A simple model for a minimal environment: the two-atom Tavis–Cummings model revisited

Abstract

Individual quantum systems may be interacting with surrounding environments having a small number of degrees of freedom. It is therefore relevant to understand the extent to which such small (but uncontrollable) environments could affect the quantum properties of the system of interest.Here we discuss a simple system-environment toy model, constituted by a two-level atom (atom 1) interacting with a single mode cavity field. The field is also assumed to be (weakly) coupled to an external noisy subsystem, the small environment, modeled as a second two-level atom (atom 2). We investigate the action of the minimal environment on the dynamics of the linear entropy (state purity) and the atomic dipole squeezing of atom 1, as well as the entanglement between atom 1 and the field. We also obtain the full analytical solution of the two atom Tavis-Cummings model for both arbitrary coupling strengths and frequency detunings, necessary to analyze the influence of the field-environment detuning on the evolution of the above mentioned quantum properties. For complementarity, we discuss the role of the degree of mixedness of the environment by analyzing the time-averaged linear entropy of atom 1.1

Sudden death of entanglement induced by a minimal thermal environment

“…In fact, even a single uncontrollable subsystem coupled to the system of interest may cause a considerable disturbance. As examples of possible minimal environments, we may cite spins [20,21], a single two level system [22,23,24] and one or two modes of the quantized electromagnetic field [25,26,27,28]. In summary, we may be facing multiple challenges regarding the study of coupled quantum systems immersed in environments that might also be of different sizes, and in which the perturbative methods normally employed, e.g., local approaches, may not be applicable.…”

Two coupled qubits under the influence of a minimal, phase-sensitive environment

“…(8) we used 11 values of θ from θ = 0 to θ = π, whereas in Fig. (9) we used also 11 values of c, from c = 0 to c = 1/ √ 2 (squares in the plots in both figures). Interestingly, we verified a behaviour that is very close to a linear relation between the long-term average linear entropy and the fluctuations in the initial state of the environment for both photon and variance noise cases, despite the fact that they are distinct types of noise.…”

“…In fact, it has been experimentally demonstrated that a single electron can constitute a minimal environment causing decoherence in a H 2 molecule system [4]. There are discussions in the literature about the disturbances suffered by quantum systems due to their interaction with small, uncontrollable environments constituted by either a few two-level systems [5][6][7][8][9][10] or a few modes of the electromagnetic field [11][12][13][14][15]. Also, the contribution of a single two-level system to the decoherence of a qubit in combination with a thermal bath has been addressed in [16,17].…”

Tavis-Cummings model revisited: A perspective from macroscopic quantum electrodynamics

“…The collective coupling effects provide scientists with a new strategy to alter and control the physical and chemical properties of molecules. To explore the origin of these phenomena, the Tavis-Cummings (TC) model [9], which describes a collection of N identical molecules interacting equally with a single photonic mode, has been widely used to investigate the collective effect in hybrid lightmatter systems [10][11][12][13][14][15][16]. It is well-known that the TC model gives the N-times decay rate of single-photon superradiance and the N √ -times coupling strength between the molecular ensemble and the electromagnetic field.…”