Difference between revisions of "Recent Research"

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laser wavelengths close to certain incommensurate ratios.
 
laser wavelengths close to certain incommensurate ratios.
  
Ref. arXiv:1905.08277
+
Ref. PhysRevB.100.144202
  
link: https://arxiv.org/pdf/1905.08277.pdf
+
link: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.100.144202
  
 
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exhibits characteristic ground-state and thermal properties absent in conventional quantum manybody systems, especially the striking temperature-oscillating behavior of its physical observables.
 
exhibits characteristic ground-state and thermal properties absent in conventional quantum manybody systems, especially the striking temperature-oscillating behavior of its physical observables.
  
Ref. arXiv:1902.09747
+
Ref. Chin. Phys. Lett. 37 050503 (2020)
  
Link: https://arxiv.org/pdf/1902.09747.pdf
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Link: https://iopscience.iop.org/article/10.1088/0256-307X/37/5/050503
  
 
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Revision as of 19:20, 5 August 2020

Fast scrambling without appealing to holographic duality

Motivated by the question of whether all fast scramblers are holographically dual to black holes, we study the dynamics of a non-integrable spin chain model composed of two ingredients - a nearest neighbor Ising coupling, and an infinite range XX interaction. Unlike other fast scrambling many-body systems, this model is not known to be dual to a black hole. We quantify the spreading of quantum information using an out-of time-ordered correlator (OTOC), and demonstrate that our model exhibits fast scrambling for a wide parameter regime. Simulation of its quench dynamics finds that the rapid decline of the OTOC is accompanied by a fast growth of the entanglement entropy, as well as a swift change in the magnetization. Finally, potential realizations of our model are proposed in current experimental setups. Our work establishes a promising route to create fast scramblers.

https://arxiv.org/abs/2004.11269

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Dynamical singularities of Floquet higher-order topological insulators

We propose a versatile framework to dynamically generate Floquet higher-order topological insulators by multi-step driving of topologically trivial Hamiltonians. Two analytically solvable examples are used to illustrate this procedure to yield Floquet quadrupole and octupole insulators with zero- and/or π-corner modes protected by mirror symmetries. We introduce dynamical topological invariants from the full unitary return map and show its phase bands contain Weyl singularities whose topological charges form dynamical multipole moments in the Brillouin zone. Combining them with the topological index of Floquet Hamiltonian gives a pair of Z2 invariant ν0 and νπ which fully characterize the higher-order topology and predict the appearance of zero- and π-corner modes. Our work establishes a systematic route to construct and characterize Floquet higher-order topological phases.

PhysRevLett.124.057001

link: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.057001

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Superfluid phases and excitations in a cold gas of d-wave interacting bosonic atoms and molecules

Motivated by recent advance in orbitally tuned Feshbach resonance experiments, we analyze the ground-state phase diagram and related low-energy excitation spectra of a d-wave interacting Bose gas. A two-channel model with d-wave symmetric interactions and background s-wave interactions is adopted to characterize the gas. The ground state is found to show three interesting phases: atomic, molecular, and atomic-molecular superfluidity. Remarkably differently from what was previously known in the p-wave case, the atomic superfluid is found to be momentum-independent in the present d-wave case. Bogoliubov spectra above each superfluid phase are obtained both analytically and numerically. arXiv:1905.03727 (accepted by PRL, waiting to be announced)

https://arxiv.org/pdf/2001.04331.pdf


Exactly Solvable Points and Symmetry Protected Topological Phases of Quantum Spins on a Zig-Zag Lattice

A large number of symmetry-protected topological (SPT) phases have been hypothesized for strongly interacting spin-1=2 systems in one dimension. Realizing these SPT phases, however, often demands finetunings hard to reach experimentally. And the lack of analytical solutions hinders the understanding of their many-body wave functions. Here we show that two kinds of SPT phases naturally arise for ultracold polar molecules confined in a zigzag optical lattice. This system, motivated by recent experiments, is described by a spin model whose exchange couplings can be tuned by an external field to reach parameter regions not studied before for spin chains or ladders. Within the enlarged parameter space, we find the ground state wave function can be obtained exactly along a line and at a special point, for these two phases, respectively. These exact solutions provide a clear physical picture for the SPT phases and their edge excitations. We further obtain the phase diagram by using infinite time-evolving block decimation and discuss the phase transitions between the two SPT phases and their experimental signatures.

