Ultrafast pump-probe technique is a powerful tool to understand and manipulate properties of materials for designing novel quantum devices. An intense, single cycle terahertz pulse can change the intrinsic properties of semiconductor quantum dots to
have different luminescence. In a hybrid system of plasmon and exciton, the coherence and coupling between these two degrees of freedom play an important role on their optical properties. Therefore, we consider a terahertz pump optical probe experiment in the hybrid systems where the terahertz pump pulse couples to the exciton degrees of freedom on the quantum dot. The time resolved photoluminescence of the hybrid system shows that the response of the characteristic frequency shifts according to the overlap between the pump and probe pulses. Furthermore, the resonance between the exciton and plasmons can be induced by the terahertz pump pulse in some parameter regimes. Our results show the terahertz driven hybrid system can be a versatile tool for manipulating the material properties and open a new route to design modern optical devices.
We investigate the dynamics of an electron coupled to dispersionless optical phonons in the Holstein model, at high temperatures. The dynamics is conventionally believed to be diffusive, as the electron is repeatedly scattered by optical phonons. In
a semiclassical approximation, however, the motion is not diffusive. In one dimension, the electron moves in a constant direction and does not turn around. In two dimensions, the electron follows and then continues to retrace a fractal trajectory. Aspects of these nonstandard dynamics are retained in more accurate calculations, including a fully quantum calculation of the electron and phonon dynamics.
Understanding the physics of light emitter in quantum nanostructure regarding scalability, geometry, structure of the system and coupling between different degrees of freedom is important as one can improve the design and further provide controls of
quantum devices rigorously. The couplings between these degrees of freedom, in general, depends on the external field, the geometry of nano particles, and the experimental design. An effective model is proposed to describe the plasmon-exciton hybrid systems and its optical absorption spectrums are studied in details by exact diagonalization. Two different designs are discussed: nano particle planet surrounded by quantum dot satellites and quantum dot planet surrounded by nano particle satellites. In both setups, details of many quantum dots and nano particles are studied, and the spectrums are discussed in details regarding the energy of transition peaks and the weight distribution of allowed transition peaks. Also, different polarization of external fields are considered which results in anisotropic couplings, and the absorption spectrums clearly reveal the difference qualitatively. Finally, the system will undergo a phase transition in the presence of attractive interaction between excitons. Our work sheds the light on the design of nano scale quantum systems to achieve photon emitter/resonator theory in the plasmon-exciton hybrid systems.
Recent advance in quantum simulations of interacting photons using superconducting circuits offers opportunities for investigating the Bose-Hubbard model in various geometries with hopping coefficients and self-interactions tuned to both signs. Here
we investigate phenomena related to localized states associated with a flat-band supported by the saw-tooth geometry. A localization-delocalization transition emerges in the non-interacting regime as the sign of hopping coefficient is changed. In the presence of interactions, patterns of localized states approach a uniform density distribution for repulsive interactions while interesting localized density patterns can arise in strongly attractive regime. The density patterns indicate the underlying inhomogeneity of the simulator. Two-particle correlations can further distinguish the nature of the localized states in attractive and repulsive interaction regimes. We also survey possible experimental implementations of the simulator.
We connect explicitly the classical $O(2)$ model in 1+1 dimensions, a model sharing important features with $U(1)$ lattice gauge theory, to physical models potentially implementable on optical lattices and evolving at physical time. Using the tensor
renormalization group formulation, we take the time continuum limit and check that finite dimensional projections used in recent proposals for quantum simulators provide controllable approximations of the original model. We propose two-species Bose-Hubbard models corresponding to these finite dimensional projections at strong coupling and discuss their possible implementations on optical lattices using a $^{87}$Rb and $^{41}$K Bose-Bose mixture.
We study density wave instabilities in a doubly-degenerate Fermi-Fermi mixture with $SU(2)times SU(2)$ symmetry on a square lattice. For sufficiently large on-site inter-species repulsion, when the two species of fermions are both at half-filling, tw
o conventional ($s$-wave) number density waves are formed with a $pi$-phase difference between them to minimize the inter-species repulsion. Upon moving one species away from half-filling, an unconventional density wave with $d_{xy}$-wave symmetry emerges. When both species are away from the vicinity of half-filling, superconducting instabilities dominate. We present results of a functional renormalization-group calculation that maps out the phase diagram at weak couplings. Also, we provide a simple explanation for the emergence of the $d_{xy}$-density wave phase based on a four-patch model. We find a robust and general mechanism for $d_{xy}$-density-wave formation that is related to the shape and size of the Fermi surfaces. The density imbalance between the two species of fermions in the vicinity of half-filling leads to phase-space discrepancy for different inter-species Umklapp couplings. Using a phase space argument for leading corrections in the one-loop renormalization group approach to fermions, we show that the phase-space discrepancy in our system causes opposite flows for the two leading intra-species Umklapp couplings and that this triggers the $d_{xy}$-density-wave instability.
We study the phase diagram of the extended Hubbard model on a two-dimensional square lattice, including on-site (U) and nearest-neighbor (V) interactions, at weak couplings. We show that the charge-density-wave phase that is known to occur at half-fi
lling when 4V > U gives way to a d_{xy} -wave superconducting instability away from half-filling, when the Fermi surface is not perfectly nested, and for sufficiently large repulsive and a range of on-site repulsive interaction. In addition, when nesting is further suppressed and in presence of a nearest-neighbor attraction, a triplet time-reversal breaking (p_x + ip_y)-wave pairing instability emerges, competing with the d_{x2+y2} pairing state that is known to dominate at fillings just slightly away from half. At even smaller fillings, where the Fermi surface no longer presents any nesting, the (p_x +ip_y)-wave superconducting phase dominates in the whole regime of on-site repulsions and nearest-neighbor attractions, while d_{xy}-pairing occurs in the presence of on-site attraction. Our results suggest that zero-energy Majorana fermions can be realized on a square lattice in the presence of a magnetic field. For a system of cold fermionic atoms on a two-dimensional square optical lattice, both an on-site repulsion and a nearest-neighbor attraction would be required, in addition to rotation of the system to create vortices. We discuss possible ways of experimentally engineering the required interaction terms in a cold atom system.
We study a two species fermion mixture with different populations on a square lattice modeled by a Hubbard Hamiltonian with on-site inter-species repulsive interaction. Such a model can be realized in a cold atom system with fermionic atoms in two di
fferent hyperfine states loaded on an optical lattice and with tunable inter-species interaction strength via external fields. For a two-dimensional square lattice, when at least one of the fermion species is close to half-filling, the system is highly affected by lattice effects. With the majority species near half-filling and varying densities for the minority species, we find that several correlated phases emerge as the ground state, including a spin density wave state, a charge density wave state with stripe structure, and various p-wave BCS pairing states for both species. We study this system using a functional renormalization group method, determine its phase diagram at weak coupling, discuss the origin and characteristics of each phase, and provide estimates for the critical temperatures.
We calculate the ground-state properties of fermionic dipolar atoms or molecules in a one-dimensional double-tube potential by using the Luttinger liquid theory and the density matrix renormalization-group calculation. When the external field is appl
ied near a magic angle with respect to the double-tube plane, the long-ranged dipolar interaction can generate a spontaneous correlation between fermions in different tubes, even when the bare intertube tunneling rate is negligibly small. Such interaction-induced correlation strongly enhances the contrast of the interference fringes and therefore can be easily observed in the standard time-of-flight experiment.
