Schedule of winter semester (start from 13:00 @ #933)

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Oct. 6 Ken Funo: Topological Quantum Computing I
Oct. 13 Ken Funo: Topological Quantum Computing II
Oct. 20 Yuki Kawaguchi
Oct. 27 Shunsuke Furukawa
Nov. 3 (skip, National holiday)
Nov. 4 (Fri) Kai Stannigel
Nov. 17 Zhifang Xu
Nov. 24 Emi Yukawa
Nov. 29 (Tue)Zhifang Xu (informal)
Dec. 1 Yu Watanabe
Dec. 8 Shingo Kobayashi
Dec. 15 Shimpei Endo
Dec. 22 Nguyen Thanh Phuc
Dec. 29 (skip, winter vacation)
Jan. 5 (occasional date)
Jan. 18 (Wed) Tatsuhiko N. Ikeda @#1320,1324
Jan. 19 Yui Kuramochi
Jan. 26 Ken Funo
Feb. 2 B4
Feb. 16 Naoyuki Sakumichi

Abstract

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speaker	Yuki Kawaguchi
title	Many-body dynamics in a spinor BEC
abstract	The many-body ground state of a spinor BEC is known to be fragmented when the spin-exchange interaction is not ferromagnetic: condensation of a spin-singlet pair or a spin-singlet trimmer occurs. In this seminar, I show that the Goldstone mode in the Bogoliubov spectrum of a single condensate, i.e., a mean-field ground state, naturally includes the instability towards the fragmented ground state. However, when we take into account the effect of thermal components, the mean-field state is stabilized.

speaker	Shunsuke Furukawa
title	Bose physics in quantum magnets with coupled-dimer structures
abstract	In the first part of my talk, I will review the Bose physics that emerges in quantum magnets with coupled-dimer structures [1]. In these magnets, a local triplet excitation (triplon) behaves like a Bose particle, and such particles condense or crystallize just li ke cold atoms on optical lattices. The second part of the talk will focus on our recent study [2] on a specific spin model proposed for (CuCl)LaNb2O7. In this model, antiferromagnetic dimers are ferromagnetically coupled to each other on the distort ed Shastry-Sutherland lattice. We showed that the triplons undergo a Bose condensation or a phase separation depending on the model parameters. These are observed as a smooth increase or a jump, respectively, in the magnetization process. Implications of our results for (CuCl)LaNb2O7 and related compounds are presented. [1] T. Giamarchi, Ch. Ruegg, and O. Tchernyshyov, Nat. Phys. 4, 198 (2008). [2] S.F., T. Dodds, and Y.B. Kim, Phys. Rev. B 84, 054432 (2011).

speaker	Kai Stannigel
title	Free-space coupling of a micro-mechanical oscillator to an atomic ensemble
abstract	We discuss a hybrid quantum system where the motion of a micro-mechanical membrane is coupled to an atomic ensemble via a free-space laser beam. The well-developed toolbox available for the control of the atoms enables indirect manipulation of the membrane, such as, e.g., sympathetic cooling of its motion. Starting from a microscopic model of the system, we derive an effective description for the interactions between membrane and atoms, which we cast into the form of a (partly cascaded) master-equation. We discuss major imperfections in the system and analyze the prospects for cooling the membrane to its quantum-mechanical ground state. [1] http://arxiv.org/abs/1002.4646

speaker	Zhifang Xu
title	Mixtures of two spin-1 condensates
abstract	In this talk, I will discuss related physical phenomena of binary mixtures of spin-1 Bose-Einstein condensates. Under mean-field and single-mode approximations, we have derived ground-state phase diagram, in which one interesting ground state with axisymmetry broken exists for the case of strong enough interspecies anti-ferromagnetic spin-exchange interactions. Including quantum fluctuations, the spin-dependent Hamiltonian contains noncommuting terms, as the s-wave scattering channel between interspecies does not conform to a fixed symmetry. Making use of the spin total angular momentum conservation, we numerically derive the information of the building blocks and evaluate von Neumann entropy to quantify the ground states, which show fragmented and entangled behaviors within large parameter spaces of interspecies spin-exchange and singlet-pairing interactions. Lastly, I will briefly discuss how to determine interspecies spin-exchange and singlet-pairing interactions from subsequent spin mixing dynamics, by preparing suitable initial states and properly tuning external magnetic fields.

