近畿大学理工学部物理学コースの量子制御研究室、量子多体物理学研究室、物性理論研究室が合同で運営する量子物理学および量子技術に関するセミナーです。学期中は基本的に毎週水曜日10:45-12:15に開催しています。

### 今後の予定

2023年度

前期

日時： 2023年7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： 數田 裕紀（量子多体）

題目：Quantum and classical simulations of non-ergodic behavior in a disorder-free Bose-Hubbard system

概要：In this work, following the protocol proposed in Ref. [1], we analyze non-ergodic dynamics in a one-dimensional Bose-Hubbard system by means of a quantum simulator built with ultracold Bose gases in optical lattices. Specifically, we analyze dynamics starting from two different initial states. In the first (second) state, one particle occupies (two particles occupy) each odd-numbered site while no particle occupies each even-numbered site. We observe the time evolution of the atomic density in order to show that in the case of the second state the atomic density is not relaxed to equilibrium even after long-time evolution, exhibiting non-ergodic behavior. In order to provide quantitative references to the quantum-simulation outputs, we present numerical simulations of the experiments with use of matrix product states.

[1] M. Kunimi and I. Danshita, Phys. Rev. A **104**, 043322 (2021).

日時： 2023年7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：Composite Quantum Gates and Geometric Phase Gates

概要：After reviewing geometric phases, I shall introduce two examples of geometric phase gates applied (proposed) for Rydberg atoms (*PhysRevA.96.052316, **PhysRevResearch.2.043130). Then*, geometric properties of composite quantum gates are discussed (arXiv:2301.05627, JPSJ.80.054002). Some questionable points (= what I cannot understand) in the above papers are also discussed.

### 過去の講演

2023年度

前期

日時： 2023年4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： 小久保 治哉（物性理論）

題目： Size dependence of the critical velocity for quantum vortex formation by the superfluid wake with a plate obstacle

概要： The wake generated by an object moving through a fluid depends on the size and velocity of the obstacle and is associated with various physical phenomena such as vortex formation and turbulent transition. The wake has been studied experimentally and theoretically in superfluids. In cold atomic systems, optical potentials have been used in superfluid wake experiments [1-2]. In numerical simulations [3-4], Gaussian potential is often assumed as obstacles. However, the dynamics of the wake and the critical velocity for vortex formation depend on the specifics of the obstacle potential, complicating the universal discussion. Plate obstacle is comparatively easy to handle both theoretically and numerically. The size of the obstacle can be characterized only by the width of the plate, making it easy to study its effects.In this study, the size dependence of the critical velocity for quantum vortex formulation in the wake of a 2D Bose-Einstein condensate with the plate obstacle is investigated.

[1]Woo Jin Kwon, Joon Hyun Kim, Sang Won Seo, and Y. Shin, Phys. Rev. Lett. 117, 245301 (2016)

[2]Younghoon Lim, et al, New J. Phys. 24, 083020 (2022)

[3]Kazuki Sasaki, Naoya Suzuki, and Hiroki Saito, Phys. Rev. Lett. 104, 150404 (2010)

[4]M. T. Reeves, et al, Phys. Rev. Lett. 114, 155302 (2015)

日時： 2023年4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： 笠松 健一（物性理論）

題目： Recent understanding and problems on vortex dynamics in binary Bose-Einstein condensates

概要： I review some recent progress and remaining problems on the properties of quantized vortices in two-component (binary) Bose-Einstein condensates (BECs). A vortex in binary BECs takes a rich variety of structures, forming a half-quantized vortex, as a result of the presence of multiple order parameters. This vortex exhibits nontrivial structure and dynamics when we consider the system of several or lots of vortices. In this talk, we will discuss (i) Interactions and dynamics of two separated vortices [1,2], (ii) Structures of vortex lattices in a rotating potential [3], (iii) Quantum turbulence by stirring of a localized potential [4].

[1] K. Kasamatsu, M. Eto, and M. Nitta, Phys. Rev. A, 93, 013615 (2016).

[2] J. Han, K. Kasamatsu, and M. Tsubota, J. Phys. Soc. Jpn. 91, 024401 (2022).

[3] K. Kasamatsu, M. Tsubota and M. Ueda, Int. J. Mod. Phys. B 19, 1835 (2005).

[4] T. Mithun, K. Kasamatsu, B. Dey, and P. G. Kevrekidis, Phys. Rev. A 103, 023301 (2021).

日時： 2023年5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： 鏡原 大地（量子多体）

題目：Classical simulation of non-Hermitian boson sampling dynamics using matrix product states

概要：Sampling complexity means the difficulty of sampling from a distribution close to the desired (e.g., quantum system) probability distribution and is discussed in the context of quantum supremacy. A famous example where sampling complexity is often discussed is boson sampling [1], which consists of sampling from the distribution of identical bosons generated by a linear interferometer. An interferometer is characterized by a unitary matrix. It is shown that boson sampling is hard by classical computers for random unitary matrices. Recently, by considering the sampling problem of identical bosons time-evolved by a quadratic Hamiltonian from a product state, a transition from the state where sampling can be done easily to one where it is difficult has been proposed [2]. Furthermore, it has been pointed out that when time evolution is extended to be non-unitary by considering open systems, there is a transition in sampling complexity that has not been observed in unitary systems [3].

