We study the inflationary quantum-to-classical transition for the adiabatic curvature perturbation due to quantum decoherence, focusing on the role played by squeezed-limit mode couplings. We evolve the quantum state in the Schrodinger picture, for a generic cubic coupling to additional environment degrees of freedom. Focusing on the case of minimal gravitational interactions, we find the evolution of the reduced density matrix for a given long-wavelength fluctuation by tracing out the other (mostly shorter wavelength) modes of as an environment. We show that inflation produces phase oscillations in the wave functional , which suppress off-diagonal components of the reduced density matrix, leaving a diagonal mixture of different classical configurations. Gravitational nonlinearities thus provide a minimal mechanism for generating classical stochastic perturbations from inflation. We identify the time when decoherence occurs, which is delayed after horizon crossing due to the weak coupling, and find that Hubble-scale modes act as the decohering environment. We also comment on the observational relevance of decoherence and its relation to the squeezing of the quantum state.
Nonequilibrium fluctuation-dissipation inequality and nonequilibrium uncertainty principle
C. H. Fleming, B. L. Hu, Albert RouraThe fluctuation-dissipation relation is usually formulated for a system interacting with a heat bath at finite temperature, and often in the context of linear response theory, where only small deviations from the mean are considered. We show that for an open quantum system interacting with a nonequilibrium environment, where temperature is no longer a valid notion, a fluctuation-dissipation inequality exists. Instead of being proportional, quantum fluctuations are bounded below by quantum dissipation, whereas classically the fluctuations vanish at zero temperature. The lower bound of this inequality is exactly satisfied by (zero-temperature) quantum noise and is in accord with the Heisenberg uncertainty principle, in both its microscopic origins and its influence upon systems. Moreover, it is shown that there is a coupling-dependent nonequilibrium fluctuation-dissipation relation that determines the nonequilibrium uncertainty relation of linear systems in the weak-damping limit.
Nested Trampoline Resonators for Optomechanics
M. J. Weaver et alTwo major challenges in the development of optomechanical devices are achieving a low mechanical and optical loss rate and vibration isolation from the environment. We address both issues by fabricating trampoline resonators made from low pressure chemical vapor deposition (LPCVD) Si3N4 with a distributed bragg reflector (DBR) mirror. We design a nested double resonator structure with 80 dB of mechanical isolation from the mounting surface at the inner resonator frequency, and we demonstrate up to 45 dB of isolation at lower frequencies in agreement with the design. We reliably fabricate devices with mechanical quality factors of around 400,000 at room temperature. In addition these devices were used to form optical cavities with finesse up to 181,000 ± 1,000. These promising parameters will enable experiments in the quantum regime with macroscopic mechanical resonators.
That’s a real optical photograph! And they think that they will cool it to the ground state in the future.
Quantum Cognition: The possibility of processing with nuclear spins in the brain
Matthew P. A. FisherThe possibility that quantum processing with nuclear spins might be operative in the brain is proposed and then explored. Phosphorus is identified as the unique biological element with a nuclear spin that can serve as a qubit for such putative quantum processing - a neural qubit - while the phosphate ion is the only possible qubit-transporter. We identify the "Posner molecule", Ca9(PO4)6, as the unique molecule that can protect the neural qubits on very long times and thereby serve as a (working) quantum-memory. A central requirement for quantum-processing is quantum entanglement. It is argued that the enzyme catalyzed chemical reaction which breaks a pyrophosphate ion into two phosphate ions can quantum entangle pairs of qubits. Posner molecules, formed by binding such phosphate pairs with extracellular calcium ions, will inherit the nuclear spin entanglement. A mechanism for transporting Posner molecules into presynaptic neurons during a "kiss and run" exocytosis, which releases neurotransmitters into the synaptic cleft, is proposed. Quantum measurements can occur when a pair of Posner molecules chemically bind and subsequently melt, releasing a shower of intra-cellular calcium ions that can trigger further neurotransmitter release and enhance the probability of post-synaptic neuron firing. Multiple entangled Posner molecules, triggering non-local quantum correlations of neuron firing rates, would provide the key mechanism for neural quantum processing. Implications, both in vitro and in vivo, are briefly mentioned.
LaTeX in commentsInclude [latexpage] to render LaTeX in comments. (More.)
- Comments on Weingarten's preferred branch (4)
- Jess Riedel Also, as a separate issue, note that the "branch decomposition ambiguity" you describe in Eq.... – Nov 22, 9:41 PM
- Jess Riedel Hi Don, Thanks very much for your comments, and sorry for the big delay in... – Nov 22, 8:38 PM
- Don Weingarten Hi Jess, 1. I agree that the fuzziness of many-worlds + decoherence is simply repackaged.... – Oct 31, 11:31 PM
- Legendre transform (4)
- Branches and matrix-product states (6)
- Jess Riedel This prompted me to take an old email where I listed some models of branching... – Oct 12, 3:16 AM
- interstice Thanks. Do you know of any systems, toy or real, where we can identify a... – Oct 11, 10:06 PM
- Jess Riedel Great question. It is not obvious that we should define branches from the tensor structure... – Oct 10, 8:00 PM
- interstice Right, so to argue that the branches evolve independently, one must first define what branches... – Oct 10, 4:19 PM
- Jess Riedel You're right that the criteria for defining branches I give in the paper doesn't make... – Oct 05, 2:33 PM
- Comments on Weingarten's preferred branch (4)
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