speaker	Emi Yukawa
title	Hydrodynamic description of spin-1 Bose-Einstein condensates
abstract	Properties of the spinor Bose-Einstein condensates (BEC), such as the low-lying collective modes and the ground states, have been explored extensively in the mean-field regime by solving the Gross-Pitaevskii (GP) equation. However, the GP description based on wave functions that cannot be observed directly prevents us from an intuitive understanding of the spinor BEC. In order to give a more clear-cut picture of the spinor BEC, the nematic tensor that indicates the anisotropy of the wave functions in the spin-space is introduced, and then the hydrodynamic equations in an arbitrary state of the F=1 spinor BEC are derived in terms of the density, the spin vector, and the nematic tensor. Here, the obtained equations are equivalent to the GP equation and do not involve the wave functions. By applying the single-mode approximation to these hydrodynamic equations, we reveal that the spin vector acts on the nematic tensor like torque. In this way, the hydrodynamic equations help us directly understand the physics of the spinor BEC.

speaker	Zhifang Xu
title	Synthetic Non-Abelian Gauge Fields in Ultracold Neutral Atoms

speaker	Yu Watanabe
title	Formulation of Uncertainty Relations between Error and Disturbance in Quantum Measurement by using Quantum Estimation Theory
abstract	It is necessary to involve quantum estimation theory for formulating error and disturbance in quantum measurement. We formulate the error and disturbance in quantum measurement by using the Fisher information that bounds the variance of the estimated value of ⟨X⟩, where ⟨X⟩ is the expectation value of the observable X. We show uncertainty relations between the error of two non-commuting observables [1], and between the error and disturbance [2]. [1] Physical Review A 84, 042121 (2011). [2] arXiv:1106.2526 (2011).

speaker	Shingo Kobayashi
title	Vortex core states in spin-1 Bose-Einstein condensates
abstract	In my talk, I introduce possible vortex core states in spin-1 Bose-Einstein condensates (BECs) with respective to a symmetry of system. The homotopy theory has been so far applied to a classification of vortices in terms of the map from the boundary of vortices to the order parameter space. However it does not determine the vortex core structures since field configurations leave from the order parameter space near the vortex core. Here, we will extend this conventional homtopy theory classification in order to deal with the core structure of vortices. To this end, we will study a map from the whole space including a core to a space of the whole degrees of freedom of an order parameter, which is lager than the order parameter space. As a result, we find many possible vortex core structures including conventional vortex cores, which have been obtained in a numerical simulation by a number of researchers.

speaker	Shimpei Endo
title	Universal trimers and Efimov trimers
abstract	For a three-body system interacting via resonant two-body interaction, there exist three-body bound states called Emov states. Emov states have attracted a lot of interest since their recent experimental realizations with ultracold atoms [1]. One of the intriguing features of the Emov states is their universal property: they can be characterized completely by two parameters, the s-wave scattering length and a short-range three-body parameter, and are unaffected by all other details of the potential. Recently, however, novel three-body bound states have been predicted theoretically [2], which depend only on the s-wave scattering length. Although the origin of these trimers is closely related to the Efimov effect, they have a distinct nature. We will discuss on the relationship between these two kinds of three-body bound states [3,4]. [1] F. Ferlaino, and R. Grimm, Physics, 3, 9 (2010) [2] O. I. Kartavtsev, and A. V. Malykh, J. Phys. B, 40, 1429 (2007) [3] S. Endo, P. Naidon, and M. Ueda, Few-body Systems, 51, 207 (2011) [4] S. Endo, P. Naidon, and M. Ueda, in preparation

