Kindai QPT Seminar | 近畿大学量子多体物理学研究室

今後の予定

日時：2024年10月30日15:00-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：安藤京介（物性理論）

題目：Machine learning analysis of Fully Frustrated XY Model (FFXY) in two-dimensional square lattice

概要： The recent remarkable development of artificial neural networks in image recognition, image classification, and natural language processing has influenced many scientific fields, and the search for new discoveries by applying this technology to any problem has begun. In the field of classical statistical physics, machine learning algorithms were introduced to identify symmetry-broken phase [1-3], and in some of these cases neural networks were shown to be able to learn order parameters and other thermodynamic parameters [1,3]. Having been able to apply machine learning techniques to conventional phase transitions, it is natural to ask whether the algorithm can be applied to unconventional phase transitions. As an example of such a system, we focus on the 2D Fully Frustrated XY Model (FFXY) [4]. The FFXY model has an Ising model-like transition and an XY model-like transition.

The purpose of this study is to see if machine learning algorithms trained by the XY and Ising models can detect phase transitions for the two-dimensional square lattice FFXY model. The two neural networks used were trained from the spin configuration of the Ising model and the vortex configuration of the XY model. The FFXY model detects vortices from spin configurations obtained from Monte Carlo simulations, and inputs them to the learning model.

[1] J. Carrasquilla and R. G. Melko, Nat. Phys. 13, 431 (2017).

[2] E. P. L. van Nieuwenburg, Y.-H. Liu, and S. D. Huber, Nat. Phys.13, 435 (2017).

[3] S. J. Wetzel and M. Scherzer, Phys. Rev. B 96, 184410 (2017).

[4] Stephen Teitel, 40 Years of Berezinskii–Kosterlitz–Thouless Theory (World Scientific), pp. 201-235 (2013).

日時：2024年11月6日15:00-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：宮井誠一郎（量子多体）

題目：Toward an analysis of correlation propagation in the Bose-Hubbard model with dipole-dipole interactions

概要：Rapid technological advances in preparing and manipulating cold atoms have offered unique opportunities for studies of non-equilibrium dynamics of quantum many-body systems. One of the fundamental questions to be addressed is how correlations propagate in these systems. Specifically, such correlation propagation dynamics have been analyzed in experiments with Bose gases in optical lattices [1,2], which can be well described by the Bose-Hubbard model. Moreover, quantum simulations including long-range interactions such as atoms with strong magnetic dipole-dipole interactions, Rydberg atoms, and cold polar molecules have recently been developed [3,4,5,6]. These experiments have opened up new possibilities for studying effects of the long-range interactions on correlation propagation dynamics. In this work, we aim to theoretically investigate correlation spreading in the Bose-Hubbard model with dipole-dipole interactions using the linear spin-wave theory (LSWT) [7]. In this presentation, we will review analyses using the unconstrained fermion approximation [8] in order to gain analytical insights on the correlation propagation in the Bose-Hubbard model. We also review calculations of dispersion relations of quasi-particle excitations based on the LSWT both in the absence [7] and presence [9] of the nearest-neighbor interaction.

[1] M. Cheneau et al., Nature, 481,487 (2012).

[2] Y. Takasu et al., Science Advances 6, eaba9255 (2020).

[3] S. Baier et al., Science 352, 201(2016).

[4] L. Su et al., Nature 622, 724 (2023).

[5] S. Ebadi et al., Nature 595, 227 (2021).

[6] J. S. Rosenberg et al., Nature Physics 18, 1062 (2022).

[7] S. D. Huber et al., Phys. Rev. B 75, 085106 (2007).

[8] P. Barmettler et al., Phys. Rev. A 85, 053625 (2012).

[9] D. L. Kovrizhin et al., Europhys. Lett. 72, 162 (2005).

日時：2024年11月13日15:00-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：小久保治哉（物性理論）

題目：Critical velocity in a superfluid wake behind a plate-shaped obstacle

概要：When an obstacle potential moves within a superfluid at speeds exceeding the critical velocity, quantum vortices are generated. It is well known that this critical velocity depends strongly on the shape of the obstacle [1-2]. In this study, we investigate the critical velocity for quantum vortex formation around a plate-shaped obstacle moving within a uniform Bose-Einstein condensate. Numerical calculations based on the Gross-Pitaevskii theory reveal that the critical velocity decreases as the plate size increases, showing proportionality to $L^{-1/2}$ for large obstacles. Additionally, we find that smaller plate sizes deviate from this power law. We show that this numerical result is reproduced by applying perturbation analysis that incorporates compressibility into potential flow theory [3].

