We propose a protocol for realizing the stripe phase in two spin models on a two-dimensional square lattice, which can be implemented with strongly magnetic atoms (Cr, Dy, Er, etc.) in optical lattices by encoding spin states into Zeeman sublevels of the ground state manifold. The protocol is tested with cluster-mean-field time-dependent variational ansätze, validated by comparison with exact results for small systems, which enable us to simulate the dynamics of systems with up to 64 sites during the state-preparation protocol. This allows, in particular, to estimate the time required for preparation of the stripe phase with high fidelity under real experimental conditions.
We analyze a technique for the preparation of low entropy many body states of atoms in optical lattices based on adiabatic passage. In particular, we show that this method allows preparation of strongly correlated states as stable highest energy states of Hamiltonians that have trivial ground states. As an example, we analyze the generation of antiferromagnetically ordered states by adiabatic change of a staggered field acting on the spins of bosonic atoms with ferromagnetic interactions.
In spinor Bose-Einstein condensates, spin-changing collisions are a remarkable proxy to coherently realize macroscopic many-body quantum states. These processes have been, e.g., exploited to generate entanglement, to study dynamical quantum phase transitions, and proposed for realizing nematic phases in atomic condensates. In the same systems dressed by Raman beams, the coupling between spin and momentum induces a spin dependence in the scattering processes taking place in the gas. Here we show that, at weak couplings, such modulation of the collisions leads to an effective Hamiltonian which i…
We examine the adiabatic preparation of crystalline phases of Rydberg excitations in a one-dimensional lattice gas by frequency sweep of the excitation laser, as proposed by Pohl et al. [Phys. Rev. Lett. 104, 043002 (2010)] and recently realized experimentally by Schauß et al. [Science 347, 1455 (2015)]. We find that the preparation of crystals of a few Rydberg excitations in a unitary system of several tens of atoms requires exceedingly long times for the adiabatic following of the ground state of the system Hamiltonian. Using quantum stochastic (Monte-Carlo) wavefunction simulations, we show…
We analyze the possibility to prepare a Heisenberg antiferromagnet with cold fermions in optical lattices, starting from a band insulator and adiabatically changing the lattice potential. The numerical simulation of the dynamics in 1D allows us to identify the conditions for success, and to study the influence that the presence of holes in the initial state may have on the protocol. We also extend our results to two-dimensional systems.
We analyze a scheme for preparation of magnetically ordered states of two-component bosonic atoms in optical lattices. We compute the dynamics during adiabatic and optimized time-dependent ramps to produce ground states of effective spin Hamiltonians, and determine the robustness to decoherence for realistic experimental system sizes and timescales. Ramping parameters near a phase transition point in both effective spin-1/2 and spin-1 models produces entangled spin-symmetric states that have potential future applications in quantum enhanced measurement. The preparation of these states and thei…
We study the growth dynamics of ordered structures of strongly interacting polar molecules in optical lattices. Using dipole blockade of microwave excitations, we map the system onto an interacting spin-1/2 model possessing ground states with crystalline order, and describe a way to prepare these states by non-adiabatically driving the transitions between molecular rotational levels. The proposed technique bypasses the need to cross a phase transition and allows for the creation of ordered domains of considerably larger size compared to approaches relying on adiabatic preparation.
