arXiv subjects

Chih-Chun Chien

Publications and source records attributed to Chih-Chun Chien.

At least 73 records · Page 4Linked to original sources

arXiv2018

Tunable current circulation in triangular quantum-dot metastructures

Advances in fabrication and control of quantum dots allow the realization of metastructures that may exhibit novel electrical transport phenomena. Here, we investigate the electrical current passing through one such metastructure, a system composed of quantum dots placed at the vertices of a triangle. The wave natural of quantum particles leads to internal current circulation within the metastructure in the absence of any external magnetic field. We uncover the relation between its steady-state total current and the internal circulation. By calculating the electronic correlations in quantum transport exactly, we present phase diagrams showing where different types of current circulation can be found as a function of the correlation strength and the coupling between the quantum dots. Finally, we show that the regimes of current circulation can be further enhanced or reduced depending on the local spatial distribution of the interactions, suggesting a single-particle scattering mechanism is at play even in the strongly-correlated regime. We suggest experimental realizations of actual quantum-dot metastructures where our predictions can be directly tested.

cond-mat.mes-hall↗

arXiv2018

Topological quantization of energy transport in micro- and nano-mechanical lattices

Topological effects typically discussed in the context of quantum physics are emerging as one of the central paradigms of physics. Here, we demonstrate the role of topology in energy transport through dimerized micro- and nano-mechanical lattices in the classical regime, i.e., essentially "masses and springs". We show that the thermal conductance factorizes into topological and non-topological components. The former takes on three discrete values and arises due to the appearance of edge modes that prevent good contact between the heat reservoirs and the bulk, giving a length-independent reduction of the conductance. In essence, energy input at the boundary mostly stays there, an effect robust against disorder and nonlinearity. These results bridge two seemingly disconnected disciplines of physics, namely topology and thermal transport, and suggest ways to engineer thermal contacts, opening a direction to explore the ramifications of topological properties on nanoscale technology.

cond-mat.mes-hall↗

arXiv2018

Thermodynamics and structural transition of binary atomic Bose-Fermi mixtures in box or harmonic potentials: A path-integral study

Experimental realizations of a variety of atomic binary Bose-Fermi mixtures have brought opportunities for studying composite quantum systems with different spin-statistics. The binary atomic mixtures can exhibit a structural transition from a mixture into phase separation as the boson-fermion interaction increases. By using a path-integral formalism to evaluate the grand partition function and thermodynamic grand potential, we obtain the effective potential of binary Bose-Fermi mixtures. Thermodynamic quantities in a broad range of temperatures and interactions are also derived. The structural transition can be identified as a loop of the effective potential curve, and the volume fraction of phase separation can be determined by the lever rule. For $^6$Li-$^7$Li and $^6$Li-$^{41}$K mixtures, we present the phase diagrams of the mixtures in a box potential at zero and finite temperatures. Due to the flexible densities of atomic gases, the construction of phase separation is more complicated when compared to conventional liquid or solid mixtures where the individual densities are fixed. For harmonically trapped mixtures, we use the local density approximation to map out the finite-temperature density profiles and present typical trap structures, including the mixture, partially separated phases, and fully separated phases.

cond-mat.quant-gas↗

arXiv2017

Topology, edge states, and zero-energy states of ultracold atoms in 1D optical superlattices with alternating onsite potentials or hopping coefficients

One-dimensional superlattices with periodic spatial modulations of onsite potentials or tunneling coefficients can exhibit a variety of properties associated with topology or symmetry. Recent developments of ring-shaped optical lattices allow a systematic study of those properties in superlattices with or without boundaries. While superlattices with additional modulating parameters are shown to have quantized topological invariants in the augmented parameter space, we also found localized or zero-energy states associated with symmetries of the Hamiltonians. Probing those states in ultracold-atoms is possible by utilizing recently proposed methods analyzing particle depletion or the local density of states. Moreover, we summarize feasible realizations of configurable optical superlattices using currently available techniques.

cond-mat.quant-gas↗

arXiv2017

Quantification of the memory effect of steady-state currents from interaction-induced transport in quantum systems

