Topological Bogoliubov Quasiparticles from Bose-Einstein Condensate in a Flat Band System.

For bosons with flat energy dispersion, condensation can occur in different symmetry sectors. Here, we consider bosons in a kagome lattice with π-flux hopping, which, in the presence of mean-field interactions, exhibit degenerate condensates in the Γ and the K point. We analyze the excitation above both condensates and find strikingly different properties: For the K-point condensate, the Bogoliubov-de Gennes (BdG) Hamiltonian has broken particle-hole symmetry and exhibits a topologically trivial quasiparticle band structure. However, band flatness plays a key role in breaking the time-reversal symmetry of the BdG Hamiltonian for a Γ-point condensate. Consequently, its quasiparticle band structure exhibits nontrivial topology, characterized by nonzero Chern numbers and by the presence of edge states. Although quantum fluctuations energetically favor the K-point condensate, the interesting properties of the Γ-point condensate become relevant for anisotropic hopping. The topological properties of the Γ-point condensate get even richer in the presence of extended Bose-Hubbard interactions. We find a topological phase transition into a topological condensate characterized by high Chern number and also comment on the realization and detection of such excitations.

Detecting Majorana Zero Modes via Strong Field Dynamics.

We propose a protocol to detect topological phase transitions of one-dimensional p-wave superconductors from their harmonic emission spectra in strong fields. Specifically, we identify spectral features due to radiating edge modes, which characterize the spectrum and the density of states in the topological phase and are absent in the trivial phase. These features allow us to define a measurable signature, obtained from emission measurements, that unambiguously differentiates between the two phases. Local probing provides insight into the localized and topologically protected nature of the modes. The presented results establish that high-harmonic spectroscopy can be used as an all-optical tool for the detection of Majorana zero modes.

High-harmonic spectroscopy of quantum phase transitions in a high-Tc superconductor.

We report on the nonlinear optical signatures of quantum phase transitions in the high-temperature superconductor YBCO, observed through high harmonic generation. While the linear optical response of the material is largely unchanged when cooling across the phase transitions, the nonlinear optical response sensitively imprints two critical points, one at the critical temperature of the cuprate with the exponential growth of the surface harmonic yield in the superconducting phase and another critical point, which marks the transition from strange metal to pseudogap phase. To reveal the underlying microscopic quantum dynamics, a strong-field quasi-Hubbard model was developed, which describes the measured optical response dependent on the formation of Cooper pairs. Further, the theory provides insight into the carrier scattering dynamics and allows us to differentiate between the superconducting, pseudogap, and strange metal phases. The direct connection between nonlinear optical response and microscopic dynamics provides a powerful methodology to study quantum phase transitions in correlated materials. Further implications are light wave control over intricate quantum phases, light-matter hybrids, and application for optical quantum computing.

Phonon-Induced Pairing in Quantum Dot Quantum Simulator.

Quantum simulations can provide new insights into the physics of strongly correlated electronic systems. A well-studied system, but still open in many regards, is the Hubbard-Holstein Hamiltonian, where electronic repulsion is in competition with attraction generated by the electron-phonon coupling. In this context, we study the behavior of four quantum dots in a suspended carbon nanotube and coupled to its flexural degrees of freedom. The system is described by a Hamiltonian of the Hubbard-Holstein class, where electrons on different sites interact with the same phonon. We find that the system presents a transition from the Mott insulating state to a polaronic state, with the appearance of pairing correlations and the breaking of the translational symmetry. These findings will motivate further theoretical and experimental efforts to employ nanoelectromechanical systems to simulate strongly correlated systems with electron-phonon interactions.

Fractional Angular Momentum and Anyon Statistics of Impurities in Laughlin Liquids.

The elementary excitations of a fractional quantum Hall liquid are quasiparticles or quasiholes that are neither bosons nor fermions, but are so-called anyons. Here we study impurity particles immersed in a quantum Hall liquid that bind to the quasiholes via repulsive interactions with the liquid. We show that the angular momentum of an impurity is given by the multiple of a fractional "quantum" of angular momentum, and can directly be observed from the impurity density. In a system with several impurities bound to quasiholes, their total angular momentum interpolates between the values for free fermions and for free bosons. This interpolation is characterized by the fractional statistical parameter of the anyons, which is typically defined via their braiding behavior.

Critical phase boundaries of static and periodically kicked long-range Kitaev chain.

