Erratum: Theory of Frequency-Filtered and Time-Resolved N-Photon Correlations [Phys. Rev. Lett. 109, 183601 (2012)].

This corrects the article DOI: 10.1103/PhysRevLett.109.183601.

Dissipative Optomechanical Preparation of Macroscopic Quantum Superposition States.

The transition from quantum to classical physics remains an intensely debated question even though it has been investigated for more than a century. Further clarifications could be obtained by preparing macroscopic objects in spatial quantum superpositions and proposals for generating such states for nanomechanical devices either in a transient or a probabilistic fashion have been put forward. Here, we introduce a method to deterministically obtain spatial superpositions of arbitrary lifetime via dissipative state preparation. In our approach, we engineer a double-well potential for the motion of the mechanical element and drive it towards the ground state, which shows the desired spatial superposition, via optomechanical sideband cooling. We propose a specific implementation based on a superconducting circuit coupled to the mechanical motion of a lithium-decorated monolayer graphene sheet, introduce a method to verify the mechanical state by coupling it to a superconducting qubit, and discuss its prospects for testing collapse models for the quantum to classical transition.

Nonclassical radiation from thermal cavities in the ultrastrong coupling regime.

Thermal or chaotic light sources emit radiation characterized by a slightly enhanced probability of emitting photons in bunches, described by a zero-delay second-order correlation function g((2))(0)=2. Here we explore photon-coincidence counting statistics of thermal cavities in the ultrastrong coupling regime, where the atom-cavity coupling rate becomes comparable to the cavity resonance frequency. We find that, depending on the system temperature and coupling rate, thermal photons escaping the cavity can display very different statistical behaviors, characterized by second-order correlation functions approaching zero or greatly exceeding two.

Spontaneous conversion from virtual to real photons in the ultrastrong-coupling regime.

We show that a spontaneous release of virtual photon pairs can occur in a quantum optical system in the ultrastrong coupling regime. In this regime, which is attracting interest both in semiconductor and superconducting systems, the light-matter coupling rate Ω(R) becomes comparable to the bare resonance frequency of photons ω(0). In contrast to the dynamical Casimir effect and other pair creation mechanisms, this phenomenon does not require external forces or time dependent parameters in the Hamiltonian.

Theory of frequency-filtered and time-resolved N-photon correlations.

A theory of correlations between N photons of given frequencies and detected at given time delays is presented. These correlation functions are usually too cumbersome to be computed explicitly. We show that they are obtained exactly through intensity correlations between two-level sensors in the limit of their vanishing coupling to the system. This allows the computation of correlation functions hitherto unreachable. The uncertainties in time and frequency of the detection, which are necessary variables to describe the system, are intrinsic to the theory. We illustrate the power of our formalism with the example of the Jaynes-Cummings model, by showing how higher order photon correlations can bring new insights into the dynamics of open quantum systems.

Photon blockade in the ultrastrong coupling regime.

We explore photon coincidence counting statistics in the ultrastrong coupling regime, where the atom-cavity coupling rate becomes comparable to the cavity resonance frequency. In this regime, usual normal order correlation functions fail to describe the output photon statistics. By expressing the electric-field operator in the cavity-emitter dressed basis, we are able to propose correlation functions that are valid for arbitrary degrees of light-matter interaction. Our results show that the standard photon blockade scenario is significantly modified for ultrastrong coupling. We observe parametric processes even for two-level emitters and temporal oscillations of intensity correlation functions at a frequency given by the ultrastrong photon emitter coupling. These effects can be traced back to the presence of two-photon cascade decays induced by counterrotating interaction terms.

Generation of mesoscopic entangled states in a cavity coupled to an atomic ensemble.

We propose a novel scheme for the efficient production of entangled states for N photons of the form |N>(a)|0>(b) + |0>(a)|N>(b) (NOON states) based on the resonant interaction of a pair of quantized cavity modes with an ensemble of atoms. We show that, in the strong-coupling regime, the adiabatic evolution of the system tends to a limiting state that describes mesoscopic entanglement between photons and atoms which can easily be converted to a purely photonic or atomic NOON state. We also demonstrate the remarkable property that the efficiency of this scheme increases exponentially with the cavity cooperativity factor, which gives efficient access to high number NOON states. The experimental feasibility of the scheme is discussed, and its efficiency is demonstrated numerically.

