Solving condensed-matter ground-state problems by semidefinite relaxations

We present a new generic approach to the condensed-matter ground-state problem which is complementary to variational techniques and works directly in the thermodynamic limit. Relaxing the ground-state problem, we obtain semidefinite programs (SDP). These can be solved efficiently, yielding strict lower bounds to the ground-state energy and approximations to the few-particle Green's functions. As the method is applicable for all particle statistics, it represents in particular a novel route for the study of strongly correlated fermionic and frustrated spin systems in D>1 spatial dimensions. It is demonstrated for the XXZ model and the Hubbard model of spinless fermions. The results are compared against exact solutions, quantum Monte Carlo, and Anderson bounds, showing the competitiveness of the SDP method.Comment: 8 pages, 3 figures; original title "Approaching condensed matter ground states from below"; improved numerics, added references; published version, including appendice

Towards experimental quantum-field tomography with ultracold atoms

The experimental realization of large-scale many-body systems in atomic- optical architectures has seen immense progress in recent years, rendering full tomography tools for state identification inefficient, especially for continuous systems. To work with these emerging physical platforms, new technologies for state identification are required. Here we present first steps towards efficient experimental quantum-field tomography. Our procedure is based on the continuous analogues of matrix-product states, ubiquitous in condensed-matter theory. These states naturally incorporate the locality present in realistic physical settings and are thus prime candidates for describing the physics of locally interacting quantum fields. To experimentally demonstrate the power of our procedure, we quench a one- dimensional Bose gas by a transversal split and use our method for a partial quantum-field reconstruction of the far-from-equilibrium states of this system. We expect our technique to play an important role in future studies of continuous quantum many-body systems

Confocal Imaging of Transmembrane Voltage by SEER of di-8-ANEPPS

Imaging, optical mapping, and optical multisite recording of transmembrane potential (Vm) are essential for studying excitable cells and systems. The naphthylstyryl voltage-sensitive dyes, including di-8-ANEPPS, shift both their fluorescence excitation and emission spectra upon changes in Vm. Accordingly, they have been used for monitoring Vm in nonratioing and both emission and excitation ratioing modes. Their changes in fluorescence are usually much less than 10% per 100 mV. Conventional ratioing increases sensitivity to between 3 and 15% per 100 mV. Low sensitivity limits the value of these dyes, especially when imaged with low light systems like confocal scanners. Here we demonstrate the improvement afforded by shifted excitation and emission ratioing (SEER) as applied to imaging membrane potential in flexor digitorum brevis muscle fibers of adult mice. SEER—the ratioing of two images of fluorescence, obtained with different excitation wavelengths in different emission bands—was implemented in two commercial confocal systems. A conventional pinhole scanner, affording optimal setting of emission bands but less than ideal excitation wavelengths, achieved a sensitivity of up to 27% per 100 mV, nearly doubling the value found by conventional ratioing of the same data. A better pair of excitation lights should increase the sensitivity further, to 35% per 100 mV. The maximum acquisition rate with this system was 1 kHz. A fast “slit scanner” increased the effective rate to 8 kHz, but sensitivity was lower. In its high-sensitivity implementation, the technique demonstrated progressive deterioration of action potentials upon fatiguing tetani induced by stimulation patterns at \u3e40 Hz, thereby identifying action potential decay as a contributor to fatigue onset. Using the fast implementation, we could image for the first time an action potential simultaneously at multiple locations along the t-tubule system. These images resolved the radially varying lag associated with propagation at a finite velocity

Long-term modification of cortical synapses improves sensory perception

Synapses and receptive fields of the cerebral cortex are plastic. However, changes to specific inputs must be coordinated within neural networks to ensure that excitability and feature selectivity are appropriately configured for perception of the sensory environment. Long-lasting enhancements and decrements to rat primary auditory cortical excitatory synaptic strength were induced by pairing acoustic stimuli with activation of the nucleus basalis neuromodulatory system. Here we report that these synaptic modifications were approximately balanced across individual receptive fields, conserving mean excitation while reducing overall response variability. Decreased response variability should increase detection and recognition of near-threshold or previously imperceptible stimuli, as we found in behaving animals. Thus, modification of cortical inputs leads to wide-scale synaptic changes, which are related to improved sensory perception and enhanced behavioral performance