Dissipative dynamics of quantum fluctuations

Abstract

One way to look for complex behaviours in many-body quantum systems is to let the number N of degrees of freedom become large and focus upon collective observables. Mean-field quantities scaling as 1/N tend to commute, whence complexity at the quantum level can only be inherited from complexity at the classical level. Instead, fluctuations of microscopic observables scale as 1/ √ N and exhibit collective Bosonic features, typical of a mesoscopic regime half-way between the quantum one at the microscopic level and the classical one at the level of macroscopic averages. Here, we consider the mesoscopic behaviour emerging from an infinite quantum spin chain undergoing a microscopic dissipative, irreversible dynamics and from global states without long-range correlations and invariant under lattice translations and dynamics. We show that, from the fluctuations of one site spin observables whose linear span is mapped into itself by the dynamics, there emerge bosonic operators obeying a mesoscopic dissipative dynamics mapping Gaussian states into Gaussian states. Instead of just depleting quantum correlations because of decoherence effects, these maps can generate entanglement at the collective, mesoscopic level, a phenomenon with no classical analogue that embodies a peculiar complex behaviour at the interface between micro and macro regimes.

Quantum fluctuations in mesoscopic systems

“…More general and involved situations can surely be considered [119,120]; the simplified model discussed here results nevertheless quite adequate for showing a general physical phenomenon, namely bath-mediated, mesoscopic entanglement generation. (69) and (70), with L as in (92), one can now explicitly construct the emergent mesoscopic dynamics Φ t on the Weyl algebra of fluctuations W(X , σ (β) ).…”

Generating a Squeezed‐Coherent‐Cat State in a Double‐Cavity Optomechanical System

“…Different from the superposition of coherent of cavity field, [14,31,32] the superposition of the coherent state of the mechanical oscillator is real Schrödinger cat state since the mechanical oscillator is macroscopic or mesoscopic massive object. [33][34][35] Quantum fluctuations originating from the Heisenberg uncertainty principle restrict the application in precision measurements, [36][37][38] because quantum fluctuation in the optomechanical systems can broaden the optical response spectrum and affect the sensitivity of detection. Therefore, squeezing quantum fluctuation is necessary for the application in precision.…”

Dynamical Phases and Quantum Correlations in an Emitter-Waveguide System with Feedback

“…We employ the theory of quantum fluctuations [58][59][60][61] to investigate the quantum correlations in the many-body state of the emitter ensemble. This mathematically rigorous approach, which becomes exact in the thermodynamic limit, has been used for isolated systems [62][63][64][65][66][67][68][69][70][71], to explore critical phenomena [72][73][74], as well as in open quantum systems [75][76][77][78][79], for instance to witness dissipative generation of entanglement in mesoscopic systems [80][81][82]. Here, we use it to investigate spin squeezing of the emitter ensemble and to demonstrate critical power-law dynamics of quantum correlations at the boundary between two different non-equilibrium phases.…”

“…Recently, spin squeezing in the steady state of dissipative systems has been explored in cavity QED setups [90] and in the non-equilibrium dynamics of an ensemble of superconduncting qubits [91]. In order to study quantum correlations within the emitter ensemble we will exploit the theory of quantum fluctuation operators [58][59][60][61], applied to open quantum systems [76][77][78][79][80][81][82]. For our model, this allows us to obtain rigorous analytical results in the thermodynamic limit.…”