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arXiv2013

Bounds on universal quantum computation with perturbed 2d cluster states

Motivated by the possibility of universal quantum computation under noise perturbations, we compute the phase diagram of the 2d cluster state Hamiltonian in the presence of Ising terms and magnetic fields. Unlike in previous analysis of perturbed 2d cluster states, we find strong evidence of a very well defined cluster phase, separated from a polarized phase by a line of 1st and 2nd order transitions compatible with the 3d Ising universality class and a tricritical end point. The phase boundary sets an upper bound for the amount of perturbation in the system so that its ground state is still useful for measurement-based quantum computation purposes. Moreover, we also compute the local fidelity with the unperturbed 2d cluster state. Besides a classical approximation, we determine the phase diagram by combining series expansions and variational infinite Projected entangled-Pair States (iPEPS) methods. Our work constitutes the first analysis of the non-trivial effect of few-body perturbations in the 2d cluster state, which is of relevance for experimental proposals.

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arXiv2013

Orbital phases of fermions in an asymmetric optical ladder

We study a quantum ladder of interacting fermions with coupled s and p orbitals. Such a model describes dipolar molecules or atoms loaded into a double-well optical lattice, dipole moments being aligned by an external field. The two orbital components have distinct hoppings. The tunneling between them is equivalent to a partial Rashba spin-orbital coupling when the orbital space (s, p) is identified as spanned by pseudo-spin 1/2 states. A rich phase diagram, including incommensurate orbital density wave, pair density wave and other exotic superconducting phases, is proposed with bosonization analysis. In particular, superconductivity is found in the repulsive regime.

cond-mat.quant-gas↗

arXiv2013

Topological superfluid phases of an atomic Fermi gas with in- and out-of-plane Zeeman fields and equal Rashba-Dresselhaus spin-orbit coupling

We analyze the effects of in- and out-of-plane Zeeman fields on the BCS-BEC evolution of a Fermi gas with equal Rashba-Dresselhaus (ERD) spin-orbit coupling (SOC). We show that the ground state of the system involves novel gapless superfluid phases that can be distinguished with respect to the topology of the momentum-space regions with zero excitation energy. For the BCS-like uniform superfluid phases with zero center-of-mass momentum, the zeros may correspond to one or two doubly-degenerate spheres, two or four spheres, two or four concave spheroids, or one or two doubly-degenerate circles, depending on the combination of Zeeman fields and SOC. Such changes in the topology signal a quantum phase transition between distinct superfluid phases, and leave their signatures on some thermodynamic quantities. We also analyze the possibility of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like nonuniform superfluid phases with finite center-of-mass momentum and obtain an even richer phase diagram.

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arXiv2013

Quantum Ising dynamics and Majorana-like edge modes in the Rabi lattice model

The atomic dipoles in the Rabi lattice model exhibit quantum Ising dynamics in the limit of strong atom-photon interaction. It governs the para- to ferro-electric phase transition in the ground state. On an open chain, it implies the existence of two Majorana-like, albeit topologically unprotected, edge modes in the ordered phase. The relation ρ^x_{1L}=p^8 between the end-to-end dipole correlation, ρ^x_{1L}, and the spontaneous polarization, p, is proposed as an observable signature of these edge modes. The DMRG calculations on the one-dimensional Rabi lattice support the strong coupling quantum Ising behavior, and correctly yield the proposed end-to-end dipole correlation. The conditions which protect the edge modes against the adverse perturbations are also identified.

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arXiv2013

Exploring exchange mechanisms with a cold atom gas

Fermionic atoms trapped in a double well potential are an ideal setting to study fundamental exchange mechanisms. We use exact diagonalization and complementary analytic calculations to demonstrate that two trapped fermions deliver a minimal model of the direct exchange mechanism. This is an ideal quantum simulator of the Heisenberg antiferromagnet, exposes the competition between covalent and ionic bonding, and can create, manipulate, and detect quantum entanglement. Three trapped atoms form a faithful simulator of the double exchange mechanism that is the fundamental building block behind many Heisenberg ferromagnets.

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arXiv2013

Spin-orbit coupling induced Fulde-Ferrell-Larkin-Ovchinnikov-like Cooper pairing and skyrmion-like polarization textures in trapped optical lattices

We study the interplay between the Zeeman field and spin-orbit coupling (SOC) in harmonically trapped Fermi gases loaded into a two-dimensional single-band tight-binding optical lattice. Using the Bogoliubov-de Gennes theory, we find that the Zeeman field combined with a Rashba SOC gives rise to $(i)$ Fulde-Ferrell-like superfluidity and $(ii)$ skyrmion-like polarization textures near the edges of the system. We also discussed the effects of interaction, temperature, SOC anisotropy and Zeeman field anisotropy on the superfluid ground state and polarization textures.

