Microscopy of quantum many-body systems out of equilibrium

Quantensimulatoren können die Grenzen von analytischen und numerischen Methoden überwinden und detaillierte Informationen über stark korrelierte Vielteilchensysteme liefern. Für die experimentelle Erforschung komplexer Problemstellungen bieten Quantengase vielfältige Möglichkeiten und profitieren von der herausragenden Isolation von externen Störungen. Diese Promotionsarbeit befasst sich mit dem experimentellen Studium von Quantensystemen, die kontrolliert aus dem Gleichgewicht gebracht werden. Mit Einzelplatz aufgelöster Abbildung von bosonischen Rubidium Atomen in optischen Gittern wird die zeitliche Entwicklung festgehalten. Quantenmagnetismus ist der erste behandelte Schwerpunkt in dieser Arbeit. Zuerst zeigen wir, dass im Regime von starker Wechselwirkung,in welchem sich ein Mott Isolator bildet, ein zwei komponentiges Gas exzellent das Heisenberg Model simuliert. Hierzu vermessen wir die kohärente Ausbreitung eines Magnons mit der spinselektiven Abbildung nach einer lokalen Anregung eines einzelnen Spins. Spinprojektionen auf die $z$-Achse und den Äquator der Bloch-Kugel belegen die Entstehung und Propagation von verschränkten Zuständen. Detaillierte Informationen werden in diesem Experiment durch eine neu entwickelte Abbildung gewonnen, welche an Stern-Gerlach Messungen angelehnt ist. Bei der Anregung zweier benachbarter Spins wird des Weiteren die Entstehung gebundener Zustände beobachtet und deren Ausbreitungsgeschwindigkeit sowie Zerfallszeit charakterisiert. In weiterführenden Messungen erzeugen wir hochangeregte Spiralzustände, die in einen homogenen Gleichgewichtszustand zerfallen und keine kohärente Zeitentwicklung aufweisen. Die Geschwindigkeit der beobachteten Zerfälle ist abhängig von der Windungsstärke und weist in eindimensionalen Systemen auf ein diffusives Verhalten hin. Im Gegensatz dazu deuten die Ergebnisse in zweidimensionalen Systemen auf ein sub-diffusive Propagation hin. Der zweite Schwerpunkt dieser Arbeit behandelt die Thermalisierung von hoch angeregten Systemen. Wir ermitteln wie stark eine zusätzlich eingestrahlte computergenerierte zufällige Potentiallandschaft sein muss, um zu einer Lokalisierung der Atome zu führen. Von diesen entstehenden lokalisierten Vielteilchenzustände wird die Zerfallslänge der Dichteverteilung bestimmt, welche am Phasenübergang eine Divergenz zeigt. Die in dieser Arbeit beschriebenen Experimente demonstrieren unterschiedliche Realisierungen von Quantensimulationen. Viele weitere Effekte im Bereich der Quantenmechanik können mit der hier dargelegten Technik untersucht werden. Weitere Messungen profitieren insbesondere von der nachgewiesenen präzisen Anfangszustandspräparation, basierend auf der Kontrolle jedes einzelnen Atomes in wechselwirkenden Vielteilchensystemen, und der ortsaufgelösten Erfassung von einzelnen Atomen. Dieses wird in Zukunft einen wesentlichen Beitrag zur Informationsgewinnung über komplexe verschränkte Systeme liefern können.Quantum simulators can overcome the limits of analytical and numerical methods and deliver detailed information about strongly correlated many-body systems. For the experimental exploration of complex problems, quantum gases offer versatile possibilities and profit from the outstanding isolation from external disturbances. This doctoral thesis deals with the experimental study of quantum systems, which are controllably moved out of equilibrium. The temporal evolution is recorded with single-site resolved imaging of bosonic Rubidium atoms in optical lattices. Quantum magnetism is the first examined main topic of this thesis. At first, we reveal that a two component gas is well suited to simulate the Heisenberg model in the regime of strong interaction and under the formation of a Mott insulating state. Therefore, we survey, after a local excitation of a single spin, the coherent expansion of a magnon with spin selective imaging. Utilizing spin projections on the $z$-axis and the equator of the Bloch sphere, the creation and propagation of entangled states is observed. In this experiment, detailed information are extracted with the newly developed Stern-Gerlach like imaging. Furthermore, the emergence and expansion velocity of bound states after the excitation of two neighboring spins is surveyed. The experiments are extended to highly excited spiral states, which decay to homogeneous equilibrium states and do not indicate coherent evolution. The determined decay rate depends on the winding strength and manifests a diffusive behavior in one dimensional systems. In contrast, measurements in two dimensional systems point towards a sub-diffusive evolution. The second main focus of this theses is the thermalization of highly excited states. We investigate how strong an additional computer generated random potential needs to be in order to lead to localization of the atoms. The decay length of the corresponding density distribution of the arising many-body localized states is quantified, which diverges at the phase transition. The experiments characterized in this thesis demonstrate different realizations of quantum simulation. Several further effects in the field of quantum mechanics can be studied with the here demonstrated techniques. Further research will in particular benefit from the precise initial state manipulation, based on the control of every single atom within the many-body interacting system, and the spin selective spatial resolved detection of single atoms. In the future, this will yield a substantial contribution to the acquisition of information on complex entangled systems

