Mar 2017

Mar 1-Mar 10 Biao Huang, Mar 11-Mar 20 Haiyuan Zou, Mar 21-Mar 28 Zehan Li

Mar 20
arXiv:1703.05842 [pdf, other]
Realizing the Haldane phase with bosons in optical lattices
Junjun Xu, Qiang Gu, Erich J. Mueller
Comments: 5 pages, 5 figures
Subjects: Quantum Gases (cond-mat.quant-gas)
We analyze an experimentally realizable model of bosons in a zig-zag optical lattice, showing that by rapidly modulating the magnetic field one can tune interaction parameters and realize an analog of the Haldane phase. We explain how quantum gas microscopy can be used to detect this phase's non-local string order and its topological edge states. We model the detection process. We also find that this model supports a supersolid phase, but argue that it only occurs at parameter values which would be challenging to realize in an experiment.

Mar 17
arXiv:1703.05402 [pdf, other]
Experimental Quantum Hamiltonian Learning
Jianwei Wang, Stefano Paesani, Raffaele Santagati, Sebastian Knauer, Antonio A. Gentile, Nathan Wiebe, Maurangelo Petruzzella, Jeremy L. O'Brien, John G. Rarity, Anthony Laing, Mark G. Thompson
Subjects: Quantum Physics (quant-ph)

Efficiently characterising quantum systems, verifying operations of quantum devices and validating underpinning physical models, are central challenges for the development of quantum technologies and for our continued understanding of foundational physics. Machine-learning enhanced by quantum simulators has been proposed as a route to improve the computational cost of performing these studies. Here we interface two different quantum systems through a classical channel - a silicon-photonics quantum simulator and an electron spin in a diamond nitrogen-vacancy centre - and use the former to learn the latter's Hamiltonian via Bayesian inference. We learn the salient Hamiltonian parameter with an uncertainty of approximately 10−5. Furthermore, an observed saturation in the learning algorithm suggests deficiencies in the underlying Hamiltonian model, which we exploit to further improve the model itself. We go on to implement an interactive version of the protocol and experimentally show its ability to characterise the operation of the quantum photonic device. This work demonstrates powerful new quantum-enhanced techniques for investigating foundational physical models and characterising quantum technologies.

Mar 16
arXiv:1703.04663 [pdf, other]
Clean Floquet Time Crystals: Models and Realizations in Cold Atoms
Biao Huang, Ying-Hai Wu, W. Vincent Liu
Comments: 6+8 pages, 4 figures
Subjects: Quantum Gases (cond-mat.quant-gas); Strongly Correlated Electrons (cond-mat.str-el)

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.

Mar 14
arXiv:1703.04074 [pdf, other]
Theory of interacting fermions in shaken square optical lattice
Ahmet Keles, Erhai Zhao, W. Vincent Liu
Comments: 12 pages with 5 figures. Comments and reference suggestions are welcome
Subjects: Quantum Gases (cond-mat.quant-gas)

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.

Mar 13
arXiv:1703.03420 [pdf, other]
Entanglement Complexity in Quantum Many-Body Dynamics, Thermalization and Localization
Zhi-Cheng Yang, Alioscia Hamma, Salvatore M. Giampaolo, Eduardo R. Mucciolo, Claudio Chamon
Comments: 5 pages, 3 figures
Subjects: Strongly Correlated Electrons (cond-mat.str-el); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)

Entanglement is usually quantified by von Neumann entropy, but its properties are much more complex than what can be expressed with a single number. We show that the three distinct dynamical phases known as thermalization, Anderson localization, and many-body localization are marked by different patterns of the spectrum of the reduced density matrix for a state evolved after a quantum quench. While the entanglement spectrum displays Poisson statistics for the case of Anderson localization, it displays universal Wigner-Dyson statistics for both the cases of many-body localization and thermalization, albeit the universal distribution is asymptotically reached within very different time scales in these two cases. We further show that the complexity of entanglement, revealed by the possibility of disentangling the state through a Metropolis-like algorithm, is signaled by whether the entanglement spectrum level spacing is Poisson or Wigner-Dyson distributed.


Mar 09
Floquet topological phases protected by time glide symmetry
Takahiro Morimoto, Hoi Chun Po, Ashvin Vishwanath
(Submitted on 7 Mar 2017)

We study Floquet topological phases in periodically driven systems that are protected by "time glide symmetry", a combination of reflection and half time period translation. Time glide symmetry is an analog of glide symmetry with partial time translation replacing the partial space translation, and hence, is an intrinsically dynamical symmetry which may be engineered in periodically driven systems by exploiting the controllability of driving. We present lattice models of time glide symmetric Floquet topological insulators in two and three dimensions. The topological numbers characterizing those Floquet topological phases are derived from the half period time evolution operator along with time glide operator. Moreover, we classify Floquet topological phases protected by time glide symmetry in general dimensions using a Clifford algebra approach. The obtained classification table is similar to that for topological crystalline insulators protected by static reflection symmetry, but shows nontrivial entries in different combination of symmetries, which clarifies that time glide symmetric Floquet topological phases are a distinct set of topological phases from topological crystalline insulators. We also classify Floquet topological phases with "time screw symmetry," defined as a two-fold spatial rotation accompanied by half-period time translation.




Mar 06

https://arxiv.org/abs/1703.01304v1
Geometric theory of anisotropic quantum Hall states
Andrey Gromov, Barry Bradlyn
(Submitted on 3 Mar 2017)

We construct a low energy effective theory of anisotropic fractional quantum Hall (FQH) states. We develop a formalism similar to the one used in the bi-metric approach to massive gravity and apply it to describe abelian anisotropic FQH states in the presence of external electromagnetic and geometric backgrounds. We derive a relationship between the shift, the Hall viscosity, and the response of the system to changes in anisotropy. We also study in detail the case when the anisotropy is due to an emergent nematic order and derive exactly the Berry phase term in the effective action for the nematic order parameter. Our results clarify certain disagreements that exist in the literature about the meaning of the coefficient of the Berry phase term.

https://arxiv.org/abs/1703.01113v1
Universal non-analytic behavior of the non-equilibrium Hall conductance in Floquet topological insulators
Markus Schmitt, Pei Wang
(Submitted on 3 Mar 2017)

We study the Hall conductance in a Floquet topological insulator in the long time limit after sudden switches of the driving amplitude. Based on a high frequency expansion of the effective Hamiltonian and the micromotion operator we demonstrate that the Hall conductance as function of the driving amplitude follows universal non-analytic laws close to phase boundaries, namely a logarithmic divergence for gapped initial states and jumps of a definite height for gapless initial states.




Mar 01


https://arxiv.org/abs/1703.00430


Realizing and Adiabatically Preparing Bosonic Integer and Fractional Quantum Hall states in Optical Lattices

Yin-Chen He, Fabian Grusdt, Adam Kaufman, Markus Greiner, Ashvin Vishwanath

(Submitted on 1 Mar 2017)

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 nb with flux nϕ per unit cell, which determines a filling ν=nb/nϕ. 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 to the bosonic Jain sequence (ν=p/(p+1)) pointing towards an underlying composite fermion picture. In addition to identifying Hamiltonians whose ground states realize these phases, we discuss their preparation beginning in the independent chain limit of 1D Luttinger liquids, and ramping up interchain couplings. Using time dependent DMRG simulations, these are shown to reliably produce states close to the ground state for experimentally relevant system sizes. We utilize a simple physical signature of these phases, the non-monotonic behavior of a two-point correlation, a direct consequence of edge states in a finite system, to numerically assess the effectiveness of the preparation scheme. Our proposal only utilizes existing experimental capabilities.