We study the static and dynamical properties of a long-range Kitaev chain, i.e. a p -wave superconducting chain in which the superconducting pairing decays algebraically as [Formula: see text], where l is the distance between the two sites and [Formula: see text] is a positive constant. Considering very large system sizes, we show that when [Formula: see text], the system is topologically equivalent to the short-range Kitaev chain with massless Majorana modes at the ends of the system; on the contrary, for [Formula: see text], there exist symmetry protected massive Dirac end modes. We further study the dynamical phase boundary of the model when periodic [Formula: see text]-function kicks are applied to the chemical potential; we specially focus on the case [Formula: see text] and analyze the corresponding Floquet quasienergies. Interestingly, we find that new topologically protected massless end modes are generated at the quasienergy [Formula: see text] (where T is the time period of driving) in addition to the end modes at zero energies which exist in the static case. By varying the frequency of kicking, we can produce topological phase transitions between different dynamical phases. Finally, we propose some bulk topological invariants which correctly predict the number of massless end modes at quasienergies equal to 0 and [Formula: see text] for a periodically kicked system with [Formula: see text].

Exploring the possibilities of dynamical quantum phase transitions in the presence of a Markovian bath.

We explore the possibility of dynamical quantum phase transitions (DQPTs) occurring during the temporal evolution of a quenched transverse field Ising chain coupled to a particle loss type of bath (local in Jordan-Wigner fermion space) using two versions of the Loschmidt overlap (LO), namely, the fidelity induced LO and the interferometric phase induced LO. The bath, on the one hand, dictates the dissipative evolution following a sudden quench and on the other, plays a role in dissipative mixed state preparation in the later part of the study. During a dissipative evolution following a sudden quench, no trace of DQPTs are revealed in both the fidelity and the interferometric phase approaches; however, remarkably the interferometric phase approach reveals the possibility of inter-steady state DQPTs in passage from one steady state to the other when the system is subjected to a quench after having reached the first steady state. We further probe the occurrences of DQPTs when the system evolves unitarily after being prepared in a mixed state of engineered purity by ramping the transverse field in a linear fashion in the presence of the bath. In this case though the fidelity approach fails to indicate any DQPT, the interferometric approach indeed unravels the possibility of occurrence of DQPTs which persists even up to a considerable loss of purity of the engineered initial state as long as a constraint relation involving the dissipative coupling and ramping time (rate) is satisfied. This constraint relation also marks the boundary between two dynamically inequivalent phases; in one the LO vanishes for the critical momentum mode (and hence DQPTs exist) while in the other no such critical mode can exist and hence the LO never vanishes.

Phase transition in the periodically pulsed Dicke model.

We study the effect of pulsed driving and kicked driving of the interaction term on the nonequilibrium phase transition in the Dicke model. Within the framework of Floquet theory, we observe the emergence of new nontrivial phases on impingement by such periodic pulses. Notably, our study reveals that a greater control over the dynamical quantum criticality is possible through the variation of multiple parameters related to the pulse, as opposed to a single parameter control in a monochromatic drive. Furthermore, the probability of the system remaining trapped in a metastable state during the observed first order transition from the superradiant to normal phase is found to be higher for small number of kicks (or pulses) in comparison to the sinusoidal perturbation.

Reply to "Comment on 'Exploring chaos in the Dicke model using ground-state fidelity and Loschmidt echo' ".

Although we agree with the fact reported in García-Mata et al. [Phys. Rev. E 91, 036901 (2015)] that a computational error resulted in misinterpretation of the behavior of the ground-state fidelity only, we emphasize below that this does not alter the main conclusion of our paper. That is the main claim that we had made about the use of quantum information measures to study chaos in the Dicke model still holds true.

Exploring chaos in the Dicke model using ground-state fidelity and Loschmidt echo.

We study the quantum critical behavior of the Dicke Hamiltonian with finite number of atoms and explore the signature of quantum chaos using measures like the ground-state fidelity and the Loschmidt echo and the time-averaged Loschmidt echo. We show that these quantities clearly point to the classically chaotic nature of the system in the superradiant (SR) phase. While the ground-state fidelity shows aperiodic oscillations as a function of the coupling strength, the echo shows aperiodic oscillations in time and decays rapidly when the system is in the SR phase. We clearly demonstrate how the time-averaged value of the echo already incorporates the information about the ground-state fidelity and stays much less than unity, indicating the classically chaotic nature of the model in the SR phase.