Long-Lived Mesoscopic Entanglement Between Two Damped Infinite Harmonic Chains

Abstract

We consider two chains, each made of N independent oscillators, immersed in a common thermal bath and study the dynamics of their mutual quantum correlations in the thermodynamic, large-N limit. We show that dissipation and noise due to the presence of the external environment are able to generate collective quantum correlations between the two chains at the mesoscopic level. The created collective quantum entanglement between the two many-body systems turns out to be rather robust, surviving for asymptotically long times even for non vanishing bath temperatures.

Quantum fluctuations in mesoscopic systems

“…As in the case of spin chains discussed earlier, let us take as initial state the mesoscopic Gaussian state Ω β , further squeezed with a real parameter r along the first two modes. The entanglement content of the reduced state at any later time t can then be analyzed by looking at the corresponding logarithmic negativity E(t) as defined in (100), which also in this can be analytically computed [123,125]. One easily sees that E(t) become positive in a finite time, reaching a maximum, whose value increases as the dissipative parameter λ gets larger and the initial bath temperature lowers.…”

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.…”

Dynamical phases and quantum correlations in an emitter-waveguide system with feedback

“…The measurement of the light emitted into the right-propagating mode via homodyne detection is fed back as a modulation of the laser field with strength g. 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], to explore critical phenomena [70][71][72], as well as in open quantum systems [73][74][75][76][77], for instance to witness dissipative generation of entanglement in mesoscopic systems [78][79][80]. 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 nonequilibrium phases.…”

“…Recently, spin squeezing in the steady state of dissipative systems has been explored in cavity QED setups [88] and in the non-equilibrium dynamics of an ensemble of superconduncting qubits [89]. 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 [74][75][76][77][78][79][80]. For our model, this allows us to obtain rigorous analytical results in the thermodynamic limit.…”