Tactile responses in the granule cell layer of cerebellar folium crus IIa of freely behaving rats.

We recorded activity from the granule cell layer (GCL) of cerebellar folium Crus IIa as freely moving rats engaged in a variety of natural behaviors, including grooming, eating, and free tactile exploration. Multiunit responses in the 1000-4500 Hz range were found to be strongly correlated with tactile stimulation of lip and whisker (perioral) regions. These responses occurred regardless of whether the stimulus was externally or self-generated and during both active and passive touch. In contrast, perioral movements that did not tactually stimulate this region of the face (e.g., chewing) produced no detectable increases in GCL activity. In addition, GCL responses were not correlated with movement extremes. When rats used their lips actively for palpation and exploration, the tactile responses in the GCL were not detectably modulated by ongoing jaw movements. However, active palpation and exploratory behaviors did result in the largest and most continuous bursts of GCL activity: responses were on average 10% larger and 50% longer during palpation and exploration than during grooming or passive stimulation. Although activity levels differed between behaviors, the position and spatial extent of the peripheral receptive field was similar over all behaviors that resulted in tactile input. Overall, our data suggest that the 1000-4500 Hz multiunit responses in the Crus IIa GCL of awake rats are correlated with tactile input rather than with movement or any movement parameter and that these responses are likely to be of particular importance during the acquisition of sensory information by perioral structures.

Applications of video mixing and digital overlay to neuroethology.

Neuroethological experiments often require video images of animal behavior and recordings of physiological data to be acquired simultaneously, synchronized with each other, stored, and analyzed together. The use of inexpensive multimedia computers offers new possibilities for mixing video images, analog voltages, and computer data, storing these combined signals to videotape, and extracting quantitative data for analysis. In this paper, we summarize methods for mixing images from multiple video cameras and a Macintosh computer display to facilitate manipulation of data generated during our neurophysiological and behavioral research. These technologies enhance accuracy, speed, and flexibility during experiments, and facilitate selecting and extracting quantitative data from the videotape for further analysis. Three applications are presented: (A) we used an analog video mixer to synchronize neurophysiological recordings with ongoing behaviors of freely moving rats; (B) we used a chroma keyed digital overlay to generate positional data for the rat's face during drinking behavior; and (C) we combined a computer model of a rat's head and whiskers with videos of exploratory behaviors to better track and quantify movements in three dimensions. Although the applications described here are specific to our neuroethological work, these methods will be useful to anyone wishing to combine the signals from multiple video sources into a single image or to extract series of positional or movement data from video frames without frame grabbing.

Oscillatory activity in the cerebellar hemispheres of unrestrained rats.

We recorded multiunit neural activity in the granule cell layer of cerebellar folium Crus IIa in unrestrained rats. Seven- to 8-Hz oscillatory activity was seen during behavioral states in which the animal was immobile; any movement the animal made coincided with termination of the oscillations. However, nearly one-third of oscillatory episodes appeared to cease spontaneously, in the absence of any observable sensory input or movement. Oscillations were synchronized both within and between cerebellar hemispheres, demonstrating precise temporal coordination among multiple, bilateral levels of the somatosensory system. We interpret these data in the context of similar oscillations observed in other brain structures and suggest that the oscillations are an underlying dynamic property of the entire somatosensory network.

Applications of multimedia computers and video mixing to neuroethology.

Inexpensive multimedia computers offer new possibilities for mixing video and computer images, videotaping these mixed images, and extracting quantitative data from videotape. In this paper we describe methods for mixing images from a video camera and a Macintosh computer display using chroma keying, and we describe a simple circuit for analog video mixing and frame-counting. We present three applications of these video mixing methods to our neurophysiological and behavioral research with awake, behaving animals. These technologies enhance accuracy, speed, and flexibility during experiments, by allowing us to record an information-rich videotape of the subject and state of the experimental apparatus. After the experiment, these technologies facilitate selecting and extracting quantitative data from the videotape for further analysis. The videotape is especially useful in resolving minor inconsistencies or incomplete information in the notes and data files that often arise during analysis of complex experiments.