40 research outputs found
Coupled Atomic Wires in a Synthetic Magnetic Field
We propose and study systems of coupled atomic wires in a perpendicular
synthetic magnetic field as a platform to realize exotic phases of quantum
matter. This includes (fractional) quantum Hall states in arrays of many wires
inspired by the pioneering work [Kane et al. PRL {\bf{88}}, 036401 (2002)], as
well as Meissner phases and Vortex phases in double-wires. With one continuous
and one discrete spatial dimension, the proposed setup naturally complements
recently realized discrete counterparts, i.e. the Harper-Hofstadter model and
the two leg flux ladder, respectively. We present both an in-depth theoretical
study and a detailed experimental proposal to make the unique properties of the
semi-continuous Harper-Hofstadter model accessible with cold atom experiments.
For the minimal setup of a double-wire, we explore how a sub-wavelength spacing
of the wires can be implemented. This construction increases the relevant
energy scales by at least an order of magnitude compared to ordinary optical
lattices, thus rendering subtle many-body phenomena such as Lifshitz
transitions in Fermi gases observable in an experimentally realistic parameter
regime. For arrays of many wires, we discuss the emergence of Chern bands with
readily tunable flatness of the dispersion and show how fractional quantum Hall
states can be stabilized in such systems. Using for the creation of optical
potentials Laguerre-Gauss beams that carry orbital angular momentum, we detail
how the coupled atomic wire setups can be realized in non-planar geometries
such as cylinders, discs, and tori
Unitary -designs via random quenches in atomic Hubbard and Spin models: Application to the measurement of R\'enyi entropies
We present a general framework for the generation of random unitaries based
on random quenches in atomic Hubbard and spin models, forming approximate
unitary -designs, and their application to the measurement of R\'enyi
entropies. We generalize our protocol presented in [Elben2017:
arXiv:1709.05060, to appear in Phys. Rev. Lett.] to a broad class of atomic and
spin lattice models. We further present an in-depth numerical and analytical
study of experimental imperfections, including the effect of decoherence and
statistical errors, and discuss connections of our approach with many-body
quantum chaos.Comment: This is a new and extended version of the Supplementary material
presented in arXiv:1709.05060v1, rewritten as a companion paper. Version
accepted to Phys. Rev. A. Minus sign corrected in Eq (5
Information scan of quantum states based on entropy-power uncertainty relations
We use Renyi-entropy-power-based uncertainty relations to show how the information probability distribution associated with a quantum state can be reconstructed in a process that is analogous to quantum-state tomography. We illustrate our point with the so-called "cat states", which are of both fundamental interest and practical use in schemes such as quantum metrology, but are not well described by standard variance-based approaches
Modulation of Human Time Processing by Subthalamic Deep Brain Stimulation
Timing in the range of seconds referred to as interval timing is crucial for cognitive operations and conscious time processing. According to recent models of interval timing basal ganglia (BG) oscillatory loops are involved in time interval recognition. Parkinsońs disease (PD) is a typical disease of the basal ganglia that shows distortions in interval timing. Deep brain stimulation (DBS) of the subthalamic nucleus (STN) is a powerful treatment of PD which modulates motor and cognitive functions depending on stimulation frequency by affecting subcortical-cortical oscillatory loops. Thus, for the understanding of BG-involvement in interval timing it is of interest whether STN-DBS can modulate timing in a frequency dependent manner by interference with oscillatory time recognition processes. We examined production and reproduction of 5 and 15 second intervals and millisecond timing in a double blind, randomised, within-subject repeated-measures design of 12 PD-patients applying no, 10-Hz- and ≥130-Hz-STN-DBS compared to healthy controls. We found under(re-)production of the 15-second interval and a significant enhancement of this under(re-)production by 10-Hz-stimulation compared to no stimulation, ≥130-Hz-STN-DBS and controls. Milliseconds timing was not affected. We provide first evidence for a frequency-specific modulatory effect of STN-DBS on interval timing. Our results corroborate the involvement of BG in general and of the STN in particular in the cognitive representation of time intervals in the range of multiple seconds
Probing Scrambling Using Statistical Correlations between Randomized Measurements
We propose and analyze a protocol to study quantum information scrambling using statistical correlations between measurements, which are performed after evolving a quantum system from randomized initial states. We prove that the resulting correlations precisely capture the so-called out-of-time-ordered correlators and can be used to probe chaos in strongly interacting, many-body systems. Our protocol requires neither reversing time evolution nor auxiliary degrees of freedom, and it can be realized in state-of-the-art quantum simulation experiments
Differential modulation of STN-cortical and cortico-muscular coherence by movement and levodopa in Parkinson's disease
Previous research suggests that oscillatory coupling between cortex, basal ganglia and muscles plays an important role in motor behavior. Furthermore, there is evidence that oscillatory coupling is altered in patients with movement disorders such as Parkinson's disease (PD)