speaker	Nguyen Thanh Phuc
title	Effects of quantum depletion on the energy spectrum of a ferromagnetic Bose-Einstein condensate
abstract	In contrast to scalar Bose-Einstein condensates (BECs), in, for example, 87Rb spinor BECs, due to the large ratio of spin-independent to spin-exchange interaction, the effect of a small fraction of noncondensed atoms on the system's order parameter is remarkable and leads to a significant modification of the ground-state phase diagram [1]. Similarly, the effect of quantum depletion on the energy spectra of the elementary excitations of a spinor BEC cannot be neglected in priori. In another aspect, for spinor BECs, the atoms posess unfrozen spin degrees of freedom, which leads to the existence of spin-wave excitations in addition to ordinary density-wave excitations in scalar Bose gases. Here, we investigate the effect of quantum depletion on the energy spectrum and propose an experimental setup to probe this effect based on the nature of spin-wave excitations. [1] N. T. Phuc, Y. Kawaguchi, M. Ueda, PRA 84, 043645 (2011).

speaker	Tatsuhiko N. Ikeda
title	Two thermalization mechanisms and their interplay examined in one-dimensional Bose gas
abstract	Thermalization is the phenomenon in which equilibrated value of an observable corresponds to the prediction of statistical mechanics. To understand thermalization in closed quantum systems, there proposed two conjectures, eigenstate thermalization hypothesis(ETH) and eigenstate randomization hypothesis(ERH). Both of these are the statements on the property of the expectation values of observables taken over each many-body eigenstate. In this seminar, we briefly review these hypotheses and examine the validities of them by invoking the Lieb-Liniger model, which describe the one-dimensional Bose gas with delta-function interaction. After the examination, we discuss the interplay between the ETH and ERH.

speaker	Yui Kuramochi
title	Theory of quantum continuous measurement in diffusive and jump type
abstract	The continuous quantum measurement is a quantum measurement process of continuous output in time. This measurement process can be mathematically described by stochastic master equation (SME) or stochastic Schrödinger equation (SSE) of which two types h ave been mainly discussed; jump type and dissusive type SSE's. The jump type SSE describes discrete outputs continuous measurement such as a photon counting measurement of photon field, while the measurement described by diffusive type SSE has continuous outputs such as a homodyne measurement of quadrature amplitude. In this seminar we generalize these two types of measuerement process to a measurement in which these two types of outputs exist. Then, we discuss the simultaneous measurement of photon counting and homodyne measurement as an example of this generalized process. We derive analytical expression of the time evolution of the wave function under given outputs and, using this, derive probability distribution of the two measurement outputs. This general results are applied to typical initial states: coherent states, number states, and squeezed states. These calculations shows that the correlation between the two measurement outputs comes from non-classicality of the state.

speaker	Ken Funo
title	Formulation of generalized Second law with feedback control on quantum correlated states
abstract	Quantum Maxwell's demon is a feedback controller for quantum states. This demon controls the quantum fluctuation and extracts work from the system. There has been a previous study of feedback control of the thermal fluctuation[1]. In this work, the information content and thermodynamic variables are treated on an equal footing. We want to generalize this work on states that are quantum correlated (or entangled), and find out the appropriate quantum information content on an equal footing with thermodynamic variables. We discuss a feedback control for states that are quantum correlated and derive a generalized Second law. [1] T. Sagawa and M. Ueda, Phys. Rev. Lett. 100, 80403 (2008)

speaker	Naoto Shiraishi
title	New Definition of Work in Thermodynamics of Small Systems
abstract	Thermodynamic relations of small systems such as Jarzynski equality have been studied. However, the usual definition of work doesn't mean usable work. So, we give a reasonable definition of usable work, and show a relation for this newly defined work. The relation suggests that we need extra energy kT for each operation.

speaker	Daiki Nishiguchi
title	Derivation and interpretation of Jarzynski equality
abstract	Jarzynski equality is the relation connecting the free energies of equilibrium states and the work performed during the nonequilibrium process. This equality has been proven for both Hamiltonian dynamics and stochastic dynamics. In this presentation, I will talk about the differences and the meanings of these derivations. I also discuss the critical assumptions which these derivations rely on.

speaker	Yoshihito Hotta
title	Robustness of edge states in quantum walks
abstract	The quantum walk is a generalization of the classical random walk to quantum systems. Quantum walks can be analyzed using topology of energy bands, like topological insulators. Because of the simplicity of the model, analytic solutions can be easily obtained, for example, for edge states. In this presentation, we show that robustness of edge states in spacially inhomogeneous systems which stems from topological nature both by numerical simulation and phase diagrams.