[1]Woo Jin Kwonet al., Phys. Rev. A 91, 053615 (2015)
[2]Haneul Kwak, Jong Heum Jung, and Y. Shin, Phys. Rev. A 107, 023310 (2023)
[3]Sergio Rica, Physica D : Nonlinear Phenomena, Volume 148, Issues 3–4 (2001)

日時：2024年11月20日15:00-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：植田健太（量子多体）

題目：TBA

概要：TBA

日時：2024年11月27日15:00-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：Sidharth Rammohan（量子多体）

題目：TBA

概要：TBA

日時：2024年12月4日15:00-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：百合巧（大阪大学）

題目：TBA

概要：TBA

日時：2024年12月11日15:00-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：TBA

題目：TBA

概要：TBA

日時：2024年12月18日15:00-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：TBA

題目：TBA

概要：TBA

日時：2025年1月8日15:00-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：TBA

題目：TBA

概要：TBA

日時：2024年1月22日15:00-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：TBA

題目：TBA

概要：TBA

日時：2024年1月29日15:00-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：TBA

題目：TBA

概要：TBA

過去のセミナー

日時：2024年4月17日10:45-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：植田健太（量子多体）

題目：Anomalous tunneling of collective excitations in a Rydberg atomic system

概要：We study tunneling properties of low-energy excitations through a potential barrier in a spin-1/2 ferromagnetic XY model with dipole-dipole interactions, which has been realized with Rydberg atoms in an optical tweezer array [1]. In a system with spontaneous breaking of U(1) symmetry and short-range interaction, it is known that low-energy excitations exhibit anomalous tunneling behavior, in which the transmission probability increases with decreasing the excitation energy and the barrier is completely transparent at the zero-energy limit [2]. We aim to elucidate how the long-range nature of the dipole-dipole interaction affects such tunneling properties of the low-energy excitations. Specifically, within a mean field theory, we numerically calculate the transmission probability. As a result, we find that anomalous tunneling indeed occurs. We also discuss physical properties unique to the systems with long-range interactions.

[1] C. Chen et al., Nature, 616, 691 (2023).

[2] Yu. Kagan et al., Phys. Rev. Lett. 90, 130402 (2003).

日時：2024年5月8日10:45-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：Rammohan, Sidharth（量子多体）

題目：Studying quantum phases in dipolar Bosons in planar array using cluster mean-field

概要：Dipolar bosons in optical lattices have emerged as a promising candidate for the quantum simulation of the condensed matter systems. These systems have been widely employed to study phase transitions in spin models because of their tunability with regard to the interaction strengths. These prospects now motivate scientists even more to explore for interesting phases in these kinds of systems, such Luttinger liquids. A theoretical study conducted in 2008 employed dipolar bosons in planar arrays to investigate the formation of the "sliding Luttinger liquid" (SLL) phase [1]. Since it is difficult to observe the SLL phase experimentally, the main objective of this work was to propose one such platform that would allow for the observation of the SLL phase utilizing dipolar bosons.

Despite the usual challenges associated with experimental advancements, experimental research has recently accelerated, and dipolar bosons can already be realized in optical lattices in laboratories. In 2023, Griener's group investigated the formation of dipolar quantum solids in a Hubbard quantum simulator [2]. Given the current status of the research field, we think that adopting a different approach, like a cluster mean-field method, to the problem will help to develop a computationally efficient solution and open the door to studying the real-time dynamics of the systems. We believe that the cluster mean field strategy introduced in [3] will work nicely for this.

While [3] studies the phase transition in a hardcore Bose-Hubbard model, this method can also be effectively applied to the dipolar boson in planar array case.Thus, in my talk, I will be talking about this proposal, focusing mostly on the concepts of the cluster mean-field approach from [3] and the current state of the exploration of phase transition in dipole bosons in planar array. Finally, I will provide a quick summary of the cluster mean-field approach's potential for this purpose at the end of my session.

[1] C. Kollath et.al., PRL 100, 130403 (2008).

[2] Lin Su et.al., Nature 622 (2023).

[3] D. Yamamoto et.al., PRB 86, 054516 (2012).

