Measurement plays a crucial role in a quantum system beyond just learning about the system state: it changes the post-measurement state and hence influences the subsequent time evolution; further, measurement can even create entanglement in the post-measurement conditional state. In this work, we study how careful choice of parameters for a typical measurement process on cold atoms systems -- phase contrast imaging -- has a strong impact on both what the experimentalist observes but also on the backaction the measurement has on the system, including the creation and diffusion of quasiparticles emerging from the quantum many-body dynamics. We focus on the case of a Bose-Einstein-condensate array, in the low-temperature and low-momentum limit. Our theoretical investigation reveals regimes where the imaging light probes either the bare particle or quasiparticle dynamics. Moreover, we find a path to selectively measuring quasiparticle modes directly, as well as controlling over the measurement-induced creation and diffusion of quasiparticles into different momentum states. This lays a foundation for understanding the effects of both experimental approaches for probing many-body systems, but also more speculative directions such as observable consequences of `spontaneous collapse' predictions from novel models of quantum gravity on aspects of the Standard Model.
Measurement plays a crucial role in a quantum system beyond just learning about the system state: it changes the post-measurement state and hence influences the subsequent time evolution; further, measurement can even create entanglement in the post-measurement conditional state. In this work, we study how careful choice of parameters for a typical measurement process on cold atoms systems -- phase contrast imaging -- has a strong impact on both what the experimentalist observes but also on the backaction the measurement has on the system, including the creation and diffusion of quasiparticles emerging from the quantum many-body dynamics. We focus on the case of a Bose-Einstein-condensate array, in the low-temperature and low-momentum limit. Our theoretical investigation reveals regimes where the imaging light probes either the bare particle or quasiparticle dynamics. Moreover, we find a path to selectively measuring quasiparticle modes directly, as well as controlling over the measurement-induced creation and diffusion of quasiparticles into different momentum states. This lays a foundation for understanding the effects of both experimental approaches for probing many-body systems, but also more speculative directions such as observable consequences of `spontaneous collapse' predictions from novel models of quantum gravity on aspects of the Standard Model.
The first successful experimental realization of a Bose-Einstein condensate (BEC) in 1995 sparked a still growing research activity that in the meantime has led to beautiful and surprising results, such as the interference of matter waves [4], the Mott-superfluid phase transition [49] or the direct observation of Anderson localization of matter waves [10]. The strong interest in BECs arises, among others, from the possibility to investigate known but hard to study quantum systems on a rather macroscopic scale: for example one can load ultra-cold bosons into an optical lattice created by a standing light wave, and thereby simulate a solid state device. When it comes to a measurement on the BEC, however, essentially all measurement techniques result in the destruction of the condensate: for example in the so called “time of flight method” the optical lattice is switched off to observe the expansion of the trapped atoms and thereby directly visualize their momentum distribution, which highlights the condensed component [11]. In this thesis we elaborate on a means to probe a Bose-Einstein condensate from outside, with a scattering particle. The interaction between the probe particle and the bosons allows energy exchange between them, i.e., this setup includes inelastic scattering. After the scattering process, the condensate is still confined in the optical lattice and can therefore be used for further investigations. Of course, this method of probing a BEC is only then a serious alternative if the properties of the BEC can be inferred from the scattering signal. Besides outlining the scattering formalism, the central aim of this work is to show how the properties of the BEC can be deduced from those quantities accessible in a scattering experiment, like for example the transmission or the inelastic cross section. The other, equally strong motivation of this work concerns the signature of the interaction between the bosons in the scattering quantities. The dynamics of an analog classical system depends strongly on the interaction strength, which can induce a complex structure of the underlying phase space like, e.g., the appearance of a separatrix or even the emergence of chaotic dynamics in a globally mixed regular-chaotic phase space. We are interested to which extent such phase-space metamorphosis is reflected in the properties of the scattering particle. Currently light scattering (Bragg spectroscopy) on an optical lattice [78, 77] or rather on an optical lattice embedded into a cavity [62,68,19] is under intense investigation. These efforts predominantly aim at a characterization of the Mott-superfluid transition by specific scattering properties. In the present thesis we focus on condensates loaded in two and three lattice sites, with a large number of bosons. These systems exhibit a diversity of important physical effects (as we will see below) and thus are of paradigmatic relevance for a detailed understanding of multiparticle quantum dynamics in periodic potentials.
