Experimental characterization of a quantum many-body system via higher-order correlations.

Quantum systems can be characterized by their correlations. Higher-order (larger than second order) correlations, and the ways in which they can be decomposed into correlations of lower order, provide important information about the system, its structure, its interactions and its complexity. The measurement of such correlation functions is therefore an essential tool for reading, verifying and characterizing quantum simulations. Although higher-order correlation functions are frequently used in theoretical calculations, so far mainly correlations up to second order have been studied experimentally. Here we study a pair of tunnel-coupled one-dimensional atomic superfluids and characterize the corresponding quantum many-body problem by measuring correlation functions. We extract phase correlation functions up to tenth order from interference patterns and analyse whether, and under what conditions, these functions factorize into correlations of lower order. This analysis characterizes the essential features of our system, the relevant quasiparticles, their interactions and topologically distinct vacua. From our data we conclude that in thermal equilibrium our system can be seen as a quantum simulator of the sine-Gordon model, relevant for diverse disciplines ranging from particle physics to condensed matter. The measurement and evaluation of higher-order correlation functions can easily be generalized to other systems and to study correlations of any other observable such as density, spin and magnetization. It therefore represents a general method for analysing quantum many-body systems from experimental data.

Scattering correcting wavefront shaping for three-photon microscopy.

Three-photon (3P) microscopy is getting traction due to its superior performance in deep tissues. Yet, aberrations and light scattering still pose one of the main limitations in the attainable depth ranges for high-resolution imaging. Here, we show scattering correcting wavefront shaping with a simple continuous optimization algorithm, guided by the integrated 3P fluorescence signal. We demonstrate focusing and imaging behind scattering layers and investigate convergence trajectories for different sample geometries and feedback non-linearities. Furthermore, we show imaging through a mouse skull and demonstrate a novel, to the best of our knowledge, fast phase estimation scheme that substantially increases the speed at which the optimal correction can be found.

Non-invasive chemically selective energy delivery and focusing inside a scattering medium guided by Raman scattering.

Raman scattering is a chemically selective probing mechanism with diverse applications in industry and clinical settings. Yet, most samples are optically opaque limiting the applicability of Raman probing at depth. Here, we demonstrate chemically selective energy deposition behind a scattering medium by combining prior information on the chemical's spectrum with the measurement of a spectrally resolved Raman speckle as a feedback mechanism for wavefront shaping. We demonstrate unprecedented sixfold signal enhancement in an epi-geometry, realizing targeted energy deposition and focusing on individual Raman active particles.

Speckle Engineering through Singular Value Decomposition of the Transmission Matrix.

Speckle patterns are ubiquitous in optics and have multiple applications for which the control of their spatial correlations is essential. Here, we report on a method to engineer speckle correlations behind a scattering medium through the singular value decomposition of the transmission matrix. We not only demonstrate control over the speckle grain size and shape but also realize patterns with nonlocal correlations. Moreover, we show that the reach of our method extends also along the axial dimension, allowing volumetric speckle engineering behind scattering layers.

Designing arbitrary one-dimensional potentials on an atom chip.

We use laser light shaped by a digital micro-mirror device to realize arbitrary optical dipole potentials for one-dimensional (1D) degenerate Bose gases of 87Rb trapped on an atom chip. Superposing optical and magnetic potentials combines the high flexibility of optical dipole traps with the advantages of magnetic trapping, such as effective evaporative cooling and the application of radio-frequency dressed state potentials. As applications, we present a 160 µm long box-like potential with a central tuneable barrier, a box-like potential with a sinusoidally modulated bottom and a linear confining potential. These potentials provide new tools to investigate the dynamics of 1D quantum systems and will allow us to address exciting questions in quantum thermodynamics and quantum simulations.

Chiral prethermalization in supersonically split condensates.

We study the dynamics of phase relaxation between a pair of one-dimensional condensates created by a supersonic unzipping of a single condensate. We use the Lorentz invariance of the low energy sector of such systems to show that dephasing results in an unusual prethermal state, in which right- and left-moving excitations have different, Doppler-shifted temperatures. The chirality of these modes can be probed experimentally by measuring the interference fringe contrasts with the release point of the split condensates moving at another supersonic velocity. Further, an accelerated motion of the release point can be used to observe a spacelike analog of the Unruh effect. A concrete experimental realization of the quantum zipper for a BEC of trapped atoms on an atom chip is outlined.

Single-pixel transmission matrix recovery via two-photon fluorescence.

Imaging at depth in opaque materials has long been a challenge. Recently, wavefront shaping has enabled notable advance for deep imaging. Nevertheless, most noninvasive wavefront-shaping methods require cameras, lack the sensitivity for deep imaging under weak optical signals, or can only focus on a single "guidestar." Here, we retrieve the transmission matrix (TM) noninvasively using two-photon fluorescence exploiting a single-pixel detection combined with a computational framework, allowing to achieve single-target focus on multiple guidestars spread beyond the memory effect range. In addition, if we assume that memory effect correlations exist in the TM, we are able to substantially reduce the number of measurements needed.

Recurrences in an isolated quantum many-body system.

The complexity of interacting quantum many-body systems leads to exceedingly long recurrence times of the initial quantum state for all but the smallest systems. For large systems, one cannot probe the full quantum state in all its details. Thus, experimentally, recurrences can only be determined on the level of the accessible observables. Realizing a commensurate spectrum of collective excitations in one-dimensional superfluids, we demonstrate recurrences of coherence and long-range order in an interacting quantum many-body system containing thousands of particles. Our findings will enable the study of the coherent dynamics of large quantum systems even after they have reached a transient thermal-like state.

Experimental observation of a generalized Gibbs ensemble.

The description of the non-equilibrium dynamics of isolated quantum many-body systems within the framework of statistical mechanics is a fundamental open question. Conventional thermodynamical ensembles fail to describe the large class of systems that exhibit nontrivial conserved quantities, and generalized ensembles have been predicted to maximize entropy in these systems. We show experimentally that a degenerate one-dimensional Bose gas relaxes to a state that can be described by such a generalized ensemble. This is verified through a detailed study of correlation functions up to 10th order. The applicability of the generalized ensemble description for isolated quantum many-body systems points to a natural emergence of classical statistical properties from the microscopic unitary quantum evolution.