arXiv subjects

Tommaso Roscilde

Publications and source records attributed to Tommaso Roscilde.

At least 37 records · Page 2Linked to original sources

arXiv2024

Measuring bipartite spin correlations of lattice-trapped dipolar atoms

We demonstrate a bipartition technique using a super-lattice architecture to access correlations between alternating planes of a mesoscopic array of spin-3 chromium atoms trapped in a 3D optical lattice. Using this method, we observe that out-of-equilibrium dynamics driven by long-range dipolar interactions lead to spin anti-correlations between the two spatially separated subsystems. Our bipartite measurements reveal a subtle interplay between the anisotropy of the 3D dipolar interactions and that of the lattice structure, without requiring single-site addressing. We compare our results to theoretical predictions based on a truncated cumulant expansion and a new cluster semi-classical method that we use to investigate correlations at the microscopic scale. Comparison with a high-temperature analytical model reveals quantum thermalization at a high negative spin temperature.

cond-mat.quant-gas↗

arXiv2024

Quantum degeneracy and spin entanglement in ideal quantum gases

Quantum degeneracy is the central many-body feature of ideal quantum gases stemming from quantum mechanics. In this work we address its relationship to the most fundamental form of non-classicality in many-body system, i.e. many-body entanglement. We aim at establishing a quantitative link between quantum degeneracy and entanglement in spinful ideal gases, using entanglement witness criteria based on the variance of the collective spin of the spin ensemble. We show that spin-1/2 ideal Bose gases do not possess entanglement which can be revealed from such entanglement criteria. On the contrary, ideal spin-1/2 Fermi gases exhibit spin entanglement revealed by the collective-spin variances upon entering quantum degeneracy, due to the formation of highly non-local spin singlets. We map out the regime of detectable spin entanglement for Fermi gases in free space as well as in a parabolic trap, and probe the robustness of spin entanglement to thermal effects and spin imbalance. Spin entanglement in degenerate Fermi gases is amenable to experimental observation using state-of-the-art spin detection techniques in ultracold atoms.

quant-ph↗

arXiv2023

Scalable spin squeezing in two-dimensional arrays of dipolar large-$S$ spins

Controlling the quantum many-body state of arrays of qudits, possessing a large local Hilbert space, opens the path to a broad range of possibilities for many-particle entanglement, interesting both for fundamental quantum science, as well as for potential metrological applications. In this work we theoretically show that the spin-spin interactions realized in two-dimensional Mott insulators of large-spin magnetic atoms (such as Cr, Er or Dy) lead to scalable spin squeezing along the non-equilibrium unitary evolution initialized in a coherent spin state. An experimentally relevant perturbation to the collective squeezing dynamics is offered by a quadratic Zeeman shift, which leads instead to squeezing of individual spins. Making use of a truncated cumulant expansion for the quantum fluctuations of the spin array, we show that, for sufficiently small quadratic shifts, the spin squeezing dynamics is akin to that produced by the paradigmatic one-axis-twisting (OAT) model -- as expected from an effective separation between collective spin and spin-wave variables. Spin squeezing with OAT-like scaling is shown to be protected by the robustness of long-range ferromagnetic order to quadratic shifts in the equilibrium phase diagram of the system, that we reconstruct via quantum Monte Carlo and mean-field theory.

quant-ph↗

arXiv2023

Scalable spin squeezing in a dipolar Rydberg atom array

The standard quantum limit bounds the precision of measurements that can be achieved by ensembles of uncorrelated particles. Fundamentally, this limit arises from the non-commuting nature of quantum mechanics, leading to the presence of fluctuations often referred to as quantum projection noise. Quantum metrology relies on the use of non-classical states of many-body systems in order to enhance the precision of measurements beyond the standard quantum limit. To do so, one can reshape the quantum projection noise -- a strategy known as squeezing. In the context of many-body spin systems, one typically utilizes all-to-all interactions (e.g. the one-axis twisting model) between the constituents to generate the structured entanglement characteristic of spin squeezing. Motivated by recent theoretical work, here we explore the prediction that short-range interactions -- and in particular, the two-dimensional dipolar XY model -- can also enable the realization of scalable spin squeezing. Working with a dipolar Rydberg quantum simulator of up to 100 atoms, we demonstrate that quench dynamics from a polarized initial state lead to spin squeezing that improves with increasing system size up to a maximum of -3.5 dB (prior to correcting for detection errors, or approximately -5 dB after correction). Finally, we present two independent refinements: first, using a multistep spin-squeezing protocol allows us to further enhance the squeezing by approximately 1 dB, and second, leveraging Floquet engineering to realize Heisenberg interactions, we demonstrate the ability to extend the lifetime of the squeezed state by freezing its dynamics.

