Quantum information processes in protein microtubules of brain neurons

We study biologically ‘orchestrated’ coherent quantum processes in collections of protein microtubules of brain neurons, which correlate with, and regulate, neuronal synaptic and membrane activity. In this situation the continuous Schrodinger evolution of each such process terminates in accordance with the specific Diosi-Penrose (DP) scheme of ‘objective reduction’ (‘OR’) of the quantum state. This orchestrated OR activity (‘Orch OR’) is taken to result in moments of conscious awareness and/or choice. We analyze Orch OR in light of advances and developments in quantum physics, computational neuroscience and quantum biology. Much attention is also devoted to the ‘beat frequencies’ of faster microtubule vibrations as a possible source of the observed electroencephalographic (‘EEG’) correlates of consciousness

(a) The resonance fluorescence spectrum of two atoms for Δ = 0.1, Ω₀ = 15 (dashed); Δ = 0.1, Ω₀ = 18 (dotted); and Δ = 0.3, Ω₀ = 40 (solid) (units of γ)

<p><strong>Figure 4.</strong> (a) The resonance fluorescence spectrum of two atoms for Δ = 0.1, Ω₀ = 15 (dashed); Δ = 0.1, Ω₀ = 18 (dotted); and Δ = 0.3, Ω₀ = 40 (solid) (units of γ). (b) The second correlation function at τ = 0 for the whole localization regime of the atom <em>b</em> in the anti-node. In both figures we use γ<em>t</em> = 0.1.</p> <p><strong>Abstract</strong></p> <p>The resonance fluorescence emitted by two three-level atoms dressed in a strong laser field is studied. A stark dynamics shift based on photon statistics is discussed. The appearance of coherent Rabi oscillations (quantum beats) of the atoms located in the non-symmetric positions of the anti-nodes and the modification of the quantum correlations at the Stokes and anti-Stokes cooperative emission are described. For some positions of the atoms, we observed the violation of the Cauchy–Schwarz inequality, finding antibunching in the scattered light. We present a scheme to control the position of atoms dressed with the standing field via the resonance fluorescence.</p

Second-order correlation versus delay time for γ<em>t</em> = 0.1

<p><strong>Figure 3.</strong> Second-order correlation versus delay time for γ<em>t</em> = 0.1. Figure (a) shows the total correlation function while (b)–(d) show Stokes, anti-Stokes and cross correlations. All curves correspond to atom <em>a</em> fixed in the point <em>k</em>₀<em>r_a</em> = 0.2, and <em>k</em>₀<em>r_b</em> is varied at various positions in the vicinity of the antinode.</p> <p><strong>Abstract</strong></p> <p>The resonance fluorescence emitted by two three-level atoms dressed in a strong laser field is studied. A stark dynamics shift based on photon statistics is discussed. The appearance of coherent Rabi oscillations (quantum beats) of the atoms located in the non-symmetric positions of the anti-nodes and the modification of the quantum correlations at the Stokes and anti-Stokes cooperative emission are described. For some positions of the atoms, we observed the violation of the Cauchy–Schwarz inequality, finding antibunching in the scattered light. We present a scheme to control the position of atoms dressed with the standing field via the resonance fluorescence.</p

Time dependence of the atomic correlations for <em>k</em>₀<em>r_a</em> = 0.2, and <em>k</em>₀<em>r_b</em> = 0.6 (plot 1), 1.57 (plot 2), 3 (plot 3)

<p><strong>Figure 2.</strong> Time dependence of the atomic correlations for <em>k</em>₀<em>r_a</em> = 0.2, and <em>k</em>₀<em>r_b</em> = 0.6 (plot 1), 1.57 (plot 2), 3 (plot 3). Curves (a),(b) correspond to μ = Δ/Ω₀ = 0.05 and 0.01 respectively. The insert in figure <a href="http://iopscience.iop.org/0953-4075/46/15/155501/article#jpb467388f2" target="_blank">2</a>(a) shows the case when the atoms are localized in equivalent anti-node positions at the distance <em>k</em>₀<em>r</em> = 2.7.</p> <p><strong>Abstract</strong></p> <p>The resonance fluorescence emitted by two three-level atoms dressed in a strong laser field is studied. A stark dynamics shift based on photon statistics is discussed. The appearance of coherent Rabi oscillations (quantum beats) of the atoms located in the non-symmetric positions of the anti-nodes and the modification of the quantum correlations at the Stokes and anti-Stokes cooperative emission are described. For some positions of the atoms, we observed the violation of the Cauchy–Schwarz inequality, finding antibunching in the scattered light. We present a scheme to control the position of atoms dressed with the standing field via the resonance fluorescence.</p

Geometrical representation of the dressed atoms in the standing wave

<p><strong>Figure 1.</strong> Geometrical representation of the dressed atoms in the standing wave.</p> <p><strong>Abstract</strong></p> <p>The resonance fluorescence emitted by two three-level atoms dressed in a strong laser field is studied. A stark dynamics shift based on photon statistics is discussed. The appearance of coherent Rabi oscillations (quantum beats) of the atoms located in the non-symmetric positions of the anti-nodes and the modification of the quantum correlations at the Stokes and anti-Stokes cooperative emission are described. For some positions of the atoms, we observed the violation of the Cauchy–Schwarz inequality, finding antibunching in the scattered light. We present a scheme to control the position of atoms dressed with the standing field via the resonance fluorescence.</p