Atom-field dressed states in slow-light waveguide QED

Calajò, Giuseppe; Ciccarello, Francesco; Chang, Darrick E.; Rabl, Peter

doi:10.1103/physreva.93.033833

Cited by 188 publications

(172 citation statements)

References 73 publications

(154 reference statements)

Supporting

Mentioning

163

Contrasting

Order By: Relevance

“…, represent the symmetric and anti-symmetric superpositions of two local single-excitation bound states around the QEs. However, as we will show below (and already derived in [26]), only the symmetric bound state survives in certain parameter regimes. In the regime where both bound states exist, the Hamiltonian can be projected into the subspace spanned by these two bound states, which gives rise to the following effective model for the low energy part of the spectrum:…”

Section: Two Qessupporting

confidence: 55%

See 1 more Smart Citation

Effective many-body Hamiltonians of qubit-photon bound states

Shi

González-Tudela

et al. 2018

New J. Phys.

View full text Add to dashboard Cite

Quantum emitters (QEs) coupled to structured baths can localize multiple photons around them and form qubit-photon bound states. In the Markovian or weak coupling regime, the interaction of QEs through these single-photon bound states is known to lead to effective many-body QE Hamiltonians with tuneable but yet perturbative interactions. In this work we study the emergence of such models in the non-Markovian or strong coupling regime in different excitation subspaces. The effective models for the non-Markovian regime with up to three excitations are characterized using analytical methods, uncovering the existence of doublons or triplon states. Furthermore, we provide numerical results for systems with multiple excitations and demonstrate the emergence of polariton models with optically tuneable interactions, whose many-body ground state exhibits a superfluid-Mott insulator transition.intuitive picture [21] is that the single-photon bound state acts as an off-resonant cavity mode that mediates interaction between the QEs. The strength and functional form of these interactions depend on the QE-bath coupling strength, detuning as well as the band-dispersion relation. Although, these interactions can be made relatively strong to overcome other dissipative mechanism, their predicted strength is ultimately limited by the Markovian conditions under which these effective description has been derived.In this work, we study the effective many-body Hamiltonians emerging when QEs couple to structured baths beyond the Markovian limit, and investigate to which point the dipole-dipole description survives in this regime. Furthermore, we study the consequences on the effective QE interactions of the emergence of multiphoton bound states, which were recently predicted in the single QE regime [15, 23-26], but whose impact in the multi QE situation has not yet been fully considered. Our analysis allows us to uncover qualitatively different interaction Hamiltonians, in which multi-photon bound states (doublons/triplons) hop from QE to the other, and analytically characterize them up to three excitations. With more excitations, we numerically characterize the emergent polariton models using density matrix renormalization group (DMRG), and show that their interactions can be controlled optically through the QE-bath interactions, allowing us to probe the quantum phase transition between superfluid and Mott insulator.This manuscript is organized as follows. In section 2, we explain the model that will be used throughout the paper and review the results in the Markovian limit to have them as reference for the next section. In section 3, we study the single excitation subspace, deriving an effective Hamiltonian to describe the dipole-dipole interaction for two and many QEs. In sections 4-6, we study the two-excitation subspace for both the two and many QE regimes. Since the phenomenology in this regime differs significantly from what is expected in a Markovian description, we use section 4 to explain the analytical tools we use to charact...

show abstract

Section: Two Qessupporting

confidence: 55%

“…In this section we study the physics of the single excitation subspace. This regime has been extensively studied in the literature (see, for instance, [26] and references therein). Here, we will review results that are relevant for the other sections, and also derive simple formulas for the emergent effective models.…”

Section: Single Excitationmentioning

confidence: 99%

Effective many-body Hamiltonians of qubit-photon bound states

Shi

González-Tudela

et al. 2018

New J. Phys.

