Towards superfluidity of dipolar excitons in a TMDC double layer

We study formation and superfluidity of dipolar excitons in double layer heterostructures formed by two transition metal dichalcogenide (TMDC) atomically thin layers. Considering screening effects for an electron-hole interaction via the harmonic oscillator approximation for the Keldysh potential, the analytical expressions for the exciton energy spectrum and the mean field critical temperature $T_{c}$ for the superfluidity are obtained. It is shown that binding energies of A excitons are larger than for B excitons. The mean field critical temperature for a two-component dilute exciton system in a TMDC double layer is analyzed and shown that latter is an increasing function of the factor $Q$, determined by the effective masses of A and B excitons and their reduced mass. Comparison of the calculations for $T_{c}$ performed by employing the Coulomb and Keldysh interactions demonstrates the importance of screening effects in TMDC.Comment: 14 pages, 5 figure

High-temperature superfuidity of the two-component Bose gas in a TMDC bilayer

The high-temperature superfluidity of two-dimensional dipolar excitons in two parallel TMDC layers is predicted. We study Bose-Einstein condensation in the two-component system of dipolar A and B excitons. The effective mass, energy spectrum of the collective excitations, the sound velocity and critical temperature are obtained for different TMDC materials. It is shown that in the Bogolubov approximation the sound velocity in the two-component dilute exciton Bose gas is always larger than in any one-component. The difference between the sound velocities for two-component and one-component dilute gases is caused by the fact that the sound velocity for two-component system depends on the reduced mass of A and B excitons, which is always smaller than the individual mass of A or B exciton. Due to this fact, the critical temperature Tc for superfluidity for the two-component exciton system in TMDC bilayer is about one order of magnitude higher than Tc in any one-component exciton system. We propose to observe the superfluidity of two-dimensional dipolar excitons in two parallel TMDC layers, which causes two opposite superconducting currents in each TMDC layer.Comment: 18 pages, 4 figure

Superfluidity of Dipolar Excitons in a Black Phosphorene Double Layer

We study the formation of dipolar excitons and their superfluidity in a black phosphorene double layer. The analytical expressions for the single dipolar exciton energy spectrum and wave function are obtained. It is predicted that a weakly interacting gas of dipolar excitons in a double layer of black phosphorus exhibits superfluidity due to the dipole-dipole repulsion between the dipolar excitons. In calculations are employed the Keldysh and Coulomb potentials for the interaction between the charge carriers to analyze the influence of the screening effects on the studied phenomena. It is shown that the critical velocity of superfluidity, the spectrum of collective excitations, concentrations of the superfluid and normal component, and mean field critical temperature for superfluidity are anisotropic and demonstrate the dependence on the direction of motion of dipolar excitons. The critical temperature for superfluidity increases if the exciton concentration and the interlayer separation increase. It is shown that the dipolar exciton binding energy and mean field critical temperature for superfluidity are sensitive to the electron and hole effective masses. The proposed experiment to observe a directional superfluidity of excitons is addressed.Comment: 19 pages, 7 figure

Laplace transform approach for the dynamics of N qubits coupled to a resonator

An approach to use the method of Laplace transform for the perturbative solution of the Schr\"{o}dinger equation at any order of the perturbation for a system of $N$ qubits coupled to a cavity with $n$ photons is suggested. We investigate the dynamics of a system of $N$ superconducting qubits coupled to a common resonator with time-dependent coupling. To account for the contribution of the dynamical Lamb effect to the probability of excitation of the qubit, we consider counter-rotating terms in the qubit-photon interaction Hamiltonian. As an example, we illustrate the method for the case of two qubits coupled to a common cavity. The perturbative solutions for the probability of excitation of the qubit show excellent agreement with the numerical calculations.Comment: 8 pages, 1 figur

Time evolution of the quantum entanglement between NN qubits due to dynamical Lamb effect in the presence of dissipation

A theoretical framework to investigate the time evolution of the quantum entanglement due to the dynamical Lamb effect between $N$ superconducting qubits coupled to a coplanar waveguide in the presence of different sources of dissipation is developed. We quantitatively analyze the case of $N=2$ and $3$ qubits under the assumptions of single switching of the coupling and absence of dissipation within a perturbative approach. The same systems are analyzed for the general case of periodic switching of the coupling in the presence of dissipation via numerical calculations. Different measures of entanglement compatible with mixed states are adopted. It is demonstrated that the different measures show different level of details of the latter. The concurrence and the negativity are obtained in the two qubits case, the three-$\pi$ and the negativity in the three qubits case. It is shown that time-dependent Greenberger-Horne-Zeilinger states can be created even in presence of dissipation. To maximize the quantum entanglement between the qubits, the effects of tuning several parameters of the system are investigated.Comment: 21 pages, 7 figure

