arXiv subjects

F. Nur Ünal

Publications and source records attributed to F. Nur Ünal.

28 records · Page 2Linked to original sources

arXiv2019

Hopf characterization of two-dimensional Floquet topological insulators

We present a topological characterization of time-periodically driven two-band models in 2+1 dimensions as Hopf insulators. The intrinsic periodicity of the Floquet system with respect to both time and the underlying two-dimensional momentum space constitutes a map from a three dimensional torus to the Bloch sphere. As a result, we find that the driven system can be understood by appealing to a Hopf map that is directly constructed from the micromotion of the drive. Previously found winding numbers are shown to correspond to Hopf invariants, which are associated with linking numbers describing the topology of knots in three dimensions. Moreover, after being cast as a Hopf insulator, not only the Chern numbers, but also the winding numbers of the Floquet topological insulator become accessible in experiments as linking numbers. We exploit this description to propose a feasible scheme for measuring the complete set of their Floquet topological invariants in optical lattices.

cond-mat.quant-gas↗

arXiv2019

How to Directly Measure Floquet Topological Invariants in Optical Lattices

The classification of topological Floquet systems with time-periodic Hamiltonians transcends that of static systems. For example, spinless fermions in periodically driven two-dimensional lattices are not completely characterized by the Chern numbers of the quasienergy bands, but rather by a set of winding numbers associated with the quasienergy gaps. We propose a scheme for measuring these winding numbers in a system of fermionic cold atoms in a periodically driven optical lattice efficiently and directly. It is based on the construction of a one-parameter family of experimentally feasible drives, continuously connecting the Floquet system of interest to a trivial reference system. The winding numbers are then determined by the identification and the tomography of the band-touching singularities occurring on the way. As a byproduct, we also propose a method for probing spectral properties of time evolution operators via a time analog of crystallography.

cond-mat.quant-gas↗

arXiv2019

Measuring topology by dynamics: Chern number from linking number

Integer-valued topological indices, characterizing nonlocal properties of quantum states of matter, are known to directly predict robust physical properties of equilibrium systems. The Chern number, e.g., determines the quantized Hall conductivity of an insulator. Using fermionic atoms in a periodically driven optical lattice, here we demonstrate experimentally that the Chern number determines also the far-from-equilibrium dynamics of a quantum system. Following the proposal of ref. [Wang et al., Phys. Rev. Lett. 118, 185701 (2017)] and extending it to Floquet systems, we measure the linking number that characterizes the trajectories of momentum-space vortices emerging after a strong quench. We observe that it directly corresponds to the ground-state Chern number. This one-to-one relation between a dynamical and a static topological index allows us to experimentally map out the phase diagram of our system. Furthermore, we measure the instantaneous Chern number and show that it remains zero under the unitary dynamics.

cond-mat.quant-gas↗

arXiv2019

Creating, probing, and manipulating fractionally charged excitations of fractional Chern insulators in optical lattices

We propose a set of schemes to create and probe fractionally charged excitations of a fractional Chern insulator state in an optical lattice. This includes the creation of localized quasiparticles and quasiholes using both static local defects and the dynamical local insertion of synthetic flux quanta. Simulations of repulsively interacting bosons on a finite square lattice with experimentally relevant open boundary conditions show that already a four-particle system exhibits signatures of charge fractionalization in the quantum-Hall-like state at the filling fraction of $1/2$ particle per flux quantum. This result is favorable for the prospects of adiabatic preparation of fractional Chern insulators. Our work is inspired by recent experimental breakthroughs in atomic quantum gases: the realization of strong artificial magnetic fields in optical lattices, the ability of single-site addressing in quantum gas microscopes, and the preparation of low-entropy insulating states by engineering an entropy-absorbing metallic reservoir.

cond-mat.quant-gas↗

arXiv2018

Floquet engineering of optical solenoids and quantized charge pumping along tailored paths in two-dimensional Chern insulators

The insertion of a local magnetic flux, as the one created by a thin solenoid, plays an important role in gedanken experiments of quantum Hall physics. By combining Floquet engineering of artificial magnetic fields with the ability of single-site addressing in quantum-gas microscopes, we propose a scheme for the realization of such local solenoid-type magnetic fields in optical lattices. We show that it can be employed to manipulate and probe elementary excitations of a topological Chern insulator. This includes quantized adiabatic charge pumping along tailored paths inside the bulk, as well as the controlled population of edge modes.