In the previous QPT seminar, we studied the Rényi entanglement entropy in the non-Hermitian boson sampling dynamics discussed in Ref. [3] and found that low-entangled states appear in some parameter regions. In this talk, we consider a classical simulation using matrix product states (MPS) with the expectation that low-entangled states would be well described using MPS and therefore an efficient classical simulation of the sampling would be possible. We investigate the dynamics of the bond dimension, which corresponds to the number of Schmidt states kept in MPS, because it is closely related to the efficiency of sampling [4]. Our results clarify the region where an efficient classical simulation can be performed using MPS.

[1] S. Aaronson and A. Arkhipov, in Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing (Association for Computing Machinery, New York, 2011), pp. 333–342.

[2] A. Deshpande, B. Fefferman, M. C. Tran, M. Foss-Feig, and A. V. Gorshkov, Phys. Rev. Lett. **121**, 030501 (2018).

[3] K. Mochizuki and R. Hamazaki, Phys. Rev. Res. **5**, 013177 (2023).

[4] H.-L. Huang, W.-S. Bao, and C. Guo, Phys. Rev. A **100**, 032305 (2019); C. Oh, K. Noh, B. Fefferman, and L. Jiang, Phys. Rev. A **104**, 022407 (2021).

日時： 2023年5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： Polo, Juan（Quantum Research Center, Technology Innovation Institute）

題目：Fractionalization of the angular momentum in SU(N) atomtronic circuits

概要：Neutral atoms guided in ring-shaped atomtronic circuits present quantized values of the angular momentum per particle. Depending on the specific parameters characterizing the system (eg: nature of the particle statistics, interactions), the winding number present different quantizion properties. In this talk, I will showcase how such a phenomenon occurs in an atomtronic circuit with a quantum fluid consisting of strongly interacting N component fermions, the so-called SU(N) fermions. For repulsive interactions a specific emerging phenomenon of attraction from repulsion appears, providing a quantization with similar properties to the attracting bosonic case. For attractive interactions, the quantization is determined by the number of components N . The suggested implementation of our work is provided by cold atoms therefore, I will also present how the fractionalization of the winding number can be read-out experimentally.

日時： 2023年5月31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：Correlation-spreading dynamics after a quantum quench in low-dimensional Ising models with transverse field

概要：Recent advances in controlling and manipulating Rydberg atoms trapped with an optical tweezer array have made it possible to utilize this platform as a quantum simulator of quantum Ising models, where dynamics of spin-spin correlations can be measured at a single-site resolution. Motivated by such experimental development, we theoretically study dynamics of spatial spreading of equal-time spin-spin correlations in the transverse-field Ising model subjected to a sudden change of the transverse field [1]. We assume that the initial state is a state polarized completely along the transverse direction, which is the ground state in the large-field limit. In one spatial dimension (1D), we use the exact analytical method and the linear spin-wave approximation (LSWA). We compare the outputs of the former with those of the latter in order to show that the latter can quantitatively capture the exact group velocity of the correlations as long as the transverse-field after the quench is sufficiently large compared to the spin-spin interaction. However, it fails to capture the detailed time dependence of the correlation functions. In 2D, with use of LSWA, we give a specific estimate of the group velocity in the large-field region. We also utilize the projected entangled pair states algorithm in order to provide quantitatively accurate time-evolution of the correlation functions for a relatively short time.

[1] R. Kaneko and I. Danshita, arXiv:2301.01407 [cond-mat.quant-gas].

日時： 2023年6月14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： Mikkelsen, Mathias（量子多体）

題目：Correlation spreading dynamics in SU(N) Fermi-Hubbard models

概要：For local Hamiltonians the propagation front of correlations is generally bounded by a light-cone like structure, where an initially localized correlation spreads to distant sites with a maximum velocity [1,2]. Loose bounds on this velocity can be found in a range of models using the Lieb-Robinson bound [1], but the actual speed is usually much slower. These concepts have been studied [3] and experimentally confirmed [2] quenching from a Mott-state to a finitely-interacting Bose-Hubbard (BH) model. These investigations have shown that a dip in the density-density correlations will propagate with a velocity which depends on the interaction strength U. For large U the physics can be effectively described in terms of doublon-holon excitations. Similarly SU(N) Fermi-Hubbard (FH) models will have excitations corresponding to doublon pairs with different flavors.

