Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Multi-level quantum emitter in an optical waveguide: paradoxes and resolutions

Ben Lang

TL;DR

The paper develops a general, non-cascaded, multi-level QE–WG scattering framework based on a Green's-function formalism, treating forward and backward WG modes and incorporating loss via $\mathbf{G}_{\text{loss}}$ and a matrix $\overline{\Gamma}$ for excited-state interactions. It reveals two paradoxical phenomena: transiently, two non-orthogonal QE states can produce opposite-direction photon flux without violating unitarity; and an isotropically polarizable QE can switch between full transmission and full reflection with infinitesimal polarization changes, with losses smoothing the transition. It further shows that a four-level IXI QE enables a non-destructive two-mode parity measurement of the photon number in the WG, potentially useful for quantum information processing. These results underscore the sensitivity of QE–WG coupling to local polarization and the practical importance of losses, while offering a framework for exploring chiral and parity-based photonic devices.

Abstract

We theoretically investigate the optical dipole interaction between a multi-level quantum system and a single-mode optical waveguide of any local polarisation. We investigate several paradoxical seeming situations, for example we find a situation in which there exist two non-orthogonal quantum states, each of which results in a photon flux in the opposite direction to the other. We show how, despite appearances, this does not break the unitary requirements of quantum mechanics. We also find that an isotropic quantum emitter can be either reflective or transmissive to light depending on the waveguide polarisation at the emitter location, indeed in the zero loss limit such a system changes from 100% transmission to 100% reflection due to an infinitesimal polarisation rotation. An example case for a four level system is also considered, which is found to operate as a non-destructive parity measurement of the photon number.

Multi-level quantum emitter in an optical waveguide: paradoxes and resolutions

TL;DR

The paper develops a general, non-cascaded, multi-level QE–WG scattering framework based on a Green's-function formalism, treating forward and backward WG modes and incorporating loss via and a matrix for excited-state interactions. It reveals two paradoxical phenomena: transiently, two non-orthogonal QE states can produce opposite-direction photon flux without violating unitarity; and an isotropically polarizable QE can switch between full transmission and full reflection with infinitesimal polarization changes, with losses smoothing the transition. It further shows that a four-level IXI QE enables a non-destructive two-mode parity measurement of the photon number in the WG, potentially useful for quantum information processing. These results underscore the sensitivity of QE–WG coupling to local polarization and the practical importance of losses, while offering a framework for exploring chiral and parity-based photonic devices.

Abstract

We theoretically investigate the optical dipole interaction between a multi-level quantum system and a single-mode optical waveguide of any local polarisation. We investigate several paradoxical seeming situations, for example we find a situation in which there exist two non-orthogonal quantum states, each of which results in a photon flux in the opposite direction to the other. We show how, despite appearances, this does not break the unitary requirements of quantum mechanics. We also find that an isotropic quantum emitter can be either reflective or transmissive to light depending on the waveguide polarisation at the emitter location, indeed in the zero loss limit such a system changes from 100% transmission to 100% reflection due to an infinitesimal polarisation rotation. An example case for a four level system is also considered, which is found to operate as a non-destructive parity measurement of the photon number.
Paper Structure (14 sections, 54 equations, 4 figures)

This paper contains 14 sections, 54 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Model
  3. Results
  4. Distinguishing non-orthogonal Quantum states
  5. Basis Symmetry
  6. Scattering from an Isotopically polarisable QE
  7. Multiple Ground States
  8. Conclusion
  9. Scattering Derivation
  10. Long Photon Limit
  11. Even orders
  12. Emission Derivation
  13. Interaction Picture
  14. Green's function Hamiltonian

Figures (4)

  • Figure 1: Diagram of the interaction between a Quantum Emitter (QE) and Waveguide (WG). The QE is characterized by a set of energy levels with each transition between energy levels controlled by a complex vector transition dipole. The WG possesses a forward and backward optical mode, with the forward mode electric polarisation at the location of the QE controlling the interaction. Loss into non-waveguide modes is also possible.
  • Figure 2: Time evolution of QE-WG system. Inset: picture of a V-like system with degenerate excited states and orthogonal linear transition dipoles. The WG has local forward mode has polarisation $E_f = (2, \text{i} )/\sqrt{5}$
  • Figure 3: Photon scattering from an isotropic QE system, represented by V type energy levels as shown in the inset. The transmission ($t$) and reflection ($r$) coefficients are plotted for two different levels of non-WG mode loss mode coupling (see text), as a function of the polarisation of the WG at the QE location, depicted along the $x$-axis.
  • Figure 4: Photon scattering from a four-level QE as drawn in the inset, as a function of the polarisation of the WG at the QE location, depicted along the $x$-axis. For circular polarisation the photon transmits while toggling the ground state of the QE, as shown for one of the two circular polarisations in the bubble. Green circle on insets: initial state.