quant-ph↗

arXiv2023

Quantum and classical correlations in open quantum-spin lattices via truncated-cumulant trajectories

The study of quantum many-body physics in Liouvillian open quantum systems becomes increasingly important with the recent progress in experimental control on dissipative systems and their technological exploitation . A central question in open quantum systems concerns the fate of quantum correlations, and the possibility of controlling them by engineering the competition between the Hamiltonian dynamics and the coupling to a bath. Such a question is challenging from a theoretical point of view, as numerical methods faithfully accounting for quantum correlations are either relying on exact diagonalization, limiting drastically the sizes that can be treated; or on approximations on the range or strength of quantum correlations, associated to the choice of a specific Ansatz for the density matrix. In this work we propose a new method to treat open quantum-spin lattices, based on stochastic quantum trajectories for the solution of the open-system dynamics. Along each trajectory, the hierarchy of equations of motion for many-point spin-spin correlators is truncated to a given finite order, assuming that multivariate $k$-th order cumulants vanish for $k$ exceeding a cutoff $k_c$. This allows tracking the evolution of quantum spin-spin correlations up to order $k_c$ for all length scales. We validate this approach in the paradigmatic case of the phase transitions of the dissipative 2D XYZ lattice, subject to spontaneous decay. We convincingly assess the existence of steady-state phase transitions from paramagnetic to ferromagnetic, and back to paramagnetic, upon increasing one of the Hamiltonian couplings; as well as their classical Ising nature. Moreover, the approach allows us to show the presence of significant quantum correlations in the vicinity of the dissipative critical point, and to unveil the presence of spin squeezing, a tight lower bound to the quantum Fisher information.

quant-ph↗

arXiv2023

Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions

In this paper we study the transitions of entanglement complexity in an exemplary family of states - the Rokhsar-Kivelson-sign wavefunctions - whose degree of entanglement is controlled by a single parameter. This family of states is known to feature a transition between a phase exhibiting volume-law scaling of entanglement entropy and a phase with sub-extensive scaling of entanglement, reminiscent of the many-body-localization transition of disordered quantum Hamiltonians [Physical Review B 92, 214204 (2015)]. We study the singularities of the Rokhsar-Kivelson-sign wavefunctions and their entanglement complexity across the transition using several tools from quantum information theory: fidelity metric; entanglement spectrum statistics; entanglement entropy fluctuations; stabilizer Rényi Entropy; and the performance of a disentangling algorithm. Across the whole volume-law phase the states feature universal entanglement spectrum statistics. Yet a "super-universal" regime appears for small values of the control parameter in which all metrics become independent of the parameter itself; the entanglement entropy as well as the stabilizer Rényi entropy appear to approach their theoretical maximum; the entanglement fluctuations scale to zero as in output states of random universal circuits, and the disentangling algorithm has essentially null efficiency. All these indicators consistently reveal a complex pattern of entanglement. In the sub-volume-law phase, on the other hand, the entanglement spectrum statistics is no longer universal, entanglement fluctuations are larger and exhibiting a non-universal scaling; and the efficiency of the disentangling algorithm becomes finite. Our results, based on model wavefunctions, suggest that a similar combination of entanglement scaling properties and of entanglement complexity features may be found in high-energy Hamiltonian eigenstates.