Ref. Phys. Rev. Lett. 122, 180401 (2019)

link: https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.122.180401

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Spontaneous formation of polar superfluid droplets in a p-wave interacting Bose gas

We study the quantum fluctuations in the condensates of a mixture of bosonic atoms and molecules with interspecies p-wave interaction. Our analysis shows that the quantum phase of coexisting atomic and molecular condensates is unstable at the mean-field level. Unlike the mixture of s-wave interaction, the Lee-Huang-Yang correction of p-wave interaction is unexpectedly found here to exhibit an opposite sign with respect to its mean-field term above a critical particle density. This quantum correction to the mean-field energy provides a remarkable mechanism to self-stabilize the phase. The order parameter of this superfluid phase carries opposite finite momenta for the two atomic species while the molecular component is a polar condensate. Such a correlated order spontaneously breaks a rich set of global U(1) gauge, atomic spin, spatial rotation and translation, and time-reversal symmetries. For potential experimental observation, the phenomenon of anisotropic polar superfluid droplets is predicted to occur, when the particle number is kept finite.

Ref. Phys. Rev. A 100, 053620

link: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.100.053620

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Moire Localization in Two Dimensional Quasi-Periodic Systems

We discuss a two-dimensional system under the perturbation of a Moire potential, which takes the same geometry and lattice constant as the underlying lattices but mismatches up to relative rotation. Such a selfdual model belongs to the orthogonal class of a quasi-periodic system whose features have been evasive in previous studies. We find that such systems enjoy the same scaling exponent as the one-dimensional AubryAndre model ν ≈ 1, which saturates the Harris bound ν > 2/d = 1 in two-dimensions. Meanwhile, there exist an infinite number of mobility edges different from the typical one-dimensional situation where only a few or no mobility edges show up. An experimental scheme based on optical lattices is discussed. It allows for using lasers of arbitrary wavelengths and therefore is more applicable than the one-dimensional situations requiring laser wavelengths close to certain incommensurate ratios.

Ref. PhysRevB.100.144202

link: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.100.144202

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Imaginary time crystal of thermal quantum matter

Spontaneous symmetry breaking is responsible for rich quantum phenomena from crystalline structures to superconductivity. This concept was boldly extended to the breaking of time translation, opening an avenue to finding exotic phases of quantum matter with collective “time” modulation and correlation. Here we report that a thermally open quantum ensemble manifests in the dual space of imaginary time with crystalline ordering due to a bath-induced retarded interaction. Exact quantum Monte Carlo simulations are performed to show that this imaginary time crystal phase exhibits characteristic ground-state and thermal properties absent in conventional quantum manybody systems, especially the striking temperature-oscillating behavior of its physical observables.

Ref. Chin. Phys. Lett. 37 050503 (2020)

Link: https://iopscience.iop.org/article/10.1088/0256-307X/37/5/050503

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Higher-Order Floquet Topological Insulators with Anomalous Corner States

Higher order topological insulators have emerged as a new class of phases, whose robust in-gap “corner” modes arise from the bulk higher-order multipoles beyond the dipoles in conventional topological insulators. Despite rapid theoretical and experimental breakthroughs, all discussions have been constrained to the static scenario due to the lack of specific schemes to compute higher-order dynamical topological invariant. Here we provide a concrete model and explicit constructions of topological invariants for a Floquet-driven system exhibiting anomalous corner states. The bulk quadrupolar moment for the eigenstates of static Floquet operators vanishes identically, while the anomalous topological invariant associated with full-time evolution correctly describes the quantized corner charges. The signature of such a phase in cold atom experiments is discussed through corner particle dynamics and a Floquet-Bloch band tomography

Ref. arXiv:1811.00555

Link: https://arxiv.org/pdf/1811.00555.pdf

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Scrambling dynamics and many-body chaos in a random dipolar spin model

