Bulletin of the American Physical Society
APS March Meeting 2018
Volume 63, Number 1
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session R27: Non-Equilibrium Physics in AMO Systems II: Floquet Physics and Time Crystals |
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Sponsoring Units: DAMOP DCMP Chair: Netanel Lindner, Technion Room: LACC 404B |
Thursday, March 8, 2018 8:00AM - 8:12AM |
R27.00001: Floquet Phase Transitions in Strongly-Driven Optical Lattices Kurt Fujiwara, Kevin Singh, Zachary Geiger, Mikhail Lipatov, Ethan Simmons, David Weld Ultracold neutral atoms in driven optical lattices provide a rich test bed for exploring non-equilibrium physics. We report on experimental characterization of a Floquet phase diagram using ultracold bosonic lithium in a strongly-driven optical lattice. As the drive frequency and amplitude are tuned,we observe a sharp transition line between stable and unstable behavior. For deep lattices and zero interactions, this transition corresponds to the classically-expected threshold for chaos. We explore the effect of Feshbach-tunable interactions and lattice-tunable tunneling on the properties of this Floquet phase diagram. |
Thursday, March 8, 2018 8:12AM - 8:24AM |
R27.00002: Topological transitions to chaos in quasi-periodically driven quantum systems Philip Crowley, Anushya Chandran, Ivar Martin A quantum system with time-translational symmetry has a quasi-periodic response. Driving with two incommensurate tones is the simplest protocol without this symmetry. In this talk I will analyze the response of a finite quantum system to this quasi-periodic driving. |
Thursday, March 8, 2018 8:24AM - 8:36AM |
R27.00003: A Long Range, Pre-thermal Time Crystal in One Dimension Gregory Meyer, Francisco Machado, Dominic Else, Chetan Nayak, Norman Yao Periodically driven (Floquet) systems provide an ideal platform for exploring out-of-equilibrium dynamics. In this talk, we present the numerical observation of time crystalline order in a prethermal one dimensional spin chain with long range interactions. We demonstrate that power-law interactions, with exponent α < 2, are essential to stabilize such order in 1D. In particular, we compare to the case of short-range interactions, where a robust prethermal regime is also observed, but where the time-crystalline order decays rapidly. Finally, we examine the dynamics of domain walls in the long-range system and discuss recent experiments in trapped ions. |
Thursday, March 8, 2018 8:36AM - 8:48AM |
R27.00004: Critical Time Crystals in Dipolar Systems Wen Wei Ho, Soonwon Choi, Mikhail Lukin, Dmitry Abanin We analyze the quantum dynamics of periodically driven, disordered systems in the presence of long-range interactions. Focusing on the stability of discrete time crystalline (DTC) order in such systems, we use a perturbative procedure to evaluate its lifetime. For 3D systems with dipolar interactions, we show that the corresponding decay is parametrically slow, implying that robust, long-lived DTC order can be obtained. We further predict a sharp crossover from the stable DTC regime into a regime where DTC order is lost, reminiscent of a phase transition. These results are in good agreement with the recent experiments utilizing a dense, dipolar spin ensemble in diamond [Nature 543, 221-225 (2017)]. They demonstrate the existence of a novel, critical DTC regime that is stabilized not by many-body localization but rather by slow, critical dynamics. Our analysis shows that the DTC response can be used as a sensitive probe of nonequilibrium quantum matter. [ PRL 119, 010602 (2017)] |
Thursday, March 8, 2018 8:48AM - 9:00AM |
R27.00005: Discrete Lorentz Symmetry and Discrete Time Translational Symmetry Pei Wang The Lorentz symmetry and the space and time translational symmetry are fundamental symmetries of nature. Crystals are the manifestation of the continuous space translational symmetry being spontaneously broken into a discrete one. We argue that, following the space translational symmetry, the continuous Lorentz symmetry should also be broken into a discrete one, which further implies that the continuous time translational symmetry is broken into a discrete one. We deduce all the possible discrete Lorentz and discrete time translational symmetries in 1+1-dimensional spacetime, and show how to build a field theory or a lattice field theory that has these symmetries. |
Thursday, March 8, 2018 9:00AM - 9:12AM |
R27.00006: Tuning the scattering length by periodic modulation Christoph Dauer, Axel Pelster, Sebastian Eggert We consider a 3D interacting gas with a small time-periodic modulation of the attractive potential, which can be achieved by using a Feshbach resonance. The steady state is described by the Floquet formalism, which leads to a simple recurrence formula for an effective scattering length a_{eff}. For frequencies corresponding to the bound-state of the potential without driving, we observe strong resonances, which allow the tuning to very large positive and negative values of a_{eff} with relatively small imaginary parts. |