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arXiv2013

Exact Density-Functionals with Initial-State Dependence and Memory

We analytically construct the wave function that, for a given initial state, produces a prescribed density for a quantum ring with two non-interacting particles in a singlet state. In this case the initial state is completely determined by the initial density, the initial time-derivative of the density and a single integer that characterizes the (angular) momentum of the system. We then give an exact analytic expression for the exchange-correlation potential that relates two non-interacting systems with different initial states. This is used to demonstrate how the Kohn-Sham procedure predicts the density of a reference system without the need of solving the reference system's Schrödinger equation. We further numerically construct the exchange-correlation potential for an analytically solvable system of two electrons on a quantum ring with a squared cosine two-body interaction. For the same case we derive an explicit analytic expression for the exchange-correlation kernel and analyze its frequency-dependence (memory) in detail. We compare the result to simple adiabatic approximations and investigate the single-pole approximation. These approximations fail to describe the doubly-excited states, but perform well in describing the singly-excited states.

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arXiv2013

Transverse spin diffusion in strongly interacting Fermi gases

We compute spin diffusion in a dilute Fermi gas at arbitrary temperature, polarization and strong interaction in the normal phase using kinetic theory. While the longitudinal spin diffusivity depends weakly on polarization and diverges for small temperatures, the transverse spin diffusivity D_\perp has a strong polarization dependence and approaches a finite value for T->0 in the Fermi liquid phase. For a 3D unitary Fermi gas at infinite scattering length the diffusivities reach a minimum near the quantum limit of diffusion \hbar/m in the quantum degenerate regime and are strongly suppressed by medium scattering, and we discuss the importance of the spin-rotation effect. In two dimensions, D_\perp attains a minimum at strong coupling -1 < ln(kFa2D) < 1 and reaches D_\perp~0.2...0.3\hbar/m at large polarization. These values are consistent with recent measurements of two-dimensional ultracold atomic gases in the strong coupling regime.

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arXiv2013

Quantum-statistics-induced flow patterns in driven ideal Fermi gases

While classical or quantum interacting liquids become turbulent under sufficiently strong driving, it is not obvious what flow pattern an ideal quantum gas develops under similar conditions. Unlike classical noninteracting particles which exhibit rather trivial flow, ideal fermions have to satisfy the exclusion principle, which acts as a form of collective repulsion. We thus study the flow of an ideal Fermi gas as it is driven out of a narrow orifice of width comparable to the Fermi wavelength, employing both a microcanonical approach to transport, and solving a Lindblad equation for Markovian driving leads. Both methods are in good agreement and predict an outflowing current density with a complex microscopic pattern of vorticity in the steady state. Applying a bias of the order of the chemical potential results in a short-range correlated antiferromagnetic vorticity pattern, corresponding to local moments of the order of a tenth of a magneton, $e\hbar/2m$, if the fermions are charged. The latter may be detectable by magnetosensitive spectroscopy in strongly driven cold gases (atoms) or clean electronic nanostructures (electrons).

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arXiv2013

Unconventional Fulde-Ferrell-Larkin-Ovchinnikov pairing states in a Fermi gas with spin-orbit coupling

We study the phase diagram in a two-dimensional Fermi gas with the synthetic spin-orbit coupling that has recently been realized experimentally. In particular, we characterize in detail the properties and the stability region of the unconventional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in such a system, which are induced by spin-orbit coupling and Fermi surface asymmetry. We identify several distinct nodal FFLO states by studying the topology of their respective gapless contours in momentum space. We then examine the phase structure and the number density distributions in a typical harmonic trapping potential under the local density approximation. Our studies provide detailed information on the FFLO pairing states with spin-orbit coupling and Fermi surface asymmetry, and will facilitate experimental detection of these interesting pairing states in the future.

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arXiv2013

Phases of attractive spin-imbalanced fermions in square lattices

We determine the relative stability of different ground-state phases of spin-imbalanced popula- tions of attractive fermions in square lattices. The phases are systematically characterized by the symmetry of the order parameter and the real- and momentum-space structures using Hartree- Fock-Bogoliubov theory. We find several type of unidirectional Larkin-Ovchinikov-type phases. We discuss the effect of commensuration between the ordering wave vector and the density imbalance, and describe the mechanism of Fermi surface reconstruction and pairing for various orders. A robust supersolid phase is shown to exist when the ordering wave vector is diagonally directed.

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arXiv2013

Partial Multipartite Entanglement in the Matrix Product State Formalism

We present a method to apply the well-known matrix product state (MPS) formalism to partially separable states in solid state systems. The computational effort of our method is equal to the effort of the standard density matrix renormalisation group (DMRG) algorithm. Consequently, it is applicable to all usually considered condensed matter systems where the DMRG algorithm is successful. We also show in exemplary cases, that polymerisation properties of ground states are closely connected to properties of partial separability, even if the ground state itself is not partially separable.

quant-ph↗

arXiv2013

Superfluid phases of ultracold Fermi gases on a checkerboard superlattice

We analyze the ground-state phase diagram of two-component Fermi gases loaded into a two-dimensional checkerboard superlattice, i.e. a double-well optical lattice, potential within the BCS mean-field theory. We show that, by coupling the two s-wave sublattice superfluid order parameters, a checkerboard potential gives rise to a Hamiltonian that has the form of a two-band superfluidity with three (two intraband and an interband) nonlocal order parameters. We study the evolution of these order parameters as a function of particle filling, interaction strength and checkerboard potential, and find that the system always prefers the 0-phase solutions, i.e. the phase difference between sublattice order parameters is 0, but never the $π$-phase one. In addition, we find that the ground-state of the system undergo a superfluid-normal quantum phase transition at half fillings beyond a critical checkerboard potential $C$, the threshold of which is precisely determined by the magnitude of the order parameter at $C = 0$, and that the normal state rapidly turns into a checkerboard insulator as $C$ increases.