We present a joint experimental and theoretical analysis to assess the adiabatic experimental preparation of ultracold bosons in optical lattices aimed at simulating the three-dimensional Bose-Hubbard model. Thermometry of lattice gases is realized from the superfluid to the Mott regime by combining the measurement of three-dimensional momentum-space densities with ab-initio quantum Monte Carlo (QMC) calculations of the same quantity. The measured temperatures across the superfluid-to-Mott transition are in agreement with isentropic lines reconstructed via QMC for the experimental parameters o…
In the present work, we develop an adiabatic invariant approach for the evolution of quasi-one-dimensional (stripe) solitons embedded in a two-dimensional Bose-Einstein condensate. The results of the theory are obtained both for the one-component case of dark soliton stripes, as well as for the considerably more involved case of the two-component dark-bright (alias "filled dark") soliton stripes. In both cases, analytical predictions regarding the stability and dynamics of these structures are obtained. One of our main findings is the determination of the instability modes of the waves as a fu…
Adiabatic preparation of a fractional quantum Hall fluid by coherently pumping atoms from a Bose-Einstein condensate
Pitaevskii BEC Center, INO-CNR and Dipartimento di Fisica, Università di Trento（皮塔耶夫斯基玻色-爱因斯坦凝聚中心，意大利国家研究委员会物质研究所和特伦托大学物理系）；Department of Physics, TU Dortmund University（多特蒙德大学物理系）；Technische Universität Berlin, Institut für Physik und Astronomie（柏林工业大学物理与天文学研究所）
We examine the adiabatic preparation of spatially-ordered Rydberg excitations of atoms in finite one-dimensional lattices by frequency-chirped laser pulses, as realized in a number of recent experiments simulating quantum Ising model. Our aims are to unravel the microscopic mechanism of the phase transition from the unexcited state of atoms to the antiferromagnetic-like state of Rydberg excitations by traversing an extended gapless phase, and to estimate the preparation fidelity of the target state in a moderately sized system amenable to detailed numerical analysis. We find that, in the basis…
We theoretically study the adiabatic preparation of an antiferromagnetic phase in a mixed Mott insulator of two bosonic atom species in a one-dimensional optical lattice. In such a system one can engineer a tunable parabolic inhomogeneity by controlling the difference of the trapping potentials felt by the two species. Using numerical simulations we predict that a finite parabolic potential can assist the adiabatic preparation of the antiferromagnet. The optimal strength of the parabolic inhomogeneity depends sensitively on the number imbalance between the two species. We also find that during…
The implementation of static artificial magnetic fields in ultracold atomic systems has become a powerful tool, e.g. for simulating quantum-Hall physics with charge-neutral atoms. Taking an interacting bosonic flux ladder as a minimal model, we investigate protocols for adiabatic state preparation via magnetic flux ramps. Considering the fact that it is actually the artificial vector potential (in the form of Peierls phases) that can be experimentally engineered in optical lattices, rather than the magnetic field, we find that the time required for adiabatic state preparation dramatically depe…
We model the bang-bang optimization protocol as a shortcut to adiabaticity in the ground-state preparation of an ion-trap-based quantum simulator. Compared to a locally adiabatic evolution, the bang-bang protocol produces a somewhat lower ground-state probability, but its implementation is so much simpler than the locally adiabatic approach, that it remains an excellent choice to use for maximizing ground-state preparation in systems that cannot be solved with conventional computers. We describe how one can optimize the shortcut and provide specific details for how it can be implemented with c…
We discuss how an $η$-condensate, corresponding to an exact excited eigenstate of the Fermi-Hubbard model, can be produced with cold atoms in an optical lattice. Using time-dependent density matrix renormalisation group methods, we analyse a state preparation scheme beginning from a band insulator state in an optical superlattice. This state can act as an important test case, both for adiabatic preparation methods and the implementation of the many-body Hamiltonian, and measurements on the final state can be used to help detect associated errors.
By engineering appropriate artificial gauge potentials, a Bose-Einstein condensate can be adiabatically loaded into a current carrying state that resembles a vortex lattice of a rotating uniform Bose gas. We give two explicit, experimentally feasible protocols by which vortex lattices can be smoothly formed from a condensate initially at rest. In the first example we show how this can be achieved by adiabatically loading a uniform BEC into an optical flux lattice, formed from coherent optical coupling of internal states of the atom. In the second example we study a tight binding model that is …
The preparation of a quantum degenerate gas of heteronuclear molecules has been an outstanding challenge. We use path integral Quantum Monte Carlo simulations to understand the role of interactions and finite temperature effects in the protocol currently employed to adiabatically prepare a low-entropy gas of polar molecules in a lattice starting from an ultracold Bose-Fermi mixture. We find that interspecies interactions affect the final temperature of the mixture after the adiabatic loading procedure and detrimentally limit the molecular peak filling. Our conclusions are in agreement with rec…
We argue that a Bose-Einstein condensate can be transformed into a Floquet condensate, that is, into a periodically time-dependent many-particle state possessing the coherence properties of a mesoscopically occupied single-particle Floquet state. Our reasoning is based on the observation that the denseness of the many-body system's quasienergy spectrum does not necessarily obstruct effectively adiabatic transport. Employing the idealized model of a driven bosonic Josephson junction, we demonstrate that only a small amount of Floquet entropy is generated when a driving force with judiciously ch…
