arXiv subjects

M. Iskin

Publications and source records attributed to M. Iskin.

At least 73 records · Page 4Linked to original sources

arXiv2011

Mass-imbalanced Fermi gases with spin-orbit coupling

We use the mean-field theory to analyze the ground-state phase diagrams of spin-orbit coupled mass-imbalanced Fermi gases throughout the BCS-BEC evolution, including both the population-balanced and -imbalanced systems. Our calculations show that the competition between the mass and population imbalance and the Rashba-type spin-orbit coupling (SOC) gives rise to very rich phase diagrams, involving normal, superfluid and phase separated regions. In addition, we find quantum phase transitions between the topologically trivial gapped superfluid and the nontrivial gapless superfluid phases, opening the way for the experimental observation of exotic phenomena with cold atom systems.

cond-mat.quant-gas↗

arXiv2011

Quantum phases of atomic Fermi gases with anisotropic spin-orbit coupling

We consider a general anisotropic spin-orbit coupling (SOC) and analyze the phase diagrams of both balanced and imbalanced Fermi gases for the entire BCS--Bose-Einstein condensate (BEC) evolution. In the first part, we use the self-consistent mean-field theory at zero temperature, and show that the topological structure of the ground-state phase diagrams is quite robust against the effects of anisotropy. In the second part, we go beyond the mean-field description, and investigate the effects of Gaussian fluctuations near the critical temperature. This allows us to derive the time-dependent Ginzburg-Landau theory, from which we extract the effective mass of the Cooper pairs and their critical condensation temperature in the molecular BEC limit.

cond-mat.quant-gas↗

arXiv2011

Stability of spin-orbit coupled Fermi gases with population imbalance

We use the self-consistent mean-field theory to analyze the effects of Rashba-type spin-orbit coupling (SOC) on the ground-state phase diagram of population-imbalanced Fermi gases throughout the BCS-BEC evolution. We find that the SOC and population imbalance are counteracting, and that this competition tends to stabilize the uniform superfluid phase against the phase separation. However, we also show that the SOC stabilizes (destabilizes) the uniform superfluid phase against the normal phase for low (high) population imbalances. In addition, we find topological quantum phase transitions associated with the appearance of momentum space regions with zero quasiparticle energies, and study their signatures in the momentum distribution.

cond-mat.quant-gas↗

arXiv2011

Route to supersolidity for the extended Bose-Hubbard model

We use the Gutzwiller ansatz and analyze the phase diagram of the extended Bose-Hubbard Hamiltonian with on-site (U) and nearest-neighbor (V) repulsions. For $d$-dimensional hypercubic lattices, when 2dV < U, it is well-known that the ground state alternates between the charge-density-wave (CDW) and Mott insulators, and the supersolid (SS) phase occupies small regions around the CDW insulators. However, when 2dV > U, in this paper, we show that the ground state has only CDW insulators, and more importantly, the SS phase occupies a much larger region in the phase diagram, existing up to very large hopping values which could be orders of magnitude higher than that of the well-known case. In particular, the SS-superfluid phase boundary increases linearly as a function of hopping when 2dV \gtrsim 1.5U, for which the prospects of observing the SS phase with dipolar Bose gases loaded into optical lattices is much higher.

cond-mat.quant-gas↗

arXiv2011

Isothermal sweep theorems for ultra-cold quantum gases in a canonical ensemble

After deriving the isothermal Hellmann-Feynman theorem (IHFT) that is suitable for mixed states in a canonical ensemble, we use this theorem to obtain the isothermal magnetic-field sweep theorems for the free, average and trapping energies, and for the entropy, specific heat, pressure and atomic compressibility of strongly-correlated ultra-cold quantum gases. In particular, we apply the sweep theorems to two-component Fermi gases in the weakly-interacting BCS and BEC limits, showing that the temperature dependence of the contact parameter can be determined by the variation of either the entropy or specific heat with respect to the scattering length. We also use the IHFT to obtain the Virial theorem in a canonical ensemble, and discuss its implications for quantum gases.

cond-mat.quant-gas↗

arXiv2010

Ultra-cold fermions in real or fictitious magnetic fields: The BCS-BEC evolution and the type-I--type-II transition

We study ultra-cold neutral fermion superfluids in the presence of fictitious magnetic fields, as well as charged fermion superfluids in the presence of real magnetic fields. Charged fermion superfluids undergo a phase transition from type-I to type-II superfluidity, where the magnetic properties of the superfluid change from being a perfect diamagnet without vortices to a partial diamagnet with the emergence of the Abrikosov vortex lattice. The transition from type-I to type-II superfluidity is tunned by changing the scattering parameter (interaction) for fixed density. We also find that neutral fermion superfluids such as $^6$Li and $^{40}$K are extreme type-II superfluids, and that they are more robust to the penetration of a fictitious magnetic field in the BCS-BEC crossover region near unitarity, where the critical fictitious magnetic field reaches a maximum as a function of the scattering parameter (interaction).