speaker	Naoyuki Sakumichi
title	Criteria of off-diagonal long-range order in Bose and Fermi systems based on the Lee-Yang cluster expansion method
abstract	In this seminar, we extend the quantum-statistical cluster expansion method of Lee and Yang [1] to investigate off-diagonal long-range order (ODLRO) in one- and multi-component mixtures of bosons or fermions [2]. Our formulation is formally applicable to a uniform system and a trapped system without local-density approximation and allows systematic expansions of one- and multi-particle reduced density matrices in terms of cluster functions which are defined for the same system with Boltzmann statistics. Each term in this expansion can be associated with a Lee-Yang graph. In the case of Bose statistics, an infinite series of Lee-Yang 1-graphs is shown to converge and gives the criteria of ODLRO at the one-particle level. In the case of Fermi statistics, an infinite series of Lee-Yang 2-graphs is shown to converge and gives the criteria of ODLRO at the two-particle level. [1] T. D. Lee and C. N. Yang, Phys. Rev. 113, 1165 (1958); 117, 22 (1960) [2] NS, Norio Kawakami and Masahito Ueda, arXiv:1112.5768

Schedule of summer semester (start from 13:00 @ #933)

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Apr. 14(Thu) Naoyuki Sakumichi
    "Variational Formulations of Equilibrium Statistical Mechanics"
    C. De Dominicis, J. Math. Phys. 3, (1962) 983-1002

Apr. 21(Thu) Yu Watanabe
    "General state changes in quantum theory"
    K. Kraus, Annals of Physics Volume 64, Issue 2, June 1971, Pages 311-335

Apr. 28(Thu) Shingo Kobayashi
    "Non-Abelian Statistics of Half-Quantum Vortices in p-Wave Superconducters"
    D. A. Ivanov, Phys. Rev. Lett. 86, 268 (2001)
    "Geometric phases quantum entanglement as building blocks for non-Abelian quasiparticle statistics"
    A. Stern, F. V. Oppen, and E. Mariani, Phys. Rev. B, 70, 205338 (2004)

May. 11(Wed) @445 Shimpei Endo
    "Energy levels arising from resonant two-body forces in a three-body system"
   V. Efimov, Phys Lett B 33 563 (1970)
    "Weakly-Bound States of Three Resonatly-Interacting Particles"
   V. Efimov, Sov. Jouur. Nucl. Phys. vol. 12, 589 (1971)
    "Rewiew Article about the History of Efimov Physics."
    Francesca Ferlaino and Rudolf Grimm, Physics 3, 9 (2010)

May. 26(Thu) Emi Yukawa
    "Bose-Einstein Condensation and Liquid Herium"
   Oliver Penrose and Lars Onsager, Phys. Rev. 104, 576 (1956)

speaker	Muneto Nitta (Keio University)
title	Majorana meets Coxeter: Novel Non-Abelian Statistics from Non-Abelian Majorana Fermions
abstract	First I will review non-Abelian statistics of vortices having zero-energy Majorana fermion found by Ivanov. Second, I will discuss statistics of vortices having multiple zero-energy Majorana fermions inside them (non-Abelian Majorana fermions). Considering the system of multiple non-Abelian vortices, we derive a non-Abelian statistics that differs from the one of Ivanov. The new non-Abelian statistics presented here is given by a tensor product of two different groups, namely the non-Abelian statistics obeyed by the Abelian Majorana fermions and the Coxeter group. As the simplest example, we consider the case in which a vortex contains three Majorana fermions that are mixed with each other under the SO(3) transformations. I will make a comment that such a system is so far realized in a color superconductor of high density QCD, but I will discuss a possibility that it may be realized in cold atomic gasses. This talk is based on the work with Shigehiro Yasui, Kazunori Itakura, Phys.Rev.B83:134518,2011 [arXiv:1010.3331 [cond-mat.mes-hall]].