Microscopy of a scalable superatom

Strong interactions can amplify quantum effects such that they become important on macroscopic scales. Controlling these coherently on a single particle level is essential for the tailored preparation of strongly correlated quantum systems and opens up new prospects for quantum technologies. Rydberg atoms offer such strong interactions which lead to extreme nonlinearities in laser coupled atomic ensembles. As a result, multiple excitation of a Micrometer sized cloud can be blocked while the light-matter coupling becomes collectively enhanced. The resulting two-level system, often called "superatom", is a valuable resource for quantum information, providing a collective Qubit. Here we report on the preparation of two orders of magnitude scalable superatoms utilizing the large interaction strength provided by Rydberg atoms combined with precise control of an ensemble of ultracold atoms in an optical lattice. The latter is achieved with sub shot noise precision by local manipulation of a two-dimensional Mott insulator. We microscopically confirm the superatom picture by in-situ detection of the Rydberg excitations and observe the characteristic square root scaling of the optical coupling with the number of atoms. Furthermore, we verify the presence of entanglement in the prepared states and demonstrate the coherent manipulation of the superatom. Finally, we investigate the breakdown of the superatom picture when two Rydberg excitations are present in the system, which leads to dephasing and a loss of coherence.Comment: 7 pages, 5 figure

Microscopy of quantum many-body systems out of equilibrium

Quantensimulatoren können die Grenzen von analytischen und numerischen Methoden überwinden und detaillierte Informationen über stark korrelierte Vielteilchensysteme liefern. Für die experimentelle Erforschung komplexer Problemstellungen bieten Quantengase vielfältige Möglichkeiten und profitieren von der herausragenden Isolation von externen Störungen. Diese Promotionsarbeit befasst sich mit dem experimentellen Studium von Quantensystemen, die kontrolliert aus dem Gleichgewicht gebracht werden. Mit Einzelplatz aufgelöster Abbildung von bosonischen Rubidium Atomen in optischen Gittern wird die zeitliche Entwicklung festgehalten. Quantenmagnetismus ist der erste behandelte Schwerpunkt in dieser Arbeit. Zuerst zeigen wir, dass im Regime von starker Wechselwirkung,in welchem sich ein Mott Isolator bildet, ein zwei komponentiges Gas exzellent das Heisenberg Model simuliert. Hierzu vermessen wir die kohärente Ausbreitung eines Magnons mit der spinselektiven Abbildung nach einer lokalen Anregung eines einzelnen Spins. Spinprojektionen auf die $z$-Achse und den Äquator der Bloch-Kugel belegen die Entstehung und Propagation von verschränkten Zuständen. Detaillierte Informationen werden in diesem Experiment durch eine neu entwickelte Abbildung gewonnen, welche an Stern-Gerlach Messungen angelehnt ist. Bei der Anregung zweier benachbarter Spins wird des Weiteren die Entstehung gebundener Zustände beobachtet und deren Ausbreitungsgeschwindigkeit sowie Zerfallszeit charakterisiert. In weiterführenden Messungen erzeugen wir hochangeregte Spiralzustände, die in einen homogenen Gleichgewichtszustand zerfallen und keine kohärente Zeitentwicklung aufweisen. Die Geschwindigkeit der beobachteten Zerfälle ist abhängig von der Windungsstärke und weist in eindimensionalen Systemen auf ein diffusives Verhalten hin. Im Gegensatz dazu deuten die Ergebnisse in zweidimensionalen Systemen auf ein sub-diffusive Propagation hin. Der zweite Schwerpunkt dieser Arbeit behandelt die Thermalisierung von hoch angeregten Systemen. Wir ermitteln wie stark eine zusätzlich eingestrahlte computergenerierte zufällige Potentiallandschaft sein muss, um zu einer Lokalisierung der Atome zu führen. Von diesen entstehenden lokalisierten Vielteilchenzustände wird die Zerfallslänge der Dichteverteilung bestimmt, welche am Phasenübergang eine Divergenz zeigt. Die in dieser Arbeit beschriebenen Experimente demonstrieren unterschiedliche Realisierungen von Quantensimulationen. Viele weitere Effekte im Bereich der Quantenmechanik können mit der hier dargelegten Technik untersucht werden. Weitere Messungen profitieren insbesondere von der nachgewiesenen präzisen Anfangszustandspräparation, basierend auf der Kontrolle jedes einzelnen Atomes in wechselwirkenden Vielteilchensystemen, und der ortsaufgelösten Erfassung von einzelnen Atomen. Dieses wird in Zukunft einen wesentlichen Beitrag zur Informationsgewinnung über komplexe verschränkte Systeme liefern können.Quantum simulators can overcome the limits of analytical and numerical methods and deliver detailed information about strongly correlated many-body systems. For the experimental exploration of complex problems, quantum gases offer versatile possibilities and profit from the outstanding isolation from external disturbances. This doctoral thesis deals with the experimental study of quantum systems, which are controllably moved out of equilibrium. The temporal evolution is recorded with single-site resolved imaging of bosonic Rubidium atoms in optical lattices. Quantum magnetism is the first examined main topic of this thesis. At first, we reveal that a two component gas is well suited to simulate the Heisenberg model in the regime of strong interaction and under the formation of a Mott insulating state. Therefore, we survey, after a local excitation of a single spin, the coherent expansion of a magnon with spin selective imaging. Utilizing spin projections on the $z$-axis and the equator of the Bloch sphere, the creation and propagation of entangled states is observed. In this experiment, detailed information are extracted with the newly developed Stern-Gerlach like imaging. Furthermore, the emergence and expansion velocity of bound states after the excitation of two neighboring spins is surveyed. The experiments are extended to highly excited spiral states, which decay to homogeneous equilibrium states and do not indicate coherent evolution. The determined decay rate depends on the winding strength and manifests a diffusive behavior in one dimensional systems. In contrast, measurements in two dimensional systems point towards a sub-diffusive evolution. The second main focus of this theses is the thermalization of highly excited states. We investigate how strong an additional computer generated random potential needs to be in order to lead to localization of the atoms. The decay length of the corresponding density distribution of the arising many-body localized states is quantified, which diverges at the phase transition. The experiments characterized in this thesis demonstrate different realizations of quantum simulation. Several further effects in the field of quantum mechanics can be studied with the here demonstrated techniques. Further research will in particular benefit from the precise initial state manipulation, based on the control of every single atom within the many-body interacting system, and the spin selective spatial resolved detection of single atoms. In the future, this will yield a substantial contribution to the acquisition of information on complex entangled systems