Motivated by recent progress in the experimental manipulation of cold atoms in optical lattices, we study three different protocols for non-adiabatic quantum state preparation and state transport in chains of Rydberg atoms. The protocols we discuss are based on the blockade mechanism between atoms which, when excited to a Rydberg state, interact through a van der Waals potential, and rely on single-site addressing. Specifically, we discuss protocols for efficient creation of an antiferromagnetic GHZ state, a class of matrix product states including a so-called Rydberg crystal and for the state…
An energy gap develops near quantum critical point of quantum phase transition in a finite many-body (MB) system, facilitating the ground state transformation by adiabatic parameter change. In real application scenarios, however, the efficacy for such a protocol is compromised by the need to balance finite system life time with adiabaticity, as exemplified in a recent experiment that prepares three-mode balanced Dicke state near deterministically [PNAS {\bf 115}, 6381 (2018)]. Instead of tracking the instantaneous ground state as unanimously required for most adiabatic crossing, this work repo…
We investigate the fate of hardcore bosons in a Harper-Hofstadter model which was experimentally realized by Aidelsburger et al. [Nature Physics 11 , 162 (2015)] at half filling of the lowest band. We discuss the stability of an emergent fractional Chern insulator (FCI) state in a finite region of the phase diagram that is separated from a superfluid state by a first-order transition when tuning the band topology following the protocol used in the experiment. Since crossing a first-order transition is unfavorable for adiabatically preparing the FCI state, we extend the model to stabilize a fea…
There have been considerable research efforts devoted to quantum simulations of Fermi-Hubbard model with ultracold atoms loaded in optical lattices. In such experiments, the antiferromagnetically ordered quantum state has been achieved at half filling in recent years. The atomic lattice away from half filling is expected to host d-wave superconductivity, but its low temperature phases have not been reached. In a recent work, we proposed an approach of incommensurate quantum adiabatic doping, using quantum adiabatic evolution of an incommensurate lattice for preparation of the highly correlated…
We analyze state preparation within a restricted space of local control parameters between adiabatically connected states of control Hamiltonians. We formulate a conjecture that the time integral of energy fluctuations over the protocol duration is bounded from below by the geodesic length set by the quantum geometric tensor. The conjecture implies a geometric lower bound for the quantum speed limit (QSL). We prove the conjecture for arbitrary, sufficiently slow protocols using adiabatic perturbation theory and show that the bound is saturated by geodesic protocols, which keep the energy varia…
Fractional quantum Hall systems are among the most exciting strongly correlated systems. Accessing them microscopically via quantum simulations with ultracold atoms would be an important achievement toward a better understanding of this strongly correlated state of matter. A promising approach is to confine a small number of bosonic atoms in a quasi-two-dimensional rotating trap, which mimics the magnetic field. For rotation frequencies close to the in-plane trapping frequency, the ground state is predicted to be a bosonic analog of the Laughlin state. Here, we study the problem of the adiabat…
Adiabatic protocols are employed across a variety of quantum technologies, from implementing state preparation and individual operations that are building blocks of larger devices, to higher-level protocols in quantum annealing and adiabatic quantum computation. The problem of speeding up these processes has garnered a large amount of interest, resulting in a menagerie of approaches, most notably quantum optimal control and shortcuts to adiabaticity. The two approaches are complementary: optimal control manipulates control fields to steer the dynamics in the minimum allowed time while shortcut…
We propose a method to obtain optimal protocols for adiabatic ground-state preparation near the adiabatic limit, extending earlier ideas from [D. A. Sivak and G. E. Crooks, Phys. Rev. Lett. 108, 190602 (2012)] to quantum non-dissipative systems. The space of controllable parameters of isolated quantum many-body systems is endowed with a Riemannian quantum metric structure, which can be exploited when such systems are driven adiabatically. Here, we use this metric structure to construct optimal protocols in order to accomplish the task of adiabatic ground-state preparation in a fixed amount of …
In the present work we examine the statics and dynamics of multiple parallel dark soliton stripes in a two-dimensional Bose-Einstein condensate. Our principal goal is to study the effect of the interaction between the stripes on the transverse instability of the individual stripes. We use a recently developed adiabatic invariant formulation to derive a quasi-analytical prediction for the stripe equilibrium position and for the Bogoliubov-de Gennes spectrum of excitations of stationary stripes. The cases of two-, three- and four-stripe states are studied in detail. We subsequently test our pred…
We describe forms of adiabatic transport that arise for dressed-state atoms in optical lattices. Focussing on the limit of weak tunnel-coupling between nearest-neighbour lattice sites, we explain how adiabatic variation of optical dressing allows control of atomic motion between lattice sites: allowing adiabatic particle transport in a direction that depends on the internal state, and force measurements via spectroscopic preparation and readout. For uniformly filled bands these systems display topologically quantised particle transport.
