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arXiv:1107.0905 · International Journal of Modern Physics B

FLUCTUATIONS ASSISTED STATIONARY ENTANGLEMENT IN DRIVEN QUANTUM SYSTEMS

Dimitris G. Angelakis, STEFANO MANCINI

Published Nov 1, 2012• 1 citation
arXivHTMLPDF

Abstract

We analyze quantum correlations arising in two coupled dimer systems in the presence of independent losses and driven by a fluctuating field. For the case of the interaction being of a Heisenberg exchange type, we first analytically show the possibility for stationary entanglement and then analyze its robustness as a function of the signal-to-noise ratio of the pump. We find that for a common fluctuating driving field, stochastic resonance effects appear as function of the ratio between field strength and noise strength. The effect disappears in the case of uncorrelated or separate pumps. Our result is general and could be applied to different quantum systems ranging from electron spins in solid state, to ions trap technologies and cold atom set ups.

DOI
10.1142/s0217979213450379

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We analyze quantum correlations arising in two coupled dimer systems in the presence of independent losses and driven by a fluctuating field. For the case of the interaction being of a Heisenberg exchange type, we first analytically show the possibility for stationary entanglement and then analyze its robustness as a function of the signal-to-noise ratio of the pump. We find that for a common fluctuating driving field, stochastic resonance effects appear as function of the ratio between field strength and noise strength. The effect disappears in the case of uncorrelated or separate pumps. Our result is general and could be applied to different quantum systems ranging from electron spins in solid state, to ions trap technologies and cold atom set ups.
We discuss stochastic resonance–like effects in the context of coupled quantum spin systems. We focus here on an information–theoretic approach and analyze the steady state quantum correlations (entanglement) as well as the global correlations in the system when subject to different forms of local decoherence. In the presence of decay, it has been shown that the system displays quantum correlations only when the noise strength is above a certain threshold. We extend this result to the case of a Heisenberg XY Z exchange interaction and revise and clarify the mechanisms underlying this behaviour. In the presence of pure dephasing, we show that the system always remains separable in the steady state. When both types of noise are present, we show that the system can still exhibit entanglement for long times, provided that the pure dephasing rate is not too large.
We discuss stochastic resonance (SR) effects in weakly driven coupled quantum systems. We show that both dynamical and information theoretic measures of the system's response can be introduced that exhibit a non-monotonic behaviour as a function of the noise strength. We analyze the relation between lack of monotonicity in the response and the presence of quantum correlations, showing that there are parameter regimes where the breakdown of a linear response can be associated to the presence of entanglement. We also show that a chain of coupled spin systems can exhibit an array-enhanced response, where the sensitivity of a single resonator to a weak driving signal is enhanced as a result of the nearest-neighbour coupling. These results enlarge the domain where SR effects exist and should be observable in state-of-the-art arrays of superconducting qubits.
We discuss stochastic resonance (SR) effects in driven coupled quantum systems. We construct dynamical and information-theoretic measures of the system's response that exhibit a nonmonotonic behavior as a function of the noise strength. We analyze the relation between lack of monotonicity in the response and the presence of quantum correlations and identify parameter regimes where the breakdown of a linear response can be linked to the presence of entanglement. We also show that a chain of coupled spin systems can exhibit an array-enhanced response, where the sensitivity of a single resonator is enhanced as a result of nearest-neighbor coupling. These results enlarge the domain where SR effects exist and should be observable in arrays of superconducting qubits.
We analytically investigate the fidelity dynamics of a Jaynes--Cummings qubit coupled to a single-mode cavity in the presence of stochastic fluctuations of the qubit--cavity coupling. Such fluctuations naturally arise in cavity- and circuit-QED platforms due to fabrication imperfections, control-field noise, mechanical vibrations, and environmental disturbances. Since the qubit--cavity coupling governs the rate of coherent energy and information exchange, understanding the effects of its fluctuations is essential for assessing the performance of quantum communication, quantum sensing, and quantum information-processing protocols. We consider both Gaussian white noise and Ornstein--Uhlenbeck noise with finite correlation time as models for the coupling fluctuations. Exploiting the closed dynamics within each excitation manifold, we derive exact analytical expressions for the noise-averaged density matrix and the fidelity relative to the ideal noiseless evolution. We show that the fidelity is determined by a single decoherence factor governed by the integrated noise correlation function, establishing a direct connection between microscopic coupling fluctuations and macroscopic coherence loss. In the white-noise limit, the fidelity decays exponentially, whereas finite noise correlation times produce nonexponential decay and slower coherence loss. We further show that the crossover between Markovian-like and non-Markovian regimes is controlled by the ratio of the noise correlation rate to the coherent coupling strength, and that decoherence increases with photon number because of the enhanced effective qubit--cavity coupling. These results provide a unified analytical framework for quantifying decoherence induced by stochastic coupling fluctuations and for evaluating the robustness of cavity-QED protocols under correlated noise.
A system of coherently driven two-level atoms is analysed in the presence of two independent stochastic perturbations: one due to collisions and a second due to phase fluctuations of the driving field. The behaviour of the quantum interference induced by the collisional noise is considered in detail. The quantum-trajectory method is utilized to reveal the phase correlations between the dressed states involved in the interfering transition channels. It is shown that the quantum interference induced by the collisional noise is remarkably robust against phase noise. This effect is due to the fact that the phase noise, similarly to collisions, stabilizes the phase difference between the dressed states.
We investigate the properties of angular-momentum states which yield high sensitivity to rotation. We discuss the application of these ``squeezed-spin'' or correlated-particle states to spectroscopy. Transitions in an ensemble of N two-level (or, equivalently, spin-1/2) particles are assumed to be detected by observing changes in the state populations of the particles (population spectroscopy). When the particles' states are detected with 100% efficiency, the fundamental limiting noise is projection noise, the noise associated with the quantum fluctuations in the measured populations. If the particles are first prepared in particular quantum-mechanically correlated states, we find that the signal-to-noise ratio can be improved over the case of initially uncorrelated particles. We have investigated spectroscopy for a particular case of Ramsey's separated oscillatory method where the radiation pulse lengths are short compared to the time between pulses. We introduce a squeezing parameter ${\ensuremath{\xi}}_{\mathit{R}}$ which is the ratio of the statistical uncertainty in the determination of the resonance frequency when using correlated states vs that when using uncorrelated states. More generally, this squeezing parameter quantifies the sensitivity of an angular-momentum state to rotation. Other squeezing parameters which are relevant for use in other contexts can be defined. We discuss certain states which exhibit squeezing parameters ${\ensuremath{\xi}}_{\mathit{R}}$\ensuremath{\simeq}${\mathit{N}}^{\mathrm{\ensuremath{-}}1/2}$. We investigate possible experimental schemes for generation of squeezed-spin states which might be applied to the spectroscopy of trapped atomic ions. We find that applying a Jaynes-Cummings--type coupling between the ensemble of two-level systems and a suitably prepared harmonic oscillator results in correlated states with ${\ensuremath{\xi}}_{\mathit{R}}$1.