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分化理論による量子現象の統一的解釈量子場から測定までを結ぶ基礎的解釈枠組み

昌続新関

本稿は、量子場、波動性と粒子性、重ね合わせ、量子確率、測定、量子トンネル、量子もつれ、不確定性原理、スピン、粒子の生成と消滅、真空を、分化理論の観点から統一的に読み直すための基礎的解釈枠組みを提示する。本稿における分化とは、複数の可能性を含む状態から、相互作用を通して区別可能な状態または関係が成立し、その区別が物理的記録として保持されることを指す。量子を場の励起、重ね合わせを複数の分化可能性が保持された状態、測定を区別可能な記録が成立する過程として解釈する。ただし、本枠組みは量子力学の数学的形式を置き換えるものではなく、独立した予測を行う完成した物理理論でもない。ボルン則、スピン、質量、結合定数、色荷および世代構造の数理的導出が未解決であることを明示する。キーワード分化理論、量子場、重ね合わせ、測定、量子もつれ、量子基礎論

Sep 14, 20260 citations

Vortex lattices in binary Bose–Einstein condensates: collective modes, quantum fluctuations, and intercomponent entanglement

Takumi Yoshino, Shunsuke Furukawa, Masahito Ueda

Abstract We study binary Bose–Einstein condensates subject to synthetic magnetic fields in mutually parallel or antiparallel directions. Within the mean-field theory, the two types of fields have been shown to give the same vortex-lattice phase diagram. We develop an improved effective field theory to study properties of collective modes and ground-state intercomponent entanglement. Here, we point out the need to introduce renormalized coupling constants for coarse-grained densities. We show that the low-energy excitation spectra for the two types of fields are related to each other by suitable rescaling with the renormalized coupling constants. By calculating the entanglement entropy, we find that for an intercomponent repulsion (attraction), the two components are more strongly entangled in the case of parallel (antiparallel) fields, in qualitative agreement with recent studies for a quantum (spin) Hall regime. We also find that the entanglement spectrum exhibits an anomalous square-root dispersion relation, which leads to a subleading logarithmic term in the entanglement entropy. All of these are confirmed by numerical calculations based on the Bogoliubov theory with the lowest-Landau-level approximation. Finally, we investigate the effects of quantum fluctuations on the phase diagrams by calculating the correction to the ground-state energy due to zero-point fluctuations in the Bogoliubov theory. We find that the boundaries between rhombic-, square-, and rectangular-lattice phases shift appreciably with a decrease in the filling factor.

arXiv:2108.13219Journal of Physics B Atomic Molecular and Optical PhysicsApr 20, 20220 citations

人工知能を用いた量子アルゴリズムの探索

大門　俊介, 松下雄一郎

量子コンピュータの実用的計算への応用を目指して、様々な量子アルゴリズムが提案されている。しかしながら現在の不完全な量子コンピュータ上では、従来提案されてきた量子アルゴリズムの実行が困難である場合が多く、より効率的な量子アルゴリズムの発見が求められている。そこで我々は、人工知能に量子計算の大量のデータを学習させることによって、量子アルゴリズムを学習させた。構築した人工知能は、少ないデータから量子計算の規則性を見出し、未知の入力に対しても正しい量子計算手順を出力できることが明らかになった。これは、開発した人工知能が少数のデータに内在する規則性を量子アルゴリズムとして理解し、未知のデータに対しても応用しているということを示している。

Dec 10, 20240 citations

人工ゲージ場下の二成分ボース・アインシュタイン凝縮体の理論的研究

Takumi Yoshino

Bose-Einstein condensates (BECs) in ultracold atomic gas have been studied intensively, since the state of atoms is well controlled by lasers and external electromagnetic fields.Synthetic gauge fields can be induced in a charge-neutral system by mechanical rotation of the system or by using lasers.In a BEC under a synthetic gauge fields, a quantized vortex or a vortex lattice, where multiple quantized vortices are periodically located, are observed.In binary BECs composed of bosonic atoms in two hyperfine states, parallel and antiparallel synthetic gauge fields are induced by the former (mechanical rotation) and the latter (laser) techniques, respectively.In the mean-field theory, vortex lattices appear with various configurations which depend on the ratio of the intercomponent interaction to the intracomponent one.While the ground-state phase diagrams for parallel and antiparallel fields are the same in the mean-field regime, two phase diagrams are significantly different in the quantum Hall regime, where a magnetic field is strong.In the first part of this thesis, we study the excitation spectra, correlation functions and the quantum depletion of vortex lattices by means of the effective-field theory and the Bogoliubov theory under the lowest-Landau-level (LLL) approximation.We obtain the effective-field theory of vortex lattices in binary BECs by introducing the missing elastic energy term from the symmetry consideration.By renormalizing the coupling constants, we find the effective-field theory for strong magnetic fields so that we can compare it with the Bogoliubov theory.We obtain the analytical expression of the dispersion relations for parallel and antiparallel fields by diagonalizing the effective Hamiltonian and the rescaling relations between them.From the rescaling relations, we clarify that the different excited states for parallel and antiparallel fields are indeed related to each other.By calculating the correlation function, we show that a one-particle density matrix exhibits a quasi-longrange order and that the fraction of depletion increases logarithmically with respect to the number of fluxes.By means of the Bogoliubov theory, we numerically obtain energy spectra with quadratic and linear dispersion relations for parallel and antiparallel fields and confirm the rescaling relations for all the phases.We find that the quantum depletion depends crucially on the direction of synthetic gauge fields and diverges logarithmically with respect to the number of fluxes.By calculating the correction to the ground-state energy due to zero-point fluctuations by the Bogoliubov theory, we show that the transition points shift appreciably due to quantum fluctuations.Furthermore, we show that the variations of an inner angle and an aspect ratio with respect to the ratio of interactions are altered from those obtained by the mean-field theory for rhombic and rectangular lattices, respectively.We find that the quantum fluctuation changes the ground-state phase diagram and leads to the distinction between the phase diagrams for parallel and antiparallel fields which are unique to binary BECs.Moreover, we relate the quantum depletion to shifts of the transition points since the phase diagram is largely modified when the quantum depletion which characterizes the quantum fluctuation is also large.In the second part of the present thesis, we study the intercomponent entanglement spectrum (ES) and entanglement entropy (EE) of vortex lattices in binary BECs by exploiting the formalisms developed in the first part.By means of the effective-field theory, we show that the ES exhibits a square-root dispersion relation for all the phases and that the rescaling relation holds between the ESs for parallel and antiparallel fields, similarly to the energy spectra.We confirm these predictions through a numerical calculation by List of PublicationsThis Thesis is based on the following publications. Collective modes of vortex lattices in two-component Bose-Einstein condensates under synthetic gauge fields

