Few-photon transport in many-body photonic systems: A scattering approach

Abstract

We study the quantum transport of multi-photon Fock states in one-dimensional Bose-Hubbard lattices implemented in QED cavity arrays (QCAs). We propose an optical scheme to probe the underlying many-body states of the system by analyzing the properties of the transmitted light using scattering theory. To this end, we employ the Lippmann-Schwinger formalism within which an analytical form of the scattering matrix can be found. The latter is evaluated explicitly for the two particle/photon-two site case using which we study the resonance properties of two-photon scattering, as well as the scattering probabilities and the second-order intensity correlations of the transmitted light. The results indicate that the underlying structure of the many-body states of the model in question can be directly inferred from the physical properties of the transported photons in its QCA realization. We find that a fully-resonant two-photon scattering scenario allows a faithful characterization of the underlying many-body states, unlike in the coherent driving scenario usually employed in quantum Master equation treatments. The effects of losses in the cavities, as well as the incoming photons' pulse shapes and initial correlations are studied and analyzed. Our method is general and can be applied to probe the structure of any many-body bosonic models amenable to a QCA implementation including the Jaynes-Cummings-Hubbard, the extended Bose-Hubbard as well as a whole range of spin models.

Linked cluster expansions for open quantum systems on a lattice

“…Once the coefficients {a n } are known, it is straightforward to evaluate the coefficients of the polynomials P L and Q M through Eq. (17). Further details about this procedure can be found in App.…”

“…Recently, a large body of theoretical works has been devoted to the investigation of the collective behavior emerging in dynamical response 12 , many-body spectroscopy [13][14][15] , transport [16][17][18][19][20] , as well as stationary properties. In the latter context, a careful engineering of the coupling between the system and the environment can stabilize interesting many-body phases in the steady state 21,22 .…”

Generalized cluster decomposition principle illustrated in waveguide quantum electrodynamics

“…(QED) systems, where a few waveguide photons interact with a local quantum system [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Numerical linked-cluster expansion for the dissipative XYZ model on a triangular lattice

“…The NLCE study on the steady-state susceptibility is implemented via three steps: of each topological distinct cluster c n ; (ii) compute the per-site α-direction magnetization sŝ s á ñ a in the thermodynamic limit with NLCE; (iii) compute the components c ab of the susceptibility tensor and consequently the averaged av c according to equation (8).…”

“…In contrast to the equilibrium case, the properties of the dissipative system are featured by the evolved steady state rather than the ground state of the Hamiltonian. Recently, a large body of work has be devoted to investigate the properties of the dissipative quantum many-body systems including the dynamics [2][3][4][5][6], transport properties [7][8][9][10][11], steady-state phases [12][13][14][15]16] and phase transitions [17][18][19][20][21], quantum states engineering [22][23][24], as well as the possible applications in quantum sensing [25,26]. Thanks to the experiment progress, dissipative phase transitions have been observed in circuit QED arrays [27] and ensembles of Rydberg atoms [28,29].…”