Response of two-band systems to a single-mode quantized field

Abstract

The response of topological insulators (TIs) to an external weakly classical field can be expressed in terms of Kubo formula, which predicts quantized Hall conductivity of the quantum Hall family. The response of TIs to a single-mode quantized field, however, remains unexplored. In this work, we take the quantum nature of the external field into account and define a Hall conductance to characterize the linear response of a two-band system to the quantized field. The theory is then applied to topological insulators. Comparisons with the traditional Hall conductance are presented and discussed.

Hall conductance for open two-band system beyond rotating-wave approximation

“…H can be diagonalized by a unitary matrix U : , where we have omitted the term because this term represents a energy shift to the system much smaller than the energy difference in H 0 26 . Here, , and , with , , , and …”

“…For example, zero-temperature Hall conductance subjected to decoherence 14 , topological order by dissipation 15 – 17 , density-matrix Chern insulator subjected to thermal noise 18 , 19 , topological phases induced photocurrent 20 , 21 , and optical Hall conductivity 22 – 25 . Taking the quantum nature of the external field into account, a Hall conductance to characterize the linear response of a quantum system to a single-mode quantized electronmagnetic field was also defined and explored 26 . However, most of these studies are based on the reduced density matrix of the system, hence the environment is traced out before proceeding to analyze the response of the system.…”

Simulating Z_2 topological insulators via a one-dimensional cavity optomechanical cells array

“…Besides, the topological classification and the essentially topological features of the system can be captured by a topological invariant. These novel properties stimulate that many theoretical models and experimental schemes have been proposed to investigate topological insulators, including graphene ribbons [3,4], cold atoms trapped in optical lattices [5][6][7][8][9], open system [10][11][12], p-orbit optical ladder systems [13], off-diagonal bichromatic optical lattices [14], and circuit-QED lattices [15][16][17][18]. It has been verified that these systems can be used to simulate and investigate topological insulators exhibiting QH edge states via the synthetic gauge field, dimensional reduction, etc.…”

Quantum light and topological surface states

“…Recently, progress has been made to carry out a full quantum treatment where light is quantized. The issues discussed included the linear response of a two-band system to the quantized field [23], metal-insulator transition in graphene induced by circularly polarized photons [24] and frequencydriven quantum oscillations in a graphene layer under a circularly polarized photon field [25], to mention a few of them.…”