cond-mat.quant-gas↗

arXiv2010

Mean-field theory for the Mott insulator-paired superfluid transition in the two-species Bose-Hubbard model

The standard mean-field theory for the Mott insulator-superfluid phase transition is not sufficient to describe the Mott insulator-paired superfluid phase transition. Therefore, by restricting the two-species Bose-Hubbard Hamiltonian to the subspace of paired particles, and using perturbation theory, here we derive an analytic mean-field expression for the Mott insulator-paired superfluid transition boundary.

cond-mat.quant-gas↗

arXiv2010

Strong-coupling expansion for the two-species Bose-Hubbard model

To analyze the ground-state phase diagram of Bose-Bose mixtures loaded into $d$-dimensional hypercubic optical lattices, we perform a strong-coupling power-series expansion in the kinetic energy term (plus a scaling analysis) for the two-species Bose-Hubbard model with onsite boson-boson interactions. We consider both repulsive and attractive interspecies interaction, and obtain an analytical expression for the phase boundary between the incompressible Mott insulator and the compressible superfluid phase up to third order in the hoppings. In particular, we find a re-entrant quantum phase transition from paired superfluid (superfluidity of composite bosons, i.e. Bose-Bose pairs) to Mott insulator and again to a paired superfluid in all one, two and three dimensions, when the interspecies interaction is sufficiently large and attractive. We hope that some of our results could be tested with ultracold atomic systems.

cond-mat.quant-gas↗

arXiv2010

Cooper pairing and BCS-BEC evolution in mixed-dimensional Fermi gases

Similar to what has recently been achieved with Bose-Bose mixtures [Lamporesi et al., Phys. Rev. Lett. 104, 153202 (2010)], mixed-dimensional Fermi-Fermi mixtures can be created by applying a species-selective one-dimensional optical lattice to a two-species Fermi gas ($σ\equiv \{\uparrow, \downarrow \}$), such a way that only one of the species feel the lattice potential and is confined to a quasi-two-dimensional geometry, while having negligible effect on the other, that is leaving it three dimensional. We investigate the ground state phase diagram of superfluidity for such mixtures in the BCS-BEC evolution, and find normal, gapped superfluid, gapless superfluid, and phase separated regions. In particular, we find a stable gapless superfluid phase where the unpaired $\uparrow$ and $\downarrow$ fermions coexist with the paired (or superfluid) ones in different momentum space regions. This phase is in some ways similar to the Sarma state found in mixtures with unequal densities, but in our case, the gapless superfluid phase is unpolarized and most importantly it is stable against phase separation.

cond-mat.quant-gas↗

arXiv2010

Phase diagram of the hardcore Bose-Hubbard model on a checkerboard superlattice

We obtain the complete phase diagram of the hardcore Bose-Hubbard model in the presence of a period-two superlattice in two and three dimensions. First we acquire the phase boundaries between the superfluid phase and the `trivial' insulating phases of the model (the completely-empty and completely-filled lattices) analytically. Next, the boundary between the superfluid phase and the half-filled Mott-insulating phase is obtained numerically, using the stochastic series expansion (SSE) algorithm followed by finite-size scaling. We also compare our numerical results against the predictions of several approximation schemes, including two mean-field approaches and a fourth-order strong-coupling expansion (SCE), where we show that the latter method in particular is successful in producing an accurate picture of the phase diagram. Finally, we examine the extent to which several approximation schemes, such as the random phase approximation and the strong-coupling expansion, give an accurate description of the momentum distribution of the bosons inside the insulating phases.

cond-mat.quant-gas↗

arXiv2010

Dimer-atom scattering between two identical fermions and a third particle

We use the diagrammatic $T$-matrix approach to analyze the three-body scattering problem between two identical fermions and a third particle (which could be a different species of fermion or a boson). We calculate the s-wave dimer-atom scattering length for all mass ratios, and our results exactly match the results of Petrov. In particular, we list the exact dimer-atom scattering lengths for all available two-species Fermi-Fermi and Bose-Fermi mixtures. In addition, unlike that of the equal-mass particles case where the three-body scattering $T$-matrix decays monotonically as a function of the outgoing momentum, we show that, after an initial rapid drop, this function changes sign and becomes negative at large momenta and then decays slowly to zero when the mass ratio of the fermions to the third particle is higher than a critical value (around 6.5). As the mass ratio gets higher, modulations of the $T$-matrix become more apparent with multiple sign changes, related to the "fall of a particle to the center" phenomenon and to the emergence of three-body Efimov bound states.

cond-mat.quant-gas↗

arXiv2009

Dynamical mean-field theory for light fermion--heavy boson mixtures on optical lattices