View full text Add to dashboard Cite

show abstract

“…In this work, we provide a further evidence of the validity of this assumptions by demonstrating a limited version of equation (8) Unfortunately, this result is insufficient for treating the most general case. It is well known that the Hamiltonian (2) may support excited eigenstates which are localized around the scattering center [34,35,44,45], which in the literature are usually referred as ground states. Two paradigmatic examples of scatterer with multiple ground states are the three-level Λ atom, with two electronic ground state, and a twolevel system coupled to a cavity array in the ultrastrong coupling regime [35].…”

Section: Sufficient Conditions For Having a Well-defined Scattering Tmentioning

confidence: 99%

Emergent causality and theN-photon scattering matrix in waveguide QED

et al. 2018

View full text Add to dashboard Cite

In this work we discuss the emergence of approximate causality in a general setup from waveguide QEDi.e. a one-dimensional propagating field interacting with a scatterer. We prove that this emergent causality translates into a structure for the N-photon scattering matrix. Our work builds on the derivation of a Lieb-Robinson-type bound for continuous models and for all coupling strengths, as well as on several intermediate results, of which we highlight: (i) the asymptotic independence of space-like separated wave packets, (ii) the proper definition of input and output scattering states, and (iii) the characterization of the ground state and correlations in the model. We illustrate our formal results by analyzing the two-photon scattering from a quantum impurity in the ultrastrong coupling regime, verifying the cluster decomposition and ground-state nature. Besides, we generalize the cluster decomposition if inelastic or Raman scattering occurs, finding the structure of the S-matrixin momentum space for linear dispersion relations. In this case, we compute the decay of the fluorescence (photon-photon correlations) caused by this S-matrix. models do not satisfy Lorentz or translational invariance, they are typically dispersive, and the photon-matter interaction may become highly non-perturbative. Experimental implementations include dielectrics [14,15], cavity arrays [16], metals [17], diamond structures [18,19], and superconductors [20][21][22][23][24] interacting with atoms, molecules, quantum dots, color centers in diamond or superconducting qubits. The focus of waveguide QED is set on quantum processes involving few photons and scatterers. In this regard, it is not surprising that there exists an extensive theoretical literature for waveguide-QED systems [13], which develops a variety of analytical and numerical methods for the study of the N-photon S-matrix [25][26][27][28][29][30][31][32][33][34][35][36].The main result in this work is the structure of the N-photon S-matrixin waveguide QED, rigorously deduced from emergent causality constraints. Our result builds on a general model of light-matter interactions, without any approximations such as the rotating-wave approximation (RWA), the Markovian limit, or weak light-matter coupling. To derive the S-matrixdecomposition we are assisted by several intermediate and important results, of which we remark: (i) the freedom of wave packets far away from the scatterer, (ii) Lieb-Robinson-like independence relations and approximate light-cones for propagating wave packets, (iii) a characterization of the ground state correlation properties, and (iv) a proper definition and derivation of scattering input and output states.We illustrate our results with two representative examples. The first one is a numerical study of scattering in the ultrastrong coupling limit [35,37], where we demonstrate the clustering decomposition and the nature of the ground state predicted by our intermediate results. The second is an analytical study of a non-dispersive medium interacting ...

show abstract

“…Dimensional reduction can be implemented in a range of experimental platforms, that include cold atoms in tightly focused fields [15][16][17], photonic crystals [18][19][20][21], optical fibers [22,23], quantum dots in photonic nanowires [24,25], and superconducting qubits in integrated circuit waveguides [26][27][28][29]. Theoretical studies focused on the interplay between the spectral features of the field and the structure of the emitters [30][31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Long-lived entanglement of two multilevel atoms in a waveguide

et al. 2018

View full text Add to dashboard Cite

We study the presence of nontrivial bound states of two multilevel quantum emitters and the photons propagating in a linear waveguide, when the emitters can be modeled as harmonic oscillators. We characterize the conditions for the existence of such states and determine their general properties, focusing in particular on the entanglement between the two emitters, that increases with the number of excitations. We discuss the relevance of our results for entanglement preservation and generation by spontaneous relaxation processes. We finally introduce a perturbative method for determining the existence of long-lived states, for general level spacings and couplings.

show abstract

Atom-field dressed states in slow-light waveguide QED

Cited by 188 publications

References 73 publications

Effective many-body Hamiltonians of qubit-photon bound states

Effective many-body Hamiltonians of qubit-photon bound states

Emergent causality and theN-photon scattering matrix in waveguide QED

Long-lived entanglement of two multilevel atoms in a waveguide

Contact Info

Product

Resources

About