Thursday, March 8, 2018 9:12AM - 9:24AM |
R27.00007: Floquet engineering of exchange interaction in multi-orbital Mott insulators Kasra Hejazi, Jianpeng Liu, Leon Balents We consider driving multi-orbital Mott insulators using laser radiation. We derive general expressions for periodically driven spin-orbital models using time-dependent perturbation theory. We show that the effective exchange interactions of the Floquet spin-orbital Hamiltonians are highly tunable by the frequency, amplitude, and polarization of the laser. We also take the effect of finite bandwidth of excitations into account and study possible heating effects. We further apply our formalism to orthorhombic titanates YTiO_{3} and LaTiO_{3} based on first-principles calculations, and find that the spin exchange interactions in these compounds can be engineered to a large extent by tuning the frequency and electric-field amplitude of the laser. |
Thursday, March 8, 2018 9:24AM - 9:36AM |
R27.00008: Floquet Quantum Criticality William Berdanier, Michael Kolodrubetz, Siddharth Parameswaran, Romain Vasseur It has recently been shown that periodically driven (Floquet) systems can, in the presence of disorder, support well-defined phase structure, including possibilities unique to this non-equilibrium setting. However, the nature of the critical points separating such phases has been largely unexplored. We introduce a real-space renormalization group procedure for Floquet systems and apply it to the periodically driven interacting Ising chain. Using analytical arguments and numerical calculations of the entanglement entropy scaling, we identify the criticality along the Floquet eigenstate phase transitions and at the multi-critical point of the non-interacting model, finding criticality not found in the un-driven case. We then discuss the stability of such critical points to interactions, and comment on applications to other Floquet phase transitions. |
Thursday, March 8, 2018 9:36AM - 9:48AM |
R27.00009: Voltage noise in one-dimensional Floquet topological insulators. Martin Rodriguerz-Vega, Herbert Fertig, Babak Seradjeh We consider a periodically-driven SSH model coupled to two external leads at the edges. Using a Floquet-Green's functions approach, we determine the fluctuations in occupation numbers in the system as a function of position, chemical potential, frequency (power spectrum), and drive frequency, which can be related to voltage noise in the system. For a static SSH model in the topological regime, the noise power spectrum presents a zero-frequency peak when the chemical potential of both leads is set to zero. This peak originates from transitions between the two zero-energy modes localized at the edges, and is absent in the trivial regime. We will present results for the analogue of this in a driven SSH model. We also consider disorder in the form of a random static potential, and identify the robust features in the power spectrum. Finally, we discuss the relevance of our results for experiments. |
Thursday, March 8, 2018 9:48AM - 10:00AM |
R27.00010: Absence of Thermalization in Finite Isolated Interacting Floquet Systems Karthik Seetharam, Paraj Titum, Michael Kolodrubetz, Gil Refael Conventional wisdom suggests that the long time behavior of isolated interacting periodically driven (Floquet) systems is a featureless maximal entropy state characterized by an infinite temperature. Efforts to thwart this uninteresting fixed point include adding sufficient disorder to realize a Floquet many-body localized phase or working in a narrow region of drive frequencies to achieve glassy non-thermal behavior at long time. Here we show that in clean systems the Floquet eigenstates can exhibit non-thermal behavior due to finite system size. We consider a one-dimensional system of spinless fermions with nearest-neighbor interactions where the interaction term is driven. Interestingly, even with no static component of the interaction, the quasienergy spectrum contains gaps and a significant fraction of the Floquet eigenstates, at all quasienergies, have non-thermal average doublon densities. We show that this non-thermal behavior arises due to emergent integrability at large interaction strength and discuss how the integrability breaks down with power-law behavior in system size. |
Thursday, March 8, 2018 10:00AM - 10:12AM |
