Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session H13: Dynamical and Chaotic Quantum Systems |
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Sponsoring Units: DAMOP Chair: Kaden Hazzard, Rice University Room: 272 |
Tuesday, March 14, 2017 2:30PM - 2:42PM |
H13.00001: Quantum-coherent phase oscillations in synchronization Talitha Weiss, Stefan Walter, Florian Marquardt Recently, synchronization of quantum systems has attracted increasing attention. So far, in these studies the synchronization dynamics itself remained overdamped and thus necessarily incoherent. We study the generic model of a quantum Van der Pol oscillator synchronized to an external drive and show that regimes of underdamped and even quantum-coherent phase motion exist. To this end, we derive an effective quantum model which allows us to quantify the quality of quantum coherence. We identify the quantum-coherent regime and illustrate the long-lived coherence by showing that initial negativities of a Wigner density can persist many oscillations of the system dynamics. Possible experimental implementations can be envisioned with optomechanical systems, trapped ions, and microwave circuits. [Preview Abstract] |
Tuesday, March 14, 2017 2:42PM - 2:54PM |
H13.00002: Phase transition from maximal quantum chaos to a charge glass in a generalized Sachdev-Ye-Kitaev model Ionut-Dragos Potirniche, Snir Gazit, Ehud Altman The Sachdev-Ye-Kitaev (SYK) model is a solvable model of interacting Fermions showing a maximally chaotic non-Fermi liquid fixed point. We extend this model by adding 2-site density-density interactions, which, if sufficiently strong, give rise to a dynamical quantum phase transition from the chaotic state to a non-ergodic charge glass phase. We investigate this transition numerically using exact diagonalization and analytically using an expansion in fluctuations around the non-fermi liquid fixed point. In particular, we study the instabilities toward replica symmetry breaking induced by the 2-site interactions. [Preview Abstract] |
Tuesday, March 14, 2017 2:54PM - 3:06PM |
H13.00003: Lyapunov Exponent and Four-Point Correlatorâ€™s Growth Rate in a Chaotic System Efim Rozenbaum, Sriram Ganeshan, Victor Galitski It was proposed recently that the out-of-time-ordered four-point correlator (OTOC) may serve as a characteristic of quantum-chaotic behavior, because in the semi-classical limit, $\hbar \to 0$, its rate of exponential growth resembles the classical Lyapunov exponent. We calculate OTOC for the classical and quantum kicked rotor and compare its growth rate at initial times with the standard definition of the classical Lyapunov exponent. We show that the OTOC's growth rate and the Lyapunov exponent are in general distinct quantities, corresponding to the logarithm of phase-space-averaged divergence rate of classical trajectories and to the phase-space average of the logarithm, respectively. The difference approaches a constant in the regime of high kicking strength, where classical chaos is global. We also show that the quantum correlator as a function of time exhibits a clear singularity at the Ehrenfest time $t_E$: transitioning from a time-independent value of $t^{-1}\ln{C(t)}$ at $t < t_E$ to its monotonous decrease with time at $t > t_E$. Besides that, deep in the quantum regime, $\hbar = 1$, we show that the two-point correlator averaged over very large time windows reveals classical regular-to-chaotic transition as a function of the kicking strength. [Preview Abstract] |
Tuesday, March 14, 2017 3:06PM - 3:18PM |
H13.00004: Interacting ultracold atomic kicked rotors: loss of dynamical localization Pinquan Qin, Alexei Andreanov, Hee Chul Park, Sergej Flach We study the fate of dynamical localization of two quantum kicked rotors with contact interaction, which relates to experimental realizations of the rotors with ultra-cold atomic gases. A single kicked rotor is known to exhibit dynamical localization, which takes place in momentum space. The contact interaction affects the evolution of the relative momentum $k$ of a pair of interacting rotors in a non-analytic way. Consequently the evolution operator $U$ is exciting large relative momenta with amplitudes which decay only as a power law $1/k^4$. This is in contrast to the center-of-mass momentum $K$ for which the amplitudes excited by $U$ decay superexponentially fast with $K$ . Therefore dynamical localization is preserved for the center-of-mass momentum, but destroyed for the relative momentum for any nonzero strength of interaction. [Preview Abstract] |
Tuesday, March 14, 2017 3:18PM - 3:30PM |
H13.00005: Probing microscopic dynamics of a two-dimensional disordered dipolar spin system Alexander Sushkov We investigate the microscopic dynamics of disordered many-body dipolar spin systems using nitrogen-vacancy (NV) centers in diamond. Naturally-occurring electronic spins on the surface of a diamond crystal form a two-dimensional dipolar spin system, which is probed and manipulated via a shallow NV center, a few nanometers below the surface. We observe slow decay of the spin autocorrelation functions under a variety of experimental conditions. [Preview Abstract] |
