A simple kinetic model is proposed to investigate the effect of nonlinearity and the role of fluctuations in the metastable behavior of spin systems. Nonlinearity is introduced by a sum-rule condition for spin-correlation functions. There appear a long-lived flat part of the magnetizations and transient enhancements of the long-range fluctuations in the course of relaxations from thermodynamically unstable state. An effective, time-dependent potential picture is also obtained by eliminating the fluctuations. The transient enhancements of long-range fluctuations suppress the central potential barrier. In other words this can be interpreted as a by-pass effect caused by the degrees of freedom of spatial fluctuations.A simple kinetic model is proposed to investigate the effect of nonlinearity and the role of fluctuations in the metastable behavior of spin systems. Nonlinearity is introduced by a sum-rule condition for spin-correlation functions. There appear a long-lived flat part of the magnetizations and transient enhancements of the long-range fluctuations in the course of relaxations from thermodynamically unstable state. An effective, time-dependent potential picture is also obtained by eliminating the fluctuations. The transient enhancements of long-range fluctuations suppress the central potential barrier. In other words this can be interpreted as a by-pass effect caused by the degrees of freedom of spatial fluctuations.

Progress of Theoretical Physics SupplementJan 1, 19785 citations

Emergent Coherent Transport and Synthetic Geometry in Simulated Floquet-Driven Rydberg Arrays via Vacuum--Photonic Quasienergy Channels

Cinque McFarlane - Blake

We simulate periodically driven Rydberg arrays with purely imaginary-phase driving, showing that it reshapes both internal dynamics and the structure of coupled vacuum fluctuations. In a driven Rydberg array, this interplay produces\emph{hybrid vacuum--photonic quasienergy channels}---coherent,directional modes arising from Floquet-induced modulation of theelectromagnetic local density of states (LDOS). These channels enable a coherent mapping of correlation structure far beyond the nominal dipolar range andexhibit stability characteristic of attractor-like Floquet fixed points. Using a microscopic Hamiltonian with spatiotemporally structureddipole--vacuum coupling, we derive a Floquet--Magnus expression for theeffective LDOS: $\rho_{\rm eff}(\omega)=\sum_m J_m^2(A)\,\rho_0(\omega+m\Omega),$ revealing how the drive imprints anisotropic vacuum structure.Large-scale open-system simulations confirm that this LDOS reshapingproduces long-lived, quasienergy-resolved photonic corridors, alongwhich correlation fronts propagate with direction-dependent velocities. We further show that the system's long-time behavior is well describedby an \emph{effective geometric picture}: anisotropic correlationfronts define a synthetic light cone, LDOS-induced anisotropies definean emergent spatial metric, and wavepacket bundle separation obeys ageodesic-deviation-like equation whose curvature is determined directlyfrom simulated trajectories over thousands of drive periods. We conclude with a speculative perspective: if driven matter can imprintstable geometric structure onto the vacuum LDOS, then controlled analogspacetime engineering---without material waveguides or externalphotonic scaffolds---may be achievable.We simulate periodically driven Rydberg arrays with purely imaginary-phase driving, showing that it reshapes both internal dynamics and the structure of coupled vacuum fluctuations. In a driven Rydberg array, this interplay produces\emph{hybrid vacuum--photonic quasienergy channels}---coherent,directional modes arising from Floquet-induced modulation of theelectromagnetic local density of states (LDOS). These channels enable a coherent mapping of correlation structure far beyond the nominal dipolar range andexhibit stability characteristic of attractor-like Floquet fixed points. Using a microscopic Hamiltonian with spatiotemporally structureddipole--vacuum coupling, we derive a Floquet--Magnus expression for theeffective LDOS:\[\rho_{\rm eff}(\omega)=\sum_m J_m^2(A)\,\rho_0(\omega+m\Omega),\]revealing how the drive imprints anisotropic vacuum structure.Large-scale open-system simulations confirm that this LDOS reshapingproduces long-lived, quasienergy-resolved photonic corridors, alongwhich correlation fronts propagate with direction-dependent velocities. We further show that the system's long-time behavior is well describedby an \emph{effective geometric picture}: anisotropic correlationfronts define a synthetic light cone, LDOS-induced anisotropies definean emergent spatial metric, and wavepacket bundle separation obeys ageodesic-deviation-like equation whose curvature is determined directlyfrom simulated trajectories over thousands of drive periods. We conclude with a speculative perspective: if driven matter can imprintstable geometric structure onto the vacuum LDOS, then controlled analogspacetime engineering---without material waveguides or externalphotonic scaffolds---may be achievable.

