Spectral functions and negative density of states of a driven-dissipative nonlinear quantum resonator

Abstract

Keywords: open quantum systems, quantum van der pol oscillator, driven and dissipative quantum systems AbstractWe study the spectral properties of Markovian driven-dissipative quantum systems, focusing on the nonlinear quantum van der Pol oscillator as a paradigmatic example. We discuss a generalized Lehmann representation, in which single-particle Greenʼs functions are expressed in terms of the eigenstates and eigenvalues of the Liouvillian. Applying it to the quantum van der Pol oscillator, we find a wealth of phenomena that are not apparent in the steady-state density matrix alone. Unlike the steady state, the photonic spectral function has a strong dependence on interaction strength. Further, we find that the interplay of interaction and non-equilibrium effects can result in a surprising 'negative density of states', associated with a negative temperature, even in absence of steady state population inversion.

Exact solutions of interacting dissipative systems via weak symmetries

“…( 1) has an obvious weak U (1) symmetry, as it is invariant under â → e −iθ â. This gives L a block-diagonal structure [2-4, 8, 29], which has been used previously to simplify numerical calculations [7,8]. We show below that something more powerful is possible: despite the nonlinearity, the weak symmetry can also be used to analytically diagonalize each block and thus all of L. Our analysis complements and extends previous studies that derive exact results for this model without explicit use of weak symmetry [11][12][13][14].…”

“…the Liouvillian) has a block-diagonal structure, it does not guarantee the existence of a true conserved quantity. Hence, while such weak symmetries can simplify numerical calcuations [7,8], they are not a priori a useful tool for obtaining analytic solutions.…”

Theory of relaxation and pumping of quantum oscillator non-resonantly coupled with the other oscillator

“…Effective research of attenuating quantum systems were made possible due to the introduction of the notion of a kinetic equation (master equation) into the mathematical apparatus of nonlinear and quantum optics [1][2][3].In [4][5], the general form of the kinetic equation is established, that is now commonly referred to as the Lindblad-type of the kinetic equation. Many recently published papers on the analysis of open quantum systems dynamics start with the definition (as initial ones) of precisely kinetic equations in the Lindblad form with a predefined Lindblad operators.In view of this, researchers consider atomic systems interacting with electromagnetic fields of various nature [6-9], photon systems consisting of photons of cavity modes interacting with other cavity systems, with intracavity and boundary atoms [10][11][12][13], and other optical problems.Since the relaxation channels are already defined by the appropriate terms and Lindblad operators in the initial equations, the majority of further approximations, and, in particular, dispersion approximation do not adequately describe the case under study. In fact, in optics, the initial Hamiltonian of two non-resonantly interacting atoms has both rapidly and slowly varying terms.…”

Steady-State Quantum Zeno Effect of Driven-Dissipative Bosons with Dynamical Mean-Field Theory

“…and which encode, respectively, the spectrum and occupation of single-particle excitations on top of the stationary state [48,58]. Once the DMFT self-consistency has been reached, these functions coincide with the analogous quantities at the impurity site; we plot them in Fig.…”