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Matteo Rizzi

Publications and source records attributed to Matteo Rizzi.

At least 73 records · Page 4Linked to original sources
arXiv2017

Continuous matrix product states with periodic boundary conditions and an application to atomtronics

We introduce a time evolution algorithm for one-dimensional quantum field theories with periodic boundary conditions. This is done by applying the Dirac-Frenkel time-dependent variational principle to the set of translational invariant continuous matrix product states with periodic boundary conditions. Moreover, the ansatz is accompanied with additional boundary degrees of freedom to study quantum impurity problems. The algorithm allows for a cutoff in the spectrum of the transfer matrix and thus has an efficient computational scaling. In particular we study the prototypical example of an atomtronic system - an interacting Bose gas rotating in a ring shaped trap in the presence of a localised barrier potential.

quant-ph↗
arXiv2016

High-momentum tails as magnetic structure probes for strongly-correlated $SU(κ)$ fermionic mixtures in one-dimensional traps

A universal $k^{-4}$ decay of the large-momentum tails of the momentum distribution, fixed by Tan's contact coefficients, constitutes a direct signature of strong correlations in a short-range interacting quantum gas. Here we consider a repulsive multicomponent Fermi gas under harmonic confinement, as in the experiment of Pagano et al. [Nat. Phys. {\bf 10}, 198 (2014)], realizing a gas with tunable $SU(κ)$ symmetry. We exploit an exact solution at infinite repulsion to show a direct correspondence between the value of the Tan's contact for each of the $κ$ components of the gas and the Young tableaux for the $S_N$ permutation symmetry group identifying the magnetic structure of the ground-state. This opens a route for the experimental determination of magnetic configurations in cold atomic gases, employing only standard (spin-resolved) time-of-flight techniques. Combining the exact result with matrix-product-states simulations, we obtain the Tan's contact at all values of repulsive interactions. We show that a local density approximation (LDA) on the Bethe-Ansatz equation of state for the homogeneous mixture is in excellent agreement with the results for the harmonically confined gas. At strong interactions, the LDA predicts a scaling behavior of the Tan's contact. This provides a useful analytical expression for the dependence on the number of fermions, number of components and on interaction strength. Moreover, using a virial approach in the limit of infinite interactions, we show that the contact increases with the temperature and the number of components. At zero temperature, we predict that the weight of the momentum distribution tails increases with interaction strength and the number of components if the population per component is kept constant. This latter property was experimentally observed in Ref.~[Nat. Phys. {\bf 10}, 198 (2014)].

cond-mat.quant-gas↗
arXiv2016

Phases of Attractive Fermi Gases in Synthetic Dimensions

A novel way to produce quantum Hall ribbons in a cold atomic system is to use M hyperfine states of atoms in a 1D optical lattice to mimic an additional "synthetic dimension". A notable aspect here is that the SU(M) symmetric interaction between atoms manifests as "infinite ranged" along the synthetic dimension. We study the many body physics of fermions with attractive interactions in this system. We use a combination of analytical field theoretic and numerical density matrix renormalization group (DMRG) methods to reveal the rich ground state phase diagram of the system, including novel phases such as squished baryon fluids. Remarkably, changing the parameters entails unusual crossovers and transitions, e. g., we show that increasing the magnetic field (that produces the Hall effect) may convert a "ferrometallic" state at low fields to a "squished baryon superfluid" (with algebraic pairing correlations) at high fields. We also show that this system provides a unique opportunity to study quantum phase separation in a multiflavor ultracold fermionic system.

cond-mat.quant-gas↗
arXiv2016

Quantum memories with zero-energy Majorana modes and experimental constraints

In this work we address the problem of realizing a reliable quantum memory based on zero-energy Majorana modes in the presence of experimental constraints on the operations aimed at recovering the information. In particular, we characterize the best recovery operation acting only on the zero-energy Majorana modes and the memory fidelity that can be therewith achieved. In order to understand the effect of such restriction, we discuss two examples of noise models acting on the topological system and compare the amount of information that can be recovered by accessing either the whole system, or the zero-modes only, with particular attention to the scaling with the size of the system and the energy gap. We explicitly discuss the case of a thermal bosonic environment inducing a parity-preserving Markovian dynamics in which the introduced memory fidelity decays exponentially in time, independent from system size, thus showing the impossibility to retrieve the information by acting on the zero-modes only. We argue, however, that even in the presence of experimental limitations, the Hamiltonian gap is still beneficial to the storage of information.

quant-ph↗
arXiv2016

Superfluid density and quasi-long-range order in the one-dimensional disordered Bose-Hubbard model

We study the equilibrium properties of the one-dimensional disordered Bose-Hubbard model by means of a gauge-adaptive tree tensor network variational method suitable for systems with periodic boundary conditions. We compute the superfluid stiffness and superfluid correlations close to the superfluid to glass transition line, obtaining accurate locations of the critical points. By studying the statistics of the exponent of the power-law decay of the correlation, we determine the boundary between the superfluid region and the Bose glass phase in the regime of strong disorder and in the weakly interacting region, not explored numerically before. In the former case our simulations are in agreement with previous Monte Carlo calculations.

