Engineering nonlinear coherent states as photon-added and photon-subtracted coherent states

Abstract

We show that the two-photon Jaynes-Cummings model, feasible of experimental realization in cavity or ion-trap quantum electrodynamics, can approximately produce nonlinear coherent states of the field. We introduce these nonlinear coherent states of the field as 2m-photon added or subtracted coherent states in terms of raising and lowering field operators, also known as London phase operators or Susskind-Glogower operators.

Exact analysis of the spectral properties of the anisotropic two-bosons Rabi model

“…For such systems, the localized levels are provided by the excitonic levels of the quantum dot; remarkably, two photon process in quantum dots were observed through photoluminiscence experiments [6]. The two-mode Rabi models also emerge in circuit QED involving superconducting qubits in the ultra strong regime in which non-linear couplings become realistic [7][8][9] and in ion traps [10,11]. Finally, a two-mode boson field can be implied in the dynamics of a charged particle in a magnetic field [26].…”

Underlying SUSY in a generalized Jaynes-Cummings model

“…An algebraic generalizaton was proposed to study coherent states for an anharmonic perturbation to the JC model. Some of us studied a, slightly complicated in hindsight, generalization [24][25][26][27][28][29] that reduces to our general scheme in the following section.…”

Invariant approach to the driven Jaynes-Cummings model

“…Such generalizations intend to address more involved and realistic aspects of the interaction between atoms and fields, beyond the simplifications of the original model [6][7][8][9]. These include the generalized JCM (which incorporates multiple atomic levels [10][11][12] or field modes [13,14]), the dispersive JCM [15], models including nonlinear effects [16][17][18] and losses [19,20], among others [21][22][23][24][25].…”