We present evidence of a direct, continuous quantum phase transition between a Bose superfluid and the $ν=1/2$ fractional Chern insulator in a microscopic lattice model. In the process, we develop a detailed field theoretic description of this transition in terms of the low energy vortex dynamics. The theory explicitly accounts for the structure of lattice symmetries and predicts a Landau forbidden transition that is protected by inversion. That the transition is continuous enables the quasi-adiabatic preparation of the fractional Chern insulator in non-equilibrium, quantum optical systems.
Interaction-induced topological systems have attracted a growing interest for their exotic properties going beyond the single-particle picture of topological insulators. In particular, the interplay between strong correlations and finite doping can give rise to nonhomogeneous solutions that break the translational symmetry. In this work, we report the appearance of a topological stripe state in an interaction-induced Chern insulator around half-filling. In contrast to similar stripe phases in nontopological systems, here we observe the appearance of chiral edge states on top of the domain wall…
Periodic driving has emerged as a powerful experimental tool to engineer physical properties of isolated, synthetic quantum systems. However, due to the lack of energy conservation and heating effects, non-trivial (e.g., topological) many-body states in periodically driven (Floquet) systems are generally metastable. Therefore it is necessary to find strategies for preparing long-lived many-body states in Floquet systems. We develop a theoretical framework for describing the dynamical preparation of states in Floquet systems by a slow turn-on of the drive. We find that the dynamics of the syste…
Guiding many-body systems to desired states is a central challenge of modern quantum science, with applications from quantum computation to many-body physics and quantum-enhanced metrology. Approaches to solving this problem include step-by-step assembly, reservoir engineering to irreversibly pump towards a target state, and adiabatic evolution from a known initial state. Here we construct low-entropy quantum fluids of light in a Bose Hubbard circuit by combining particle-by-particle assembly and adiabatic preparation. We inject individual photons into a disordered lattice where the eigenstate…
We study the Landau-Zener (LZ) dynamics in a setup of two Rydberg atoms with time-dependent detuning, both linear and periodic, using both the exact numerical calculations as well as the method of adiabatic impulse approximation (AIA). By varying the Rydberg-Rydberg interaction strengths, the system can emulate different three-level LZ models, for instance, bow-tie and triangular LZ models. The LZ dynamics exhibits non-trivial dependence on the initial state, the quench rate, and the interaction strengths. For large interaction strengths, the dynamics is well captured by AIA. In the end, we an…
We theoretically analyze recent experiments [G. Semeghini et al., Science 374, 1242 (2021)] demonstrating the onset of a topological spin liquid using a programmable quantum simulator based on Rydberg atom arrays. In the experiment, robust signatures of topological order emerge in out-of-equilibrium states that are prepared using a quasi-adiabatic state preparation protocol. We show theoretically that the state preparation protocol can be optimized to target the fixed point of the topological phase -- the resonating valence bond (RVB) state of hard dimers -- in a time that scales linearly with…
We observe and study a special ground state of bosons with two spin states in an optical lattice: the spin-Mott insulator, a state that consists of repulsively bound pairs which is insulating for both spin and charge transport. Because of the pairing gap created by the interaction anisotropy, it can be prepared with low entropy and can serve as a starting point for adiabatic state preparation. We find that the stability of the spin-Mott state depends on the pairing energy, and observe two qualitatively different decay regimes, one of which exhibits protection by the gap.
We study the ground states of 2D lattice bosons in an artificial gauge field. Using state of the art DMRG simulations we obtain the zero temperature phase diagram for hardcore bosons at densities $n_b$ with flux $n_ϕ$ per unit cell, which determines a filling $ν=n_b/n_ϕ$. We find several robust quantum Hall phases, including (i) a bosonic integer quantum Hall phase (BIQH) at $ν=2$, that realizes an interacting symmetry protected topological phase in 2D (ii) bosonic fractional quantum Hall phases including robust states at $ν=2/3$ and a Laughlin state at $ν=1/2$. The observed states correspond …
