We investigate the relaxation of two collective spins in double domain system, which are individually coupled to a single bosonic reservoir, by varying the total number of spins in each domain and their initial spin configurations. A particularly interesting situation occurs when the spin domains are set in an antiparallel configuration. Further for an unbalanced configuration where the number of spins are in the excited state initially is much greater than that in the ground state, the spin ensemble prepared in the ground state relaxes towards a negative-temperature state.PACS numbers: 42.50. Nn, Introduction.-In recent years, the hybridization of quantum systems has become a key technique to design and demonstrate novel quantum behaviors [1][2][3]. With the rapid progress in quantum coherent manipulation, hybrid quantum systems have now entered the regime where we can observe unexpected or rather counterintuitive behavior even in the presence of imperfections and noise [4][5][6][7]. Such hybrid systems have not only shown the capability to achieve superior properties each individual system alone cannot achieve [5,8], but they also shred light on the fundamental complexity of such quantum systems including coupling structures and decoherence mechanisms [9]. Currently a number of such hybrid systems have been proposed (and realized in some cases) with various elements coming from atomic molecular & optical systems to solid-state systems. Example include for instance, trapped ions [10], optical cavities & resonators [11,12], electron and nuclear spin ensembles in quantum dots (QD) or nitrogen-vacancy centers in diamond [13][14][15], superconducting circuits in quantum electrodynamic systems [2] and mechanical resonators [15,16]. This large diversity of component systems really allows one to explore the unique space hybridization potentially allows.

At the filling factor ν=2, the bilayer quantum Hall system has three phases, the spin-ferromagnet phase, the spin singlet phase and the canted antiferromagnet (CAF) phase, depending on the relative strength between the Zeeman energy and interlayer tunneling energy. We present a systematic method to derive the effective Hamiltonian for the Goldstone modes in these three phases. We then investigate the dispersion relations and the coherence lengths of the Goldstone modes. To explore a possible emergence of the interlayer phase coherence, we analyze the dispersion relations in the zero tunneling energy limit. We find one gapless mode with the linear dispersion relation in the CAF phase. PACS. 73.21.-b Collective excitations in nanoscale systems -73.43.Nq Phase transitions quantum Hall effects

The spin and layer (pseudospin) degrees of freedom are entangled coherently in the canted antiferromagnetic phase of the bilayer quantum Hall system at the filling factor ν = 2. There emerges a complex Goldstone mode describing such a combined degree of freedom. In the zero tunneling-interaction limit (∆SAS → 0), its phase field provokes a supercurrent carrying both spin and charge within each layer. The Hall resistance is predicted to become anomalous precisely as in the ν = 1 bilayer system in the counterflow and drag experiments. Furthermore, it is shown that the total current flowing in the bilayer system is a supercurrent carrying solely spins in the counterflow geometry. It is intriguing that all these phenomena occur only in imbalanced bilayer systems.

When the spontaneous symmetry breaking occurs for systems without Lorentz covariance, there arises possible mismatch, NNG < NBG, between numbers of Nambu-Goldstone (NG) bosons (NNG) and the numbers of broken generators (NBG). In such a situation, so-called type-II NG bosons emerge. We study how the gauge bosons acquire masses through the Higgs mechanism under this mismatch by employing gauge theories with complex scalar field at finite chemical potential and by enforcing "charge" neutrality. To separate the physical spectra from unphysical ones, the R ξ gauge is adopted. Not only massless NG bosons but also massive scalar bosons generated by the chemical potential are absorbed into spatial components of the gauge bosons. Although the chemical potential induces a non-trivial mixings among the scalar bosons and temporal components of the gauge bosons, it does not affect the structure of the physical spectra, so that the total number of physical modes is not modified even for NNG < NBG.

Spin collective phenomena including superradiance are even today being intensively investigated with experimental tests performed based on state-of-the-art quantum technologies. Such attempts are not only for the simple experimental verification of predictions from the last century but also as a motivation to explore new applications of spin collective phenomena and the coherent control of the coupling between spin ensembles and reservoirs. In this paper, we investigate the open quantum dynamics of two spin ensembles (double spin domains) coupled to a common bosonic reservoir. We analyze in detail the dynamics of our collective state and its structure by focusing on both the symmetry and asymmetry of this coupled spin system. We find that when the spin size of one of the double domains is larger than that of the other domain, at the steady state this system exhibits two novel collective behaviors: the negative-temperature state relaxation in the smaller spin domain and the reservoir-assisted quantum entanglement between the two domains. These results are the consequence of the asymmetry of this system and the decoherence driven by the common reservoir.