日時：2024年5月15日10:45-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：段下一平（量子多体）

題目：Creating Ising model with sign-inverted next-nearest-neighbor interaction by using Rydberg atoms:

Application to studies of surface criticality

概要：We propose a way to realize a system quantitatively described by a mixed-field Ising model, in which the sign of the next-nearest-neighbor (NNN) interaction is opposite to that of nearest-neighbor one [1], with use of Rydberg atoms in an optical-tweezer array. We theoretically show that the proposed system is suited to studying surface criticality associated with discontinuous quantum phase transitions [2,3]. Specifically, we derive the Ginzburg-Landau (GL) equation of the Ising model with the sign-inverted NNN interaction, which provides us with analytical insights of the surface criticality. By presenting numerical calculations based on a mean-field theory, we confirm the validity of the GL equation near the quantum tricritical point (QTCP). We also find that the logarithmic divergence behavior, which is a characteristic of the surface criticality, persists even away from the QTCP.

[1] Y. Kato and T. Misawa, Phys. Rev. B 92, 174419 (2015).

[2] R. Lipowsky, Phys. Rev. Lett. 49, 1575 (1982).

[3] I. Danshita, D. Yamamoto, and Y. Kato, Phys. Rev. A 91, 013603 (2015).

日時：2024年5月22日10:45-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：百合巧（大阪大学）

題目：Construction of Many-Body Quantum Simulators Using Phonons in Trapped Ions

概要：Quantum simulation, which uses a well-controlled quantum system to simulate another quantum system [1], is gaining attention as a new method for exploring the properties of matter, and research in this area is becoming increasingly active. Arrays of ions trapped by electromagnetic fields in a vacuum are a promising choice for quantum simulation due to their high coherence and controllability. In quantum information processing using ions, both qubits (internal states) and phonons (vibrational quantum states of ions) play important roles. The internal states of cooled ions can be controlled with high precision, making them ideal quantum bits. Experiments using ion arrays, from a few to many ions, have primarily focused on the internal states [2~4]. On the other hand, the phonon degrees of freedom have more energy levels and can handle more information. However, due to the difficulty of controlling phonons, experiments focusing on phonons have so far only been reported with a few ions [5~8]. This research aims to conduct experimental studies of quantum many-body systems described by the Jaynes-Cummings- Hubbard (JCH) model using phonons in ion arrays. In this talk, as preparation for observing quantum phase transitions in the JCH model, I will present results from measurements of Rabi oscillations and sideband cooling with ten ions using a macroscopic light addressing beam, as well as results from Rabi oscillations and sideband cooling with 20 ions. I will also discuss plans for future research.

[1] R. P. Feynman, Intl. J. Theor. Phys. 21, 467(1982).

[2] B. P. Lanyon et. al., Science 334, 57 (2011).

[3] Q.-X. Nei et. al., PRL 128, 100504 (2022).

[4] M.-W. Li et. al., PRL 129, 140501(2022).

[5] E. K. Irish et. al., PRA 77, 033811(2008).

[6] K. Toyoda et. al., PRL 111, 160501(2013).

[7] R. Ohira et. al., PRA 100, 06031(R) (2019).

[8] S. Muralidharan et. al., PRA 104, 062410(2021).

日時：2024年5月29日10:45-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：小久保治哉（物性理論）

題目：Size Dependence of the critical velocity of the superfluid wake

概要：Wake is a flow that occurs behind an obstacle moving through fluids, the dynamics of which is determined by the size and velocity of the obstacle, and is associated with various fluid phenomena such as vortex formation and turbulent transition. Wake in superfluid has been studied both experimentally and theoretically in weakly interacting Bose systems, and it has been shown that the critical velocity depends on the shape of the obstacle. In numerical simulations, Gaussian potentials are often used to simulate an optical laser obstacle. However, it is difficult to measure the dependence of the critical velocity on the shape of the obstacle due to the unclear effects of the tail in the Gaussian potential. In this work, we consider the wake with a plate-shaped obstacle to evaluate the dependence of the critical velocity on the size of the obstacle. In this talk, we describe the size dependence of the critical velocity by numerical simulations for a 2-dimensional Bose-Einstein condensate and present a method for quantitative evaluation of the critical velocity using the complex potential flow.