Feb 6, 20260 citations

Long-Range Correlations in Classical and Quantum Systems

Nikolai Nikolaevich Bogoliubov, D. N. Zubarev, V. V. Tolmatchev +1 more

Jan 1, 19630 citations

Vacuum state squeezing versus squeezed classical noise: a test using conditional homodyne detection

H. J. Carmichael

Measurement of the squeezed fluctuations of an optical field by the method of conditional homodyne detection is discussed. It is shown that conditional homodyne detection is able to distinguish qualitatively between vacuum-state squeezing and squeezed classical noise. Whereas for conventional squeezed-light detection, only a quantitative distinction can be made, based on the setting of the shot-noise level, under conditional detection, the presence of classical noise changes the actual shape of the measured correlation function. The correlations show a positive peak due to the unsqeezed classical noise frequencies, set inside the negative dip associated with the squeezed fluctuations. The width in time of the positive peak is the larger of the detector response time and the inverse of the classical noise bandwidth. The fundamental distinction between vacuum-state squeezing and squeezed classical noise is that there is no positive peak, even in the limiting form of a delta-function, when the unsqueezed frequencies correspond to vacuum state modes. Implications for the literal interpretation of vacuum fluctuations, such as is adopted in stochastic electrodynamics, are discussed. The ideas are presented in general terms and illustrated by an example which treats the generation and detection of broadband squeezed light, including finite-bandwidth classical noise, within the framework of the quantum trajectory theory of cascaded open systems.Measurement of the squeezed fluctuations of an optical field by the method of conditional homodyne detection is discussed. It is shown that conditional homodyne detection is able to distinguish qualitatively between vacuum-state squeezing and squeezed classical noise. Whereas for conventional squeezed-light detection, only a quantitative distinction can be made, based on the setting of the shot-noise level, under conditional detection, the presence of classical noise changes the actual shape of the measured correlation function. The correlations show a positive peak due to the unsqeezed classical noise frequencies, set inside the negative dip associated with the squeezed fluctuations. The width in time of the positive peak is the larger of the detector response time and the inverse of the classical noise bandwidth. The fundamental distinction between vacuum-state squeezing and squeezed classical noise is that there is no positive peak, even in the limiting form of a delta-function, when the unsqueezed frequencies correspond to vacuum state modes. Implications for the literal interpretation of vacuum fluctuations, such as is adopted in stochastic electrodynamics, are discussed. The ideas are presented in general terms and illustrated by an example which treats the generation and detection of broadband squeezed light, including finite-bandwidth classical noise, within the framework of the quantum trajectory theory of cascaded open systems.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEMay 16, 20031 citation

\rho_{\rm eff}(\omega)=\sum_m J_m^2(A)\,\rho_0(\omega+m\Omega),

revealing how the drive imprints anisotropic vacuum structure.Large-scale open-system simulations confirm that this LDOS reshapingproduces long-lived, quasienergy-resolved photonic corridors, alongwhich correlation fronts propagate with direction-dependent velocities. We further show that the system's long-time behavior is well describedby an \emph{effective geometric picture}: anisotropic correlationfronts define a synthetic light cone, LDOS-induced anisotropies definean emergent spatial metric, and wavepacket bundle separation obeys ageodesic-deviation-like equation whose curvature is determined directlyfrom simulated trajectories over thousands of drive periods. We conclude with a speculative perspective: if driven matter can imprintstable geometric structure onto the vacuum LDOS, then controlled analogspacetime engineering---without material waveguides or externalphotonic scaffolds---may be achievable.