Abstract
We propose an experimental setup to probe the low-lying excitation modes of a parametrically oscillating planar cavity, in particular the soft Goldstone mode which appears as a consequence of the spontaneously broken $\text{U}(1)$ symmetry of signal-idler phase rotations. A strong and narrow peak corresponding to the Goldstone mode is identified in the transmission spectrum of a weak probe beam incident on the cavity. When the $\text{U}(1)$ symmetry is explicitly broken by an additional laser beam pinning the signal-idler phase, a gap opens in the dispersion and the Goldstone peak is dramatically suppressed. Quantitative predictions are given for the case of semiconductor planar cavities in the strong exciton-photon coupling regime.
Highlights
The cerebellum is crucial for the precise temporal control of motor related tasks [1] and conditioned behaviors [2]
Most Purkinje cells (PC) showed a skewed CV2 distribution, with a high proportion of low CV2 values (Figure 2B), indicating the presence of regularity in spiking patterns. This was in clear contrast to spontaneous spiking of neocortical neurons, which showed uniform CV2 distributions as previously reported [20] (Figure 2B, blue) and which are similar to realizations of inhomogeneous Poisson processes
Our main findings indicate that (1) interesting finetemporal properties of neuronal responses may be uncovered by analyzing regular pattern structure on a single trial basis; (2) PC simple spike trains contain distinctly more spike timing regularities than hitherto known; (3) the high coefficient of variation (CV) in in vivo recordings is most likely caused by mixing of different regular spiking patterns, separated by single, typically longer, interspike intervals (ISIs); (4) the onset of patterns can be synchronized in nearby PCs, but their member spikes are not synchronized; (5) most regular patterns are not influenced by complex spikes; (6) regular pattern properties change with behavioral state and tactile stimulation; and (7) regular patterns may cause epochs of close to constant synaptic conductance in downstream deep cerebellar nuclei (DCN) neurons
Summary
The cerebellum is crucial for the precise temporal control of motor related tasks [1] and conditioned behaviors [2]. Prior studies of spike time coding in the cerebellum have focused on the discharge of Purkinje cells (PCs), which form the sole output of cerebellar cortex Far these studies only considered mean firing rates of the simple spikes (SS) [3,4] or complex spikes (CS) [5,6]. Cerebellar Purkinje cells (PC) in vivo are commonly reported to generate irregular spike trains, documented by high coefficients of variation of interspike-intervals (ISI). In strong contrast, they fire very regularly in the in vitro slice preparation. Our findings indicate that the apparent irregularity in cerebellar PC simple spike trains in vivo is most likely caused by mixing of different regular spike patterns, separated by single long intervals, over time. We propose that PCs may signal information, at least in part, in regular spike patterns to downstream DCN neurons
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