Supersymmetry in quantum optics and in spin-orbit coupled systems

Abstract

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, the stationary density matrix at the supersymmetric lines in parameter space has a degenerate subspace. The dimension of this subspace is given by the Witten index and thus is topologically protected. As a consequence, the dissipative dynamics is constrained by a robust additional conserved quantity which translates information about an initial state into the stationary state. 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. 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 SUSY field theories.

Dissipative quantum phase transitions of light in a generalized Jaynes-Cummings-Rabi model

“…Although the former was originally approached through exact calculations in the thermodynamic limit for N two-state systems in thermal equilibrium, and the latter as a phenomenon of single systems, both might be engineered in many-and one-two-state-system versions, with the same underlying mean-field phenomenology and where the central issue of photon number in the presence of dissipation is governed not by the number of two-state systems only, but also the ratio of coupling strength to photon loss [25]-even one two-state system can control many photons in cavity and circuit QED [26,29]. We adopted a generalization introduced by Hepp and Lieb [30], and taken up in a number of recent publications [31][32][33][34][35][36][37][38], where the interaction Hamiltonian is made from a sum of rotating and counter-rotating terms of variable relative strength; in this way we span the continuum from the Jaynes-Cummings to the quantum Rabi interaction. We also added direct driving of the field mode, since that, not the counter-rotating interaction, creates photons in the breakdown of photon blockade.…”

“…(12)); and, second, we add external coherent driving of the field mode. The first extension was made by Hepp and Lieb [30], in a quick followup to their original paper; the generalized interaction Hamiltonian is also featured in a number of recent publications [31][32][33][34][35][36][37][38]. A key link in our unification is a phase that went unreported by Hepp and Lieb.…”

Tunable spin-orbit coupling for ultracold atoms in two-dimensional optical lattices

“…Spin-dependent optical lattices provide a realistic platform where our scheme can be used to implement Rashba and Dresselhaus SOC with fully tunable strengths. We expect that this will not only enable quantum simulations of ubiquitous model Hamiltonians known from solid-state physics, but also allows for an experimental investigation of exotic physics related to SOC, ranging from studies of supersymmetric Hamiltonians [50] to statistical transmutations induced by strong interactions [12].…”

A unified treatment of polynomial solutions and constraint polynomials of the Rabi models

“…The condition that S n (z) solves (7) is equivalent to that all the coefficients of respective powers of z of the image LS n (z) of S n (z) vanish. The latter brings us to the linear system of equations F γ−1 (n) + a n,n−1 F γ (n − 1) = 0, F γ−2 (n) + a n,n−1 F γ−1 (n − 1) + a n,n−2 F γ (n − 2) = 0, .…”

“…In what follows we shall consider the (driven) Rabi model [11][12][13][14][15], together with its nonlinear two-photon [8,11,12,16,17] and nonlinear two-mode [8,11,12] versions, and the generalized Rabi model of Refs. [6][7][8]. A typical 2nd order linear ordinary differential equation (ODE) for the Rabi models turns out to be of the form Lψ = 0, where L = l p l (z)d l z , p l (z) are polynomials, z is a one-dimensional coordinate, and d z = d/dz.…”