arXiv subjects

R. O. Umucalilar

Publications and source records attributed to R. O. Umucalilar.

15 recordsLinked to original sources

arXiv2023

Bulk density signatures of a lattice quasihole with very few particles

Motivated by the recent experimental realization of a two-particle fractional quantum Hall state of ultracold atoms in a small optical lattice [Nature 619, 495 (2023)], we propose a minimal setup to create and observe a quasihole in such a system. We find that clear signatures of a quasihole state with two or three atoms can be obtained through a standard site-resolved density measurement provided that the system is appropriately modified with simple additional potential profiles. By adding a single-site repulsive potential to pin the quasihole and superimposing a harmonic trap on top of the optical lattice to keep the particles away from the system edge, we determine via exact diagonalization an optimal range for system parameters such as the magnetic flux and the strengths of the additional potentials that would favour the creation of the quasihole state. We hope that our results will be a useful guide for a possible proof-of-principle experiment that will demonstrate the first controllable creation of a simple quasihole state in a condensed matter system, which will pave the way for the observation of the anyonic statistics of quasiholes in a more complex system.

cond-mat.quant-gas↗

arXiv2018

Real-space probe for lattice quasiholes

We propose a real-space probe that is based on density measurements to extract distinct signatures of quasihole-like states of bosons experiencing a synthetic magnetic field in a two-dimensional lattice. We numerically show that certain ratios of the mean square radii of the particle cloud, obtainable through the density profile, approach the continuum values expected from Laughlin's ansatz wave functions quickly as the magnetic flux quanta per unit cell of the lattice decrease, even in a small lattice with few particles. This method could equally be used in both ultra-cold atomic and photonic systems.

cond-mat.quant-gas↗

arXiv2017

Generation and spectroscopic signatures of a fractional quantum Hall liquid of photons in an incoherently pumped optical cavity

We theoretically investigate a driven-dissipative model of strongly interacting photons in a nonlinear optical cavity in the presence of a synthetic magnetic field. We show the possibility of using a frequency-dependent incoherent pump to create a strongly-correlated $ν= 1/2$ bosonic Laughlin state of light: thanks to the incompressibility of the Laughlin state, fluctuations in the total particle number and excitation of edge modes can be tamed by imposing a suitable external potential profile for photons. We further propose angular momentum-selective spectroscopy of the emitted light as a tool to obtain unambiguous signatures of the microscopic physics of the quantum Hall liquid of light.

cond-mat.quant-gas↗

arXiv2017

BCS theory of time-reversal-symmetric Hofstadter-Hubbard model

The competition between the length scales associated with the periodicity of a lattice potential and the cyclotron radius of a uniform magnetic field is known to have dramatic effects on the single-particle properties of a quantum particle, e.g., the fractal spectrum is known as the Hofstadter butterfly. Having this intricate competition in mind, we consider a two-component Fermi gas on a square optical lattice with opposite synthetic magnetic fields for the components, and study its effects on the many-body BCS-pairing phenomenon. By a careful addressing of the distinct superfluid transitions from the semi-metal, quantum spin-Hall insulator or normal phases, we explore the low-temperature phase diagrams of the model, displaying lobe structures that are reminiscent of the well-known Mott-insulator transitions of the Bose-Hubbard model.

cond-mat.quant-gas↗

arXiv2016

Superfluid transition in the attractive Hofstadter-Hubbard model

We consider a Fermi gas that is loaded onto a square optical lattice and subjected to a perpendicular artificial magnetic field, and determine its superfluid transition boundary by adopting a BCS-like mean-field approach in momentum space. The multi-band structure of the single-particle Hofstadter spectrum is taken explicitly into account while deriving a generalized pairing equation. We present the numerical solutions as functions of the artificial magnetic flux, interaction strength, Zeeman field, chemical potential, and temperature, with a special emphasis on the roles played by the density of single-particle states and center-of-mass momentum of Cooper pairs.

cond-mat.quant-gas↗

arXiv2013

Probing few-particle Laughlin states of photons via correlation measurements

We propose methods to create and observe Laughlin-like states of photons in a strongly nonlinear optical cavity. Such states of strongly interacting photons can be prepared by pumping the cavity with a Laguerre-Gauss beam, which has a well-defined orbital angular momentum per photon. The Laughlin-like states appear as sharp resonances in the particle-number-resolved transmission spectrum. Power spectrum and second-order correlation function measurements yield unambiguous signatures of these few-particle strongly-correlated states.

cond-mat.quant-gas↗

arXiv2013

Many-body braiding phases in a rotating strongly correlated photon gas

We present a theoretical study of a rotating trapped photon gas where a Laguerre-Gauss laser pump with a non-zero orbital angular momentum is used to inject rotating photons into a cavity with strong optical nonlinearity. The Laughlin-like few-photon eigenstates appear as sharp resonances in the transmission spectra. Using additional localized repulsive potentials, quasi-holes can be created in the quantum Hall liquid of photons and then braided around in space: an unambiguous signature of the many-body Berry phase under exchange of two quasi-holes is observed as a spectral shift of the corresponding transmission resonance.

