In statistical mechanics, any quantum system in equilibrium with its weakly coupled reservoir is described by a canonical state at the same temperature as the reservoir. Here, by studying the equilibration dynamics of a harmonic oscillator interacting with a reservoir, we evaluate microscopically the condition under which the equilibration to a canonical state is valid. It is revealed that the non-Markovian effect and the availability of a stationary state of the total system play a profound role in the equilibration. In the Markovian limit, the conventional canonical state can be recovered. In the non-Markovian regime, when the stationary state is absent, the system equilibrates to a generalized canonical state at an effective temperature; whenever the stationary state is present, the equilibrium state of the system cannot be described by any canonical state anymore. Our finding of the physical condition on such noncanonical equilibration might have significant impact on statistical physics. A physical scheme based on circuit QED is proposed to test our results.

Enabling the confinement of light to a scale far below the one of conventional optics, surface plasmon polaritons (SPPs) induced by an electromagnetic field in a metal-dielectric interface supply an ideal system to explore strong quantized light-matter coupling. The fast matter-SPP population exchange reported in previous works makes it a candidate for spin manipulation, but such reversible dynamics asymptotically vanishes accompanying the quantum matter relaxing completely to its ground state. Here, we study the exact dissipative dynamics of a quantum emitter (QE) coupled to SPPs. It is interesting to find that, qualitatively different from conventional findings, the QE can be partially stabilized in its excited state even in the presence of the lossy metal. Our analysis reveals that it is the formation of a QE-SPP bound state which results in such suppressed dissipation. Enriching the decoherence dynamics of the QE in the lossy medium, our result is helpful to understand QE-SPP interactions and apply plasmonic nanostructures in quantum devices.Introduction.-Surface plasmon polaritons (SPPs) triggered by an electromagnetic field along a metaldielectric interface supply an ideal platform to explore strong quantized light-matter coupling [1][2][3][4][5]. Such couplings were achieved conventionally in cavity and circuit QED by boosting the interaction times, but at the price of a limited optical bandwidth and diffraction size [6][7][8][9]. Realizing strong confinement of light below the diffraction limit, SPPs have inspired great interest in studying subwavelength optics and quantum plasmonics [10,11]. Much effort has been made to realize strong or even ultrastrong coupling between SPPs and a quantum emitter (QE) made of, for example, quantum dots, quantum defects, or nitrogen vacancy centers [12][13][14]. It makes surface plasmonics a promising platform to design quantum devices [15][16][17][18], where the coupling is a prerequisite. However, the dissipation induced by the lossy metal to the QE severely limits its practical use.Owing to the strong spatial confinement of the radiation field of the QE near the metal-dielectric interface, the decoherence dynamics of the QE exhibits significant reversibility. Based on the dyadic Green's tensor formalism, the quantization of an electromagnetic field in a lossy medium was developed in Ref. [19], from which the quantized interactions between QE and SPPs can be studied. It was found that the spectral density of the SPPs approaches a Lorentzian form when the QEinterface distance is much smaller than the typical wavelength of the SPPs [20]. In this regime, the decoherence of the QE caused by the SPPs can be approximately stimulated by a Markovian one with QE coupled to an artificial pseudo damping cavity mode [21][22][23][24][25][26][27][28]. Thus one can use the well-developed tools in cavity QED to study QE-SPP interactions. Based on this method, the interplay between quenching and strong coupling of QE near a metal nanoparticle [26] and the dissipative dynamics of QE ne...

Confining light to scales beyond the diffraction limit, quantum plasmonics supplies an ideal platform to explore strong light-matter couplings. The light-induced localized surface plasmons (LSPs) on the metal-dielectric interface acting as a quantum bus have wide potential in quantum information processing; however, the loss nature of light in the metal hinders their application. Here we propose a mechanism to make the reversible energy exchange and the multipartite quantum correlation of a collective of quantum emitters (QEs) mediated by the LSPs persistent. Via investigating the quantized interaction between the QEs and the LSPs supported by a spherical metal nanoparticle, we find that the diverse signatures of the quantized QE-LSP coupling in the steady state, including the complete decay, population trapping, and persistent oscillation, are essentially determined by the different number of bound states formed in the energy spectrum of the QE-LSP system. Enriching our understanding on the light-matter interactions in a lossy medium, our result is instructive in the design of quantum devices using plasmonic nanostructures.