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arXiv2013

Dynamical symmetry approach and topological field theory for path integrals of quantum spin systems

We develop a dynamical symmetry approach to path integrals for general interacting quantum spin systems. The time-ordered exponential obtained after the Hubbard-Stratonovich transformation can be disentangled into the product of a finite number of the usual exponentials. This procedure leads to a set of stochastic differential equations on the group manifold, which can be further formulated in terms of the supersymmetric effective action. This action has the form of the Witten topological field theory in the continuum limit. As a consequence, we show how it can be used to obtain the exact results for a specific quantum many-body system which can be otherwise solved only by the Bethe ansatz. To our knowledge this represents the first example of a many-body system treated exactly using the path integral formulation. Moreover, our method can deal with time-dependent parameters, which we demonstrate explicitly.

cond-mat.str-el↗

arXiv2013

Genuine fidelity gaps associated with a sequential decomposition of genuinely entangling isometry and unitary operations

We draw attention to the existence of "genuine" fidelity gaps in an ancilla-assisted sequential decomposition of genuinely entangling isometry and unitary operations of quantum computing. The gaps arise upon a bipartite decomposition of a multiqubit operation in a one-way sequential recipe in which an ancillary system interacts locally and only once with each qubit in a row. Given the known "no-go" associated with such a theoretically and experimentally desirable decomposition, various figures of merit are introduced to analyze the optimal "fidelity" with which an arbitrary genuinely entangling operation may admit such a sequential decomposition. An efficient variational matrix-product-operator (VMPO) protocol is invoked in order to obtain numerically the minimal values of the fidelity gaps incurred upon sequential decomposition of genuine entanglers. We term the values of the gaps so obtained genuine in the light of possible connections to the concept of the genuine multipartite entanglement and since they are independent of the ancilla dimension and the initial states the associated unitaries act upon.

quant-ph↗

arXiv2013

Phase diagram and pair Tomonaga-Luttinger liquid in a Bose-Hubbard model with flat bands

To explore superfluidity in flat-band systems, we consider a Bose-Hubbard model on a cross-linked ladder with $π$ flux, which has a flat band with a gap between the other band for noninteracting particles, where we study the effect of the on-site repulsion nonperturbatively. For low densities, we find exact degenerate ground states, each of which is a Wigner solid with nonoverlapping Wannier states on the flat band. At higher densities, the many-body system, when projected onto the lower flat band, can be mapped to a spin-chain model. This mapping enables us to reveal the existence of a Tomonaga-Luttinger liquid comprising it pairs of bosons. Interestingly, the high- and low- density regions have an overlap, where the two phases coexist.

cond-mat.str-el↗

arXiv2013

Study of unconventional superfluid phases and the phase dynamics in spin-orbit coupled bose system

We study the phase distribution and its dynamics in spin-orbit coupled two component ultracold Bosons for finite size system. Using an inhomogeneous meanfield analysis we demonstrate how phase distribution evolves as we tune the spin-orbit coupling $γ$ and $t$, the spin-independent hopping. For $t>>γ$ we find the homogeneous superfluid phase. As we increase $γ$, differences in the phases of the order parameter grows leading to twisted superfluid phase. For $t \sim γ$ competing orderings in the phase distribution is observed. At large $γ$ limit a Ferro-Magnetic stripe ordering appears along the diagonal. We explain that this is due to the frustration bought in by the spin-orbit interaction. Isolated vortex formation is also shown to appear. We also investigate the possible collective modes. In deep superfluid regime we derive the equation of motion for the phases following a semi-classical approximation. Imaginary frequencies indicating the damped modes are seen to appear and the dynamics of lowest normal modes are discussed.

cond-mat.str-el↗

arXiv2013

Dissipative Effects on the Superfluid to Insulator Transition in Mixed-dimensional Optical Lattices

We study the superfluid to Mott insulator transition of a mixture of heavy bosons and light fermions loaded in an optical lattice. We focus on the effect of the light fermions on the dynamics of the heavy bosons. It is shown that, when the lattice potential is sufficiently deep to confine the bosons to one dimension but allowing the fermions to freely move in three dimensions (i.e. a mixed-dimensionality lattice), the fermions act as an ohmic bath for bosons leading to screening and dissipation effects on the bosons. Using a perturbative renormalization-group analysis, it is shown that the fermion-induced dissipative effects have no appreciable impact on the transition from the superfluid to the Mott-insulator state at integer filling. On the other hand, dissipative effects are found to be very important in the half-filled case near the critical point. In this case, in the presence of a finite incommensurability that destabilizes the Mott phase, the bosons can still be localized by virtue of dissipative effects.

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