Mar 19, 20210 citations

時空の離散的サンプリングと有限解像度窓関数による客観的デコヒーレンスの導出

Taishi Namba, Mick Ichigo

【要約】量子力学におけるデコヒーレンス理論は、従来、対象系と無限の自由度を持つ外部環境とのエンタングルメントに依存して説明されてきた。しかし、このアプローチは全宇宙のような閉鎖系に適用できず、古典的観測値への境界(ハイゼンベルク切断)の物理的実体を提示できないという根本的な課題を抱えている。本研究では、時空そのものが持つ情報キャリアの有限性に着目し、最小解像度スケールを持つガウス窓関数を用いた離散サンプリング写像モデルを提案する。連続波動関数から格子上の有効密度行列への変換を解析的に計算した結果、空間的に距離離れた非対角項(コヒーレンス)が幾何学的抑制因子によって指数関数的に減衰し、マクロスケール( )において自動的に消滅することが厳密に示された。さらに、ナイキスト限界を超える高周波成分は基本帯域へエイリアシングとして射影され、激しい自己位相干渉によって熱化(位相キャンセレーション)を引き起こす。これにより、環境系への情報の散逸を仮定することなく、純粋な情報幾何学的制約のみから「客観的な波束の収縮」と「ボルン規則に基づく対角項の保存」が必然的な数理的帰結として導かれる。本モデルは、主観的な観測者やアドホックな境界線を必要とせず、ミクロとマクロの力学を単一の枠組みでシームレスに統合する新たな基盤を提供する。 I. INTRODUCTIONThe quantum measurement problem remains one ofthe deepest foundational issues in physics. Whileenvironment-induced decoherence successfully explainsthe rapid diagonalization of reduced density matrices foropen quantum systems, it suffers from severe limitationswhen applied to the entire universe as a closed system,where no external environment exists.Objective collapse models, such as the Ghirardi-Rimini-Weber (GRW) and Continuous Spontaneous Lo-calization (CSL) frameworks, introduce ad-hoc stochasticjumps or classical white noise fields to restore macroreal-ism. However, these mechanisms introduce non-unitaryphenomenological parameters without geometric origin.In this work, we propose that objective decoherence isa natural consequence of the finite information-carryingcapacity and spatial resolution of background spacetime.By utilizing Shannon-Nyquist sampling theory and har-monic analysis, we show that classicality emerges deter-ministically from geometric projections onto discrete lat-tice representations.

Sep 11, 20260 citations

Collective modes of vortex lattices in two-component Bose–Einstein condensates under synthetic gauge fields

Takumi Yoshino, Shunsuke Furukawa, Sho Higashikawa +1 more

We study collective modes of vortex lattices in two-component Bose–Einstein condensates subject to synthetic magnetic fields in mutually parallel or antiparallel directions. By means of the Bogoliubov theory with the lowest-Landau-level approximation, we numerically calculate the excitation spectra for a rich variety of vortex lattices that appear commonly for parallel and antiparallel synthetic fields. We find that in all of these cases there appear two distinct modes with linear and quadratic dispersion relations at low energies, which exhibit anisotropy reflecting the symmetry of each lattice structure. Remarkably, the low-energy spectra for the two types of fields are found to be related to each other by simple rescaling when vortices in different components overlap owing to an intercomponent attraction. These results are consistent with an effective field theory analysis. However, the rescaling relations break down for interlaced vortex lattices appearing with an intercomponent repulsion, indicating a nontrivial effect of an intercomponent vortex displacement beyond the effective field theory. We also find that high-energy parts of the excitation bands exhibit line or point nodes as a consequence of a fractional translation symmetry present in some of the lattice structures.

arXiv:1807.11666New Journal of PhysicsNov 23, 20185 citations

人工ゲージ場中のボース・アインシュタイン凝縮体における多体効果の理論的研究

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人工ゲージ場中のボース・アインシュタイン凝縮体における多体効果の理論的研究

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