Jun. 2(Thu) Nguyen Thanh Phuc
    "Energy-Spectrum of a Non-Ideal Bose Gas"
   S. T. Beliaev, Sov. Phys. JETP vol. 34, 299 (1958)

Jun. 16(Thu) Tatsuhiko Ikeda
    "Information Theory and Statistical Mechanics"
    E. T. Jaynes, Phys. Rev., 106, 620-630 (1957)
    "Information Theory and Statistical Mechanics. II"
    E. T. Jaynes, Phys. Rev., 108, 171-190 (1957)

Jun. 23(Thu) Yui Kuramochi
    "On stochastic differential equations"
    Kiyosi Itô, Mem. Amer. Math. Soc. 4, 1-51.

Jun. 30(Thu) Ken Funo
    "Quantum field theory and the Jones polynomial"
   E. Witten, Commun. Math. Phys. vol. 121, 351-339 (1989)

Jul. 7(Thu) Sunmyon Chon
    "Theory of Superconductivity"
    J. Bardeen, L. N. Cooper, and J. R. Schrieffer

Jul. 21(Thu) @201a Kohaku So (Hongbo Zeng)
    "The physics and mathematics of the second law of thermodynamics"
    Elliot H. Lieb and Jakob Yngvason, Phys.Rept. 310 (1999) 1-96

Jul. 28(Thu) Yusuke Horinouchi
    "Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture"
    Kenneth G. Wilson, Phys. Rev. B 4, 3174-3183 (1971)
    "Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical Behavior"
    Kenneth G. Wilson, Phys. Rev. B 4, 3184-3205 (1971)

speaker	北 孝文
title	Bose-Einstein凝縮理論の基礎を再考する
abstract	相互作用するBose-Einstein凝縮(BEC)相の微視的理論は，1947年のBogoliubov理論を突破口し，1960年代中盤までに場の量子論を用いてその基礎が築かれた。通常の摂動展開により得られた一般的結果は次のようにまとめられる。 (a) 一粒子グリーン関数の極がBogoliubov励起で，長波長極限で無限の寿命をもち励起エネルギーが0となる (Beliaev, 1958; Hugenholtz and Pines, 1959)。 (b) 二粒子グリーン関数は一粒子グリーン関数と共通の極を持つ(Gavoret and Nozières, 1964)。 (a)によりBogoliubov励起は伝搬波であることになり，BEC相の南部-Goldstoneモードであるとみなされている。(b)はBogoliubov励起が密度揺らぎ(=音波)であることを意味し，中性子非弾性散乱による超流動4Heのフォノン-ロトン曲線がBogoliubov励起に他ならないことを表している。一方，BEC相の場の量子論には固有の難しさがあり， (c) Goldstoneの定理と動的保存則を同時に満たす自己無撞着理論が構成できない ことが知られてきた（Hohenberg and Martin, 1965; Griffin, 1996）。 最近，(c)の問題を解決し，二つの要請を同時に満たす自己無撞着摂動展開理論を構成することができた[1]。この理論はLuttingerとWardによる正常状態の自己無撞着理論(1960)をBEC系へ拡張したものとなっており，以前に提出したBEC相の平均場理論[2]を最低次の近似として再現するものである。さらに，この理論的枠組みを用いて，二粒子グリーン関数や南部-Goldstoneモードの一般的性質も調べた[3,4]。その結果，上記の(a)および(b)とは異なる次の結果を得た。 (a')Bogoliubov励起は長波長極限でも有限の寿命を持つ[4]。 (b')二粒子グリーン関数の極は一粒子グリーン関数の極とは異なる[3,4]。 そして，(a')と(b')の両モードが南部-Goldstoneモードとみなせることも明らかになった[4]。このように、Bose-Einstein凝縮（BEC）理論の基礎に関して，いくつかの発展があり，また通説とは異なる結果も得られたので本講演で報告する。 [1] T. Kita, Phys. Rev. B 80, 214502 (2009). [2] T. Kita, J. Phys. Soc. Jpn. 74, 1891 (2005); 74, 3397(E) (2005). [3] T. Kita, Phys. Rev. B 81, 214513 (2010). [4] T. Kita, J. Phys. Soc. Jpn. 80, 084606 (2011).