cond-mat.dis-nn↗
arXiv2015

Clifford Tori and the singularly perturbed Cahn-Hilliard equation

In this paper we construct entire solutions $u_{\varepsilon}$ to the Cahn-Hilliard equation $-\varepsilon^{2}Δ(-\varepsilon^{2}Δu+W^{'}(u))+W^{"}(u)(-\varepsilon^{2}Δu+W^{'}(u))=0$, under the volume constraint $\int_{\mathbb{R}^{3}}(1-u_{\varepsilon})dx=4\sqrt{2}π^{2}$, whose nodal set approaches the Clifford Torus, that is the Torus with radii of ratio $1/\sqrt{2}$ embedded in $\mathbb{R}^{3}$, as $\varepsilon\to 0$. What is crucial is that the Clifford Torus is a Willmore hypersurface and it is non-degenerate, up to conformal transformations. The proof is based on the Lyapunov-Schmidt reduction and on careful geometric expansions of the laplacian.

math.AP↗
arXiv2015

Coherent superposition of current flows in an Atomtronic Quantum Interference Device

We consider a correlated Bose gas tightly confined into a ring shaped lattice, in the presence of an artificial gauge potential inducing a persistent current through it. A weak link painted on the ring acts as a source of coherent back-scattering for the propagating gas, interfering with the forward scattered current. This system defines an atomic counterpart of the rf-SQUID: the atomtronics quantum interference device (AQUID). The goal of the present study is to corroborate the emergence of an effective two-level system in such a setup and to assess its quality, in terms of its inner resolution and its separation from the rest of the many-body spectrum, across the different physical regimes. In order to achieve this aim, we examine the dependence of the qubit energy gap on the bosonic density, the interaction strength, and the barrier depth, and we show how the superposition between current states appears in the momentum distribution (time-of-flight) images. A mesoscopic ring lattice with intermediate-to-strong interactions and weak barrier depth is found to be a favorable candidate for setting up, manipulating and probing a qubit in the next generation of atomic experiments.

cond-mat.quant-gas↗
arXiv2015

Optimal scaling of persistent currents for interacting bosons on a ring

We consider the persistent currents induced by an artificial gauge field applied to interacting ultra-cold bosonic atoms in a tight ring trap. Using both analytical and numerical methods, we study the scaling of the persistent current amplitude with the size of the ring. In the strongly interacting regime we find a power-law scaling, in good agreement with the predictions of the Luttinger-liquid theory. By exploring all interaction regimes we find that the scaling is optimal, i.e. the current amplitude decreases slower with the system size, at intermediate interactions.

cond-mat.quant-gas↗
arXiv2015

A Perturbative Approach to Continuous-Time Quantum Error Correction

We present a novel discussion of the continuous-time quantum error correction introduced by Paz and Zurek in 1998 [Paz and Zurek, Proc. R. Soc. A 454, 355 (1998)]. We study the general Lindbladian which describes the effects of both noise and error correction in the weak-noise (or strong-correction) regime through a perturbative expansion. We use this tool to derive quantitative aspects of the continuous-time dynamics both in general and through two illustrative examples: the 3-qubit and the 5-qubit stabilizer codes, which can be independently solved by analytical and numerical methods and then used as benchmarks for the perturbative approach. The perturbatively accessible time frame features a short initial transient in which error correction is ineffective, followed by a slow decay of the information content consistent with the known facts about discrete-time error correction in the limit of fast operations. This behavior is explained in the two case studies through a geometric description of the continuous transformation of the state space induced by the combined action of noise and error correction.

quant-ph↗
arXiv2014

Symmetry properties of some solutions to some semilinear elliptic equations

In this paper we prove some symmetry results for entire solutions to the semilinear equation $-Δu=f(u)$, with $f$ nonincreasing in a right neighbourhood of the origin. We consider solutions decaying only in some directions and we give some sufficient conditions for them to be radially symmetric with respect to those variables, such as periodicity or the pointwise decay of some derivatives.

math.AP↗
arXiv2014

Optimal Persistent Currents for Interacting Bosons on a Ring with a Gauge Field

We study persistent currents for interacting one-dimensional bosons on a tight ring trap, subjected to a rotating barrier potential, which induces an artificial U(1) gauge field. We show that, at intermediate interactions, the persistent current response is maximal, due to a subtle interplay of effects due to the barrier, the interaction and quantum fluctuations. These results are relevant for ongoing experiments with ultracold atomic gases on mesoscopic rings.

cond-mat.quant-gas↗
arXiv2014

Unconstrained Tree Tensor Network: An adaptive gauge picture for enhanced performance