Is there a condensed matter system that scrambles information as fast as a black hole? The Sachev-Ye-Kitaev model can saturate the conjectured bound for chaos, but it requires random all-to-all couplings of Majorana fermions that are hard to realize in experiments. Here we examine a quantum spin model of randomly oriented dipoles where the spin exchange is long-ranged and governed by dipole-dipole interactions. The model is inspired by recent experiments on dipolar spin systems of magnetic atoms, dipolar molecules, and nitrogenvacancy centers. We map out the phase diagram of this model by computing the energy level statistics, spectral form factor, and out-of-time-order correlation (OTOC) functions. In addition to a many-body localized regime, we find a broad regime of many-body chaos where the energy levels obey Wigner-Dyson statistics and the OTOC shows distinctive behaviors at different times: Its early-time dynamics is characterized by an exponential growth, while the approach to its saturated value at late times obeys a power law. The temperature scaling of the Lyapunov exponent λL shows that while it is well below the conjectured bound 2πT at high temperatures, λL approaches the bound at low temperatures and for large number of spins. These results suggest that dipolar spin systems can offer a glimpse of the bound for chaos.

Ref. arXiv:1810.03815

Link: https://arxiv.org/pdf/1810.03815.pdf

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Clean Floquet Time Crystals: Models and Realizations in Cold Atoms

Time crystals, a phase showing spontaneous breaking of time-translation symmetry, has been an intriguing subject for systems far away from equilibrium. Recent experiments found such a phase both in the presence and absence of localization, while in theories localization by disorder is usually assumed a priori. In this work, we point out that time crystals can generally exist in systems without disorder and is not in a pre-thermal state. A series of clean quasi-one-dimensional models under Floquet driving and non-local interactions are proposed to demonstrate this unexpected result in principle. Robust time crystalline orders are found in the strongly interacting regime due to the emergent integrals of motion in the dynamical system, which can be characterized by the out-of-time-ordered correlators. We propose two cold atom experimental schemes to realize the clean Floquet time crystals, one by making use of dipolar gases and another by synthetic dimensions.

Ref. Phys. Rev. Lett. 120, 110603 (2018)

link: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.110603

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Odd-parity topological superfluidity for fermions in a bond-centered square optical lattice

We propose a physical scheme for the realization of two-dimensional topological odd-parity superfluidity in a spin-independent bond-centered square optical lattice based upon interband fermion pairing. The D4 point-group symmetry of the lattice protects a quadratic band crossing, which allows one to prepare a Fermi surface of spin-up fermions with odd parity close to the degeneracy point. In the presence of spin-down fermions with even parity populating a different energetically well-separated band, odd-parity pairing is favored. Strikingly, as a necessary prerequisite for pairing, both Fermi surfaces can be tuned to match well. As a result, topological superfluid phases emerge in the presence of merely s-wave interaction. Due to the Z2 symmetry of these odd-parity superfluids, we infer their topological features simply from the symmetry and the Fermi-surface topology as confirmed numerically.

Ref. Phys. Rev. A 96, 053607 (2017)

link. https://journals.aps.org/pra/abstract/10.1103/PhysRevA.96.053607

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Frustrated Magnetism of Dipolar Molecules on a Square Optical Lattice: Prediction of a Quantum Paramagnetic Ground State

Motivated by the experimental realization of quantum spin models of polar molecule KRb in optical lattices, we analyze the spin 1/2 dipolar Heisenberg model with competing anisotropic, longrange exchange interactions. We show that, by tilting the orientation of dipoles using an external electric field, the dipolar spin system on square lattice comes close to a maximally frustrated region similar, but not identical, to that of the J1-J2 model. This provides a simple yet powerful route to potentially realize a quantum spin liquid without the need for a triangular or kagome lattice. The ground state phase diagrams obtained from Schwinger-boson and spin-wave theories consistently show a spin disordered region between the N´eel, stripe, and spiral phase. The existence of a finite quantum paramagnetic region is further confirmed by an unbiased variational ansatz based on tensor network states and a tensor renormalization group

Ref. Phys. Rev. Lett. 119, 050401 (2017)

link. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.050401

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Theory of interacting fermions in shaken square optical lattice