Experimental access to many-body quantum systems is often limited by measurement backaction, and key dynamical properties are typically obtained by perturbing a system and measuring its response. Here we replace this active paradigm with a minimally invasive protocol based on a pair of weak quantum measurements that leverages measurement backaction as a strength. By correlating time-separated measurements with the first detecting fluctuations -- of any sort -- and the second tracking their time evolution, our method directly measures dynamical correlation functions without external perturbation. We demonstrate this technique in an atomic Bose-Einstein condensate using phase-contrast imaging to obtain the two-time density-density correlation function known as the Van Hove function and, through its Fourier transform, the dynamical structure factor. Due to the role of spatial correlations in scattering, these quantities underpin neutron and X-ray scattering and atomic Bragg spectroscopy. This approach is broadly applicable, providing access to correlation functions between any pair of observables amenable to weak measurement, thereby going beyond the capabilities of conventional strong measurements. We further isolate the role of quantum backaction through Aharonov's post-selection-based quantum weak values.
Understanding system-reservoir dynamics in many-body physics is a new frontier. An external environment can be thought of as a 'measurement reservoir' which extracts information about the quantum system. Weak (i.e. minimally destructive) measurements provide a time-resolved but noisy record of system evolution. In this talk, we propose using weak measurement and feedback to probe and manipulate spinor Bose-Einstein condensates, focusing on the trade-off between usable information obtained from measurement and the effect of measurement on the system (quantum backaction). As a prototype example, we consider the dynamics of a domain wall in a two-component BEC and show that quantum backaction due to measurement causes two primary effects: domain wall diffusion and overall heating. The system dynamics and signal-to-noise ratio depend on the choice of measurement observable. We describe a feedback protocol to create and stabilize a domain wall in the regime where domain walls are unstable, giving a prototype example of Hamiltonian engineering using measurement and feedback.
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.
In quantum physics, measurement exhibits fundamentally different behaviour to the classical case, having direct effect on the observed system. As a result, the very act of observation in quantum systems plays a non-trivial role, and can be used as a method of controlling the dynamics of the system. With the rise of quantum technologies, understanding and exploiting these phenomena offers a great boon. Here, we investigate a selection of the possibilities offered by quantum measurement for characterising and manipulating many-body systems, with particular focus on ultracold atomic gases. We first study how microscopic quantum structures can be used to indirectly probe larger systems. After deriving a general result, we consider the specific case of impurity atoms immersed in a quantum gas, and demonstrate that this enables density-related properties of the gas to be inferred from measurements of solely the impurity internal state. Following this, we explore how the backaction from measurement can be used for control of quantum systems. Utilising the quantum Zeno effect that results from persistent measurement of a quantum state, we show how fully-quantum many-body light-matter interactions enable the engineering of atomic states and dynamics through measurement of the light, leading to an abundance of interesting phenomena, including genuinely multipartite entangled states, long-range correlated tunnelling, and the quantum simulation of long-range and correlated interactions. The resulting structure imparted by the light on the matter can also be used to detect and measure atomic entanglement. Finally, we generalise quantum Zeno dynamics to the regime where the measurement timestep is finite, and demonstrate that the resulting system evolution can exhibit correlated processes.
Trapping ultracold atoms in optical lattices enabled the study of strongly correlated phenomena in an environment that is far more controllable and tunable than what was possible in condensed matter. Here, we consider coupling these systems to quantised light where the quantum nature of both the optical and matter fields play equally important roles in order to push the boundaries of what is possible in ultracold atomic systems. We show that light can serve as a nondestructive probe of the quantum state of matter. By considering a global measurement we show that it is possible to distinguish a highly delocalised phase like a superfluid from the Bose glass and Mott insulator. We also demonstrate that light scattering reveals not only density correlations, but also matter-field interference. By taking into account the effect of measurement backaction we show that the measurement can efficiently compete with the local atomic dynamics of the quantum gas. This can generate long-range correlations and entanglement which in turn leads to macroscopic multimode oscillations across the whole lattice when the measurement is weak and correlated tunnelling, as well as selective suppression and enhancement of dynamical processes beyond the projective limit of the quantum Zeno effect in the strong measurement regime. We also consider quantum measurement backaction due to the measurement of matter-phase-related variables such as global phase coherence. We show how this unconventional approach opens up new opportunities to affect system evolution and demonstrate how this can lead to a new class of measurement projections thus extending the measurement postulate for the case of strong competition with the system's own evolution.