quant-ph↗

arXiv2023

Rotor/spin-wave theory for quantum spin models with U(1) symmetry

The static and dynamics properties of finite-size lattice quantum spin models which spontaneously break a continuous $U(1)$ symmetry in the thermodynamic limit are of central importance for a wide variety of physical systems, from condensed matter to quantum simulation. Such systems are characterized by a Goldstone excitation branch, terminating in a zero mode whose theoretical treatment within a linearized approach leads to divergencies on finite-size systems, revealing that the assumption of symmetry breaking is ill-defined away from the thermodynamic limit. In this work we show that, once all its non-linearities are taken into account, the zero mode corresponds exactly to a U(1) quantum rotor, related to the Anderson tower of states expected in systems showing symmetry breaking in the thermodynamic limit. The finite-momentum modes, when weakly populated, can be instead safely linearized (namely treated within spin-wave theory) and effectively decoupled from the zero mode. This picture leads to an approximate separation of variables between rotor and spin-wave ones, which allows for a correct description of the ground-state and low-energy physics. Most importantly, it offers a quantitative treatment of the finite-size non-equilibrium dynamics -- following a quantum quench -- dominated by the zero mode, for which a linearized approach fails. Focusing on the 2$d$ XX model with power-law decaying interactions, we compare our equilibrium predictions with unbiased quantum Monte Carlo results and exact diagonalization; and our non-equilibrium results with time-dependent variational Monte Carlo. The agreement is remarkable for all interaction ranges, and it improves the longer the range. Our rotor/spin-wave theory defines a successful strategy for the application of spin-wave theory and its extensions to finite-size systems at equilibrium or away from it.

cond-mat.str-el↗

arXiv2023

Entangling dynamics from effective rotor/spin-wave separation in U(1)-symmetric quantum spin models

The non-equilibrium dynamics of quantum spin models is a most challenging topic, due to the exponentiality of Hilbert space; and it is central to the understanding of the many-body entangled states that can be generated by state-of-the-art quantum simulators. A particularly important class of evolutions is the one governed by U(1) symmetric Hamiltonians, initialized in a state which breaks the U(1) symmetry -- the paradigmatic example being the evolution of the so-called one-axis-twisting (OAT) model, featuring infinite-range interactions between spins. In this work we show that the dynamics of the OAT model can be closely reproduced by systems with power-law-decaying interactions, thanks to an effective separation between the zero-momentum degrees of freedom, associated with the so-called Anderson tower of states, and reconstructing a OAT model; and finite-momentum ones, associated with spin-wave excitations. This mechanism explains quantitatively the recent numerical observation of spin squeezing and Schrödinger-cat generation in the dynamics of dipolar Hamiltonians; and it paves the way for the extension of this observation to a much larger class of models of immediate relevance for quantum simulations.

quant-ph↗

arXiv2023

Gaussian-state Ansatz for the non-equilibrium dynamics of quantum spin lattices

The study of non-equilibrium dynamics is one of the most important challenges of modern quantum many-body physics, in relationship with fundamental questions in quantum statistical mechanics, as well as with the fields of quantum simulation and computing. In this work we propose a Gaussian Ansatz for the study of the nonequilibrium dynamics of quantum spin systems. Within our approach, the quantum spins are mapped onto Holstein-Primakoff bosons, such that a coherent spin state -- chosen as the initial state of the dynamics -- represents the bosonic vacuum. The state of the system is then postulated to remain a bosonic Gaussian state at all times, an assumption which is exact when the bosonic Hamiltonian is quadratic; and which is justified in the case of a nonlinear Hamiltonian if the boson density remains moderate. We test the accuracy of such an Ansatz in the paradigmatic case of the $S=1/2$ transverse-field Ising model, in one and two dimensions, initialized in a state aligned with the applied field. We show that the Gaussian Ansatz, when applied to the bosonic Hamiltonian with nonlinearities truncated to quartic order, is able to reproduce faithfully the evolution of the state, including its relaxation to the equilibrium regime, for fields larger than the critical field for the paramagnetic-ferromagnetic transition in the ground state. In particular the spatio-temporal pattern of correlations reconstructed via the Gaussian Ansatz reveals the dispersion relation of quasiparticle excitations, exhibiting the softening of the excitation gap upon approaching the critical field. Our results suggest that the Gaussian Ansatz correctly captures the essential effects of nonlinearities in quantum spin dynamics; and that it can be applied to the study of fundamental phenomena such as quantum thermalization and its breakdown.

cond-mat.quant-gas↗

arXiv2022

Quantum-critical scaling at the Bose-glass transition of the 3d diluted Heisenberg antiferromagnet in a field

