Two-photon Dicke model: effective Hamiltonian and strong field dynamics

A. B. Klimov, J. Negro, R Farias +1 more

We derive an effective two-photon Hamiltonian for a collection of two-level atoms interacting with a quantized field in the regime of two-photon resonance. This Hamiltonian naturally includes the dynamical Stark shift terms. Considering, in detail, the case of an initially strong quantum field, we show that the effective Hamiltonian acquires nonlinear terms in the su (2) algebra generators. For this case we find the evolution operator and prove the wavefunction factorization for special initial states. We show that collective effects modify the dynamics of the atomic inversion leading to a modulation of the collapse-revival structure.

Giuseppe Compagno, Jin Sheng Peng, Franco Persico

Shôzô Takeno, Michiyoshi Nagashima, Jun Sugimto

Coherent states and dynamics of a photon mode in the Dicke model Hamiltonian are studied by using a method of diagonal coherent-state representation. It is shown that under a strong coupling condition the ground state of the model Hamiltonian is characterized by simultaneous appearance of a photon coherent state and that due to atomic polarization. The energy eigenvalue of such a combined coherent state is shown to be lower than that of the in which all atoms in a matter system are in their ground state while no photon is present. An exact solution for the time evolution of the coherent-state representation of the photon number operator is obtained in terms of the Jacobi elliptic functions. It is shown that periodic, pulse-like and stationary solutions exist under various initial conditions.

Priyankar Banerjee, Deepti Sharma, Aranya B. Bhattacherjee

Igor Leonidovich Kirilyuk

The properties of a system consisting of two-level atoms interacting with a mode of the electromagnetic field in a cavity are considered for the case when the cavity detuning or the coefficient of the atom-field interaction is modulated. The consideration is performed with account taken of the Hamiltonian terms that are neglected in the rotating-wave approximation. It is shown that in the semiclassical equations for such a model, the effect of extension (compared to the autonomous system) of the range of variation of the quantity characterizing the number of photons can manifest itself; in this case, the energy oscillations have a chaotic character. The dependence of this phenomenon on parameters characterizing the model is studied. It is numerically demonstrated that with account taken for the relaxation, the system studied can have attractors different from the equilibrium positions, i.e., the number of photons in the mode does not tend to a constant value. The limits of validity of the rotating-wave approximation in the parametrically perturbed Dicke model are discussed.

Kong Junran, Mao Mang, Liu Huan +1 more

Nonequilibrium heat transport and quantum thermodynamics in light-matter interacting systems have received increasing attention. Quantum thermal devices, e.g., heat valve and head diode, have been realized. Recently, it has been discovered that the anisotropic light-matter interactions can greatly modify the eigenvalues and eigenvectors of hybrid quantum systems, leading to nontrivial quantum phase transitions, quantum metrology, and nonclassicality of photons. To explore the influences of anisotropic light-matter interactions on quantum transport, we investigate heat flow in the nonequilibrium anisotropic Dicke model. In this model, an ensemble of qubits collectively interacts with an anisotropic photon field. Each component interacts with bosonic thermal reservoirs. Quantum dressed master equation (DME) is included to properly study dissipative dynamics of the anisotropic Dicke model. Within the eigenbasis of the reduced anisotropic Dicke system, strong qubit-photon couplings can be properly handled. Our results demonstrate that anisotropic qubit-photon interactions are crucial for modulating steady-state heat flow. In particular, it is found that under strong coupling the heat flow is dramatically suppressed by a large anisotropic qubit-photon factor. While under moderate coupling, the anisotropic qubit-photon interactions enhance the heat flow. Moreover, the increase in the number of qubits amplifies the flow characteristics, with the peaks increasing and the valleys decreasing. Besides, we derive two analytical expressions of heat flows in thermodynamic limit approximation with limiting anisotropic factors. These heat currents exhibit the cotunneling heat transport pictures. They also serve as the upper boundaries for the heat flows in the finite-size anisotropic Dicke model. We also analyze the thermal rectification effect in the anisotropic Dicke model.