日時：2024年6月5日10:45-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：安藤京介（物性理論）

題目：Machine learning analysis of Fully Frustrated XY Model (FFXY) in two-dimensional square lattice

概要：The recent remarkable development of artificial neural networks in image recognition, image classification, and natural language processing has influenced many scientific fields, and the search for new discoveries by applying this technology to any problem has begun. In the field of classical statistical physics, machine learning algorithms were introduced to identify symmetry-broken phase [1-3], and in some of these cases neural networks were shown to be able to learn order parameters and other thermodynamic parameters [1,3]. Having been able to apply machine learning techniques to conventional phase transitions, it is natural to ask whether the algorithm can be applied to unconventional phase transitions. As an example of such a system, we focus on the 2D Fully Frustrated XY Model (FFXY) [4]. The FFXY model has an Ising model-like transition and an XY model-like transition.

[1] J. Carrasquilla and R. G. Melko, Nat. Phys. 13, 431 (2017).

[2] E. P. L. van Nieuwenburg, Y.-H. Liu, and S. D. Huber, Nat. Phys.13, 435 (2017).

[3] S. J. Wetzel and M. Scherzer, Phys. Rev. B 96, 184410 (2017).

[4] Stephen Teitel, 40 Years of Berezinskii–Kosterlitz–Thouless Theory (World Scientific), pp. 201-235 (2013).

日時：2024年6月12日10:45-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：笠松健一（物性理論）

題目：Decay of two-dimensional quantum turbulence in binary Bose-Einstein condensates

概要：We study two-dimensional quantum turbulence in miscible binary Bose-Einstein condensates in either a harmonic trap or a steep-wall trap through the numerical simulations of the Gross-Pitaevskii equations. The turbulence is generated through a Gaussian stirring potential. When the condensates have unequal intracomponent coupling strengths or asymmetric trap frequencies, the turbulent condensates undergo a dramatic decay dynamics to an interlaced array of vortex-antidark structures, a quasiequilibrium state, of like-signed vortices with an extended size of the vortex core. The time of formation of this state is shortened when the parameter asymmetry of the intracomponent couplings or the trap frequencies is enhanced. The corresponding spectrum of the incompressible kinetic energy exhibits two noteworthy features: (i) a k^{-3} power law around the range of the wave number determined by the spin healing length (the size of the extended vortex core) and (ii) a flat region around the range of the wave number determined by the density healing length. The latter is associated with the small scale phase fluctuation relegated outside the Thomas-Fermi radius and is more prominent as the strength of intercomponent interaction approaches the strength of intracomponent interaction. We also study the impact of the intercomponent interaction to the cluster formation of like-signed vortices in an elliptical steep-wall trap, finding that the intercomponent coupling gives rise to the decay of the clustered configuration.Reference
Thudiyangal Mithun, Kenichi Kasamatsu, Bishwajyoti Dey, and Panayotis G. Kevrekidis, Phys. Rev. A 103, 023301 (2021)

日時：2024年6月19日10:45-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：近藤康（量子制御）

題目：Artificial Relaxation in NMR Experiment

概要：Environmental noises cause quantum systems to relax, which can significantly impact the precision of operations. Grasping the relaxation mechanism caused by environmental noises is a crucial step in the development of quantum technologies. Relaxations can be viewed as a process of information dissipation from the system into an environment with infinite degrees of freedom (DoF). This concept has led to the proposal and demonstration of a model of artificial relaxation in NMR experiments. While the current model has successfully captured the central idea of relaxation, we have observed recursive behavior due to the limited DoF of the ``artificial environment''. This limitation hampers its ability to describe relaxation accurately. This paper aims to overcome this limitation by extending the approach and studying the relaxation-like behavior through manipulating DoF. Our study promises to provide a more comprehensive understanding of the concept of relaxation.

日時：2024年6月26日10:45-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：手塚真樹（京都大学）

題目：Quantum error correction and spectral statistics in Sachdev-Ye-Kitaev-type long-range interacting models

概要：The Sachdev-Ye-Kitaev (SYK) model is a quantum mechanical model with maximally chaotic behavior at low temperatures. The model contains N fermions with random, all-to-all interactions and can be solved in the large-N limit. Since its proposal in 2015, the model has received significant attention due to its simplicity and the potential to study quantum gravity via the holographic principle. Numerous variants of the SYK model have been proposed, including a sparse version where only O(N) couplings are nonzero.
In this talk, we discuss our results [1] on the scrambling feature of SYK-type models including the binary-coupling sparse version [2], obtained by estimating the decoding error for the Hayden-Preskill protocol, where quantum information is embedded in a larger quantum system undergoing unitary dynamics. We also briefly introduce our
proposal for a further simplified model [3] that employs spin operators instead of Majorana fermions, presenting numerical results such as eigenenergy statistics and discussing the potential for quantum simulations.