The electron-hole superfluidity in two coaxial nanotubes

The superfluid phase and Coulomb drag effect caused by the pairing in the system of spatially separated electrons and holes in two coaxial cylindrical nanotubes are predicted. It is found that the drag resistance as a function of temperature experiences a jump at the critical temperature and can be used for the manifestation of the superfluid transition. It is demonstrated that at sufficiently low temperatures the order parameter and free energy density exhibit a kink due to the electron-hole asymmetry that is controlled by the radii of the nanotubes

Phase transitions in the two-dimensional electron-hole gas

A first order phase transition between a BCS phase and an insulating Mott phase for a gas of spatially separated electrons and holes with tunable Coulomb interaction and variable density is predicted. In the framework of a BCS-like mean-field approach and a Landau expansion in terms of the pairing order parameter the phase diagram is studied. This indicates several phases and phase transitions, including an electron-hole plasma at low density and weak interaction, an intermediate BCS phase with Cooper pairs and an electron-hole plasma at high density and weak interaction. The insulating Mott phase appears for the strong interaction and low temperatures. We briefly discuss the possibilities to realize these phases in realistic systems such as coupled quantum wells and graphene double layers.Comment: 10 pages, 4 figure

Bose-Einstein condensation of polaritons in graphene in a high magnetic field

The Bose-Einstein condensation (BEC) of magnetoexcitonic polaritons in a graphene layer embedded in a optical microcavity in a high magnetic field $B$ is predicted. The essential property of this system (in contrast, e.g., to a quantum well embedded in a cavity) is stronger influence of magnetic field and weaker influence of disorder. A two-dimensional (2D) magnetoexcitonic polaritons gas is considered in a planar harmonic electric field potential applied to excitons or a parabolic shape of the optical cavity causing the trapping of microcavity photons. It is shown that the effective polariton mass $M_{\rm eff}$ increases with magnetic field as $B^{1/2}$. The BEC critical temperature $T_{c}^{(0)}$ decreases as $B^{-1/4}$ and increases with the spring constant of the parabolic trap. The Rabi splitting related to the creation of a magnetoexciton in a high magnetic field in graphene is obtained.Comment: 7 pages, 1 figur

Drag effects in the system of electrons and microcavity polaritons

The theory of the drag effects in the system of spatially separated electrons and excitons in coupled quantum wells (QW) embedded in an optical microcavity is developed. It is shown that at low temperature an electron current induces the (normal component) polariton flow, therefore, a transport of photons along the cavity. However, the electron current dragged by the polariton flow is strongly suppressed below polariton superfluid transition temperature and hence, the strong suppression of the induced electron current indicates the superfluidity of polaritons. Therefore, the transport properties of polaritons can be investigated by measuring the current or voltage in the electron subsystem. At high temperatures we study the exciton-electron drag effects. At high temperatures regime, from one hand, the existence of the electric current in an electron QW induces the exciton flow in the other QW, from the other hand, the electron current in one QW induces the exciton flow in the other QW via the drag of excitons by the electrons. The drag coefficients for the polariton-electron systems are calculated and analyzed. We discuss the possible experimental observation of the drag effects in the system of electrons and microcavity polaritons, that also allow to observe the cavity polaritons superfluidity.Comment: 16 pages, 7 figures, Physical Review B, in press (2010

Graphene nanoribbon based spaser

A novel type of spaser with the net amplification of surface plasmons (SPs) in doped graphene nanoribbon is proposed. The plasmons in THz region can be generated in a dopped graphene nanoribbon due to nonradiative excitation by emitters like two level quantum dots located along a graphene nanoribbon. The minimal population inversion per unit area, needed for the net amplification of SPs in a doped graphene nanoribbon is obtained. The dependence of the minimal population inversion on the surface plasmon wavevector, graphene nanoribbon width, doping and damping parameters necessary for the amplification of surface plasmons in the armchair graphene nanoribbon is studied.Comment: 10 pages, 5 figure