the thermodynamics of homogeneous quantum systems using trapped atomic gases. These measurements are directly compared to the predictions of theories of the quantum many-body problem. We have applied this technique to the spin-1/2 Fermi gas and the Bose with short-range interactions. Using fermionic 6Li, we explored a part of the wide parameter space by changing the interaction strength, the spin-population imbalance or the temperature of the gas. This system exhibits remarkably rich physics, such as normal/superfluid phase transitions (that can be of thermal or quantum character) or a Fermi liquid-type behaviour of the normal phase. We have also used this method to probe a Bose gas of 7Li atoms close to a Feshbach resonance. We have measured the Equation of State of the Bose gas as a function of interactions at very low temperature. For the first time, we measured quantitatively the Lee-Huang-Yang beyond mean-field correction to the ground-state energy of the system, first predicted in 1957. We compared the experimental results to Quantum Monte-Carlo calculations. We have extended this study using out-of-equilibrium measurements of the Bose gas in the strongly interacting regime, which gives a first hint on the properties of the hypothetical unitary Bose gas.
In this thesis we discuss several aspects of ultracold atomic systems and their applications to quantum simulation. These topics cover a degenerate gas near a Feshbach resonance, superfluids in an optical lattice, trapped-ion quantum computation and simulation. We study a degenerate Fermi gas when the interaction is tuned from the Bose-Einstein Condensation (BEC) side to the Bardeen-Cooper-Schrieffer (BCS) side, investigating effects due to population and mass imbalance. We identify various phases and find that an superfluid shell can be observed within a trap because of the mass mismatch. We study a Fermi gas in a quasi-two-dimensional geometry formed by optical lattices. A two-channel model is proposed to describe the BEC-BCS crossover physics. We find that the higher band excitations are significant and contribute to the closed channel as effective Feshbach ``dressed molecules''. This model predicts a decrease in the cloud size as the interaction is tuned from the BCS side to the BEC side. To investigate superfluidity of bosons in an optical lattice, we calculate the momentum distribution related to the time-of-flight (TOF) interference patterns at finite temperature. We find that a distinct bimodal distribution of the TOF image is presented as long as superfluids emerge, and hence can be used as a reliable signature indicating onset of superfluidity. We propose a large-scale quantum computer architecture by stabilizing a one-dimensional ion chain in a simple linear trap geometry. By arranging ions uniformly through optimizing the anharmonic trap potential, we show that high-fidelity quantum gates can be realized in large ion crystals under the Doppler temperature based on coupling to a near-continuum of transverse motional modes with simple shaped laser pulses. Finally, we demonstrate the trapped ion quantum simulation of the Ising model. Through control of the laser detuning, various coupling networks can be realized. We give a detailed discussion of the frustrated nature in three-ion cases and show achievable phases for larger systems. A comparison of our calculation and experimental data is presented.
Thermometry is essential for studying many-body physics with ultracold atoms. Accurately measuring low temperatures in these systems, however, remains a significant challenge due to the absence of a universal thermometer. Most widely applicable methods, such as fitting of in situ density profiles, are limited by the requirement of global thermal equilibrium and inapplicability to homogeneous systems. In this Letter, we introduce a novel in situ thermometry for quantum gases, leveraging single-atom-resolved measurements via quantum gas microscopy, and demonstrate it on an ideal Fermi gas. By analyzing number fluctuations in probe volumes containing as little as one atom on average, we extract both global and local temperatures over a broad dynamic range. Our method does not rely on the fluctuation-dissipation theorem and is based instead on the exact relationship between number fluctuations and density-density correlations. In the low-temperature regime, it allows us to observe significant deviations from fluctuation-dissipation predictions, uncovering subextensive fluctuations. Our method is applicable to systems with arbitrary trapping potentials, requiring neither precise trap calibration nor global thermal equilibrium. This thermometer for quantum gases overcomes key limitations of existing techniques, paving the way for more accurate and versatile temperature measurements in ultracold quantum systems.
Ultracold atoms are exceptional tools to explore the physics of quantum matter. In fact, the high degree of tunability of ultracold Bose and Fermi gases makes them ideal systems for quantum simulation and for investigating macroscopic manifestations of quantum effects, such as superfluidity. In ultracold gas research, a central role is played by collective oscillations. They can be used to study different dynamical regimes, such as superfluid, collisional, or collisionless limits or to test the equation of state of the system. In this thesis, we present a unified description of collective oscillations in low dimensions covering both Bose and Fermi statistics, different trap geometries and zero as well as finite temperature, based on the formalism of hydrodynamics and sum rules. We discuss the different behaviour exhibited by the second excited breathing mode in the collisional regime at low temperature and in the collisionless limit at high temperature in a 1D trapped Bose gas with repulsive contact interaction. We show how this mode exhibits a single-valued excitation spectrum in the collisional regime and two different frequencies in the collisionless limit. Our predictions could be important for future research related to the thermalization and damping phenomena in this low-dimensional system. We show that 1D uniform Bose gases exhibit a non-monotonic temperature dependence of the chemical potential characterized by an increasing-with-temperature behaviour at low temperature. This is due to the thermal excitation of phonons and reveals an interesting analogy with the behaviour of superfluids. Finally, we investigate a gas with a finite number N of atoms in a ring geometry at T = 0. We discuss explicitly the deviations of the thermodynamic behaviour in the ring from the one in the large N limit.
We study an impurity atom trapped by an anharmonic potential, immersed within a cold atomic Fermi gas with attractive interactions that realizes the crossover from a Bardeen-Cooper-Schrieffer superfluid to a Bose-Einstein condensate. Considering the qubit comprising the lowest two vibrational energy eigenstates of the impurity, we demonstrate that its dynamics probes the equilibrium density fluctuations encoded in the dynamic structure factor of the superfluid. Observing the impurity's evolution is thus shown to facilitate nondestructive measurements of the superfluid order parameter and the contact between collective and single-particle excitation spectra. Our setup constitutes a model of an open quantum system interacting with a thermal reservoir, the latter supporting both bosonic and fermionic excitations that are also coupled to each other.