[1] Y. Nakata and M. Tezuka, Phys. Rev. Research 6, L022021 (2024).
[2] M. Tezuka, O. Oktay, E. Rinaldi, M. Hanada, and F. Nori, Phys. Rev. B. 107, L081103 (2023).
[3] M. Hanada, A. Jevicki, X. Liu, E. Rinaldi, and M. Tezuka, J. High Energ. Phys. 05(2024)280.

日時：2024年7月3日10:45-

教室：31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：濱田雄大（場の量子論・素粒子論研究室）

題目：Fermion on the lattice

概要：When defining fermion fields on lattice spaces, a challenge known as the doubling problem arises. In this issue, taking the continuous limit of the fermion action on the lattice results in two fermionic degrees of freedom for each dimension. This is undesirable from the perspective of the physical properties of low-energy systems, such as asymptotic freedom. Moreover, according to the Nielsen-Ninomiya theorem, the fundamental properties of lattice fermion actions lead to a strong constraint that the doubling problem is necessarily unavoidable. In this presentation, we will explore lattice field theory and gauge invariance on the lattice. We will then examine Wilson fermions, which are commonly used to address the doubling problem, as well as domain-wall fermions, discussing their relationship with topological insulators.

日時：2024年7月10日10:45-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：宮井誠一郎（量子多体）

題目：Toward an analysis of correlation propagation in the Bose-Hubbard model with dipole-dipole interactions

Moreover, quantum simulations including long-range interactions such as dipole-dipole interactions, Rydberg atoms, and cold polar molecules have recently been developed [3,4,5,6]. These experiments have opened up new possibilities for studying effects of the long-range interactions on correlation propagation dynamics. In this work, we aim to theoretically investigate correlation spreading in the Bose-Hubbard model with dipole-dipole interactions using an approximation method based on Holsetin-Primakoff transformation [7]. In preparation for analyzing this model, this presentation will review the unconstrained fermion approximation (UF approximation) [8], which is a fundamental approximation used to analyze the 1D Bose-Hubbard model, and present a part of what has been learned about the Holstein-Primakoff transformation for the Bose-Hubbard model.

[1] Marc Cheneau, Peter Barmettler, Dario Poletti, et al., Nature 481, 484-487 (2012).

[2] Yosuke Takasu, Tomoya Yagami, Hiroto Asaka, et al., Science Advances 6, eaba9255 (2020).

[3] S. Baier, M. J. Mark, D. Petter, et al., Science 352, 201-205 (2016).

[4] Lin Su, Alexander Douglas, Michal Szurek, et al., Nature 622, 724-729 (2023).

[5] Sepehr Ebadi, Tout T. Wang, Harry Levine, et al., Nature 595, 227-232 (2021).

[6] Jason S. Rosenberg , Lysander Christakis, et al., Nature Physics 18, 1062-1066 (2022).

[7] S. D. Huber, E. Altman, et al., Physical Review B 75, 085106 (2007).

[8] Peter Barmettler, Dario Poletti, et al., Physical Review A 85, 053625 (2012).

日時：2024年7月24日10:45-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：武上響生（京都大学）

題目：Spin Green’s function approach to the Kitaev model

概要：The Kitaev model is a quantum spin system defined on a honeycomb lattice whose ground state has been shown to be a strictly spin liquid state [1,2]. Furthermore, the existence of fractionalized Majorana fermion excitations has been suggested. Although Majorana fermions are essential for obtaining the exact ground state, their physical interpretation in terms of spin operators remains unclear. In this study, we employ the Green’s function equation of motion approach for the analysis of the spin correlations in the isotropic Kitaev model while preserving SU(2) symmetry [3]. In this method, the temperature dependence of the spin-spin correlation function is obtained based on the short-range spin correlations. The spin Green's functions describe the propagation of the Z2 flux defined at each hexagonal plaquette. This approach aligns with the high-temperature expansion in the high-temperature regime. We present the temperature dependence of the nearest neighbor spin-spin correlation function, and show that its value is very close to the exact value at zero temperature. We also present some exact results for the spin-spin correlation function.

[1] A. Kitaev, Ann. Phys. 321, 2 (2006).

[2] Y. Motome and J. Nasu, J. Phys. Soc. Jpn. 89, 012002 (2020).