Dynamics of a system in general depends on its initial state and how the system is driven, but in many-body systems the memory is usually averaged out during evolution. Here, interacting quantum systems without external relaxations are shown to retain long-time memory effects in steady states. To identify memory effects, we first show quasi-steady state currents form in finite, isolated Bose and Fermi Hubbard models driven by interaction imbalance and they become steady-state currents in the thermodynamic limit. By comparing the steady state currents from different initial states or ramping rates of the imbalance, long-time memory effects can be quantified. While the memory effects of initial states are more ubiquitous, the memory effects of switching protocols are mostly visible in interaction-induced transport in lattices. Our simulations suggest the systems enter a regime governed by a generalized Fick's law and memory effects lead to initial-state dependent diffusion coefficients. We also identify conditions for enhancing memory effects and discuss possible experimental implications.

cond-mat.quant-gas↗

arXiv2017

Shear Viscosity of Uniform Fermi Gases with Population Imbalance

The shear viscosity plays an important role in studies of transport phenomena in ultracold Fermi gases and serves as a diagnostic of various microscopic theories. Due to the complicated phase structures of population-imbalanced Fermi gases, past works mainly focus on unpolarized Fermi gases. Here we investigate the shear viscosity of homogeneous, population-imbalanced Fermi gases with tunable attractive interactions at finite temperatures by using a pairing fluctuation theory for thermodynamical quantities and a gauge-invariant linear response theory for transport coefficients. In the unitary and BEC regimes, the shear viscosity increases with the polarization because the excess majority fermions cause gapless excitations acting like a normal fluid. In the weak BEC regime the excess fermions also suppress the noncondensed pairs at low polarization, and we found a minimum in the ratio of shear viscosity and relaxation time. To help constrain the relaxation time from linear response theory, we derive an exact relation connecting some thermodynamic quantities and transport coefficients at the mean-field level for unitary Fermi superfluids with population imbalance. An approximate relation beyond mean-field theory is proposed and only exhibits mild deviations from numerical results.

cond-mat.quant-gas↗

arXiv2017

Protocols for dynamically probing topological edge states and dimerization with fermionic atoms in optical potentials

Topological behavior has been observed in quantum systems including ultracold atoms. However, background harmonic traps for cold-atoms hinder direct detection of topological edge states arising at the boundary because the distortion fuses the edge states into the bulk. We propose experimentally feasible protocols to probe localized edge states and dimerization of ultracold fermions. By confining cold-atoms in a ring lattice and changing the boundary condition from periodic to open using an off-resonant laser sheet to cut open the ring, topological edge states can be generated. A lattice in a topological configuration can trap a single particle released at the edge as the system evolves in time. Alternatively, depleting an initially filled lattice away from the boundary reveals the occupied edge states. Signatures of dimerization in the presence of contact interactions can be found in selected correlations as the system boundary suddenly changes from periodic to open and exhibit memory effects of the initial state distinguishing different configurations or phases.

cond-mat.quant-gas↗

arXiv2017

Relation connecting thermodynamics and transport of atomic unitary Fermi superfluids

The shear viscosity has been shown to be equal to the product of pressure and relaxation time in normal scale-invariant fluids, but the presence of superfluidity at low temperatures can alter the relation. By using the mean-field BCS-Leggett theory with a gauge-invariant linear response theory for unitary Fermi superfluids, we present an explicit relation between thermodynamic quantities, including the pressure and chemical potential, and transport coefficients, including the shear viscosity, superfluid density, and anomalous shear viscosity from momentum transfer via Cooper pairs. The relation is modified when pairing fluctuations associated with noncondensed Cooper pairs are considered. Within a pairing fluctuation theory consistent with the BCS-Leggett ground state, we found an approximate relation for unitary Fermi superfluids. The exact mean-field relation and the approximate one with pairing flucutaions advance our understanding of relations between equilibrium and transport quantities in superfluids, and they help determine or constrain quantities which can be otherwise difficult to measure.

cond-mat.quant-gas↗

arXiv2016

Berry phase, entanglement entropy, and algebraic properties of ground states of BCS and BEC superfluids