In this work we calculate SU(2)-SU(4) equal time density correlations and compare with the BH results using the time-evolving block decimation (based on the Suzuki-Trottter decomposition) method for tensor network representations of the system [4]. Preliminary results suggest that the propagation velocity is generally lower than the BH case, particularly for the standard SU(2) FH model, but increases with N asymptotically towards the BH case (in line with Lieb-Robinson bounds which are similar to bosons in the large N limit [1]). Our study is motivated by the successful experimental implementation of SU(N) Fermi-Hubbard models using Alkaline earth(-like) atoms [5,6]. While site-resolved measurement of dynamics remains an experimental challenge our investigation shows that potentially interesting physics can be found and provides a theoretical/numerical comparison for future experiments.

[1] Z. Wang and K. R.A. Hazzard, *PRX Quantum* **1**, 010303 (2020)

[2] M. Cheneau et al., *Nature* **481**, 484–487 (2012)

[3] P. Barmettler, D. Poletti, M. Cheneau and C. Kollath, *Phys.Rev. A ***85**, 053625 (2012)

[4] E. M. Stoudenmire and Steven R White, *New J. Phys.* **12, **055026 (2010)

[5] S. Taie, R. Yamazaki, S. Sugawa, and Y. Takahashi, *Nature Physics* **8**, 825 (2012).

[6] C. Hofrichter, et al. *Phys. Rev. X ***6**, 021030 (2016).

日時： 2023年6月21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 XY models 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. An example of such a system is a two-dimensional XY model that exhibits the Kosterlitz-Thouless transition (KT transition) [4].

The purpose of this study is to check whether machine learning algorithms can reproduce the known results for the well understood two-dimensional square lattice XY model. We confirmed that the spin configurations obtained by Monte Carlo simulations reproduce the known behavior of the correlation function, and trained the model with an all-associative neural network and a convolutional neural network. Using the trained model, we confirm the accuracy and size dependence of the transition temperature at which the KT transition occurs from spin configuration.

[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] A. Krizhevsky, I. Sutskever, and G. Hinton, Commun. ACM 60, 84 (2017).

日時： 2023年6月29日13:15-

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：Numerical analysis on anomalous tunneling of Bogoliubov excitations through a Gaussian potential barrier

概要：Elementary excitations of a weakly interacting Bose gas, which are referred to as Bogoliubov excitations [1], exhibit an anomalous tunneling property in that the transmission probability approaches unity as the excitation energy decreases towards zero [2,3]. Despite more than 20 years having passed since its first prediction [2], the anomalous tunneling has not been observed in experiments. We plan to observe the anomalous tunneling of Bogoliubov excitations using the cloud-based remote experimental apparatus of ultracold atomic Bose-Einstein condensates, called Albert [4]. For identifying the anomalous tunneling in experiments, it is necessary to have theoretical values for the transmission probability of Bogoliubov excitations through the Gaussian potential barrier used in the experiment, as a reference for comparison.

The purpose of this study is to provide theoretical values for the transmission probability in this case by numerically solving the Bogoliubov equation that describes the Bogoliubov excitations. First, we review the case of a rectangular potential, which allows for an approximate analytical expression of the transmission probability [3], as an example to illustrate the important properties of the anomalous tunneling. Next, we explain the finite element method that is used to numerically calculate the transmission probability [5]. We reproduce the calculation of the transmission probability for Bogoliubov excitations in a rectangular potential [3]. Finally, we calculate the transmission probability for a Gaussian potential and discuss optimal values of the barrier width and height for observing the anomalous tunneling with Albert.

[1] L. P. Pitaevskii and S. Stringari, Bose–Einstein Condensation., (Oxford University Press, Oxford, 2003).

[2] D. L. Kovrizhin, Phys. Lett. A 46 , 392 (2001).

[3] Yu. Kagan, D. L. Kovrizhin, and L. A. Maksimov, Phys. Rev. Lett. 90, 130402 (2003).

[4] https://bec.coldquantaapis.com

[5]計算物理Ⅱ, 夏目雄平および植田毅, 朝倉書店, 2002年.

日時： 2023年7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： 木屋 晴貴（量子制御）

題目：Robust Single-Qubit Gates and Polygons on Sphere

概要：In single-qubit gates, two typical inevitable systematic errors, Pulse Length Error (PLE) and Off-Resonance Error (ORE) exist. PLE is often caused by a control field strength error, while ORE is by a resonance frequency calibration error of a qubit. These errors can be compensated by a method called Composite Quantum Gate (CQG): A single gate is replaced with a sequence of gates such that their errors are canceled with each other [1]. We discuss a symmetric CQG (sCQG) which is robust against PLE from the viewpoint of a corresponding polygon on a sphere.

We are interested in the gate times of CQGs [2] and Geometric Quantum Gates [3,4]. We hope that the graphical understanding of the PLE robust condition helps to find the shortest gate time and to deepen the understanding of CQGs.

[1] M. H. Levitt and R. Freedman, J. Magn. Reson.**33**,472(1979).

[2] S. Kukita, H. Kiya and Y. Kondo, submitted.

[3] Y. Kondo and M. Bando, J. Phys. Soc. Jpn.**80**,054002(2011).

[4] E.Sjöqvist, Int. J. Quantum Chem. 2015,**115**,1311-1326.