Spatially Resolved Detection of a Spin-Entanglement Wave in a Bose-Hubbard Chain

Entanglement is an essential property of quantum many-body systems. However, its local detection is challenging and was so far limited to spin degrees of freedom in ion chains. Here we measure entanglement between the spins of atoms located on two lattice sites in a one-dimensional Bose-Hubbard chain which features both local spin- and particle-number fluctuations. Starting with an initially localized spin impurity, we observe an outwards propagating entanglement wave and show quantitatively how entanglement in the spin sector rapidly decreases with increasing particle-number fluctuations in the chain.Comment: 6 pages, 4 figure

A new type of quantum speed meter interferometer: measuring speed to search for intermediate mass black holes

The recent discovery of gravitational waves (GW) by LIGO has impressively launched the novel field of gravitational astronomy and it allowed us to glimpse at exciting objects we could so far only speculate about. Further sensitivity improvements at the low frequency end of the detection band of future GW observatories rely on quantum non-demolition (QND) methods to suppress fundamental quantum fluctuations of the light fields used to readout the GW signal. Here we invent a novel concept of how to turn a conventional Michelson interferometer into a QND speed meter interferometer with coherently suppressed quantum back-action noise by using two orthogonal polarisations of light and an optical circulator to couple them. We carry out a detailed analysis of how imperfections and optical loss influence the achievable sensitivity and find that the configuration proposed here would significantly enhance the low frequency sensitivity and increase the observable event rate of binary black hole coalescences in the range of $10^2-10^3 M_\odot$ by a factor of up to $\sim300$.Comment: 8 pages, 5 figures. Modified figures and text in v

Local-Oscillator Noise Coupling in Balanced Homodyne Readout for Advanced Gravitational Wave Detectors

The second generation of interferometric gravitational wave detectors are quickly approaching their design sensitivity. For the first time these detectors will become limited by quantum back-action noise. Several back-action evasion techniques have been proposed to further increase the detector sensitivity. Since most proposals rely on a flexible readout of the full amplitude- and phase-quadrature space of the output light field, balanced homodyne detection is generally expected to replace the currently used DC readout. Up to now, little investigation has been undertaken into how balanced homodyne detection can be successfully transferred from its ubiquitous application in table-top quantum optics experiments to large-scale interferometers with suspended optics. Here we derive implementation requirements with respect to local oscillator noise couplings and highlight potential issues with the example of the Glasgow Sagnac Speed Meter experiment, as well as for a future upgrade to the Advanced LIGO detectors.Comment: 7 pages, 5 figure