By using Bogoliubov transformations to construct the ground states of fermionic Bardeen-Cooper-Schrieffer (BCS) superfluids and weakly-interacting Bose gases supporting Bose Einstein Condensation (BEC), their algebraic structures and implications can be analyzed in detail. Both ground states are generalized squeezed coherent states saturating a generalized Heisenberg uncertainty relation, and they acquire quantized Berry phases when the corresponding systems are transported along a closed path in their parameter spaces. While the Berry phase of the BCS ground state depends on the total particle number, the Berry phase of the BEC ground state depends only on the particles outside the BEC. The Berry phases are associated with magnetic monopoles in the parameter spaces and we found that the Dirac quantization condition is satisfied. Moreover, both ground states are entangled states of the fermion or boson quanta and we found the entanglement entropy quantifying the internal correlations. A fixed particle-number approach of fermionic superfluids does not saturate the generalized uncertainty relation, exhibits internal entanglement, and gives corresponding Berry phase. In addition, the algebraic structures of the ground states can be classified by the $q$-deformed Hopf algebra, $\bigoplus_{\mathbf{k}}h_{q_{\mathbf{k}}}(1)$ for bosons and $q$-deformed Hopf superalgebra $\bigoplus_{\mathbf{k}}h_{q_{\mathbf{k}}}(1|1)$ for fermions, respectively.

cond-mat.quant-gas↗

arXiv2016

Challenges and constraints of dynamically emerged source and sink in atomtronic circuits: From closed-system to open-system approaches

While batteries offer electronic source and sink in electronic devices, atomic analogues of source and sink and their theoretical descriptions have been a challenge in cold-atom systems. Here we consider dynamically emerged local potentials as controllable source and sink for bosonic atoms. Although a sink potential can collect bosons in equlibrium and indicate its usefulness in the adiabatic limit, sudden switching of the potential exhibits low effectiveness in pushing bosons into it. This is due to conservation of energy and particle in isolated systems such as cold atoms. By varying the potential depth and interaction strength, the systems can further exhibit averse response, where a deeper emerged potential attracts less bosonic atoms into it. To explore possibilities for improving the effectiveness, we investigate what types of system-environment coupling can help bring bosons into a dynamically emerged sink, and a Lindblad operator corresponding to local cooling is found to serve the purpose.

cond-mat.quant-gas↗

arXiv2016

Boundary-induced dynamics in 1D topological systems and memory effects of edge modes

Dynamics induced by a change of boundary conditions reveals rate-dependent signatures associated with topological properties in one-dimensional Kitaev chain and SSH model. While the perturbation from a change of the boundary propagates into the bulk, the density of topological edge modes in the case of transforming to open boundary condition reaches steady states. The steady-state density depends on the transformation rate of the boundary and serves as an illustration of quantum memory effects in topological systems. Moreover, while a link is physically broken as the boundary condition changes, some correlation functions can remain finite across the broken link and keep a record of the initial condition. By testing those phenomena in the non-topological regimes of the two models, none of the interesting signatures of memory effects can be observed. Our results thus contrast the importance of topological properties in boundary-induced dynamics.

cond-mat.mes-hall↗

arXiv2016

Hysteresis of noninteracting and spin-orbit coupled atomic Fermi gases with relaxation

Hysteresis can be found in driven many-body systems such as magnets and superfluids. Rate-dependent hysteresis arises when a system is driven periodically while relaxing towards equilibrium. A two-state paramagnet driven by an oscillating magnetic field in the relaxation approximation clearly demonstrates rate-dependent hysteresis. A noninteracting atomic Fermi gas in an optical ring potential, when driven by a periodic artificial gauge field and subjected to dissipation, is shown to exhibit hysteresis loops of atomic current due to a competition of the driving time and the relaxation time. This is in contrast to electronic systems exhibiting equilibrium persistent current driven by magnetic flux due to rapid relaxation. Universal behavior of the dissipated energy in one hysteresis loop is observed in both the magnetic and atomic systems, showing linear and inverse-linear dependence on the relaxation time in the strong and weak dissipation regimes. While interactions in general invalidate the framework for rate-dependent hysteresis, an atomic Fermi gas with artificial spin-orbit coupling exhibits hysteresis loops of atomic currents. Cold-atoms in ring-shape potentials are thus promising in demonstrating rate-dependent hysteresis and its associated phenomena.

cond-mat.quant-gas↗

arXiv2016

Superconducting circuit simulator of Bose-Hubbard model with a flat band

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.

cond-mat.supr-con↗

arXiv2016

Geometry-induced memory effects in isolated quantum systems: Observations and applications