[3] H. Takegami and T. Morinari, arXiv:2405.13309

日時：2024年9月25日15:00-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：籔内雄大（大阪公立大学）

題目：Quantum Turbulence Generated by Normal-Fluid Wall Turbulence in Co-flow of Superfluid ⁴He

概要：While the universal logarithmic law of the wall is crucial in the study of classical turbulence, there are still not enough studies on quantum turbulence. Recently, Guo’s group [1] observed the logarithmic law of the normal component in co-flowing superfluid ⁴He, where the mean velocities of the superfluid and normal fluid are in the same direction. Interestingly, the Kármán constant κ obtained by the experiment is different from the universal value κ = 0.41 of classical turbulence. To identify the cause of the change, we consider the effect of the mutual friction in a vortex tangle state under the co-flow. We performed simulations of the vortex filament model [2] between two parallel plates. Our mean velocity profile of the normal fluid consists of the viscous sublayer, the logarithmic region, and the bulk region. To introduce the turbulence of the normal component, we added an ABC flow [3] to the mean velocity profile. It is found that the turbulence in the normal component is required to create and maintain the vortex tangle under co-flow, unlike the counterflow. Our simulation shows that polarized vortex filaments are collected near the wall. This is a unique feature of the co-flow turbulence. We will discuss how the spatial distribution of mutual friction may affect the change in the Kármán constant.

[1] W. Guo, private communications

[2] K. W. Schwarz, Phys. Rev. B, Vol 38, 2398 (1988)

[3] T. Dombre, et.al., J. Fluid. Mech., Vol 167, 353 (1986)

日時：2024年10月2日15:00-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者１：西澤良彌

題目：Rydberg原子系からなる量子計算機におけるフォノンによるエラーの解析に向けて

概要：アブストラクト→量子計算機に適しているプラットフォームとして、光ピンセットを用いて配列されたRydberg原子が注目されている[1]。今後のRydberg原子系を用いた量子計算機の発展に向けて、この系の量子ビット操作技術の高度化が求められる。量子ビット操作のエラーの要因としてドップラー効果、レーザー位相ノイズ、中間状態からの自然放出などが考えられており、近年活発に議論されている[2]。エラーを引き起こしうる他の物理的現象としてフォノン散乱がある。これは上記3つのエラー要因に対して影響が小さいとされているが、研究開発の進展によってそれらの影響が軽減されてくるにつれて相対的に影響が大きくなると予想される。本研究ではフォノン散乱のRydberg原子系に対する影響を理論解析し、フォノンの影響による量子ビット操作のエラーを抑制する手法を理論面から提案することを目的とする。本発表では、エラーを抑制したい操作として2量子ビット操作の一つであるCZゲートを選び、先行研究[3]で示されたRydberg原子系でのCZゲートの実現方法について説明する。次に、Facilitation conditionというスピン揃っている領域の境界でスピンが反転しやすくなる状況を考え、フォノン散乱によってスピンが影響を受ける様子をそれらのシミュレーションについての先行研究[4]を用いて学習する。
[1] M. Morgado and S. Whitlock, AVS Quantum Sci. 3, 023501(2021)
[2] Sylvain de Léséleuc et al, Phys. Rev. A 97, 053803 (2018)
[3] Levine, H. et al., Phys. Rev. Lett. 123, 170503 (2019)
[4] Matteo Magoni, Chris Nill, and Igor Lesanovsky, Phys. Rev. Lett. 132, 133401 (2024)

発表者２：森本陸斗

題目：制限Boltzmannマシン型変分波動関数を用いたBose-Hubbard模型の数値解析に向けて

概要：2017年にCarleoとTroyerが制限Boltzmannマシン（RBM）型のニューラルネットワークを用いた変分波動関数を量子スピン系の数値解析に応用して以来[1]、RBM変分波動関数を用いた量子多体系の理論研究は急速に発展している[2]。一方で、光格子中の冷却気体系からなる量子シミュレータを用いた量子多体系の非平衡ダイナミクスの研究が近年精力的になされている[3]。そこで本研究では、RBM変分波動関数を用いて、光格子中の冷却気体系を記述する典型的な模型であるBose-Hubbard模型の非平衡ダイナミクスを解析することを目的とする。現在そのための準備としてRBM変分波動関数を用いたスピン1/2 Heisenberg模型の基底状態解析[1,4]の再現に取り組んでおり、本発表では、その進捗状況を報告する。まず初めに、文献[4]に基づいて、近年発展を続けているニューラルネットワークを用いた機械学習について概説する。つづいて、RBM変分波動関数の最適化に用いたマルコフ連鎖型モンテカルロ法と最急降下法を説明する。それらを用いて、(L^2+2L)個の変分パラメータを有するRBM波動関数を準備した場合に正しい基底状態エネルギーが得られることを確認する。続いてより大きいスピン数の場合に適応するために、並進対称性を用いて(L+2)個に変分パラメータを減らしたRBM波動関数を準備した場合でも同様に正しい基底状態エネルギーが得られることを確認する。