Tuesday, March 14, 2017 3:30PM - 3:42PM |
H13.00006: Ground State Energy and Momentum Distribution Function for a Bose Gas Within a Multi-Rods Structure O. A. Rodriguez, M. A. Solis We use the Variational Monte Carlo ({VMC}) method to calculate the ground state (gs) energy and the momentum distribution of an interacting Bose gas confined by a one-dimensional periodic multi-rods structure created by an external Kronig-Penney potential. The VMC gs energy is compared with that previously obtained using the Mean-Field theory approximation by solving analytically the Gross-Pitaevskii equation [1]. In the limit of zero external potential, we recover the well-known Lieb-Liniger gas, which for strong interactions becomes the Tonks gas. In this limit case, we compare our variational results with those obtained originally by Lieb and Liniger [2], as well as with those calculated by means of the Diffusion Monte Carlo ({DMC}) method [3]. Only in the region of high density and weak interaction, Mean-Field results are equal to DMC results and slightly better than the variational ones. [1] O.A. Rodr\'iguez and M.A. Sol\'is, ``Ground state of a Lieb-Liniger gas within multi-rods solving analytically the Gross-Pitaevskii equation", work in process. [2] E.H. Lieb and W. Liniger, PR {\bf 130}, 1605 (1963). [3] G.E. Astrakharchik and S. Giorgini, PRA {\bf 68}, 031602 (2003). We thank partial support from grants CONACyT 221030 and PAPIIT IN107616. [Preview Abstract] |
Tuesday, March 14, 2017 3:42PM - 3:54PM |
H13.00007: Extended nonergodic states in disordered many-body quantum systems E. Jonathan Torres-Herrera, Lea Santos |
Tuesday, March 14, 2017 3:54PM - 4:06PM |
H13.00008: Abstract Withdrawn We study adiabatic evolution of quantum states that exhibit bifurcation behavior and find that the classical geometric phase of the generalized harmonic oscillator can be described qualitatively by a 2+1 dimensional de Sitter universe. The fundamental frequency of vibration near the critical surface plays the role of cosmic scale factor, and the classical geometric phase is an integral of a dierential 2-form that exhibits conic singularity similar to the casual singularity at the big bang of the 2+1 dimensional de Sitter universe. |
Tuesday, March 14, 2017 4:06PM - 4:18PM |
H13.00009: Localization Protection and Symmetry Breaking in One-dimensional Potts Chains Aaron Friedman, Romain Vasseur, Andrew Potter, Siddharth Parameswaran Recent work on the 3-state Potts and $Z_3$ clock models has demonstrated that their ordered phases are connected by duality to a phase that hosts topologically protected parafermionic zero modes at the system's boundary. The analogy with Kitaev's example of the one-dimensional Majorana chain (similarly related by duality to the Ising model) suggests that such zero modes may also be stabilized in highly excited statesÂ by many-body localization (MBL). However, the Potts model has a non-Abelian $S_3$ symmetry believed to be incompatible with MBL; hence any MBL state must spontaneously break this symmetry, either completely or into one of its abelian subgroups ($Z_2$ or $Z_3$), with the topological phase corresponding to broken $Z_3$ symmetry. We therefore study the excited state phase structure of random three-state Potts and clock models in one dimension using exact diagonalization and real-space renormalization group techniques. We also investigate the interesting possibility of a direct excited-state transition between MBL phases that break either $Z_3$ or $Z_2$ symmetry, forbidden within Landau theory. [Preview Abstract] |
Tuesday, March 14, 2017 4:18PM - 4:30PM |
H13.00010: Landau-Zener extension of the Tavis-Cummings model: structure of the solution Chen Sun, Nikolai Sinitsyn We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent frequency. We derive compact and tractable expressions for transition probabilities in terms of the well known special functions. In the new form, our formulas are suitable for fast numerical calculations and analytical approximations. As an application, we obtain the semiclassical limit of the exact solution and compare it to prior approximations. We also reveal connection between DTCM and $q$-deformed binomial statistics. [Preview Abstract] |
Tuesday, March 14, 2017 4:30PM - 4:42PM |