The nature of the superfluid-to-Bose-glass (SF-BG) quantum phase transition, occurring in systems of interacting bosons immersed in a disordered environment, remains elusive. One fundamental open question is whether or not the transition obeys conventional scaling at quantum critical points (QCPs): this scaling would lock the value of the crossover exponent $ϕ$ -- dictating the vanishing of the superfluid critical temperature upon approaching the QCP -- to the value of quantum critical exponents for the ground-state transition. Yet such a relation between exponents has been called into question by several numerical as well as experimental results on the SF-BG transition. Here we revisit this issue in the case of the $S=1/2$ Heisenberg antiferromagnet on a site-diluted cubic lattice, which lends itself to efficient quantum Monte Carlo simulations. Our results show that the model exhibits a percolation transition in zero applied field, with the correlation length exponent $ν= 0.87(8)$ and $ϕ= 1.1(1)$ consistent with 3d percolation. When applying a sufficiently strong magnetic field, the dilution-induced transition decouples from geometric percolation, and it becomes a SF-BG transition; nonetheless, the $ν$ and $ϕ$ exponents maintain values consistent with those of the percolation transition. These results contradict the conventional scaling, which predicts $ϕ\geqslant 2$; and they suggest a close connection between the SF-BG transition and percolation.

cond-mat.dis-nn↗

arXiv2022

Multipartite entangled states in dipolar quantum simulators

The scalable production of multipartite entangled states in ensembles of qubits is a fundamental function of quantum devices, as such states are an essential resource both for fundamental studies on entanglement, as well as for applied tasks. Here we focus on the $U(1)$ symmetric Hamiltonians for qubits with dipolar interactions -- a model realized in several state-of-the-art quantum simulation platforms for lattice spin models, including Rydberg-atom arrays with resonant interactions. Making use of exact and variational simulations, we theoretically show that the non-equilibrium dynamics generated by this lattice spin Hamiltonian shares fundamental features with that of the one-axis-twisting model, namely the simplest interacting collective-spin model with $U(1)$ symmetry. The evolution governed by the dipolar Hamiltonian generates a cascade of multipartite entangled states -- spin-squeezed states, Schrödinger's cat states, and multi-component superpositions of coherent spin states. Investigating systems with up to $N=144$ qubits, we observe full scalability of the entanglement features of these states directly related to metrology, namely scalable spin squeezing at an evolution time ${\cal O}(N^{1/3})$; and Heisenberg scaling of sensitivity of the spin parity to global rotations for cat states reached at times ${\cal O}(N)$. Our results suggest that the native Hamiltonian dynamics of state-of-the-art quantum simulation platforms, such as Rydberg-atom arrays, can act as a robust source of multipartite entanglement.

quant-ph↗

arXiv2022

Quantum critical behavior of entanglement in lattice bosons with cavity-mediated long-range interactions

We analyze the ground-state entanglement entropy of the extended Bose-Hubbard model with infinite-range interactions. This model describes the low-energy dynamics of ultracold bosons tightly bound to an optical lattice and dispersively coupled to a cavity mode. The competition between onsite repulsion and global cavity-induced interactions leads to a rich phase diagram, which exhibits superfluid, supersolid, and insulating (Mott and checkerboard) phases. We use a slave-boson treatment of harmonic quantum fluctuations around the mean-field solution and calculate the entanglement entropy across the phase transitions. At commensurate filling, the insulator-superfluid transition is signalled by a singularity in the area-law scaling coefficient of the entanglement entropy, that is similar to the one reported for the standard Bose-Hubbard model. Remarkably, at the continuous $\mathbb{Z}_2$ superfluid-to-supersolid transition we find a critical logarithmic term, regardless of the filling. This behavior originates from the appearance of a roton mode in the excitation and entanglement spectrum, becoming gapless at the critical point, and it is characteristic of collective models.

cond-mat.quant-gas↗

arXiv2022

Thermal critical dynamics from equilibrium quantum fluctuations

We show that quantum fluctuations display a singularity at thermal critical points, involving the dynamical $z$ exponent. Quantum fluctuations, captured by the quantum variance (I. Frérot and T. Roscilde, Phys. Rev. B 94, 075121 (2016)), can be expressed via purely static quantities; this in turn allows us to extract the $z$ exponent related to the intrinsic Hamiltonian dynamics via equilibrium unbiased numerical calculations, without invoking any effective classical model for the critical dynamics. These findings illustrate that, unlike classical systems, in quantum systems static and dynamic properties remain inextricably linked even at finite-temperature transitions, provided that one focuses on static quantities that do not bear any classical analog, namely on quantum fluctuations.

cond-mat.stat-mech↗

arXiv2022

Robust spin squeezing from the tower of states of $U(1)$-symmetric spin Hamiltonians

