Rice–Mele model with topological solitons in an optical lattice

Przysiezna, A.; Dutta, Omjyoti; Zakrzewski, Jakub

doi:10.1088/1367-2630/17/1/013018

Cited by 29 publications

(47 citation statements)

References 32 publications

(49 reference statements)

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“…(21). We consider the system of ultracold bosons trapped in the quasi-1D optical lattice subject to a periodic driving with frequency fulfilling the resonance condition [94][95][96][97] …”

Section: Cold-atom Implementationmentioning

confidence: 99%

At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited

et al. 2018

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We address the question of whether the super-Heisenberg scaling for quantum estimation is indeed realizable. We unify the results of two approaches. In the first one, the original system is compared with its copy rotated by the parameter-dependent dynamics. If the parameter is coupled to the one-body part of the Hamiltonian, the precision of its estimation is known to scale at most as N −1 (Heisenberg scaling) in terms of the number of elementary subsystems used N. The second approach compares the overlap between the ground states of the parameter-dependent Hamiltonian in critical systems, often leading to an apparent super-Heisenberg scaling. However, we point out that if one takes into account the scaling of time needed to perform the necessary operations, i.e., ensuring adiabaticity of the evolution, the Heisenberg limit given by the rotation scenario is recovered. We illustrate the general theory on a ferromagnetic Heisenberg spin chain example and show that it exhibits such super-Heisenberg scaling of ground-state fidelity around the critical value of the parameter (magnetic field) governing the one-body part of the Hamiltonian. Even an elementary estimator represented by a single-site magnetization already outperforms the Heisenberg behavior providing the N −1.5 scaling. In this case, Fisher information sets the ultimate scaling as N −1.75 , which can be saturated by measuring magnetization on all sites simultaneously. We discuss universal scaling predictions of the estimation precision offered by such observables, both at zero and finite temperatures, and support them with numerical simulations in the model. We provide an experimental proposal of realization of the considered model via mapping the system to ultracold bosons in a periodically shaken optical lattice. We explicitly derive that the Heisenberg limit is recovered when the time needed for preparation of quantum states involved is taken into account.

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“…(21). We consider the system of ultracold bosons trapped in the quasi-1D optical lattice subject to a periodic driving with frequency fulfilling the resonance condition [94][95][96][97] …”

Section: Cold-atom Implementationmentioning

confidence: 99%

At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited

et al. 2018

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“…The topological time crystals we consider should not be confused with the so-called Floquet topological systems. In the latter, a crystalline structure (usually an optical lattice) is present in space and it is periodically driven so that its effective parameters can be changed and the system can reveal topological properties in space but no crystalline structure can be observed in time [46][47][48][49]. Our systems are also different from Floquet-Bloch systems where time periodicity is considered as an additional synthetic dimensional combined with a crystalline structure in space [50][51][52][53][54][55].…”

Section: Introductionmentioning

confidence: 99%

Topological time crystals

et al. 2019

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By analogy with the formation of space crystals, crystalline structures can also appear in the time domain. While in the case of space crystals we often ask about periodic arrangements of atoms in space at a moment of a detection, in time crystals the role of space and time is exchanged. That is, we fix a space point and ask if the probability density for detection of a system at this point behaves periodically in time. Here, we show that in periodically driven systems it is possible to realize topological insulators, which can be observed in time. The bulk-edge correspondence is related to the edge in time, where edge states localize. We focus on two examples: Su-Schrieffer-Heeger model in time and Bose Haldane insulator which emerges in the dynamics of a periodically driven many-body system. 5 Note that due to the negative effective mass m eff , the first energy band is the highest in energy. 2 New J. Phys. 21 (2019) 052003 where = ¢ J J i 2and J 2i−1 =J, which is identical to the SSH model [86]. The latter describes spinless fermions hopping on a 1D-lattice with staggered hopping amplitudes. Changing the ratio λ 1 /λ in (1), allows one to control the ratio ¢ J J . This effective Hamiltonian belongs to the BDI class of the periodic table of the topological insulators and superconductors [87] and is characterized by a  topological invariant, the winding number ν. For an infinite system with ¢ > J J ( ¢ < J J ), the system is in a topological (trivial) phase with winding number ν=1 (ν=0). For a finite system, the topological phase exhibits zero energy edge states protected by the topology of the bulk. The SSH model has been experimentally realized in quantum simulators and both the presence of edge states and the winding number have been measured [63][64][65]. Let us emphasize that the Wannier states w i (x, t) of equation (2) are localized wavepackets of the effective SSH Hamiltonian of equation (3). We then discuss how such states allow one to detect the topology of the SSH Hamiltonian. corresponding to quasi-energies closest to zero, see top panel. In the topological phase, these eigenstates have zero quasi-energy and are linear combinations of the edge states localized at the edge of time. That is, in the laboratory frame, a detector is placed close to the oscillating mirror (x≈0) and the probability density of clicking of the detector is shown versus time for different values of the ratio ¢ J J of the tunneling amplitudes in (3). This behavior is repeated with the period 2π/ω. At sωt/(2π)=1 and sωt/(2π)=40 there are edges where the eigenstate localizes if ¢ > J J 1. The results correspond to ω=0.067, λ=0.06 in (1) and are obtained within the quantum secular approach [84], see the appendix.

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“…Similar to the SSH model, the RM describes a conducting polymers with nontrivial topology and has been realized in cold-atom systems confined in superlattice potential [21,22]. Its topological properties have been well studied in earlier works [23]. The presence of finite t does not change qualitatively the topological features [19].…”

Section: Topological Featuresmentioning

confidence: 98%

Artificial topological models based on a one-dimensional spin-dependent optical lattice

Zheng

Zou

et al. 2017

Phys. Rev. A

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Topological matter is a popular topic in both condensed matter and cold atom research. In the past decades, a variety of models have been identified with fascinating topological features. Some, but not all, of the models can be found in materials. As a fully controllable system, cold atoms trapped in optical lattices provide an ideal platform to simulate and realize these topological models. Here we present a proposal for synthesizing topological models in cold atoms based on a one-dimensional (1D) spin-dependent optical lattice potential. In our system, features such as staggered tunneling, staggered Zeeman field, nearest-neighbor interaction, beyond-near-neighbor tunneling, etc. can be readily realized. They underlie the emergence of various topological phases. Our proposal can be realized with current technology and hence has potential applications in quantum simulation of topological matter.

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Rice–Mele model with topological solitons in an optical lattice

Cited by 29 publications

References 32 publications

At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited

At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited

Topological time crystals

Artificial topological models based on a one-dimensional spin-dependent optical lattice

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