We introduce a variational algorithm to simulate quantum many-body states based on a tree tensor network ansatz which releases the isometry constraint usually imposed by the real-space renormalization coarse-graining: This additional numerical freedom, combined with the loop-free topology of the tree network, allows one to maximally exploit the internal gauge invariance of tensor networks, ultimately leading to a computationally flexible and efficient algorithm able to treat open and periodic boundary conditions on the same footing. We benchmark the novel approach against the 1D Ising model in transverse field with periodic boundary conditions and discuss the strategy to cope with the broken translational invariance generated by the network structure. We then perform investigations on a state-of-the-art problem, namely the bilinear-biquadratic model in the transition between dimer and ferromagnetic phases. Our results clearly display an exponentially diverging correlation length and thus support the most recent guesses on the peculiarity of the transition.

cond-mat.stat-mech↗
arXiv2014

Robustness of quantum memories based on Majorana zero modes

We analyze the rate at which quantum information encoded in zero-energy Majorana modes is lost in the presence of perturbations. We show that information can survive for times that scale exponentially with the size of the chain both in the presence of quenching and time-dependent quadratic dephasing perturbations, even when the latter have spectral components above the system's energy gap. The origin of the robust storage, namely the fact that a sudden quench affects in the same way both parity sectors of the original spectrum, is discussed, together with the memory performance at finite temperatures and in the presence of particle exchange with a bath.

quant-ph↗
arXiv2011

An Optical-Lattice-Based Quantum Simulator For Relativistic Field Theories and Topological Insulators

We present a proposal for a versatile cold-atom-based quantum simulator of relativistic fermionic theories and topological insulators in arbitrary dimensions. The setup consists of a spin-independent optical lattice that traps a collection of hyperfine states of the same alkaline atom, to which the different degrees of freedom of the field theory to be simulated are then mapped. We show that the combination of bi-chromatic optical lattices with Raman transitions can allow the engineering of a spin-dependent tunneling of the atoms between neighboring lattice sites. These assisted-hopping processes can be employed for the quantum simulation of various interesting models, ranging from non-interacting relativistic fermionic theories to topological insulators. We present a toolbox for the realization of different types of relativistic lattice fermions, which can then be exploited to synthesize the majority of phases in the periodic table of topological insulators.

cond-mat.quant-gas↗
arXiv2011

From Rotating Atomic Rings to Quantum Hall States

Considerable efforts are currently devoted to the preparation of ultracold neutral atoms in the emblematic strongly correlated quantum Hall regime. The routes followed so far essentially rely on thermodynamics, i.e. imposing the proper Hamiltonian and cooling the system towards its ground state. In rapidly rotating 2D harmonic traps the role of the transverse magnetic field is played by the angular velocity. For particle numbers significantly larger than unity, the required angular momentum is very large and it can be obtained only for spinning frequencies extremely near to the deconfinement limit; consequently, the required control on experimental parameters turns out to be far too stringent. Here we propose to follow instead a dynamic path starting from the gas confined in a rotating ring. The large moment of inertia of the fluid facilitates the access to states with a large angular momentum, corresponding to a giant vortex. The initial ring-shaped trapping potential is then adiabatically transformed into a harmonic confinement, which brings the interacting atomic gas in the desired quantum Hall regime. We provide clear numerical evidence that for a relatively broad range of initial angular frequencies, the giant vortex state is adiabatically connected to the bosonic $ν=1/2$ Laughlin state, and we discuss the scaling to many particles.

cond-mat.quant-gas↗
arXiv2010

Emerging Bosons with Three-Body Interactions from Spin-1 Atoms in Optical Lattices

We study two many-body systems of bosons interacting via an infinite three-body contact repulsion in a lattice: a pairs quasi-condensate induced by correlated hopping and the discrete version of the Pfaffian wavefunction. We propose to experimentally realise systems characterized by such interaction by means of a proper spin-1 lattice Hamiltonian: spin degrees of freedom are locally mapped into occupation numbers of emerging bosons, in a fashion similar to spin-1/2 and hardcore bosons. Such a system can be realized with ultracold spin-1 atoms in a Mott Insulator with filling-factor one. The high versatility of these setups allows us to engineer spin-hopping operators breaking the SU(2) symmetry, as needed to approximate interesting bosonic Hamiltonians with three-body hardcore constraint. For this purpose we combine bichromatic spin-independent superlattices and Raman transitions to induce a different hopping rate for each spin orientation. Finally, we illustrate how our setup could be used to experimentally realize the first setup, i.e. the transition to a pairs quasi-condensed phase of the emerging bosons. We also report on a route towards the realization of a discrete bosonic Pfaffian wavefunction and list some open problems to reach this goal.

cond-mat.quant-gas↗
arXiv2008

Simulation of time evolution with the MERA

We describe an algorithm to simulate time evolution using the Multi-scale Entanglement Renormalization Ansatz (MERA) and test it by studying a critical Ising chain with periodic boundary conditions and with up to L ~ 10^6 quantum spins. The cost of a simulation, which scales as L log(L), is reduced to log(L) when the system is invariant under translations. By simulating an evolution in imaginary time, we compute the ground state of the system. The errors in the ground state energy display no evident dependence on the system size. The algorithm can be extended to lattice systems in higher spatial dimensions.

quant-ph↗