cond-mat.quant-gas↗

arXiv2017

Cooling Quantum Gases with Entropy Localization

We study the dynamics of entropy in a time dependent potential and explore how disorder influences this entropy flow. We show that disorder can trap entropy at the edge of the atomic cloud enabling a novel cooling method. We demonstrate the feasibility of our cooling technique by analyzing the evolution of entropy in a one-dimensional Fermi lattice gas with a time dependent superlattice potential.

cond-mat.quant-gas↗

arXiv2016

Non-equilibrium Fractional Hall Response After a Topological Quench

We theoretically study the Hall response of a lattice system following a quench where the topology of a filled band is suddenly changed. In the limit where the physics is dominated by a single Dirac cone, we find that the change in the Hall conductivity is two-thirds of the quantum of conductivity. We explore this universal behavior in the Haldane model, and discuss cold-atom experiments for its observation. Beyond linear response, the Hall effect crosses over from fractional to integer values. We investigate finite-size effects, and the role of the harmonic confinement.

cond-mat.quant-gas↗

arXiv2016

Pairing of Fermions with Unequal Effective Charges in an Artificial Magnetic Field

Artificial magnetic fields (AMFs) created for ultra cold systems depend sensitively on the internal structure of the atoms. In a mixture, each component experiences a different AMF depending on its internal state. This enables the study of Bardeen-Cooper-Schrieffer pairing of fermions with unequal effective charges. In this Letter, we investigate the superconducting (SC) transition of a system formed by such pairs as a function of field strength. We consider a homogeneous two-component Fermi gas of unequal effective charges but equal densities with attractive interactions. We find that the phase diagram is altered drastically compared to the usual balanced charge case. First, for some AMFs there is no SC transition and isolated SC phases are formed, reflecting the discrete Landau level (LL) structure. SC phases become reentrant both in AMF and temperature. For extremely high fields where both components are confined to their lowest LLs, the effect of the charge imbalance is suppressed. Charge asymmetry reduces the critical temperature even in the low-field semiclassical regime. We discuss a pair breaking mechanism due to the unequal Lorentz forces acting on the components of the Cooper pairs to identify the underlying physics.

cond-mat.quant-gas↗

arXiv2015

Evolution of the Hofstadter butterfly in a tunable optical lattice

Recent advances in realizing artificial gauge fields on optical lattices promise experimental detection of topologically non-trivial energy spectra. Self-similar fractal energy structures generally known as Hofstadter butterflies depend sensitively on the geometry of the underlying lattice, as well as the applied magnetic field. The recent demonstration of an adjustable lattice geometry [L. Tarruell \textit{et al.}, Nature 483, 302--305 (2012)] presents a unique opportunity to study this dependence. In this paper, we calculate the Hofstadter butterflies that can be obtained in such an adjustable lattice and find three qualitatively different regimes. We show that the existence of Dirac points at zero magnetic field does not imply the topological equivalence of spectra at finite field. As the real-space structure evolves from the checkerboard lattice to the honeycomb lattice, two square lattice Hofstadter butterflies merge to form a honeycomb lattice butterfly. This merging is topologically non-trivial, as it is accomplished by sequential closings of gaps. Ensuing Chern number transfer between the bands can be probed with the adjustable lattice experiments. We also calculate the Chern numbers of the gaps for qualitatively different spectra and discuss the evolution of topological properties with underlying lattice geometry.

cond-mat.quant-gas↗

arXiv2015

Impurity coupled to an artificial magnetic field in a Fermi gas in a ring trap

The dynamics of a single impurity interacting with a many particle background is one of the central problems of condensed matter physics. Recent progress in ultracold atom experiments makes it possible to control this dynamics by coupling an artificial gauge field specifically to the impurity. In this paper, we consider a narrow toroidal trap in which a Fermi gas is interacting with a single atom. We show that an external magnetic field coupled to the impurity is a versatile tool to probe the impurity dynamics. Using Bethe Ansatz (BA) we calculate the eigenstates and corresponding energies exactly as a function of the flux through the trap. Adiabatic change of flux connects the ground state to excited states due to flux quantization. For repulsive interactions, the impurity disturbs the Fermi sea by dragging the fermions whose momentum matches the flux. This drag transfers momentum from the impurity to the background and increases the effective mass. The effective mass saturates to the total mass of the system for infinitely repulsive interactions. For attractive interactions, the drag again increases the effective mass which quickly saturates to twice the mass of a single particle as a polaron of the impurity and one fermion is formed. For excited states with momentum comparable to number of particles, effective mass shows a resonant behavior. We argue that standard tools in cold atom experiments can be used to test these predictions.

cond-mat.quant-gas↗