Effects of static and dynamic higher-order optical modes in balanced homodyne readout for future gravitational waves detectors

With the recent detection of Gravitational waves (GW), marking the start of the new field of GW astronomy, the push for building more sensitive laser-interferometric gravitational wave detectors (GWD) has never been stronger. Balanced homodyne detection (BHD) allows for a quantum noise (QN) limited readout of arbitrary light field quadratures, and has therefore been suggested as a vital building block for upgrades to Advanced LIGO and third generation observatories. In terms of the practical implementation of BHD, we develop a full framework for analyzing the static optical high order modes (HOMs) occurring in the BHD paths related to the misalignment or mode matching at the input and output ports of the laser interferometer. We find the effects of HOMs on the quantum noise limited sensitivity is independent of the actual interferometer configuration, e.g. Michelson and Sagnac interferometers are effected in the same way. We show that misalignment of the output ports of the interferometer (output misalignment) only effects the high frequency part of the quantum noise limited sensitivity (detection noise). However, at low frequencies, HOMs reduce the interferometer response and the radiation pressure noise (back action noise) by the same amount and hence the quantum noise limited sensitivity is not negatively effected in that frequency range. We show that the misalignment of laser into the interferometer (input misalignment) produces the same effect as output misalignment and additionally decreases the power inside the interferometer. We also analyze dynamic HOM effects, such as beam jitter created by the suspended mirrors of the BHD. Our analyses can be directly applied to any BHD implementation in a future GWD. Moreover, we apply our analytical techniques to the example of the speed meter proof of concept experiment under construction in Glasgow. We find that for our experimental parameters, the performance of our seismic isolation system in the BHD paths is compatible with the design sensitivity of the experiment

Demonstration of a switchable damping system to allow low-noise operation of high-Q low-mass suspension systems

Low mass suspension systems with high-Q pendulum stages are used to enable quantum radiation pressure noise limited experiments. Utilising multiple pendulum stages with vertical blade springs and materials with high quality factors provides attenuation of seismic and thermal noise, however damping of these high-Q pendulum systems in multiple degrees of freedom is essential for practical implementation. Viscous damping such as eddy-current damping can be employed but introduces displacement noise from force noise due to thermal fluctuations in the damping system. In this paper we demonstrate a passive damping system with adjustable damping strength as a solution for this problem that can be used for low mass suspension systems without adding additional displacement noise in science mode. We show a reduction of the damping factor by a factor of 8 on a test suspension and provide a general optimisation for this system.Comment: 5 pages, 5 figure

Observation of mesoscopic crystalline structures in a two-dimensional Rydberg gas

The ability to control and tune interactions in ultracold atomic gases has paved the way towards the realization of new phases of matter. Whereas experiments have so far achieved a high degree of control over short-ranged interactions, the realization of long-range interactions would open up a whole new realm of many-body physics and has become a central focus of research. Rydberg atoms are very well-suited to achieve this goal, as the van der Waals forces between them are many orders of magnitude larger than for ground state atoms. Consequently, the mere laser excitation of ultracold gases can cause strongly correlated many-body states to emerge directly when atoms are transferred to Rydberg states. A key example are quantum crystals, composed of coherent superpositions of different spatially ordered configurations of collective excitations. Here we report on the direct measurement of strong correlations in a laser excited two-dimensional atomic Mott insulator using high-resolution, in-situ Rydberg atom imaging. The observations reveal the emergence of spatially ordered excitation patterns in the high-density components of the prepared many-body state. They have random orientation, but well defined geometry, forming mesoscopic crystals of collective excitations delocalised throughout the gas. Our experiment demonstrates the potential of Rydberg gases to realise exotic phases of matter, thereby laying the basis for quantum simulations of long-range interacting quantum magnets.Comment: 10 pages, 7 figure

Microscopic observation of magnon bound states and their dynamics

More than eighty years ago, H. Bethe pointed out the existence of bound states of elementary spin waves in one-dimensional quantum magnets. To date, identifying signatures of such magnon bound states has remained a subject of intense theoretical research while their detection has proved challenging for experiments. Ultracold atoms offer an ideal setting to reveal such bound states by tracking the spin dynamics after a local quantum quench with single-spin and single-site resolution. Here we report on the direct observation of two-magnon bound states using in-situ correlation measurements in a one-dimensional Heisenberg spin chain realized with ultracold bosonic atoms in an optical lattice. We observe the quantum walk of free and bound magnon states through time-resolved measurements of the two spin impurities. The increased effective mass of the compound magnon state results in slower spin dynamics as compared to single magnon excitations. In our measurements, we also determine the decay time of bound magnons, which is most likely limited by scattering on thermal fluctuations in the system. Our results open a new pathway for studying fundamental properties of quantum magnets and, more generally, properties of interacting impurities in quantum many-body systems.Comment: 8 pages, 7 figure