We theoretically analyze Fermi-Bose mixtures consisting of light fermions and heavy bosons that are loaded into optical lattices (ignoring the trapping potential). To describe such mixtures, we consider the Fermi-Bose version of the Falicov-Kimball model on a periodic lattice. This model can be exactly mapped onto the spinless Fermi-Fermi Falicov-Kimball model at zero temperature for all parameter space as long as the mixture is thermodynamically stable. We employ dynamical mean-field theory to investigate the evolution of the Fermi-Bose Falicov-Kimball model at higher temperatures. We calculate spectral moment sum rules for the retarded Green's function and self-energy, and use them to benchmark the accuracy of our numerical calculations, as well as to reduce the computational cost by exactly including the tails of infinite summations or products. We show how the occupancy of the bosons, single-particle many-body density of states for the fermions, momentum distribution, and the average kinetic energy evolve with temperature. We end by briefly discussing how to experimentally realize the Fermi-Bose Falicov-Kimball model in ultracold atomic systems.

cond-mat.quant-gas↗

arXiv2009

Momentum distribution of the insulating phases of the extended Bose-Hubbard model

We develop two methods to calculate the momentum distribution of the insulating (Mott and charge-density-wave) phases of the extended Bose-Hubbard model with on-site and nearest-neighbor boson-boson repulsions on $d$-dimensional hypercubic lattices. First we construct the random phase approximation result, which corresponds to the exact solution for the infinite-dimensional limit. Then we perform a power-series expansion in the hopping $t$ via strong-coupling perturbation theory, to evaluate the momentum distribution in two and three dimensions; we also use the strong-coupling theory to verify the random phase approximation solution in infinite dimensions. Finally, we briefly discuss possible implications of our results in the context of ultracold dipolar Bose gases with dipole-dipole interactions loaded into optical lattices.

cond-mat.str-el↗

arXiv2009

Strong-coupling perturbation theory for the extended Bose-Hubbard model

We develop a strong-coupling perturbation theory for the extended Bose-Hubbard model with on-site and nearest-neighbor boson-boson repulsions on ($d > 1$)-dimensional hypercubic lattices. Analytical expressions for the ground-state phase boundaries between the incompressible (Mott or charge-density-wave insulators) and the compressible (superfluid or supersolid) phases are derived up to third order in the hopping $t$. We also briefly discuss possible implications of our results in the context of ultracold dipolar Bose gases with dipole-dipole interactions loaded into optical lattices.

cond-mat.str-el↗

arXiv2009

Rotation induced superfluid-normal phase separation in trapped Fermi gases

We use the Bogoliubov-de Gennes formalism to analyze the effects of rotation on the ground state phases of harmonically trapped Fermi gases, under the assumption that quantized vortices are not excited. We find that the rotation breaks Cooper pairs that are located near the trap edge, and that this leads to a phase separation between the nonrotating superfluid (fully paired) atoms located around the trap center and the rigidly rotating normal (nonpaired) atoms located towards the trap edge, with a coexistence (partially paired) region in between. Furthermore, we show that the superfluid phase that occurs in the coexistence region is characterized by a gapless excitation spectrum, and that it is distinct from the gapped phase that occurs near the trap center.

cond-mat.supr-con↗

arXiv2008

Trapped fermion mixtures with unequal masses: a Bogoliubov-de Gennes approach

We use the Bogoliubov-de Gennes formalism to analyze the ground state phases of harmonically trapped two-species fermion mixtures with unequal masses. In the weakly attracting limit and around unitarity, we find that the superfluid order parameter is spatially modulated around the trap center, and that its global maximum occurs at a finite distance away from the trap center where the mixture is locally unpolarized. As the attraction strength increases towards the molecular limit, the spatial modulations gradually disappear while the Bardeen-Cooper-Schrieffer (BCS) type nonmodulated superfluid region expands until the entire mixture becomes locally unpolarized.

cond-mat.supr-con↗

arXiv2008

Vortex core states in superfluid Fermi-Fermi mixtures with unequal masses

We analyze the vortex core states of two-species (mass imbalanced) superfluid fermion mixtures as a function of two-body binding energy in two dimensions. In particular we solve the Bogoliubov-de Gennes equations for a population balanced mixture of $^{6}$Li and $^{40}$K atoms at zero temperature. We find that the vortex core is mostly occupied by the light-mass ($^{6}$Li) fermions and that the core density of the heavy-mass ($^{40}$K) fermions is highly depleted. This is in contrast with the one-species (mass balanced) mixtures with balanced populations where an equal amount of density depletion is found at the vortex core for both pseudospin components.

cond-mat.supr-con↗

arXiv2008

Population imbalanced fermions in harmonically trapped optical lattices

The attractive Fermi-Hubbard Hamiltonian is solved via the Bogoliubov-de Gennes formalism to analyze the ground state phases of population imbalanced fermion mixtures in harmonically trapped two-dimensional optical lattices. In the low density limit the superfluid order parameter modulates in the radial direction towards the trap edges to accommodate the unpaired fermions that are pushed away from the trap center with a single peak in their density. However in the high density limit while the order parameter modulates in the radial direction towards the trap center for low imbalance, it also modulates towards the trap edges with increasing imbalance until the superfluid to normal phase transition occurs beyond a critical imbalance. This leads to a single peak in the density of unpaired fermions for low and high imbalance but leads to double peaks for intermediate imbalance.

cond-mat.supr-con↗