cond-mat.quant-gas↗

arXiv2012

Fractional quantum Hall states of photons in an array of dissipative coupled cavities

We report a theoretical study of the collective optical response of a two-dimensional array of nonlinear cavities in the impenetrable photon regime under a strong artificial magnetic field. Taking advantage of the non-equilibrium nature of the photon gas, we propose an experimentally viable all-optical scheme to generate and detect strongly correlated photon states which are optical analogs of the Laughlin states of fractional quantum Hall physics.

cond-mat.quant-gas↗

arXiv2011

Artificial Gauge Field for Photons in Coupled Cavity Arrays

We propose and characterize solid-state photonic structures where light experiences an artificial gauge field. A suitable coupling of the propagation and polarization degrees of freedom introduces a geometrical phase for photons tunneling between adjacent sites of a coupled cavity array. We then discuss the feasibility of observing strong gauge field effects in the optical spectra of realistic systems, including the Hofstadter butterfly spectrum.

cond-mat.quant-gas↗

arXiv2010

Pairing and Vortex Lattices for Interacting Fermions in Optical Lattices with a Large Magnetic Field

We study the structure of pairing order parameter for spin-1/2 fermions with attractive interactions in a square lattice under a uniform magnetic field. Because the magnetic translation symmetry gives a unique degeneracy in the single-particle spectrum, the wave function has both zero and finite momentum components co-existing, and their relative phases are determined by a self-consistent mean-field theory. We present a microscopic calculation that can determine the vortex lattice structure in the superfluid phase for different flux densities. Phase transition from a Hofstadter insulator to a superfluid phase is also discussed.

cond-mat.quant-gas↗

arXiv2010

Fractional Quantum Hall states in the vicinity of Mott plateaus

We perform variational Monte-Carlo calculations to show that bosons in a rotating optical lattice will form analogs of fractional quantum Hall states when the tunneling is sufficiently weak compared to the interactions and the deviation of density from an integer is commensurate with the effective magnetic field. We compare the energies of superfluid and correlated states to one-another and to the energies found in full configuration-interaction calculations on small systems. We look at overlaps between our variational states and the exact ground-state, characterizing the ways in which fractional quantum Hall effect correlations manifest themselves near the Mott insulating state. We explore the experimental signatures of these states.

cond-mat.quant-gas↗

arXiv2008

P-band in a rotating optical lattice

We investigate the effects of rotation on the excited bands of a tight binding lattice, focusing particulary on the first excited (p-) band. Both the on-site energies and the hopping between lattice sites are modified by the effective magnetic field created by rotation, causing a non-trivial splitting and magnetic fine structure of the p-band. We show that Peierls substitution can be modified to describe p-band under rotation, and use this method to derive an effective Hamiltonian. We compare the spectrum of the effective Hamiltonian with a first principles calculation of the magnetic band structure and find excellent agreement, confirming the validity of our approach. We also discuss the on-site interaction terms for bosons and argue that many-particle phenomena in a rotating p-band can be investigated starting from this effective Hamiltonian.

cond-mat.other↗

arXiv2007

Trapped Fermi Gases in Rotating Optical Lattices: Realization and Detection of the Topological Hofstadter Insulator

We consider a gas of non-interacting spinless fermions in a rotating optical lattice and calculate the density profile of the gas in an external confinement potential. The density profile exhibits distinct plateaus, which correspond to gaps in the single particle spectrum known as the Hofstadter butterfly. The plateaus result from insulating behavior whenever the Fermi energy lies within a gap. We discuss the necessary conditions to realize the Hofstadter insulator in a cold atom setup and show how the quantized Hall conductance can be measured from density profiles using the Středa formula.

cond-mat.mes-hall↗

arXiv2007

Localization of an impurity particle on a boson Mott insulator background

We investigate the behavior of a single particle hopping on a three dimensional cubic optical lattice in the presence of a Mott insulator of bosons in the same lattice. We calculate the critical interaction strength between the impurity and background bosons, beyond which there is bound state (polaron) formation. We give exact results in the limit of a perfect Mott insulator, where polaron formation is equivalent to impurity localization. We calculate the effects of lattice anisotropy, higher impurity bands, and fluctuations of the Mott insulator on the localization threshold. We argue that our results can be checked experimentally by RF spectroscopy of impurity particles.

cond-mat.other↗

arXiv2007

Phase Boundary of the Boson Mott Insulator in a Rotating Optical Lattice

We consider the Bose-Hubbard model in a two dimensional rotating optical lattice and investigate the consequences of the effective magnetic field created by rotation. Using a Gutzwiller type variational wavefunction, we find an analytical expression for the Mott insulator(MI)-Superfluid(SF) transition boundary in terms of the maximum eigenvalue of the Hofstadter butterfly. The dependence of phase boundary on the effective magnetic field is complex, reflecting the self-similar properties of the single particle energy spectrum. Finally, we argue that fractional quantum Hall phases exist close to the MI-SF transition boundaries, including MI states with particle densities greater than one.

cond-mat.mes-hall↗