Effect of Emitters on Quantum State Transfer in Coupled Cavity Arrays

Abstract

Over the last decade, considerable work has been done on quantum state transfer along one dimensional arrays of coupled qubits, as modeled by quantum spin chains. Protocols for perfect quantum state transfer, requiring 'full engineering' of the exchange constants Ji have been discovered. The degradation induced by the inevitable disorder ∆Ji present in any experimental realization has also been discussed. In this paper, we consider an extension of such studies to quantum state transfer in a coupled cavity array including the effects of atoms in the cavities which can absorb and emit photons as they propagate down the array. Our model is equivalent to previously examined spin chains in the one-excitation sector and in the absence of emitters. We introduce a Monte Carlo approach to the inverse eigenvalue problem which allows the determination of the inter-cavity and cavity-emitter couplings resulting in near-perfect quantum state transfer fidelity, and examine the time dependent polariton wave function through exact diagonalization of the resulting Tavis-Cummings-Hubbard Hamiltonian. The effect of inhomogeneous emitter locations is also evaluated.

Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer

“…The XX chains, on the contrary, allow perfect QST using different strategies [8][9][10][11] or near perfect QST at transfer times close to the minimal time allowed by the quantum speed limit [12][13][14]. Regrettably, more and more experimental implementations can be modeled only by using effective Heisenberg chain Hamiltonians [15][16][17][18][19][20][21][22][23][24][25] (or more complicated interactions [26][27][28]) while the XX chains remain as an option only for simplistic highly anisotropic situations. Of course, there is always room for renewed proposals that involve the XX Hamiltonian, as is the case in some XX chains that show topological states [26][27][28].…”

Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer

“…The XX chains, on the contrary, allow perfect quantum state transfer using different strategies [8][9][10][11] or near perfect QST at transfer times close to the minimal time allowed by the Quantum Speed limit [12][13][14]. Regrettably, more and more experimental implementations can be modeled only by using effective Heisenberg chain Hamiltonians [15][16][17][18][19][20][21][22][23][24][25] (or more complicated interactions [26][27][28]) while the XX chains remain as an option only for simplistic highly anisotropic situations. Of course, there is always room for renewed proposals that involve the XX Hamiltonian, as is the case in some XX chains that show topological states [26][27][28].…”

Understanding the propagation of excitations in quantum spin chains with different kind of interactions

“…The availability of numerous physical systems where it is possible to actually implement the transfer protocols [5][6][7][8][9][10][11][12][13][14][15] has driven the study of different control strategies to achieve the propagation of excitations in a ballistic way, i.e. the propagation of a spin wave packet that propagates at constant velocity along the chain.…”