We develop a theory of weakly interacting fermionic atoms in shaken optical lattices based on the orbital mixing in the presence of time-periodic modulations. Specifically, we focus on fermionic atoms in circularly shaken square lattice with near resonance frequencies, i.e., tuned close to the energy separation between s-band and the p-bands. First, we derive a time-independent four-band effective Hamiltonian in the non-interacting limit. Diagonalization of the effective Hamiltonian yields a quasi-energy spectrum consistent with the full numerical Floquet solution that includes all higher bands. In particular, we find that the hybridized s-band develops multiple minima and therefore non-trivial Fermi surfaces at different fillings. We then obtain the effective interactions for atoms in the hybridized s-band analytically and show that they acquire momentum dependence on the Fermi surface even though the bare interaction is contact-like. We apply the theory to find the phase diagram of fermions with weak attractive interactions and demonstrate that the pairing symmetry is s + d-wave. Our theory is valid for a range of shaking frequencies near resonance, and it can be generalized to other phases of interacting fermions in shaken lattices.

Ref. Arxiv 1703.04074 (2017)

link: https://arxiv.org/pdf/1703.04074.pdf

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Frustrated magnetism of dipolar molecules on square optical lattice: evidence for a quantum paramagnetic ground state

Motivated by the experimental realization of quantum spin models of polar molecule KRb in optical lattices, we analyze the spin 1/2 dipolar Heisenberg model with competing anisotropic, longrange exchange interactions. We show that by tilting the orientation of dipoles using an external electric field, the dipolar spin system on square lattice come close to a maximally frustrated region similar, but not identical, to that of the J1-J2 model. This provides a simple yet powerful route to potentially realize quantum spin liquid without the need for triangular or kagome lattice. The ground state phase diagrams obtained from Schwinger-boson and spin-wave theories consistently show a spin disordered region between the Neel, stripe, and spiral phase. The existence of a finite quantum paramagnetic region is further confirmed by unbiased variational ansatz based on tensor network states and tensor renormalization group.

Ref. Arxiv 1702.08517 (2017)

link: https://arxiv.org/pdf/1702.08517.pdf


Detecting π-phase superfluids with p-wave symmetry in a quasi-one-dimensional optical lattice

We propose an experimental protocol to study p-wave superfluidity in a spin-polarized cold Fermi gas tuned by an s-wave Feshbach resonance. A crucial ingredient is to add a quasi-one-dimensional optical lattice and tune the fillings of two spins to the s and p band, respectively. The pairing order parameter is confirmed to inherit p-wave symmetry in its center-of-mass motion. We find that it can further develop into a state of unexpected π-phase modulation in a broad parameter regime. Experimental signatures are predicted in the momentum distributions, density of states, and spatial densities for a realistic experimental setup with a shallow trap. The π-phase p-wave superfluid is reminiscent of the π state in superconductor-ferromagnet heterostructures but differs in symmetry and physical origin. The spatially varying phases of the superfluid gap provide an approach to synthetic magnetic fields for neutral atoms. It would represent another example of p-wave pairing, first discovered in He3 liquids.

Ref. Phys. Rev. A 94, 031602 (2016)

link: http://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.031602

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π-Flux Dirac Bosons and Topological Edge Excitations in a Bosonic Chiral p-Wave Superfluid

We study the topological properties of elementary excitations in a staggered px±ipy Bose-Einstein condensate realized in recent orbital optical lattice experiments. The condensate wave function may be viewed as a configuration space variant of the famous px+ipy momentum space order parameter of strontium ruthenate superconductors. We show that its elementary excitation spectrum possesses Dirac bosons with π Berry flux. Remarkably, if we induce a population imbalance between the px+ipy and px−ipy condensate components, a gap opens up in the excitation spectrum resulting in a nonzero Chern invariant and topologically protected edge excitation modes. We give a detailed description of how our proposal can be implemented with standard experimental technology.

