Non-perturbative treatment of giant atoms using chain transformations

Abstract

Superconducting circuits coupled to acoustic waveguides have extended the range of phenomena that can be experimentally studied using tools from quantum optics. In particular giant artificial atoms permit the investigation of systems in which the electric dipole approximation breaks down and pronounced non-Markovian effects become important. While previous studies of giant atoms focused on the realm of the rotating-wave approximation, we go beyond this and perform a numerically exact analysis of giant atoms strongly coupled to their environment, in regimes where counterrotating terms cannot be neglected. To achieve this, we use a Lanczos transformation to cast the field Hamiltonian into the form of a one-dimensional chain and employ matrix-product state simulations. This approach yields access to a wide range of system-bath observables and to previously unexplored parameter regimes.

Ultrastrong waveguide QED with giant atoms

“…In contrast, our simulations indicate that entering the USC regime leads to the loss of the oscillating bound state due to the renormalization of ∆ r and eventually to the quantum phase transition. This same trend has also been recently reported in [64] where matrix product states simulations showed this same breakdown of the periodicity for the existence of oscillating bound states in parameter space with the coupling strength.…”

“…Some interest has been aroused in the existence of oscillating bound states [13,64]. They originate from the interplay of two coexisting bound states.…”

“…Different techniques are available in the literature to deal with it, such as Matrix-product states [42,44,45], density matrix renormalization group [53], hierarchical equations of motion or pseudomodes methods [54], and path integral [55,56], polaron-like [43,[57][58][59][60][61][62] or Gaussian approaches [63]. During the completion of this work, it has been recently reported [64] how to use matrix product states to describe the dynamics of giant atoms in a waveguide in the USC regime.…”

Giant atoms with time-dependent couplings

“…To date, there have been a variety of intriguing phenomena witnessed in giant-atom structures, such as frequency-dependent Lamb shifts and relaxation rates [8], decoherence-free interatomic interactions [9,[11][12][13][14], unconventional bound states [15][16][17][18][19][20][21], and phase-controlled frequency conversions [22,23]. Most recently, giant atoms have also been extended to the nonperturbative regime [24], to chiral quantum optics [12-15, 25, 26], and to synthetic dimensions [27].…”