R27.00011: Many-body dynamics and prethermalization in interacting periodically driven systems Ervand Kandelaki, Mark Rudner, Erez Berg, Netanel Lindner A wave of intense interest over the past several years has generated a rich variety of proposals for intriguing new phenomena that can be realized in periodically driven quantum many-body systems, and early experiments to observe them. Understanding the stability of such phenomena and ways to mitigate heating due to energy absorption from the drive are important for enabling further advances in the field. We investigate transient dynamics and prethermalization in the context of Floquet gap opening [1] and chiral transport [2] in interacting systems subjected to high and low frequency drives, respectively. We study the relevant dynamical timescales using non-equilibrium Green's functions, consistently capturing the heating processes, and discuss the regimes in which many-body phenomena can be observed before heating becomes significant. |
Thursday, March 8, 2018 10:12AM - 10:24AM |
R27.00012: Entanglement entropy and computational complexity of the driven Anderson impurity model Zhuoran He, Andrew Millis We do a follow up study of the growth of entanglement entropy and bond dimension in the density matrix renormalization group studies of the Anderson impurity models. We focus on the periodically driven single-impurity Anderson model in real time and applied our previously developed 4-MPS method to do the simulation. In the energy-ordered bath orbital arrangement, we find a critical driving period $T_c$, longer than which the system takes exponential time and shorter than which the system takes polynomial time to simulate. The transition was understood by the Floquet Hamiltonian of the driven system and was found to agree with our previous finding. For the interacting model, the exponential difficulty encountered when $T>T_c$ remains when the bath orbitals are reordered by the quasi-energies of the bath orbitals in the Floquet theory. |
Thursday, March 8, 2018 10:24AM - 10:36AM |
R27.00013: Generation of atypical hopping and interactions by kinetic driving Fernando Sols, Gregor Pieplow, Charles Creffield We study the effect of time-periodically varying the hopping amplitude in a one-dimensional Bose-Hubbard model, such that the time-averaged hopping is zero. Employing Floquet theory, we derive a static effective Hamiltonian in which nearest-neighbor single-particle hopping processes are suppressed, but all even higher-order processes are allowed. Unusual many-body features arise from the combined effect of nonlocal interactions and correlated tunneling. At a critical value of the driving, the system passes from a Mott insulator to a superfluid formed by two quasi-condensates with opposite nonzero momenta. Even with hard-wall boundary conditions, a many-body cat state emerges which involves the superposition of two configurations each macroscopically occupying one of the two momentum eigenstates. This work shows how driving of the hopping energy provides a novel form of Floquet engineering, which enables atypical Hamiltonians and exotic states of matter to be produced and controlled. |
Thursday, March 8, 2018 10:36AM - 10:48AM |
R27.00014: Prethermal Phases in Long-Range Interacting Systems Francisco Machado, Dominic Else, Gregory Meyer, Chetan Nayak, Norman Yao Recent work has shown that periodically driven systems can be fundamentally richer than their static counterparts, enabling the realization of out-of-equilibrium phases of matter that have no static analog. These results are in tension with the conventional expectation that periodic driving generically heats an interacting system to infinite temperature, thus destroying any non-trivial order. One resolution to this issue is the existence of an exponentially long lived prethermal regime in short-range interacting systems, during which the driven system can host novel phases of matter. In this talk, we will prove the existence of bounds enabling prethermal phases of matter in long-range interacting systems. Our result open the doors for the realization of out-of-equilibrium phases in atomic, molecular, and ionic systems with power-law interactions. |
Thursday, March 8, 2018 10:48AM - 11:00AM |
R27.00015: Quantum Time Crystal by Decoherence in Ring Systems Keiji Nakatsugawa, Toshiyuki Fujii, Satoshi Tanda A quantum time crystal is a quantum mechanical system which spontaneously breaks time translation symmetry [1]. We show that, instead of spontaneous symmetry breaking, decoherence breaks time translation symmetry of a ring system with a macroscopic ground state [2]. In particular, we show that the complex order parameter of an incommensurate charge density wave and an annular Josephson junction with a ring or Möbius ring geometry [3] coupled to their environment oscillates periodically. The Caldeira-Leggett model is used to model the environment as a bath of harmonic oscillators. The Hamiltonians considered in this model are time-independent unlike ``Floquet time crystals". Our model forms a quantum time crystal with a finite length in space and time. |
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