Ref: PhysRevLett.117.085301(2016)

link: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.117.085301

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A continuum of compass spin models on the honeycomb lattice

Quantum spin models with spatially dependent interactions, known as compass models, play an important role in the study of frustrated quantum magnetism. One example is the Kitaev model on the honeycomb lattice with spin-liquid (SL) ground states and anyonic excitations. Another example is the geometrically frustrated quantum 120° model on the same lattice whose ground state has not been unambiguously established. To generalize the Kitaev model beyond the exactly solvable limit and connect it with other compass models, we propose a new model, dubbed 'the tripod model', which contains a continuum of compass-type models. It smoothly interpolates the Ising model, the Kitaev model, and the quantum 120° model by tuning a single parameter theta' , the angle between the three legs of a tripod in the spin space. Hence it not only unifies three paradigmatic spin models, but also enables the study of their quantum phase transitions. We obtain the phase diagram of the tripod model numerically by tensor networks in the thermodynamic limit. We show that the ground state of the quantum 120° model has long-range dimer order. Moreover, we find an extended spin-disordered (SL) phase between the dimer phase and an antiferromagnetic phase. The unification and solution of a continuum of frustrated spin models as outline here may be useful to exploring new domains of other quantum spin or orbital models.

Ref. New J. Phys. 18 053040 (2016)

link: http://iopscience.iop.org/article/10.1088/1367-2630/18/5/053040/meta


Physics of higher orbital bands in optical lattices: a review

Orbital degree of freedom plays a fundamental role in understanding the unconventional properties in solid state materials. Experimental progress in quantum atomic gases has demonstrated that high orbitals in optical lattices can be used to construct quantum emulators of exotic models beyond natural crystals, where novel many-body states such as complex Bose-Einstein condensation and topological semimetals emerge. A brief introduction of orbital degree of freedom in optical lattices is given and a summary of exotic orbital models and resulting many-body phases is provided. Experimental consequences of the novel phases are also discussed.

link: http://iopscience.iop.org/article/10.1088/0034-4885/79/11/116401


Spontaneous quantum Hall effect in an atomic spinor Bose-Fermi mixture

Searching for topological states of matter has become one of the frontier topics in the field of ultracold atomic quantum gases. Tremendous efforts have been made to synthesize effective gauge fields or spin-orbit interactions by complex external manipulations. In contrast, we show that U(1) gauge fields for fermions can be spontaneously generated in an atomic spinor Bose-Fermi mixture (e.g., Rb-87 and Li-6) loaded in a triangular optical lattice. With fermions at 3/4 filling, Fermi surface nesting leads to spontaneous formation of various spin textures of bosons in the ground state, such as collinear, coplanar and even non-coplanar spin orders. Most surprisingly, a non-coplanar spin state is found and it naturally supports a quantum anomalous Hall state of fermions and crystalline superfluidity in bosons, both driven by interaction.

Ref: PhysRevLett.114.125303(2015)

link: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.125303

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Weyl Superfluidity in a Three-dimensional Dipolar Fermi Gas

Weyl superconductivity or superfluidity, a fascinating topological state of matter, features novel phenomena such as emergent Weyl fermionic excitations and anomalies. Here we report that an anisotropic Weyl superfluid state can arise as a low temperature stable phase in a 3D dipolar Fermi gas. A crucial ingredient of our model is a direction-dependent two-body effective attraction generated by a rotating external field. Experimental signatures are predicted for cold gases in radio-frequency spectroscopy. The finite temperature phase diagram of this system is studied and the transition temperature of the Weyl superfluidity is found to be within the experimental scope for atomic dipolar Fermi gases.

Ref: PhysRevLett.114.045302 (2015)

link: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.045302

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Spin-Orbital Exchange of Strongly Interacting Fermions in the p Band of a Two-Dimensional Optical Lattice

Mott insulators with both spin and orbital degeneracy are pertinent to a large number of transition metal oxides. The intertwined spin and orbital fluctuations can lead to rather exotic phases such as quantum spin-orbital liquids. Here, we consider two-component (spin 1/2) fermionic atoms with strong repulsive interactions on the p band of the optical square lattice. We derive the spin-orbital exchange for quarter filling of the p band when the density fluctuations are suppressed, and show that it frustrates the development of long-range spin order. Exact diagonalization indicates a spin-disordered ground state with ferro-orbital order. The system dynamically decouples into individual Heisenberg spin chains, each realizing a Luttinger liquid accessible at higher temperatures compared to atoms confined to the s band.

Ref:PhysRevLett.114.100406(2015)

link: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.100406

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