H13.00011: Energy Cascade in Quantum Gases X. Y. Yin, Tin-Lun Ho Energy cascade is ubiquitous in systems far from equilibrium. Facilitated by particle interactions and external forces, it can lead to highly complex phenomena like fully developed turbulence, characterized by power law velocity correlation functions. Yet despite decades of research, how these power laws emerge from first principle remains unclear. Recently, experiments show that when a Bose condensate is subjected to periodic shaking, its momentum distribution exhibits a power law behavior. The flexibility of cold atom experiments has provided new opportunities to explore the emergence of these power laws, and to disentangle different sources of energy cascade. Here, we point out that recent experiments in cold atoms imply that classical turbulence is part of a larger family of scale invariant phenomena that include ideal gases. Moreover, the property of the entire family is contained in the structure of its Floquet states. For ideal gases, we show analytically that its momentum distribution acquires a $1/q^2$ tail in each dimension when it is shaken periodically. [Preview Abstract] |
Tuesday, March 14, 2017 4:42PM - 4:54PM |
H13.00012: Floquet engineering from long-range to short-range interactions Tony Lee Quantum simulators based on atoms or molecules often have long-range interactions due to dipolar or Coulomb interactions. We present a method based on Floquet engineering to turn a long-range interaction into a short-range one. By modulating a magnetic-field gradient with one or a few frequencies, one reshapes the interaction profile, such that the system behaves as if it only had nearest-neighbor interactions. Our approach works in both one and two dimensions and for both spin-1/2 and spin-1 systems. It does not require individual addressing, and it is applicable to all experimental systems with long-range interactions: trapped ions, polar molecules, Rydberg atoms, nitrogen-vacancy centers, and cavity QED. Our approach allows one achieve a short-range interaction without relying on Hubbard superexchange. [1] T. E. Lee, Phys. Rev. A 94, 040701(R) [Preview Abstract] |
Tuesday, March 14, 2017 4:54PM - 5:06PM |
H13.00013: Floquet Dynamics of Boundary-Driven Conformal Field Theories William Berdanier, Michael Kolodrubetz, Romain Vasseur, Joel Moore We study the dynamics of quantum critical 1D systems described by a conformal field theory (CFT) subject to a periodic boundary drive. We focus on the transverse-field Ising CFT with a boundary field step-drive, and analytically and numerically calculate its entanglement entropy and Loschmidt echo. We identify three regimes with distinct dynamics, and show that two are well-described by boundary CFT: a slow-driving limit where the Loschmidt echo is given by an N-point function of boundary condition changing operators, and a fast-driving limit where the Floquet-Magnus high-frequency Hamiltonian converges to a single quench at half field, plus irrelevant terms. An intermediate regime governed by resonant processes produces extensive entropy and dynamics described by quantum field theory. We comment on generalizations to other kinds of boundary drives and CFTs, and on applications to quenches involving $\pi$-Majorana fermions. [Preview Abstract] |
Tuesday, March 14, 2017 5:06PM - 5:18PM |
H13.00014: Quantum open systems dynamics via quantum diffusion equations Dawei Luo, Jian-Qiang You, Hai-Qing Lin, Lian-Au Wu, Ting Yu, C.H. Lam Solving realistic quantum systems coupled to an environment is a challenging task. Here we develop a hierarchical functional derivative (HFD) approach for efficiently solving the non-Markovian quantum trajectories of an open quantum system embedded in a bosonic bath. An explicit expression for arbitrary order HFD equation is derived systematically. Moreover, it is found that for an analytically solvable model, this hierarchical equation naturally terminates at a given order and thus becomes exactly solvable. This HFD approach provides a systematic method to study the non-Markovian quantum dynamics of an open system coupled to a bosonic environment. [Preview Abstract] |
Tuesday, March 14, 2017 5:18PM - 5:30PM |
H13.00015: Steady states of OQBM: Central Limit Theorem, Gaussian and non-Gaussian behavior Francesco Petruccione, Ilya Sinayskiy Open Quantum Brownian Motion (OQBM) describes a Brownian particle with an additional internal quantum degree of freedom. Originally, it was introduced as a scaling limit of Open Quantum Walks (OQWs). Recently, it was noted, that for the model of free OQBM with a two-level system as an internal degree of freedom and decoherent coupling to a dissipative environment, one could use weak external driving of the internal degree of freedom to manipulate the steady-state position of the walker [Sinayskiy, I., and Petruccione, F. (2016). Fortschr. Phys.. doi:10.1002/prop.201600063]. This observation establishes a useful connection between controllable parameters of the OQBM, e.g. driving strengths and magnitude of detuning, and its steady state properties. Although OQWs satisfy a central limit theorem (CLT), it is known, that OQBM, in general, does not. The aim of this work is to derive steady states for some particular OQBMs and observe possible transitions from Gaussian to non-Gaussian behavior depending on the choice of quantum coin and as a function of diffusion coefficient and dissipation strength. [Preview Abstract] |
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