[1] G. Carleo and M. Troyer, Science 355, 602 (2017).
[2] R. G. Melko et al., Nat. Phys. 15, 887-892 (2019).
[3] F. Schäfer, et al., Nat. Rev. Phys. 2, 411 (2020).
[4] ―Pythonで実践― 基礎からの物理学とディープラーニング入門，福島健二および桂法称, 科学情報出版株式会社, 2022年.

日時：2024年10月9日15:00-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者１：小田川陽睦（量子多体）

題目：一次元Bose-Hubbard模型で記述される超伝導量子回路における量子多体傷跡状態の実現方法の提案に向けて

概要：冷却原子系などの外界から非常によく隔離された量子プラットフォームの発展に促進されて、孤立した量子多体系の熱平衡化の問題が実験・理論の両面から精力的に研究されている[1,2]。非可積分な系において一般的な初期状態は長時間発展の後に熱平衡化するが、近年の研究で、量子多体傷跡状態と呼ばれる熱平衡化しない例外的な量子状態が存在しうることが明らかになっている[3,4]。2024年に、三体制約を課したBose-Hubbard (BH) 模型の量子多体傷跡状態が理論的に発見され、光格子中のBose気体を用いてその状態を実現する方法が提案された[5]。そこでは非常に強い三体ロスによる量子ゼノ効果によって三体制約を導入することが提案されているが、現実的には粒子のロスのせいで系の寿命が相当短くなってしまう。本研究では、人工的な散逸を用いずに三体制約を実現できる超伝導量子回路系の利点を生かして、この系を用いて先行研究[5]で発見された量子多体傷跡状態を実現する方法を提案することを目的とする。本発表では、そのための準備として、まずBH模型で記述される超伝導量子回路の実現方法[6,7]を説明する。さらに、量子多体傷跡状態を実現に必要な要素として、調整可能な結合の導入方法[8]と多体系への粒子の追加方法[7]を概説する。

[1] D'Alessio, Luca, et al., Advances in Physics 65.3 (2016): 239-362.

[2] Mori, Takashi, et al., Journal of Physics B 51.11 (2016): 112001.

[3] Bernien, Hannes, et al., Nature 551.7682 (2017): 579-584.

[4] Turner, Christopher J., et al., Nature Physics 14.7 (2018): 745-749.

[5] Kaneko, Ryui, et al., Physical Review A 109.1 (2024): L011301.

[6] Saxberg, Brendan, Diss., PhD. Thesis, The University of Chicago, (2023).

[7] Ma, Ruichao, et al., Nature 566.7742 (2019): 51-57.

[8] Yan, Fei, et al., Physical Review Applied 10.5 (2018): 054062.

発表者２：中井七海（量子多体）

題目：冷却原子Bose-Einstein凝縮体におけるダークソリトンの実験観測に向けて

概要：冷却Bose原子気体からなるBose-Einstein凝縮体(BEC)が初めて実現[1,2]されて以来、その巨視的波動性に起因する様々な物性が実験・理論の両面から研究されてきた。本研究ではBECが示す興味深い物性の一つであるダークソリトン励起に注目する。ソリトンとは非線形方程式に従う孤立波でBose-Einstein凝縮においては原子間の相互作用が非線型性として働き、さまざまなソリトンが形成されうる。過去いくつかの実験で位相焼き付け法を用いてダークソリトンが生成されたがどれも寿命が短時間であり、安定なダークソリトンの観測には成功していない[3-8]。

　そこで我々は遠隔実験装置Oqtant[9]を用いてダークソリトンを観測することを目指す。Oqtantでは、軸対象な閉じ込めポテンシャル中のBECに対して青色離調レーザーからなる斥力ポテンシャルを印加して制御できる。しかしながら、同径方向の閉じ込めが大きくないために、そのままの設定ではダークソリトン状態は不安定である。そこで本研究では、斥力ポテンシャルを適切に用いれば、Oqtantで安定なダークソリトン状態を生成できることを理論的に提案する。Gross-Pitaevskii(GP)理論に基づく安定性解析により、安定したダークソリトンを観測するための実験パラメータを与える。本発表ではそのために現在まで学習したこととして、まずGP方程式及びBogoliubov方程式[10]を説明する。トラップがある場合とない場合のそれぞれに関してソリトンの不安定性を[11]を参考にして解説する。さらに、定常GP方程式とBogoliubov方程式を数値的に解く方法である直交関数展開法[12]について解説する。その計算手法を用いて得たプレリミナリーな結果を示し、今後の方針について議論する。

[1] K. B. Davis et al., Phys. Rev. Lett. 75, 3969 (1995).