Memory effects can lead to history-dependent behavior of a system, and they are ubiquitous in our daily life and have broad applications. Here we explore possibilities of generating memory effects in simple isolated quantum systems. By utilizing geometrical effects from a class of lattices supporting flat-bands consisting of localized states, memory effects could be observed in ultracold atoms in optical lattices. As the optical lattice continuously transforms from a triangular lattice into a kagome lattice with a flat band, history-dependent density distributions manifest quantum memory effects even in noninteracting systems, including fermionic as well as bosonic systems in the proper ranges of temperatures. Rapid growth in ultracold technology predicts a bright future for quantum memory-effect systems, and here two prototypical applications of geometry-induced quantum memory effects are proposed: An accelerometer recording the mechanical change rate in a coupled system and a rate-controlled memvalve where the rate of ramping the lattice potential acts as a control of the remnant density in the lattice.

cond-mat.quant-gas↗

arXiv2016

Matter-wave propagation in optical lattices: geometrical and flat-band effects

The geometry of optical lattices can be engineered allowing the study of atomic transport along paths arranged in patterns that are otherwise difficult to probe in the solid state. A question readily accessible to atomic systems is related to the speed of propagation of matter-waves as a function of the lattice geometry. To address this issue, we have investigated theoretically the quantum transport of non-interacting and weakly-interacting ultracold fermionic atoms in several 2D optical lattice geometries. We find that the triangular lattice has a higher propagation velocity compared to the square lattice, despite supporting longer paths. The body-centered square lattice has even longer paths, nonetheless the propagation velocity is yet faster. This apparent paradox arises from the mixing of the momentum states which leads to different group velocities in quantum systems. Standard band theory provides an explanation and allows for a systematic way to search and design systems with controllable matter-wave propagation. Moreover, the presence of a flat band such as in a two-leg ladder geometry leads to a dynamical density discontinuity, which contrasts the behavior of mobile and localized atoms in quantum transport. Our predictions are realizable with present experimental capability.

cond-mat.quant-gas↗

arXiv2015

Critical temperature of trapped interacting bosons from large-N based theories

Ultracold atoms provide clues to an important many-body problem regarding the dependence of Bose-Einstein condensation (BEC) transition temperature $T_c$ on interactions. However, cold atoms are trapped in harmonic potentials and theoretical evaluations of the $T_c$ shift of trapped interacting Bose gases are challenging. While previous predictions of the leading-order shift have been confirmed, more recent experiments exhibit higher-order corrections beyond available mean-field theories. By implementing two large-N based theories with the local density approximation (LDA), we extract next-order corrections of the $T_c$ shift. The leading-order large-N theory produces results quantitatively different from the latest experimental data. The leading-order auxiliary field (LOAF) theory containing both normal and anomalous density fields captures the $T_c$ shift accurately in the weak interaction regime. However, the LOAF theory shows incompatible behavior with the LDA and forcing the LDA leads to density discontinuities in the trap profiles. We present a phenomenological model based on the LOAF theory, which repairs the incompatibility and provides a prediction of the $T_c$ shift in stronger interaction regime.

cond-mat.quant-gas↗

arXiv2015

Crossover behavior of the thermal conductance and Kramers' transition rate theory

Kramers' theory frames chemical reaction rates in solution as reactants overcoming a barrier in the presence of friction and noise. For weak coupling to the solution, the reaction rate is limited by the rate at which the solution can restore equilibrium after a subset of reactants have surmounted the barrier to become products. For strong coupling, there are always sufficiently energetic reactants. However, the solution returns many of the intermediate states back to the reactants before the product fully forms. Here, we demonstrate that the thermal conductance displays an analogous physical response to the friction and noise that drive the heat current through a material or structure. A crossover behavior emerges where the thermal reservoirs dominate the conductance at the extremes and only in the intermediate region are the intrinsic properties of the lattice manifest. Not only does this shed new light on Kramers' classic turnover problem, this result is significant for the design of devices for thermal management and other applications, as well as the proper simulation of transport at the nanoscale.

cond-mat.stat-mech↗

arXiv2015

Quantum transport in ultracold atoms

Ultracold atoms confined by engineered magnetic or optical potentials are ideal systems for studying phenomena otherwise difficult to realize or probe in the solid state because their atomic interaction strength, number of species, density, and geometry can be independently controlled. This review focuses on quantum transport phenomena in atomic gases that mirror and oftentimes either better elucidate or show fundamental differences with those observed in mesoscopic and nanoscopic systems. We discuss significant progress in performing transport experiments in atomic gases, contrast similarities and differences between transport in cold atoms and in condensed matter systems, and survey inspiring theoretical predictions that are difficult to verify in conventional setups. These results further demonstrate the versatility offered by atomic systems in the study of nonequilibrium phenomena and their promise for novel applications.

cond-mat.quant-gas↗