Spin squeezing - a central resource for quantum metrology - can be generated via the non-linear, entangling evolution of an initially factorized spin state. Here we show that robust (i.e. persistent) squeezing dynamics is generated by a very large class of $S=1/2$ spin Hamiltonians with axial symmetry, in relationship with the existence of a peculiar structure of the low-lying Hamiltonian eigenstates - the so-called Anderson's tower of states. Such states are fundamentally related to the appearance of spontaneous symmetry breaking in quantum systems; and, for models with sufficiently high connectivity, they are parametrically close to the eigenstates of a planar rotor (Dicke states), in that they feature an anomalously large value of the total angular momentum. Our central insight is that, starting from a coherent spin state, a generic $U(1)$-symmetric Hamiltonian featuring the Anderson's tower of states generates the same squeezing evolution at short times as the one governed by the paradigmatic one-axis-twisting (or planar-rotor) model of squeezing dynamics. The full squeezing evolution of the planar-rotor model is seemingly reproduced for interactions decaying with distance $r$ as $r^{-α}$ when $α< 5d/3$ in $d$ dimensions. Our results connect quantum simulation with quantum metrology by unveiling the squeezing power of a large variety of Hamiltonian dynamics that are currently implemented by different quantum simulation platforms.

cond-mat.str-el↗

arXiv2022

Measuring correlations from the collective spin fluctuations of a large ensemble of lattice-trapped dipolar spin-3 atoms

We perform collective spin measurements to study the buildup of two-body correlations between $\approx10^4$ spin $s=3$ chromium atoms pinned in a 3D optical lattice. The spins interact via long range and anisotropic dipolar interactions. From the fluctuations of total magnetization, measured at the standard quantum limit, we estimate the dynamical growth of the connected pairwise correlations associated with magnetization. The quantum nature of the correlations is assessed by comparisons with short and long time expansions, and numerical simulations. Our work shows that measuring fluctuations of spin populations provides new ways to characterize correlations in quantum many-body systems, for $s>1/2$ spins

cond-mat.quant-gas↗

arXiv2021

Optimal entanglement witnesses: a scalable data-driven approach

Multipartite entanglement is the key resource allowing quantum devices to outperform their classical counterparts, and entanglement certification is fundamental to assess any quantum advantage. The only scalable certification scheme relies on entanglement witnessing, typically effective only for special entangled states. Here we focus on finite sets of measurements on quantum states (hereafter called quantum data); and we propose an approach which, given a particular spatial partitioning of the system of interest, can effectively ascertain whether or not the data set is compatible with a separable state. When compatibility is disproved, the approach produces the optimal entanglement witness for the quantum data at hand. Our approach is based on mapping separable states onto equilibrium classical field theories on a lattice; and on mapping the compatibility problem onto an inverse statistical problem, whose solution is reached in polynomial time whenever the classical field theory does not describe a glassy system. Our results pave the way for systematic entanglement certification in quantum devices, optimized with respect to the accessible observables.

quant-ph↗

arXiv2021

Quench dynamics of quasi-periodic systems exhibiting Rabi oscillations of two-level integrals of motion

The elusive nature of localized integrals of motion (or l-bits) in disordered quantum systems lies at the core of some of their most prominent features, i.e. emergent integrability and lack of thermalization. Here, we study the quench dynamics of a one-dimensional model of spinless interacting fermions in a quasi-periodic potential with a localization-delocalization transition. Starting from an unentangled initial state, we show that in the strong disorder regime an important subset of the $l$-bits can be explicitly identified with strongly localized two-level systems, associated with particles confined on two lattice sites. The existence of such subsystems forming an ensemble of nearly free l-bits is found to dominate the short-time dynamics of experimentally relevant quantities, such as the Loschmidt echo and the particle imbalance. We investigate the importance of the choice of the initial state by developing a second quench protocol, starting from the ground-state of the model at different initial disorder strengths and monitoring the quench dynamics close to the delicate ETH-MBL transition regime.

cond-mat.dis-nn↗

arXiv2021

Spin squeezing from bilinear spin-spin interactions: two simple theorems

We demonstrate two simple theorems about squeezing induced by bilinear spin-spin interactions that conserve spin parity -- including a vast majority of quantum spin models implemented by state-of-the-art quantum simulators. In particular we show that squeezing captures the first form of quantum correlations which are produced: 1) at equilibrium, by adiabatically turning on the spin-spin interactions starting from a factorized state aligned with an external, arbitrary field; 2) away from equilibrium, by evolving unitarily the same state with the interacting Hamiltonian.

quant-ph↗