[2] M. H. Anderson et al., Science 269, 198 (1995).

[3] S. Burger et al., Phys. Rev. Lett. 83, 5198 (1999).

[4] J. Denschlag et al., Science 287, 97 (2000).

[5] A. Weller et al., Phys. Rev. Lett. 101, 130401 (2008).

[6] C. Becker et al., Nat. Phys. 4, 496 (2008).

[7] C. Becker et al., New J. Phys. 15, 113028 (2013).

[8] L. M. Aycock et al., Proc. Natl. Acad. Sci. 114, 2503 (2017).

[9] https://www.infleqtion.com/oqtant

[10] L. Pitaevskii and S.Stringari, Bose-Einstein Condensattion,(Oxford University press, Oxford, 2016).

[11] A. E. Muryshev et al., Phys. Rev. A 60, R2665 (1999)

[12] M. Edwards et al., J. Res. Natl. Inst. Stand. Technol. 101, 553 (1996)

発表者３：大田裕一（量子多体）

題目：イオントラップを用いたJaynes-Cummings-Hubbard模型の量子シミュレーションの理論的サポート

概要：量子シミュレーションとは、物質中で起きる複雑な物理現象を人工的に作成した制御性の高いシステムを使ってシミュレーションすることであり、近年様々な物理系が量子シミュレーション研究に応用されている。今回の研究では、イオントラップ系をプラットホームとした量子シミュレーションに注目する。この系では、イオンの内部状態をS=1/2スピン、トラップ中の振動状態を遍歴ボース粒子とみなし、それらをレッドサイドバンド光で結合することで、Jaynes-Cummings-Hubbard模型（JCH模型）で記述される系を実現できる[1,2]。具体的には、共同研究している実験グループが、この物理系において超流動状態とMott絶縁体状態の間の量子相転移を実験で観測することを直近の一里塚的な目的としている。そこで本研究では、この目的を精密な数値計算手法を用いてサポートすることを目指す。本発表では、その準備的な研究として、JCH模型における超流動-Mott絶縁体転移を理解するために、平均場近似[3]による解析[4]をする。その近似の範囲で現状の実験パラメータをインプットした場合における基底状態の性質を議論する。

[1] K. Toyoda et al., Physical Review Letters 111, 160501 (2013).

[2] 豊田健二, 応用物理 89, 632 (2020).

[3] A. D. Greentree et al., Nature Physics 2, 12 (2006).

[4] 斉藤拓也, 物性研究・電子版 1, 012601 (2012).

日時：2024年10月11日15:00-

教室：　31号館3階シミュレーション実験室　+　Zoomでのオンライン配信

発表者：村山太洋（量子多体）

題目：二軌道Bose気体系における量子相転移ダイナミクスの数値解析に向けて

概要：二軌道Bose気体系とは、二つの異なる内部状態をもつ原子の混合気体を状態依存光格子に載せることで実現されている系である[1,2]。平均場近似を用いた近年の理論研究で、軌道間のRabi結合を変化させることで、異なる二つの超流動状態間の量子相転移が起こりうることが示された。本研究では、より精密な数値計算手法を用いて、この転移が実験で観測されうるかどうかを詳細に検討する。本発表では、そのための準備として、光格子中のBose気体がBose-Hubbard型の模型で記述されることを説明する。また、二軌道Bose気体という物理系を理解するために、Stony Brook大学のグループによる二成分⁸⁷Rb原子を用いた二軌道Bose気体に関する実験結果を概説する[1,4]。特に、Rabi結合によるバンド混成によってそれぞれの軌道の粒子の有効的なホッピングがどのように変化するのかを議論する。

[1] L. Krinnner et al., Nature 559, 589 (2018).

[2] L. Riegger, Ph.D.thesis (2019).

[3] 段下一平, 後藤慎平, 横井真理, 日本物理学会年次大会, 2021年.

[4] J. Kwon et al., Nature Physics 18, 657 (2022).