Abstract
At the quantum many-body level, atom-light interfaces generally remain challenging to solve for or understand in a non-perturbative fashion. Here, we consider a waveguide quantum electrodynamics model, where two-level atoms interact with and via propagating photons in a one-dimensional waveguide, and specifically investigate the interplay of atomic position disorder, multiple scattering of light, quantum nonlinear interactions and dissipation. We develop qualitative arguments and present numerical evidence that such a system exhibits a many-body localized~(MBL) phase, provided that atoms are less than half excited. Interestingly, while MBL is usually formulated with respect to closed systems, this system is intrinsically open. However, as dissipation originates from transport of energy to the system boundaries and the subsequent radiative loss, the lack of transport in the MBL phase makes the waveguide QED system look essentially closed and makes applicable the notions of MBL. Conversely, we show that if the system is initially in a delocalized phase due to a large excitation density, rapid initial dissipation can leave the system unable to efficiently transport energy at later times, resulting in a dynamical transition to an MBL phase. These phenomena can be feasibly realized in state-of-the-art experimental setups.
Highlights
Quantum light-matter interfaces are being actively investigated, for their many possibilities to explore fundamental science and for applications [1,2]
Considering that any physical system will consist of finite atom number, we propose that its dynamical behavior, if it begins in the delocalized phase, will consist of transport-facilitated dissipation, until it reaches an many-body localized (MBL) phase, as illustrated by the arrow showing evolution in time
We have proposed and presented numerical evidence that a system of disordered atoms coupled to a waveguide exhibits an MBL phase, provided that the density of atomic excitations is less than 1/2
Summary
The key properties of MBL can be understood from a “canonical” Hamiltonian hypothesized for all MBL systems. Because HLIOM only involves products of τz operators, each τzj commutes with the Hamiltonian and their occupancies are conserved quantities As these operators only have support on a few sites, there will be no transport of energy, and an MBL system prepared initially out of equilibrium will never thermalize. The interactions differentiate MBL from Anderson localization, and cause each local integral of motion τzi to acquire different phases in evolution depending on the occupancy of other τzj. For closed systems, this results in a dephasing for any local subsystem, due to the gradual entanglement of these degrees of freedom with others further away. Systems that do not exhibit MBL experience a ballistic growth of entanglement entropy (linear with time)
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