We provide a complete and exact quantum description of coherent light scattering in a one-dimensional multi-mode transmission line coupled to a two-level emitter. Using recently developed scattering approach we discuss transmission properties, power
spectrum, the full counting statistics and the entanglement entropy of transmitted and reflected states of light. Our approach takes into account spatial parameters of an incident coherent pulse as well as waiting and counting times of a detector. We describe time evolution of the power spectrum as well as observe deviations from the Poissonian statistics for reflected and transmitted fields. In particular, the statistics of reflected photons can change from sub-Poissonian to super-Poissonian for increasing values of the detuning, while the statistics of transmitted photons is strictly super-Poissonian in all parametric regimes. We study the entanglement entropy of some spatial part of the scattered pulse and observe that it obeys the area laws and that it is bounded by the maximal entropy of the effective four-level system.
Light-matter interaction is naturally described by coupled bosonic and fermionic subsystems. This suggests that a certain Bose-Fermi duality is naturally present in the fundamental quantum mechanical description of photons interacting with atoms. We
reveal submanifolds in parameter space of a basic light-matter interacting system where this duality is promoted to a supersymmetry (SUSY) which remains unbroken. We show that SUSY is robust with respect to decoherence and dissipation. In particular, a stationary density matrix at the supersymmetric lines in the parameter space has a degenerate subspace. A dimension of this subspace is given by the Witten index and thus topologically protected. As a consequence of this SUSY, dissipative dynamics at the supersymmetric lines is constrained by an additional conserved quantity which translates some part of information about an initial state into the stationary state subspace. We also demonstrate a robustness of this additional conserved quantity away from the supersymmetric lines. In addition, we demonstrate that the same SUSY structures are present in condensed matter systems with spin-orbit couplings of Rashba and Dresselhaus types, and therefore spin-orbit coupled systems at the SUSY lines should be robust with respect to various types of disorder and decoherences. Our findings suggest that optical and condensed matter systems at the SUSY points can be used for quantum information technology and can open an avenue for quantum simulation of the SUSY field theories.
We study the spectrum of the generalized Rabi model in which co- and counter-rotating terms have different coupling strengths. It is also equivalent to the model of a two-dimensional electron gas in a magnetic field with Rashba and Dresselhaus spin-o
rbit couplings. Like in case of the Rabi model, the spectrum of the generalized Rabi model consists of the regular and the exceptional parts. The latter is represented by the energy levels which cross at certain parameters values which we determine explicitly. The wave functions of these exceptional states are given by finite order polynomials in the Bargmann representation. The roots of these polynomials satisfy a Bethe ansatz equation of the Gaudin type. At the exceptional points the model is therefore quasi-exactly solvable. An analytical approximation is derived for the regular part of the spectrum in the weak- and strong-coupling limits. In particular, in the strong-coupling limit the spectrum consists of two quasi-degenerate equidistant ladders.
A complete characterization of quantum fluctuations in many-body systems is accessible through the full counting statistics. We present an exact computation of statistical properties of light in a basic model of light-matter interaction: a multimode
photonic field coupled to a single two-level emitter. We mostly consider an initial coherent state in a given mode and demonstrate how the original Poissonian statistics gets modified because of quantum many-body scattering effects leading to non-Poissonian distributions. We argue that measuring this statistics in a simple quantum optical setup provides an insight into many-body correlation effects with photons.
